In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

We say that a system {zmF(z)}m=0∞ is a Beurling system if F is an outer function. Beurling’s approximation theorem asserts that if F is an outer function from H2(D) then the system {zmF(z)}m=0∞ is complete in the space H2(D). We prove that a Beurling system with F∈Hp(D),1≤p<∞ is an M−bases in Hp(D) with an explicit dual system. Any function f∈Hp(D),1≤p<∞ can be expanded as a series by the system {zmF(z)}m=0∞. For different methods of summation we characterize outer functions F for which the expansion converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

Chipman contends, in stark contrast to the conventional view, that utility is not a real number but a vector and is inherently lexicographic in nature. According to these views, it will be proved that, for every preordered topological space (X,≾,t), the assumption t to be finer than the order topology t≾ on (X,t), i.e. t⊇t≾, and the assumption the quotient topology t∣∼≾ that is defined on the preordered set (X∣∼,≾∣∼) of indifference classes of ≾ to be Hausdorff imply that a cardinal number κ and a (complete) preorder ≲ on {0,1}κ that is coarser than the lexicographical ordering ≤lex on {0,1}κ, i.e. ≤lex⊂≲, can be chosen in such a way that there exists a continuous order-embedding ϑ:(X,≾,t)⟶({0,1}κ,≲,t≤lex). This theorem will be compared with a theorem that, in particular, describes necessary and sufficient conditions for ≾ to have a continuous multi-utility representation.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Vir_c with central charge c ≥ 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net of with respect to the ground state representations of Vir_c, one obtains possibly new family of Möbius covariant nets on S¹.

Starting from the analysis of the lack of positivity of the Cattaneo heat equation, the article addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, than is at least as important as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmarking example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to the overcome the parabolic diffusion model or to consider the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid.

The generation and maintenance of membrane potential is a fundamental part of Membrane Pump Theory. One of the key points of this hypothesis is based on a natural or facilitated molecular diffusion through several types of ion channels and pumps like the Na/K ATPase. Chemistry, physics and especially electrochemistry, however, bring strong contradictions to this theoretical assumption. By respecting the principles of chemistry and electrostatics, it becomes obvious that this theoretical hypothesis cannot work. The ionic diffusion that would be at the origin of this potential cannot take place. Indeed, the topology and the forces involved definitively exclude the current model, which must absolutely be revised according to the current state of our knowledge and allow an advance in the understanding of the phenomena and open new research perspectives.

For the past few decades, researchers have been intrigued with glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers during the last few years. This review also includes the applications of glassy polymer. Despite having so many applications, current researchers still have difficulty in implementing coating challenges due to issues like as physical ageing, which is briefly discussed in the review.

The term “risk” is connoted with divergent meanings in natural hazard risk research and the practice of risk management. Whilst the technical definition is accurately defined, in practice, the term “risk” is often synonymously used with “danger”. Considering this divergence as a deficiency, risk communication often aims to correct laypersons’ understanding. We suggest in reference to Breakwell (2001) to treat the variety of meanings as a resource for risk communication strategies instead. However, there is no investigation so far, of what laypersons’ meanings of risk actually comprise. To address this gap, we examine the meanings of risk applying a social representations approach (Moscovici, 2001) in a qualitative case study design. Results of the study among inhabitants of Swiss mountain villages show that differences in meanings were found according to hazard experience and community size. We found commonly shared core representations, and single peripheral ones. We conclude with suggestions on how to make usage of the knowledge on SR in risk communication.

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

The diffusion coefficient (D) is a key parameter characterizing gas transport in coal seams. Usually, the D is calculated from the desorption curve of particle coal, which cannot accurately reflect the diffusion characteristics under the stress constraint conditions of in-situ coal seams. In this paper, based on Fick's law of counter diffusion, different metamorphic deformed coals of medium and high coal rank are taken as the research object. The change laws of D under different confining pressure, gas pressure, and temperature conditions are tested and analyzed, and the influencing mechanisms on the D are discussed. The results show that the D of different metamorphic deformed coals decreases exponentially with the increase of confining pressure, and increases exponentially with the increase of gas pressure and temperature. There is a limit diffusion coefficient. The influence of confining pressure on the D is essentially determined by the change of effective stress, and the D has a negative effect of effective stress similar to permeability. The effect of gas pressure on the D involves two mechanisms, namely, mechanical and adsorption effects, which are jointly restricted by effective stress and coal particle shrinkage and expansion deformation. The effect of temperature on the D is mainly achieved by changing the root mean square speed and average free path of gas molecules. Under the same temperature and pressure conditions, the D increases first and then decreases with the increase of deformation degree, and the D of fragmented coal is the largest. Under similar deformation conditions, the D of high-rank anthracite is greater than that of medium-rank fat coal. It is considered that porosity is the key factor affecting the change of D in different metamorphic deformed coals.

An interesting anomaly of the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem, so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the cross-section and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

Increased data acquisition by uncalibrated, heterogeneous digital sensor systems such as smartphones present new challenges. Binary metrics are proposed for the quantification of cyber-physical signal characteristics and features, and a standardized constant-Q variation of the Gabor atom is developed for use with wavelet transforms. Two different continuous wavelet transform (CWT) reconstruction formulas are presented and tested under different signal to noise ratio (SNR) conditions. A sparse superposition of Nth order Gabor atoms worked well against a synthetic blast transient using the wavelet entropy and an entropy-like parametrization of the SNR as the CWT coefficient-weighting functions. The proposed methods should be well suited for sparse feature extraction and dictionary-based machine learning across multiple sensor modalities.

This paper presents a novel method to extract local features, which instead of calculating local extrema computes global maxima in a discretized scale-space representation. To avoid obtaining precise scales by interpolation and to achieve perfect rotation invariance, two essential techniques, increasing the width of kernels in pixel and utilizing disk-shaped convolution template are adopted in this method. Since the size of a convolution template is finite and finite templates can introduce computational error into convolution, we sufficiently discuss this problem and work out an upper bound of the computational error. The upper bound is utilized in the method to ensure that all features obtained are computed under a given tolerance. Besides, the technique of relative threshold to determine features is adopted to reinforce the robustness for the scene of changing illumination. Simulations show that this new method attains high performance of repeatability in various situations including scale change, rotation, blur, JPEG compression, illumination change and even viewpoint change.

It is shown by numerical modelling that anisotropic diffusion can compensate and even overcome diffusion broadening - the main limiting factor of devices working at atmospheric pressure. The thickness of ion clouds coming out of the ionisation chamber is reduced ~ 1000 times in the ADMA inlet increasing the resolution. This finding has a great potential that enables construction of a device with resolution close to that of currently available desktop ion separation devices – high pressure mass spectrometers, but with much lower cost of manufacture and with smaller dimensions. Comprehensive numerical modelling along with mathematical analysis of physical concepts enables reduction of the footprint and manufacturing costs. Modelling determined that the resolving power (RP) potential of the ADMA is greater than the RP of currently available on the market devices for the airport security market. The ADMA technology enables very fast detection of threats; at least 100 times faster than currently used in Ion Mobility Spectrometers (IMS). This potentially allows an increase in passenger throughput in airports.

A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase separations. The results on the evolution of the distribution function and other characteristics of the ensemble, which in the zero volume fraction approximation are asymptotically in good agreement with the theory and the experiment, have been obtained. The peculiarity of the created program complex is the possibility of its adaptation to the description of the decomposition of multicomponent multiphase systems. Fig. 6, list of references - 19 titles.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

In recent times, BERT based transformer models have become an inseparable part of the 'tech stack' of text processing models. Similar progress is being observed in the speech domain with a multitude of models observing state-of-the-art results by using audio transformer models to encode speech. This begs the question of what are these audio transformer models learning. Moreover, although the standard methodology is to choose the last layer embedding for any downstream task, but is it the optimal choice? We try to answer these questions for the two recent audio transformer models, Mockingjay and wave2vec2.0. We compare them on a comprehensive set of language delivery and structure features including audio, fluency and pronunciation features. Additionally, we probe the audio models' understanding of textual surface, syntax, and semantic features and compare them to BERT. We do this over exhaustive settings for native, non-native, synthetic, read and spontaneous speech datasets

A cursory look at Indian prime time news tells us much about the tone and tenor of the people associated with it. Exaggerations, hyperbole, and tempers run wild and news anchors flail in theatrical rage. News channels and news editors display their ideological affiliations subliminally. These affiliations — a factor of personal political stance, funding bodies, and investors — lead to partisan bias in the framing of news and, in some cases, can easily translate into racial prejudice. In this paper, I examine news coverage related to Muslims in India. I study the coverage of two issues specifically– love jihad and triple talaq –in prime time English news of two channels – Times Now and Republic TV. My analysis of the content, tone, and tenor of their coverage shows that these channels propagate associations between Islam and backwardness, ignorance and violence through consistent employment of the following tropes – ‘Muslim women need to be saved from Muslim men’, ‘Hindu women need to be saved from Muslim men’, and ‘Muslims are not fully Indian – they are anti-national’. I place this study of news media within the current political climate in India and briefly touch on the conversations it guides and provokes. This is also a call for further analysis on this subject to examine and evaluate how discourse manipulates public conversations and policy decisions.

