Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

The particulars of stimulus-response experiments done on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures – so that modal analysis can be used constructively in systems biology model building – for nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output data associated with a structural model – one that includes inputs and outputs explicitly – and for NL as well as linear biosystems. The methodology establishes model dimensionality (size, complexity) from particular data sets; helps select among multiple candidate models (model distinguishability); helps in designing new experiments to extract “hidden” structure; and helps to simplify (reduce) models to their essentials. For NL biosystems, results are not as comprehensive, similarly informative about their dominant dynamical properties, and unified with linear models on invariant 2-dimensional manifolds in phase space. Some automation of these highly technical aspects of biomodeling is also introduced.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

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.

A Hayward black hole and magnetically charged black hole based on rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ (${\cal F}$ is a field invariant) are considered. It was shown that the metric function in both models possesses a de Sitter core without singularities as $r\rightarrow 0$. The behavior of the Hawking temperature and the heat capacity in these models are similar. The phase transitions take place when the Hawking temperature has the maximum, and black holes are thermodynamically stable at some event horizon radii when the heat capacity is positive. We show that the source of gravity in the Hayward model is questionable.

The chiral optical Tamm state (COTS) is a special localized state at the interface of a handedness-preserving mirror and a structurally chiral medium such as a cholesteric liquid crystal or a chiral sculptured thin film. The spectral behavior of COTS, observed as reflection resonances, is described by the temporal coupled-mode theory. Mode coupling is different for two circular light polarizations because COTS has a helix structure replicating that of the cholesteric. The mode coupling for co-handed circularly polarized light exponentially attenuates with the cholesteric layer thickness since the COTS frequency falls into the stop band. Cross-handed circularly polarized light freely goes through the cholesteric layer and can excite COTS when reflected from the handedness-preserving mirror. The coupling in this case is proportional to anisotropy of the cholesteric and theoretically it is only anisotropy of magnetic permittivity that can ultimately cancel this coupling. These two couplings being equal results in a polarization crossover (the Kopp--Genack effect) for which a linear polarization is optimal to excite COTS. The corresponding cholesteric thickness and scattering matrix for COTS are generally described by simple expressions.

This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov-Smirnov type-test for change-point detection is constructed and its null distribution is provided. An estimator of the change-point location is defined. Its consistency and its limiting distribution are studied in detail. A simulation experiment is carried out to assess the performance of the results which are also applied to two sets of real data.

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

In this study, the focus is on the drop test simulation of an MR (Magnetorheological) damper-based main landing gear (MRMLG), aiming to explore multi-degree-of-freedom (DOF) dynamic models during aircraft landing. Three different 6-DOF dynamic models are proposed in this work and their drop performances are compared with results achieved one of commercial softwares. The proposed models include a nonlinear aircraft model (NLAM), a linearized approximated aircraft model (LAAM) linearizing from the nonlinear equations of motion in NLAM, and a fully approximated aircraft model (FAAM) which linearizes the MRMLG's strut force model. In order to evaluate drop performance of the aircraft landing gear system with MR dampers, a 7-DOF aircraft model incorporating the nonlinear MRMLG is formulated using RecurDyn. The principal comparative param-eters are the coefficient of determination (R2) for system response of each model with Re-curDyn model and root mean square error (RMSE) which is the ensembles of CG dis-placement data for each model. In addition, the ensemble of time series data is created for diverse drop scenarios, providing valuable insights into the performance of the proposed drop test models of the aircraft landing gear system featuring MR dampers.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

While numerous studies have explored the correlation between the built environment and ride-hailing demand, few have assessed their nonlinear interplay. Utilizing ride-hailing order data and multi-source built environment data from Nanjing, China, this paper uses the machine learning method, eXtreme Gradient Boosting (XGBoost), combined with SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to investigate the impact of built environment factors on ride-hailing travel demand, including their non-linear and threshold effects. The findings reveal that dining facilities have the most significant impact, with a contribution rate of 30.75%, on predicting ride-hailing travel demand. Additionally, financial, corporate, and medical facilities also exert considerable influence. The built environment factors need to reach a certain threshold or within a certain range to maximize the impact of ride-hailing travel demand. population density, land use mix and distance to