The term Concept has been a prominent part of investigations in psychology and neurobiology where, mostly, it is mathematically or theoretically represented. The Concepts are also studied computationally through their symbolic, distributed and hybrid representations. The majority of these approaches focused on addressing concrete concepts notion, but the view of the abstract concept is rarely explored. Moreover, most computational approaches have a predefined structure or configurations. The proposed method, Regulated Activation Network (RAN), has an evolving topology and learns representations of Abstract Concepts by exploiting the geometrical view of Concepts, without supervision. In the article, the IRIS data was used to demonstrate: the RAN's modeling; flexibility in concept identifier choice; and deep hierarchy generation. Data from IoT's Human Activity Recognition problem is used to show automatic identification of alike classes as abstract concepts. The evaluation of RAN with 8 UCI benchmarks and the comparisons with 5 Machine Learning models establishes the RANs credibility as a classifier. The classification operation also proved the RAN's hypothesis of abstract concept representation. The experiments demonstrate the RANs ability to simulate psychological processes (like concept creation and learning) and carry out effective classification irrespective of training data size.

Equipping autonomous agents for dynamic interaction and navigation is a significant challenge in intelligent transportation systems. This study aims to address this by implementing a brain-inspired model for decision-making in autonomous vehicles. We employ active inference, a Bayesian approach that models decision-making processes similar to the human brain, focusing on the agent's preferences and the principle of free energy. This approach is combined with imitation learning to enhance the vehicle's ability to adapt to new observations and make human-like decisions. The research involved developing a multi-modal self-awareness architecture for autonomous driving systems and testing this model in driving scenarios, including abnormal observations. The results demonstrated the model's effectiveness in enabling the vehicle to make safe decisions, particularly in unobserved or dynamic environments. The study concludes that the integration of active inference with imitation learning significantly improves the performance of autonomous vehicles, offering a promising direction for future developments in intelligent transportation systems.

Taste determination in small molecules is critical in food chemistry, but traditional experimental methods can be time-consuming. Consequently, computational techniques have emerged as val-uable tools for this task. In this study, we explore taste prediction using various molecular feature representations and assess the performance of different machine learning algorithms on a dataset comprising 2,601 molecules. The results reveal that GNN-based models outperform other ap-proaches in taste prediction. Moreover, consensus models that combine diverse molecular repre-sentations demonstrate improved performance. Among these, molecular fingerprints + GNN con-sensus model emerges as the top performer, highlighting the complementary strengths of GNNs and molecular fingerprints. These findings have significant implications for food chemistry research and related fields. By leveraging these computational approaches, taste prediction can be expedited, leading to advancements in understanding the relationship between molecular structure and taste perception in various food components and related compounds.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

Heart sounds and murmurprovidecrucial diagnosis information for valvular heart diseases (VHD). Phonocardiogram (PCG) combined with modern digital processing techniques, provides a complementary tool for clinicians. This article proposes a benchmark different time-frequency representations, which are spectogram, mel-spectogram and cochleagram for obtaining images, in addition to the use of two interpolation techniques to improve the quality of the images, which are Bicubic and Lanczos. Deep features are extracted from a pre-trained model called VGG16 and for feature reduction the Boruta algorithm is applied. To evaluate the models and obtain more precise results, nested cross-validation is used. The best results achieved in this study were for coclegram with 99.2% accuracy and mel-spectogram representation with the bicubic interpolation technique which reached 99.4% accuracy, both having support vector machine (SVM) as classifier 10 algorithm. Overall, this study highlights the potential of time-frequency representations of PCG 11 signals combined with modern digital processing techniques and machine learning algorithms for 12 accurate diagnosis of VHD.

: Oscillation synchronization through diffusion-based communication of active materials can lead to emergence of diverse patterns and collective behaviors. A detailed general description of the formation process of synchronization or resynchronization dynamics is a challenging task. We employ a photosensitive Belousov-Zhabotinsky reaction-diffusion model (within a gel media) to investigate the recovery process of oscillation synchronization between a pair of gel patches. The recovery time for oscillation resynchronization can be modulated by patch-distance, species of signaling molecules, intensity and duration of illumination. Analysis reveals that the “switch effect” of the gel-distance and the “promotion effect” from illumination on the oscillation resynchronization originate from the competition between processes of photo-promotion of oscillation, diffusion of signaling molecules (HBrO2 and Br-) and disproportionation of HBrO2. These results will benefit studies on bio-inspired active materials and soft motors.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In this work we study an economic-demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources the homogeneous in space wealth-population distribution is replaced by a periodic in space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Almost all modern inorganic light-emitting diode (LED) designs are based on double heterojunctions (DHJs) whose structure and current injection principle have remained essentially unchanged for decades. Although highly efficient devices based on the DHJ design have been developed and commercialized for energy-efficient general lighting, the conventional DHJ design requires burying the active region (AR) inside a pn-junction. This has hindered the development of emitters utilizing nanostructured ARs located close to device surfaces such as nanowires or surface quantum wells. Modern DHJ III-N LEDs also exhibit resistive losses which arise from the DHJ device geometry. The recently introduced diffusion-driven charge transport (DDCT) emitter design offers a novel way to transport charge carriers to unconventionally placed ARs. In a DDCT device, the AR is located apart from the pn-junction and the charge carriers are injected into the AR by bipolar diffusion. This device design allows the integration of surface ARs to semiconductor LEDs and offers a promising method to reduce resistive losses in high power devices. In this work, we present a review of the recent progress in gallium nitride (GaN) based DDCT devices, and an outlook of potential DDCT has for opto- and microelectronics.

A harmful impact of climate change and global warming has concerned various sectors of the international community. Numerous energy policies aiming at climate change mitigation have been implemented on a national and global scale. Renewable Energy Technologies (RET) play a critical role in enhancing sustainable solutions that significantly limit greenhouse gases (GHG) emissions. Such innovative technologies can facilitate energy transition through providing e.g. energy security, sustainable development, or effective usage of indigenous resources. However, the commercialization of RET becomes extremely challenging. The barriers can be of a different nature, although in this study the focus has been put on socio-economic and regulatory issues. In fact, there is ample evidence that energy policies play a central role in supporting renewables adoption. It is also claimed that RET require the whole ecosystem to support their successful diffusion. In this study, we explore multifarious barriers for a widespread RET diffusion in two European Union countries: Finland and Poland, indicating the most common barriers existing in the literature as well as analyzing major bottlenecks in the viewpoint of renewable energy companies’ executives. We also present statistics of the most commonly used RET in these countries in order to express the diffusion issues more appropriately. The outcomes of this study provide useful insight for the researchers in the energy transition field as well as practical managerial and regulatory implications aimed at overcoming these challenges.

A number of experiments suggest that the elementary particles are non-local entities. A dissipative self-organization, that treats particles as open systems may provide a better understanding of the underlying phenomena than conservative models. The proposed toy model is such an attempt. We found that self-gravitation (although accompanied by self-diffusion) may not only be compatible with the quantum phenomena but is perhaps the major reason for the existence of quantum fields. According to the proposed model, fields/particles (resemble those of the Standard Model) emerge from a dynamic self-organized medium (which we associate with vacuum dust) from competition between self-gravitation and self-diffusion. These forces produce turbulence in the form of vortices (which we call vacuum cells) that serve as the building blocks for fields and particles. Field/particle features and symmetries are based on their internal (intracellular) dynamics and vortex synchronization (intercellular dynamics). This model allows for rough estimations of relative field coupling strengths, the quantity of charges and flavors, the probabilities of quark transmutations, the dimensionality and the topologies of phase spaces, and other Standard Model parameters that came not from the theory but rather determined by experiment.

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thins films in the cases of the evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation–condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films submitted to thermal and mechanical stress, and fatigue effects; by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation y'2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that change of the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry and chronoamperometry experiments were performed in such viscous medium, where diffusion rates are much slower than in fluid solutions. Confirmation of the existence of such conditions from the log i vs. log v or log i vs. log t relationships in the current equation always yielded values lower than the expected value of 0.5. This could indicate impure linear diffusion profile, i. e. some contribution from radial diffusion (edge effect). However, performing these tests in monomeric solvents of similar viscosities, such as glycerol or propylene glycol, gave the desired value of 0.5. These results lead to the conclusion that current equations which are based on Fick’s laws may not be applicable for polymer electrolytes, where various obstruction to diffusion make it a more complicated process than in monomeric solvents.

The presence of phase diffusion can lead to the loss of the advantages of quantum measurements. Squeezing is considered to be an effective method to reduce the detrimental effect of phase diffusion on the measurement. The Mach-Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically, because the input state will change from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts in the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. The truncated MZ interferometer is simpler to build and operate than the conventional MZ interferometer, and also mitigates the phase diffusion noise by the squeezing operation, thus making it useful for applications in precision metrology.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

It is known that ammonium has a higher permeability through anion-exchange and bipolar membranes compared to K+ cation that has the same mobility in water. However, the mechanism of this high permeability is not clear enough. We develop a mathematical model based of the Nernst-Planck and Poisson equations for diffusion of ammonium chloride through an anion-exchange membrane; proton exchange reactions between ammonium, water and ammonia are taken into account. It is assumed that ammonium, chloride and OH− ions can only pass through membrane hydrophilic pores, while ammonia can also dissolve in membrane matrix fragments not containing water and diffuse through these fragments. It is found that due to the Donnan exclusion of H+ ions as coions, the pH in the membrane internal solution increases when approaching the membrane side facing distilled water. Consequently, there is a change in the principal nitrogen-atom carrier in the membrane: in the part close to the side facing the feed NH4Cl solution (pH<8.8), it is the NH4+ cation, and in the part close to distilled water, NH3 molecules. The concentration of NH4+ reaches almost zero at a point close to the middle of the membrane cross-section, which approximately halves the effective thickness of the diffusion layer for the transport of this ion. When NH3 takes over the nitrogen transport, it only needs to pass through the other half of the membrane. Leaving the membrane, it captures an H+ ion from water, and the released OH− goes towards the membrane side facing the feed solution to meet the NH4+ ions. The comparison of the simulation with experiment shows a satisfactory agreement.

Li₂MnO₃ is critical component in the well-studied Li-excess cathode materials xLi₂MnO₃•(1- x)LiMO₂ for achieving high lithium storage capacity. In this article, the diffusion of Li ions in Li₂MnO₃ is studied using molecular dynamics (MD) simulation with well-behaved empirical force fields obtained by fitting against the crystal structure from experiment and phonons calculated using Density Function Theory (DFT). We have found two possible tetrahedral hopping channels, 0-TM and 1-TM(Mn⁴⁺) channel, which are differentiated by the face sharing octahedral cations. Simulation results show that the 0-TM channel is active for Li hopping, while 1-TM(Mn4+) channel is inactive. During the delithiation process, the Li ions in the TM layered are firstly removed, then those in the Li layer. However, the Li ions will be trapped in the tetrahedral 0-TM channels as long as the four face sharing octahedral sites are cleared. Up to x=1.0 for Li₂-xMnO₃, almost all the Li ions are located at the tetrahedral sites, forming a regular array along a axis. The de-intercalation of tetrahedral Li ions requires a high voltage (>5.2 V vs. Li/Li+), limiting the practical capacities measured in lab. The diffusion of Mn ions into the Li layers is observed in a deeper delithiated structure (x=1.2 for Li₂-xMnO₃), indicating an initial phase transformation to a spinel-like structure. However, the Mn ions are mainly trapped in the tetrahedral sites in the Li layer, instead of the octahedral sites fin spinel-like structure. A few of Mn ions diffusing into the octahedral sites in Li layers have no face sharing tetrahedral Li ions, revealing a further Li de-intercalation is imperative for the complete phase transformation. Our model is not stable for x≥1.4 in Li₂-xMnO₃. Other charge compensation mechanism should be considered in this high delithiation stage, eg. oxygen release.

Hydrogel microneedles are a promising technology for the delivery of different types of medicines locally and painlessly, as well as ISF extraction. As the hydrogel microneedles are inserted into the tissue, they swell and release drugs. To improve the effectiveness of this technology in delivering medicine at controlled and desirable doses and intervals, a deep understanding of the mechanism of drug delivery inside the microneedles is required. In this work, drug diffusion inside a tapered microneedle is investigated using numerical simulation. The microneedle is divided into many small elements, and the mass transfer equation of meloxicam is solved in each element over time. The skin is simulated as the sink in the microneedle surface for drug absorption. Simulations are performed for different sizes of microneedles. For a microneedle with a height of 500 µm and a base diameter of 250 µm, the drug completely penetrates the skin within 3.2 seconds. The rate of drug diffusion from the tip of the microneedle is higher than diffusion from the side area near the microneedle base. The obtained data demonstrate that in addition to the height and the base diameter, the microneedle’s aspect ratio, h/d, also affects the time of drug diffusion. We present a nonlinear equation to predict the time of complete drug diffusion as a function of the microneedle geometrical parameter, including the height and base diameter. The proposed equation calculates the total drug diffusion time with an error of less than 7% for all studied cases. Predicting drug diffusion patterns inside microneedles can be helpful in the biomedical field, especially in the drug-controlled release system for the optimization of drug delivery.

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism a la Bisin and Verdier (2001) and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first thecase with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process : appearing, growing and then disappearing once a culture of cooperation is suffciently established in the local population.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

Ion channels are integral membrane proteins that facilitate the movement of ions across cell membranes, playing a key role in a range of biological processes. The high cost and time required for wet lab experiments to characterize ion channels has spurred the development of computational methods for this purpose. In our previous work, we demonstrated the effectiveness of protein language models for ion channel prediction, using a logistic regression classifier to distinguish ion channels from non-ion channels (TooT-BERT-C) and transporters from non-transporters (TooT-BERT-T). In this study, we build upon this approach by using a combination of classical machine learning classifiers and a Convolutional Neural Network (CNN) with fine-tuned representations from ProtBERT, ProtBERT-BFD, and MembraneBERT to discriminate ion channels from non-ion channels. The results of our experiments demonstrate that TooT-BERT-CNN-C, a combination of the representations from ProtBERT-BFD and a CNN, outperforms existing state-of-the-art methods for predicting ion channels, with a Matthews Correlation Coefficient (MCC) of 0.86 and an accuracy of 98.35% on an independent test set.

Additive manufacturing processes offer various options to fabricate metal parts, which show numerous ecological and technological advantages compared to formative and subtractive manufacturing methods. Due to quick availability and high accuracy, they are particularly suitable to produce complex prototypes. Metal fused deposition modeling is a relatively new material extrusion additive manufacturing technique based on the widely used fused filament deposition process. This study focuses on the Inconel 625 metal filament from Markforged Inc., it consists of a mixture of metal powder and a binder system, the latter being removed during washing and sintering. In this article, the mechanical properties of printed and sintered Inconel were investigated using tensile testing specimens with three different infill patterns, solid, triangular, and gyroid, printed in flatwise and upright direction. In addition, investigations into the dimensional accuracy of the printed specimens and the sintering shrinkage were carried out. The results showed that neither the dimensional accuracy nor the sintering shrinkage was significantly influenced by the printing orientation. In the context of lightweight engineering, the structures proofed beneficial especially within the elastic region. Generally, triangular infill patterns resulted in higher stiffness, while gyroids led to more ductile specimens. A mass-related evaluation of tensile testing elucidates that with aid of the infill structures weight savings of 40 % resulted in mechanical performance decreased by only 20 % on average.

The interplay between Diffuse Idiopathic Skeletal Hyperostosis (DISH) and the gut microbiota represents a compelling area of research, offering insights into the relationship between spinal degenerative diseases and the gut's microbial inhabitants. This comprehensive review seeks to unravel the complex connection, shedding light on its implications for human health and potential therapeutic avenues. A crucial section dives into the world of gut microbiota (GM), exploring its impact on human health, featuring its defining characteristics, and highlighting its role in metabolism, immunomodulation, host interaction, and how its composition changes over time. The subsequent portion delves into the relationship between microbiome composition and pathological bone development, including the link between Intervertebral Disc Degeneration (IDD) and gut inflammation, emphasizing how gut inflammation and GM dysbiosis play pivotal roles. Further dissecting the interconnections, various axes of influence, including the gut-spine axis, gut-bone axis, gut-joint axis, gut-disc axis (specific to DISH), gut-ligament axis, and gut-muscle axis, are discussed. Of particular interest is the section on the impact of GM on DISH-derived pain, addressing a critical aspect of the condition's manifestation. The review discusses the potential of GM modulation as a treatment for DISH, providing hope for therapeutic advancements. Additionally, it highlights the positive impact of lifestyle interventions, such as dietary modifications, sleep optimization, and exercise regimens, in mitigating GM dysbiosis and potentially improving DISH outcomes. Lastly, the intriguing prospect of fecal microbiome transplant and its implications for DISH management is examined, opening new avenues for research and therapeutic interventions. In conclusion, this comprehensive review underscores the intricate interplay between DISH and the gut microbiota, offering a fresh perspective on the impact of GM on spinal degenerative diseases. It emphasizes the potential for innovative treatments, such as GM modulation and lifestyle interventions, and presents fecal microbiome transplant as an exciting area for future exploration.

Carbon fibers (CFs) cannot be directly used for the preparation of CF paper because of their chemically inert nature. Herein, the surface of CF was modified via the spontaneous oxidative self-polymerization of dopamine. By taking full advantage of the spontaneous oxidation and self-polymerization properties of PD to maintain the maximum strength of CFs, a polydopamine-modified CF paper (PDA-CFP) with excellent performance was prepared using PD-modified CFs (PDA-CFs), which increased the proportion of hydrophilic functional groups on the surface of carbon fibers, increased the O/C ratio on the CF surface by 6 times, and improved the bond strength between the modified CF and the adhesive by making full use of the interaction force between polydopamine and PVA fibers. In this way, the primary properties of the CF paper was improved. Overall, the results showed that the dispersion of CF was considerably improved by the dopamine modification. In addition, the primary physical properties of PDA-CFP were better than those of virgin CF paper (CFP-0). PDA-CFP exhibited a maximum tensile strength of 2.04 kN/m2, a minimum resistivity of 0.06055 Ω·cm and a minimum porosity of 72.4%. The tightness could be increased by up to 12.1%.

Lipid mesophases are being intensively studied as potential candidates for drug-delivery purposes. Extensive experimental characterization has unveiled a wide palette of release features depending on the nature of the host lipids and of the guest molecule, as well as on the environmental conditions. However, only few simulation works have addressed the matter, which hampers a solid rationalization of the richness of outcomes observed in experiments. Particularly, to date there are no theoretical works addressing the impact of hydropathy on the transport of a molecule within lipid mesophases, despite the significant fraction of hydrophobic molecules among currently-available drugs. Similarly, the high heterogeneity of water mobility in the nanoscopic channels within lipid mesophases has also been neglected. To fill this gap, we introduce here a minimal model to account for these features in a lamellar geometry, and systematically study the role played by hydropathy and water-mobility heterogeneity by Brownian-dynamics simulations. We unveil a fine interplay between the presence of free-energy barriers, the affinity of the drug for the lipids, and the reduced mobility of water in determining the net molecular transport. More in general, our work is an instance of how multiscale simulations can be fruitfully employed to assist experiments in release systems based on lipid mesophases.

Background. To describe the characteristics of anterior mediastinal masses on conventional magnetic resonance imaging (MRI) and to assess the role of the Apparent Diffusion Coefficient (ADC) value in distinguishing benign from malignant mediastinal lesions. Methods. We conducted a retrospective cross-sectional study on 55 patients with anterior mediastinal mass who performed MRI before treatment. Biopsy and histopathological assessments were done after that. A radiologist evaluates the changes of signal intensity on these sequences: T1- weighted VIBE DIXON pre and post-contrast with Gadolinium, T2 HASTE, T2 TIRM, DWI/ADC, to determine the size, margin of the lesion, the presence of fat, cystic in it. ADCs values were calculated from the ADC maps which were constructed from b = 0 and b = 2000 Results. The study was composed of 55 patients, with 5 benign lesions and 50 malignant lesions. The ADCmean, ADCmedian, ADC10, and ADC90 in the histogram-based approach and hot-spot-ROI-based mean ADC for the malignant lesions was significantly lower than those found in benign lesions (P-value <0.05). The hot-spot-ROI-based mean ADC had the highest value in differentiation between benign and malignant mediastinal lesions, between group A (benign lesions, thymoma A, AB, B1) and group B (thymoma B2, B3 and other malignant lesions). The cut-off point of the ADC value differentiating malignant from benign mediastinal lesions was 1,17x10-3mm2/s with sensitivity of 80%, and specificity of 80%. The cut off point of the ADC value differentiating group A from group B was 0.99 x10-3mm2/s with sensitivity of 78,4%, and specificity of 88.9%. The cut-off point of the ADC value differentiating lymphoma from other malignant lesions was 0,91 x10-3mm2/s with sensitivity of 100%, and specificity of 60.5%. Conclusion. Diffusion-weighted MRI and measurement of ADC value in histogram-based approach and hot-spot-ROI-based mean ADC are very helpful in the differentiation between benign and malignant anterior mediastinal lesions.

This article responds to an identified and significant gap in the existing scholarly canon to consider the extent to which cinematic representations construct heroin users—the ‘junkie’—as a criminalised ‘Other’ which confer legitimacy on the notion that such are criminogenic and deviant. Positioned within the disciplinary bounds of cultural criminology, this article focuses on five films - Sid and Nancy (1986); The Basketball Diaries (1995); Trainspotting (1996); Requiem for a Dream (2000); and, T2 Trainspotting (2017). Drawing together Hall’s (1997) theories of representation and Hjelm’s (2014) theories of social constructionism, the findings from a narrative analysis of each of the films—individually and comparatively—explores the following themes, junkies: as criminogenic; as dangerous underclass; as embodying decay and depravity; and in relation to female junkies, as junkie whores. In doing so, this article elucidates new thinking and ideas about cinematic representations of junkies and how this shapes and influences social norms and mores.

Magnetic Nanoparticles (MNPs) is a promising technique to cure brain diseases. On the one hand, by serving as drug carriers, they can bypass the blood-brain barrier and deliver drug molecules to the brain parenchyma; on the other hand, their transport trajectory can be manipulated by applying an external magnetic field. However, due to the complex microstructure of brain tissues, e.g. the anisotropy of white matter (WM), how to achieve desired drug distribution patterns, e.g. uniform distribution, by tuning the drug delivery system is largely unknown. Here, in this study, by adopting a mathematical model capable of capturing the diffusion trajectories of MNPs in the microstructures, we systematically investigated the effects of key parameters in the MNPs delivery system on the equivalent diffusion coefficient of MNPs in the microenvironment of brain WM. The results show that uniform distribution of MNPs in anisotropic tissues can be achieved by adjusting the particle size and magnetic field. We have not only obtained a deeper understanding on how to optimise the MNPs delivery system, it can also be anticipated that an improved mathematical model could even help to achieve complex drug distribution patterns in the complicated brain environment by designing an appropriate combination of the key parameters.

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition of diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution specially when extreme situations occur (pandemics, global wars, etc.). When between jumps the dynamical evolution is governed by an Ornstein-Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continous time random walk.

The work is devoted to the investigation of virus quasispecies evolution and diversification due to mutations, competition for host cells, and cross-reactive immune responses. The model consists of a nonlocal reaction-diffusion equation for the virus density depending on the genotype considered as a continuous variable and on time. This equation contains two integral terms corresponding to the nonlocal effects of virus interaction with host cells and with immune cells. In the model, a virus strain is represented by a localized solution concentrated around some given genotype. Emergence of new strains corresponds to a periodic wave propagating in the space of genotypes. The conditions of appearance of such waves and their dynamics are described.

The relationship between Climate Change and Water is an obvious and key issue within the Sustainable Development Goals. This study aims to investigate the social representation created around this relationship in three different territorial contexts in order to evaluate the influence of the territory on the perception of the risk of Climate Change and its relationship with water. By means of a questionnaire completed by 1709 university students, the climatic literacy of the individual was evaluated in order to relate it to other dimensions on the relationship between Climate Change and Water (information, training previous on climate change and pro-environmental attitudes) in their different dimensions in three different territorial contexts. The results show that the socio-cultural context influences the social representation of Climate Change, but not from the climatological condition, so that it is reasonable to think that the social representation of this relationship is favoured by a common culture around this relationship.

Abstract: The diffusion of competition under the coexistence of multi-generation products has become one of the important challenges faced by enterprises in their daily and sustainable operations. At the same time, the competition between different brands has intensified the difficulty and complexity of decision-making in the process of multi-generation product operation, Therefore, based on the Norton-Bass model diffusion process, this paper introduces two marketing variables, dynamic price and quality level, builds a multi-generation product diffusion model under the dual-brand competition, and analyzes the impact of the company's revenue on the launch time to market, pricing, quality or technical level. By using system dynamics (SD) method, From the perspective of strong brand and weak brand enterprises, the competition diffusion model is built and simulated. The simulation shows that: i) When enterprises have the same brand competitiveness, reducing the pricing level cannot obtain more revenue, but diminish the overall revenue of the industry; Raising the pricing level can get more revenue, but also improve the revenue of competitors. ii) When the competitive strength of enterprises is different, the strong brand tends to maintain a stable pricing on the basis of improving the quality level, or slightly raise the price. Weak brands tend to raise the pricing of new products significantly on the basis of improving the quality level. iii) The launch time to market decision of new product is influenced by the degree of product quality upgrade. Therefore, the frequency of releasing new products should trade-off against the degree of technological upgrading of product quality. This paper provides the theoretical basis and new insights for the new product launch and operation decision of enterprises.

Rapid solidification during metal additive manufacturing (AM) leads to non-equilibrium microsegregation, which can result in the formation of detrimental phases and cracking. Most of the microsegregation models, assume a Scheil-type solidification, where the solidification interface is planar and there exists local equilibrium at the interface along with either zero or infinite solute diffusion in the respective participating phases - solid and liquid. This assumption leads to errors in prediction. One has to account for finite solute diffusion and the curvature at the dendritic tip for more accurate predictions. In this work, we compare different microsegregation models that do and do not consider finite diffusion and dendrite tip kinetics against the experiments. We also propose a method to couple dendrite tip kinetics with the diffusion module (DICTRA®) implemented in Thermo-Calc®. The models which accounted for both finite diffusion and dendrite tip kinetics matched well with the experimental data.

We study an air-fluidized granular monolayer, composed in this case of plastic spheres, which roll on a metallic grid. The air current is adjusted so that the spheres never loose contact with the grid, so that the dynamics may be regarded as pseudo two-dimensional (or two-dimensional, if the effects of sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all cases, we found the coexisting phases display strong energy non-equipartition. In the first transition, at weak fludization, a glassy phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at very low packing fraction and for a wide range of granular temperatures. Both phases are characterized also by a strong anti-correlated velocities upon collision. Thus, the dynamics observed for this quasi two-dimensional system unveils phase transitions with peculiar properties, very different from the predicted behavior in well know theories for their equilibrium counterparts.

Nonlinear catastrophes caused by geological fluids are a fundamental issue in rock mechanics and the geoengineering hazard field. For the consideration of hydrodynamic force on red-bed mudstone softening damage, X-ray visualization test on the fissure flow in mudstone block failure under hydrodynamic force was performed in this study based on block scale and the physical phenomena of fissure seepage and nonlinear diffusion were further explored. A new method for evaluating the hydro-damage degrees of rocks using an X-ray image analysis was proposed, and the quantitative relation of diffusion coefficients of hydro-damage and seepage was established. The research results revealed that the hydrodynamic force promoted the fluid-filled fissure behavior in mudstone specimen failure. Also, the seepage and diffusion phenomena of fluid in rocks during failures were indicated using X-ray imaging. A dual mechanical behavior was presented in the nonlinear seepage and abnormal diffusion of a red mudstone geological body under hydrodynamic conditions. The damaged degree of mudstone was aggravated by the effect of hydrodynamic force, and the initial seepage–diffusion coefficient with respect to lower hydro-damage was larger than the final seepage–diffusion coefficient with respect to higher hydro-damage of rocks with a decreasing nonlinear trend.

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

Cannabis is among the oldest human domesticates and has been subjected to intensive artificial (human-mediated) selection throughout history to create a wide array of varieties and biotypes for diverse uses, including fibre, food, biofuel, medicine and drugs. This paper briefly reviews the available literature on the taxonomy, evolutionary origin and domestication of this plant, as well as its worldwide dispersal, in both its wild and cultivated forms. Emphasis is placed on Europe and especially on the Iberian Peninsula. Today, it is accepted that Cannabis is a monospecific genus with two subspecies, C. sativa subsp. sativa and C. sativa subsp. indica, originating in Europe and Asia, respectively, by allopatric differentiation after geographic isolation fostered by Pleistocene glacial-interglacial cycles. Palynological and phylogeographic evidence situates the Cannabis ancestor on the NE Tibetan Plateau during the mid-Oligocene. The timing and place of domestication is still a matter of debate between contrasting views that defend single or multiple Neolithic domestication centres situated in different parts of the Eurasian supercontinent, notably central/southeastern China and the Caucasus region. Recent meta-analyses have suggested that wild Cannabis may have already been spread across Europe in the Pleistocene, and its domestication could have occurred during the European Copper/Bronze ages. According to the available reviews and meta-analyses, pre-anthropic dispersal of Cannabis into the Iberian Peninsula seems to have occurred only in postglacial times, and the earlier signs of cultivation date to the Early Medieval Ages. However, the palynological and archaeological evidence used to date is insufficient for a sound assessment, and the development of thorough Iberian databases to address further meta-analysis is essential for more robust conclusions. Some clues are provided for these achievements to be fulfilled.

This study aimed to evaluate potential posttreatment changes in ADC values within the tissue surrounding the enhancing lesion, particularly in areas not exhibiting MRI characteristics of in-volvement. Additionally, the objective was to investigate the correlation between ADC values, treatment response, and survival outcomes in individuals diagnosed with gliomas. This retrospective study included a total of 49 patients that underwent either stereotactic biopsy or maximal surgical resection. Histologically confirmed as Grade III or IV gliomas, all cases adhered to the 2016 and 2021 WHO classifications, with subsequent radio-chemotherapy administered post-surgery. Patients were divided into two groups: short and long survival group. Baseline and follow-up MRI scans were obtained on a 1.5T MRI scanner. Two ROI circles were positioned near the enhancing area, one ROI in the NAWM ipsilateral to the neoplasm and another symmetrically in the contralateral hemisphere on ADC maps. At follow-up there was a significant difference in both ipsilateral and contralateral NAWM be-tween the two groups, -0.0857 (p=0.004) and -0.0607 (p=0.037), respectively. There was a weak negative correlation between survival and ADC values in ipsilateral and contralateral NAWM at the baseline with the correlation coefficient -0.328 (p=0.02) and -0.302 (p=0.04), respectively. The correlation was stronger at the follow-up. The findings indicate that ADC values in normal appearing white matter (NAWM) may function as a prognostic biomarker in patients with diffuse gliomas.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

Binarization of degraded documents is an important preprocessing task for various document analysis such as OCR and historical document analysis. Existing studies have applied various convolutional neural network (CNN) models and generative models for document binarization, but they do not show generalized performance for noise that the model has not seen and it suffers from extracting elaborate text strokes. In this paper, to overcome these challenges, we utilize latent diffusion model (LDM), which is known for high-quality image generation model, for the first time in document binarization. By utilizing the iterative diffusion-denoising process in latent space, it shows high-quality cleaned binarized image generation and high generalized performance through using both data distribution and time step while training. Additionally, we apply gated U-Net to the backbone network to preserve text strokes using trainable gating value. Gated convolution can extract elaborate text stroke by allowing the model to focus on text region by combining gating value and feature. Furthermore, we maximize the effectiveness of the proposed model by training it with a combination of LDM loss and pixel-level loss, which is suitable for the model structure. Experiments on H-DIBCO and DIBCO benchmark datasets show that the proposed model outperforms existing methods.

The kinetic analysis of octogen coating with a polyurethane base containing hydroxyl-terminated polybutadi-ene (HTPB) was investigated using infrared spectroscopy. The coating process involved a solvent method, where octogen and liquid polyurethane were mixed, the solvent was evaporated, and curing took place at an elevated temperature. The ratio of HTPB to diisocyanate was equimolar. Initially, the curing process occurred in the solvent system, followed by further curing in the bulk system. The kinetic analysis was performed using a modified diffusion-autocatalytic model, which includes non-catalytic, autocatalytic, and diffusion compo-nents. This model was compared with others during the bulk reaction and proved to be effective in correcting errors, particularly in the gel time region. Thermodynamic parameters were evaluated using the Arrhenius and Eyring equations. The reaction rate was initially controlled by chemical reactivity, but after the gel time, diffusion became the controlling factor. In the HTPB-TDI system, both the non-catalytic and autocatalytic parts decreased with increasing temperature, while diffusivity increased. It is worth noting that diffusivity is temperature-dependent. Different diisocyanates, namely toluene diisocyanate (TDI), isophorone diisocyanate (IPDI), and hexamethylene diisocyanate (HMDI), were studied, revealing that HMDI exhibited higher reactivi-ty than TDI and IPDI. The catalyst effect on reaction rate HTPB-TDI system is investigated. Catalysts adding (0.1%) to HTPB-TDI system is really decrease their activation energy by efectivity DBTL>FeAA>TPB. Catalyst not change their diffusivity.

Jacobian-free Newton Krylov (JFNK) is an attractive method to solve nonlinear equations in nuclear engineering systems, and has been successfully applied to steady-state neutron diffusion (k-eigenvalue) problems and multi-physics coupling problems. Preconditioning technique plays an important role in JFNK algorithm, significantly affecting computational efficiency. The key point is how to automatically construct a high-quality preconditioning matrix that can improve the convergence rate, and perform the preconditioning matrix factorization efficiently. An efficient reordering-based ILU(k) preconditioner is proposed to achieve the above objectives. In detail, the finite difference technique combined with the coloring algorithm is utilized to construct an efficient preconditioning matrix with low computational cost automatically. Furthermore, the reordering algorithm is employed for the ILU(k) to reduce the additional non-zero elements and pursue robust computational performance. A two-dimensional LRA neutron steady-state benchmark problem is used to evaluate the performance of the proposed preconditioning technique, and steady-state neutron diffusion problem with thermal-hydraulic feedback is also utilized as a supplement. The results show that coloring algorithms can efficiently and automatically construct the preconditioning matrix. The reordering-based ILU(k) preconditioner shows excellent robustness, avoiding the effect of fill-in levels k choice in incomplete LU factorization.

The purpose of this paper is to study the influence of diffusion and thermal loading due to pulsed laser heating on a thermoelastic solid with voids in the context of the model of three-phase-lag. The non-dimensional governing equations are formulated and then the exact expressions for the temperature field, the displacement components, the stress components, the concentration field and the change in the volume fraction field are obtained using the normal mode technique. The material is an isotropic, homogeneous elastic half-space and heated by a non-Gaussian laser beam with pulse duration of ps. The magnesium crystal element is used as an application to compare the predictions induced by diffusion and laser pulse on poro-thermoelastic medium of the model of three-phase-lag with those for the theory of Green–Naghdi of type III. The results obtained for thermal changes are verified by comparison with two theories of thermoelasticity, namely the model of three-phase lag (3PHL) and the Green and Nagdi type III theory. Plot the expressions to examine the effect of the laser pulse at two different values of time and the effect void parameter. This study also yields some interesting special cases.

Background: As coronavirus (COVID-19) continues to pose a threat to the entire world, it is critical to developing strategies for containing its spread. The purpose of this study was to assess the demographic characteristics, brain tomography characteristics, and diffusion magnetic resonance findings of COVID-19 positive individuals. Material and Method: Between January 1 and December 31, 2021, 317 patients over the age of 18 were admitted to the emergency department with symptoms consistent with COVID-19. Three groups were formed based on clinical findings in patients, divided into light, medium, and severe, and four groups were formed based on radiological imaging findings. Results: The mean age of the 317 patients included in the study was 67.28±12.06 years, with a range of 28-91 years. The clinical classification of the patients was based on laboratory parameters and radiological imaging, not on their age or gender. Mild cases were classified as CO-RADS 0-4; moderate and severe cases were classified as CO-RADS 5-6 (p=0.001). While 60 (18.9%) of patients were followed outpatient, 144 (45.4%) were admitted to the hospital, 73 (23%) were admitted to the intensive care unit, and 40 (12.7%) died (p=0.001). Direct radiographs revealed bilateral involvement in 224 (70.7%) cases, peripheral involvement in 259 (81.7%) cases, and mid-lower lobe lung involvement in 194 (61.2%) cases (p=0.001). Brain tomography revealed infarction in 42 (13.2%) of the patients who were followed and hospitalized and hemorrhage in 22 (6.9%) of the patients. Magnetic resonance imaging revealed diffusion involvement in 68 (21.5%) of the cases (p=0.001). Conclusion: A standardized reporting system for COVID-19 data is required, and it must be simple to use, quick to understand, and focused on determining the risk of pneumonia. Additionally, the diagnostic role of radiological imaging, prognosis prediction, and severity scoring of lung involvement should be included.

In clinical diagnostics and longitudinal studies, the reproducibility of MRI assessments is of high importance in order to detect pathological changes, but developments in MRI hard- and software often outrun extended periods of data acquisition and analysis. This could potentially introduce artefactual changes or mask pathological alterations. However, if and how changes of MRI hardware, scanning protocols or preprocessing software affect complex neuroimaging outcomes from e.g. diffusion weighted imaging (DWI) remains largely understudied. We therefore compared DWI outcomes and artefact severity of 121 healthy participants (age range 19-54 years) who underwent two matched DWI protocols (Siemens product and Center for Magnetic Resonance Research sequence) at two sites (Siemens 3T Magnetom Verio and Skyra^fit). After different preprocessing steps, fractional anisotropy (FA) and mean diffusivity (MD) maps,obtained by tensor fitting, were processed with tract-based spatial statistics (TBSS). Inter-scanner and inter-sequence variability of skeletonised FA values reached up to 5% and differed largely in magnitude and direction across the brain. Skeletonised MD values differed up to 14% between scanners. We here demonstrate that DTI outcome measures strongly depend on imaging site and software, and that these biases vary between brain regions. These regionally inhomogeneous biases may exceed and considerably confound physiological effects such as ageing, highlighting the need to harmonise data acquisition and analysis. Future studies thus need to implement novel strategies to augment neuroimaging data reliability and replicability.

The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the correlation is often strongly non-linear. To understand this complex dependence, we consider the classical Brownian diffusion in this work. Under certain rational assumption, i.e. in the bi-component fluid mixture, the mass of the Brownian particle $M$ is far greater than that of the bath molecule $m$, we can adopt the weakly couple limit. Only considering the first-order approximation of the mass ratio $m/M$, we obtain a linear motion equation in the reference frame of the observer as a Brownian particle. Based on this equivalent equation, we get the Hamiltonian at equilibrium. Finally, using canonical ensemble method, we define a new entropy that is similar to the Kolmogorov-Sinai entropy. Further, we present an analytic expression of the relationship between the diffusion coefficient $D$ and the entropy $S$ in the thermal equilibrium, that is to say, $D =\frac{\hbar}{eM} \exp{[S/(k_Bd)]}$, where $d$ is the dimension of the space, $k_B$ the Boltzmann constant, $\hbar $ the reduced Planck constant and $e$ the Euler number. This kind of scaling relation has been well-known and well-tested since the similar one for single component is firstly derived by Rosenfeld with the expansion of volume ratio.

In the realm of artificial intelligence (AI), generative systems, most notably Midjourney, have tremendous power to generate creative images of buildings and sites of Islamic architectural heritage through text-to-image generation based on the internet. The AI-generated representations have significant potential for architects, specialists, and common users. However, the system has considerable limitations when generating images for some buildings and sites where the representations appear too far from their original represented structures. This research article attempts to answer the question: What are the limitations of using the AI system of Midjourney in producing images similar to the original buildings and sites of the Islamic architectural heritage? The research employs prompt engineering techniques based on historical sources as inputs to examine the accuracy of the output of the AI-generated images of selected examples of structures of the Islamic tradition. It compares the output with the original look by employing direct observation and critical analysis of human intelligence (HI). It categorizes these limitations into four groups: (1) limits of the prompt, (2) limits of fame, (3) limits of regionality and historical styles, and (4) limits of architectural elements and details. It concludes that while Midjourney has great capability to represent high-end AI-generated images inspired by the Islamic tradition, it currently falls short of presenting the actual appearance of some of their original structures.

The aim of this article is to understand the symbolic representations of the assistance strategies aimed at disabled children, expressed in two newspapers published on the island of Faial, in the Azores, in the second half of the 19th and early 20th centuries (covering the time horizon between the end of the monarchic period and the implementation of the First Republic). The technique of documentary analysis and a subsequent qualitative thematic content analysis of childcare news collected in two local newspapers was used. The discursive records produced by the press on the assistance strategies value, on the one hand, an axiological dimension and forms of charitable intervention and, on the other hand, aggregate and reconcile the discourses and techniques inherent to charitable and philanthropic models. This mutual assimilation underlies the achievement of the same objective: the moralisation and integration of invalid childhood and, above all, the protection of the existing social order. We conclude that, perhaps contrary to what would be expected, the charitable logic articulated in a concomitant way with the philanthropic logic survived even with the stabilization of the republican period (result of a revolution that deposed the regime of the constitutional monarchy and implemented the republican regime in 1910 in Portugal whose political elites mobilized an official discourse that advocated the separation between the State and Religion, assigning the State the function of social assistance for children and youth). This demonstrates a certain dissociation, as well as a relative autonomy of conceptions about child and youth care between republican political ideology and current social practices at least in this specific context.

A new three-dimensional numerical model of a polymer electrolyte fuel cell (PEFC) with a single straight channel has been developed to primarily investigate the important impact of the double-sided microporous layer (MPL) coating on the overall performance of the fuel cell and the distribution of the current and the oxygen concentration within the cathode gas diffusion layers (GDLs). Realistic experimentally estimated interfacial contact resistance values between the gas diffusion layer and each of the bipolar plates and the catalyst layer values were incorporated into the model, and parametric studies were performed. The results showed that the double-sided MPL coating could significantly improve the fuel cell performance by up to 30%. Also, it was shown that the neglect of the contact resistance between the MPL and the catalyst layer could overestimate the fuel cell performance by up to 6%. In addition, the results showed that the fuel cell performance and the distribution of the current and oxygen are more sensitive to the porosity of the MPL facing the bipolar plate than the porosity of the MPL facing the catalyst layer. All the above results are presented and critically discussed in detail.

Acute encephalopathy with biphasic seizures and reduced diffusion (AESD) is characterized by biphasic seizures following febrile viral infections and delayed reduced diffusion of the cerebral white matter on magnetic resonance imaging (MRI) diffusion-weighted imaging (DWI) (bright tree appearance, BTA). However, hypoxic encephalopathy with biphasic seizures and AESD-mimicking imaging findings has not been reported. Herein, we report an case of hypoxic encephalopathy due to suffocation with concomitant biphasic seizures and BTA, mimicking AESD. On day 1, a 5-month-old female was found face down with breathing cessation and deteriorating consciousness level. The electroencephalography (EEG) revealed periodic epileptic discharges, suggesting possible nonconvulsive status epilepticus. Despite the improvements in consciousness level and EEG abnormalities on day 2, her consciousness level deteriorated again with generalized tonic-clonic seizures on day 3, and head MRI-DWI revealed restricted diffusion predominantly in the subcortical areas, suggesting BTA. Treatment for acute encephalopathy resolved clinical sei-zures and EEG abnormalities. The persistence of abnormal EEG, reflecting abnormal excitation and accumulation of neurotoxic substances caused by hypoxia, may have contributed to the devel-opment of AESD-like findings. As hypoxic encephalopathy causes AESD-like biphasic seizures, monitoring the consciousness level, seizure occurrence, and EEG abnormalities even after acute symptoms have temporarily improved following hypoxia is essential.

The steady-state, coupled heat and mass transfer from a fluid flow to a sphere accompanied by an exothermal catalytic chemical reaction on the surface of the sphere is analysed taking into consideration the effect of thermal radiation. The flow past the sphere is considered steady, laminar and incompressible. The radiative transfer is modeled by P₀ and P₁ approximations. The mathematical model equations were discretized by the finite difference method. The discrete equations were solved by the defect correction – multigrid method. The influence of thermal radiation on the sphere surface temperature, concentration and reaction rate was analysed for three parameter sets of the dimensionless reaction parameters. The numerical results show that only for very small values of the Prater number the effect of thermal radiation on the surface reaction is not significant.

Nowadays, the imidazolium-based ionic liquids containing acetate counter-ions are attracting much attention as both highly selective absorbents of the acidic gases and CO₂ carriers in the supported ionic liquid membranes. In this regard, the investigation of the gas transport properties of such membranes may be appropriate for better understanding of various factors affecting the separation performance and the selection of the optimal operating conditions. In this work, we have tested CH₄, CO₂ and H₂S permeability across the SILM impregnated by 1-butyl-3-methylimidazolium acetate (bmim[ace]) with the following determination of the ideal selectivity in order to compare the facilitated transport membrane performance with the SILM that dissolves acidic gases physically, namely, containing 1-butyl-3-methylimidazolium tetrafluoroborate (bmim[BF₄]). Both SILMs have showed modest individual gases permeability and ideal selectivity of CO₂/CH₄ and H₂S/CH₄ separation that achieves values up to 15 and 32, respectively. The effect of the feed gas mixture composition on the permeability of acidic gases and permeselectivity of the gas pair was investigated. It turned out that the permeation behavior for the bmim[ace]-based SILM toward the binary CO₂/CH₄, H₂S/CH₄ and ternary CO₂/H₂S/CH₄ mixtures was featured with high acidic gases selectivity due to the relatively low methane penetration through the liquid phase saturated by acidic gases.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

The service life of the reinforced concrete structure in the marine environment can be impaired significantly due to chloride-induced corrosion. However, how the chloride diffusion in pre-cracked concrete structures is affected by the hydrostatic pressure magnitude is poorly understood. This study experimentally examined the effect of hydrostatic pressure on the chloride diffusion in pre-cracked concrete. Cracks with five different widths, i.e., 20 μm, 40 μm, 60 μm, 80 μm, and 100 μm, were manually created using a splitting tensile apparatus respectively. The chloride diffusion in the concrete with a certain crack was then studied under four different hydrostatic pressures of 0 MPa, 0.1 MPa, 0.3 MPa, and 0.5 MPa. Experimental results show that the chloride diffusion in concrete with a crack greatly relies on both the hydrostatic pressure and the crack width. The chloride concentration increases as the hydrostatic pressure grows, particularly for the wider cracks with width ranging from 60 μm to 100 μm. Surprisingly, the hydrostatic pressure has a negligible effect on the chloride distribution in the concrete with a crack width no larger than 40 μm. Both the chloride diffusion coefficient and the surface chloride concentration of concrete increased gradually as the hydrostatic pressure increased. The experimental findings enrich our understanding of the behavior of pre-cracked concrete when exposed to chloride-induced corrosion at different depths of marine environments.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

Pseudomonas aeruginosa is a Gram-negative bacillus included among the six "ESKAPE" microbial species with an outstanding ability to "escape" currently used antibiotics and developing new antibiotics against it is of the highest priority. Whereas minimum inhibitory concentration (MIC) values against Pseudomonas aeruginosa have been used previously for QSAR model development, disk diffusion results (inhibition zones) have not been apparently used for this purpose in the literature, and we decided to explore their use in this sense. We developed multiple QSAR methods using several machine learning algorithms (Support vector classifier, K Nearest Neighbors, Random Forest Classifier, Decision Tree Classifier, AdaBoost Classifier, Logistic Regression, and Naive Bayes Classifier). The main descriptors used in building the models belonged to the families of adjacency matrix, constitutional descriptors, first highest eigenvalue of Burden matrix, centered Moreau-Broto autocorrelation, and averaged and centered Moreau-Broto autocorrelation descriptors. A total of 32 models were built, of which 28 were selected and stacked to create a meta-model. In terms of balanced accuracy, the best performance was provided by KNN, SVM and AdaBoost algorithms, but the ensemble method had slightly superior results in nested cross-validation.

False positives on multiparametric (mp)-MRI result in a large number of unnecessary biopsies in men with clinically insignificant diseases. This study investigates whether quantitative diffusion MRI can improve differentiation between false positives, true positives and normal tis-sue. Twenty-three patients underwent mp-MRI and Vascular, Extracellular and Restricted Diffu-sion for Cytometry in Tumours (VERDICT)-MRI, followed by transperineal biopsy. The patients were categorised into two groups following biopsy: (1) significant cancer - true positive (2) atro-phy/inflammation/high-grade prostatic intraepithelial neoplasia (PIN) - false positive. The clinical apparent diffusion coefficient (ADC) values of the lesions were obtained, and the intravoxel inco-herent motion (IVIM), diffusion kurtosis imaging (DKI) and VERDICT models were fitted using a deep learning approach. Significant differences (p < 0.05) between true positive and false positive lesions were found in ADC, IVIM perfusion fraction (f) and diffusivity (D), DKI diffusivity (DK) and kurtosis (K) and VERDICT intracellular volume fraction (fIC), extracellular-extravascular vol-ume fraction (fEES) and diffusivity (dEES) values. Significant differences between false positives and normal tissue were only found for the VERDICT fIC. These results demonstrate that model-based diffusion MRI could reduce the number of unnecessary biopsies due to false positive prostate lesions and shows promising sensitivity to benign diseases that mimic cancer.

The main objective of this work was to evaluate the application of individual and ensemble machine learning models to classify malignant and benign breast masses using features from two-dimensional (2D) correlated spectroscopy spectra extracted from five-dimensional Echo Planar-Correlated Spectroscopic Imaging (5D EP-COSI) and Diffusion-weighted imaging (DWI). Twenty-four different metabolite and lipid ratios with respect to 2D diagonal peaks at 1.4ppm and 5.4ppm, and water from one-dimensional non-water-suppressed (NWS) spectra were used as the features. Additionally, water fraction, fat fraction and water-to-fat ratios from NWS spectra and apparent diffusion coefficients (ADC) from DWI were included. Nine most important features were identified using recursive feature elimination. XGBoost (AUC:93.0%, Accuracy:85.7%, F1-score:87.6%), GradientBoost (AUC:94.4%, Accuracy:87.0%, F1-score:89.4%), CatBoost (AUC:95.2%, Accuracy:86.9%, F1-score:88.4%) and RandomForest (AUC:92.2%, Accuracy:85.3%, F1-score:87.6%) were the best performing models. While the conventional biomarkers like choline, myo-Inositol, and glycine were statistically significant predictors, the key features contributing to the classification were ADC, 2D diagonal peaks at 0.9ppm, 2.1ppm and 2.3ppm, cross peaks between 1.4 and 0.9ppm, 4.3 and 4.1ppm, 2.1 and 1.4ppm and the triglyceryl-fat cross peak. The results highlight the contribution of the 2D spectral peaks to the model, and they demonstrate the potential of 5D EP-COSI for early breast cancer detection.

Objectives: To explore the potential of Radiomics alone and in combination with diffusion-weighted derived quantitative parameter namely apparent diffusion co-efficient (ADC) using supervised classification algorithms in predicting outcomes and prognosis. Materials and Methods: Retrospective evaluation of the imaging was done for a study cohort of uterine cervical cancer, candidates for radical treatment with chemo radiation. ADC values were calculated from the darkest part of the tumor, both before (labeled preADC) and post treatment (labeled postADC) with chemo radiation. Post extraction of 851 Radiomics features and feature selection by taking the union of the features which had Pearson correlation >0.35 for recurrence, >0.49 for lymph node and >0.40 for metastasis, analysis was done to predict clinical outcomes. Results: The study enrolled 52 patients who presented with variable FIGO stages and age range 28–79 (Median = 53 years) with median follow-up of 26.5 months (range, 7–76 months). Disease recurrence occurred in 12 patients (23%). Metastasis occurred in 15 patients (28%). A model generated with 24 radiomics features and preADC using a monotone multi-layer perceptron neural network to predict the recurrence yields AUC of 0.80 and kappa value as 0.55 and shows that addition of radiomics features on ADC values improves the statistical metrics by 40% approximately for AUC and 223% approximately for Kappa. Similarly, neural network model for prediction of metastasis re-turns AUC of 0.84 and kappa value as 0.65 over performs by 25% for AUC and 140% for Kappa approximately. There was a significant input of GLSZM features (SALGLE and LGLZE) and GLDM features (SDLGLE and DE) correlation with clinical outcomes of recurrence and metastasis. Conclusions: The study is an effort to bridge the unmet need of translational predictive biomarkers in stratification of uterine cervical cancer patients based on prognosis.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of (globally) exponentially stable positive stationary solution of delayed reaction-diffusion cell neural networks under Dirichlet zero boundary value, including the global stability criteria \textbf{in the classical meaning}. Next, sufficient conditions are proposed to guarantee the global stability invariance of ordinary differential systems under the influence of diffusions. New theorems show that the diffusion is a double-edged sword in judging the stability of diffusion systems. Besides, an example is constructed to illuminate that any non-zero constant equilibrium point must be not in the phase plane of dynamic system under Dirichlet zero boundary value, or it must lead to a contradiction. Next, under Lipschitz assumptions on active function, another example is designed to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks via a Saddle point theorem. Finally, a numerical example illustrates the feasibility of the proposed methods.

Background: Early identification and prevention of hypoxic ischemic encephalopathy (HIE) may reduce neonatal mortality and morbidity. Objective: We aimed to correlate between urinary Activin-A and MRI (conventional and Diffusion-weighted) and the severity of HIE in full-term neonates. Methods: Forty-five full-term neonates with HIE admitted to NICU and 15 normal neonates were enrolled into the study. The concentration of urinary Activin-A was determined using enzyme immunoassay kits and MRI were done. Correlations between urinary Activin-A and MRI with the degree of HIE were done. Results: Urinary Activin-A levels were significantly higher in neonates with HIE than controls (P<0.001). It was positively correlated with the clinical grading of HIE and a cutoff value of 0.08µg/l on day-1 after birth had a sensitivity of 98.6% and specificity of 97.1% for prediction of HIE. DW-MRI detected HIE with a high sensitivity (85%) compared to the low sensitivity of conventional MRI (35%). An ADC value of ≤ 0.8 was the best sensitivity-specificity cutoff point for detecting severe ischemic injury. DW-MRI imaging was positively correlated with Urinary Activin-A and both of them were positively correlated with the clinical grades of HIE (P < 0.001). Conclusions: DW-MRI imaging is correlated well with urinary Activin-A in full-term neonates with HIE and both of them are correlated with the degree of HIE. Early determination of urinary Activin-A combined with DW-MRI imaging can early detect HIE and its severity in full-term neonates with HIE.

One of the most important problems in the presence of epidemics and pandemics is an accurate prediction and preparedness. Scholars and experts argue that future pandemics and/or epidemics are almost inevitable events and is not whether next pandemics will happen, but when a new heath emergency will emerge. Epidemiologic models for prediction of Coronavirus Disease 2019 (COVID-19) have shown many limitations because of unpredictable dynamics of the new viral agent SARS-CoV-2 in environment and society. The main goals of this study are twofold: first, the analysis of anthropogenic activities and factors that may trigger pandemic threats; second, the planning of new directions for strategies to reduce risks that a pandemic threat emerges and/or in the initial phase to reduce vast diffusion and negative impact of new viral agents that can generate hazards and problems in public health, environment and socioeconomic systems. In particular, the investigation and understanding of sources and driving factors concerning the emergence and diffusion of new pandemics have critical aspects for strategic actions of forecast, prevention and preparation of effective policy responses to cope with next pandemic crises and health emergencies. Insights here endeavor, whenever possible, to clarify these problems to increase the knowledge of the sources and factor determining the emergence of new viral agents in order to design optimal response policies to face next pandemic diseases similar to COVID-19. .

Subgrid scale models for unresolved turbulent fluxes are investigated with a focus on combustion for space propulsion applications. An extension to the gradient model is proposed, introducing a dependency on the local burning regime. The dynamic behavior of the model's coefficients is investigated, and scaling laws are studied. The discussed models are validated using a DNS database of a high-pressure turbulent fuel-rich methane-oxygen diffusion flame. The operating point and turbulence characteristics are selected to resemble those of modern combustors for space propulsion applications to support the future usage of the devised model in this context.

We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

This work investigates a new nanostructured gas-diffusion-layer (nano-GDL) to improve performance of air-cathode Single-Chamber-Microbial-Fuel-Cells (a-SCMFCs). The new nano-GDLs improves the direct oxygen-reduction-reaction by exploiting the best of nanofibers from electrospinning in terms of high surface ratio to volume and high porosity, and laser-based processing to promote adhesion. Nano-GDLs by electrospinning were fabricated directly collecting two nanofibers mats on the same carbon-based electrode, acting as the substrate. Each layer was designed with a specific function: water resistant, oxygen permeable polyvinylidene-difluoride (PVDF) nanofibers served as a barrier to prevent water-based electrolyte leakage, while an inner layer of cellulose nanofibers was added to promote oxygen diffusion towards the catalytic sites. The maximum current density obtained for a-SCMFCs with the new nano-GDLs is (132.2 ± 10.8) mA m^-2, and it doubles the current density obtained with standard PTFE-based GDL (58.5 ± 2.4 mA m^-2), used as reference material. The energy recovery (EF) factor, i.e. the ratio of the power output to the inner volume of the device, was then used to evaluate the overall performance of a-SCMFCs. a-SCMFCs with nano-GDL provided an EF value of 60.83 mJ m^-3: one order of magnitude higher than the value of 3.92 mJ m^-3 obtained with standard GDL

Porous materials can be characterized by well-trained neural networks. In this study, fibrous paper-type gas diffusion layers were trained with artificial data created by a stochastic geometry model. The features of the data were calculated by means of transport simulations using the Lattice–Boltzmann method based on stochastic micro-structures. A convolutional neural network was developed that can predict the permeability and tortuosity of the material, through-plane and in-plane. The characteristics of real data, both uncompressed and compressed, were predicted. The data was represented by reconstructed images of different sizes and image resolutions. Image artifacts are also a source of potential errors in the prediction. The Kozeny–Carman trend was used to evaluate the prediction of permeability and tortuosity of compressed real data. Using this method, it was possible to decide if the predictions on compressed data were appropriate.

In this paper a combined Laplace transform (LT) and boundary element method (BEM) is used to find numerical solutions to problems of anisotropic functionally graded media which are governed by the transient diffusion-convection-reaction equation. First, the variable coefficients governing equation is reduced to a constant coefficients equation. Then, the Laplace-transformed constant coefficients equation is transformed a boundary-only integral equation. Using a BEM, the numerical solutions in the frame of Laplace transform may then be obtained from this integral equation. Then the solutions are inversely transformed numerically using the Stehfest formula. Some problems considered are those of compressible or incompressible flow, and of media which are quadratically, exponentially and trigonometrically graded materials. The results obtained show that the analysis used to transform the variable coefficients equation into the constant coefficients equation is valid, and the mixed LT-BEM is easy to implement for obtaining the numerical solutions. The numerical solutions are verified by showing their accuracy and steady state. For symmetric problems, the symmetry of solutions is also justified. Moreover, the effect of the anisotropy and inhomogeneity of the material on the solutions are also shown, as to suggest that it is important to take the anisotropy and inhomogeneity into account when doing experimental studies.

In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been recognized as the most promising technologies for the removal of organic pollutants from water. In this paper, we propose a 1D convection-diffusion-reaction model concerning the transport and oxidation of oxalic acid (OA) and oxygen evolution in the flow-through electrochemical oxidation system with REM. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in calculated and experimental data at different transmembrane pressures and initial concentrations of OA. The model provides an understanding of the processes occurring in the system and gives the concentration, current density, potential and overpotential distributions in REM. The dispersion coefficient was determined as a fitting parameter and it is in good agreement with literary data for similar REMs. It is shown, that the oxygen evolution reaction plays an important role in the process even under the kinetic limit, and its contribution decreases with increasing total organic carbon flux through the REM.

The diffusion coefficients of ions are measured in a microchip filled with a cationic charged 3D hydrogel in order to study the effect of cationic charged 3D hydrogel on the diffusivity of ions. In this study, poly-diallyl-dimethyl-ammoniumchloride (poly-DADMAC) is used to produce a 3D hydrogel. Four different fluorophores are used in the 3D hydrogel rhodamine 6G, rhodamine-BSA, fluorescein isothio-cyanate (FITC) and FITC-BSA. The rhodamine 6G and rhodamine-BSA are positively charged (cations), while fluorescein isothio-cyanate (FITC) and FITC-BSA are negatively charged (anions). Two widely used techniques which are short time diffusivity measurement technique and long time diffusivity measurement techniques are used to measure the diffusion coefficients. For the short time measurement, Fluorescence recovery after photo-bleaching (FRAP) is used by a 3D confocal microscope. For the long time measurement, fluorescence images are taken for 11 days to observe a pure diffusivity without any convective movement. As a result, the diffusivity of the cations was found to be lower than that of the anions in the cationic charged hydrogel.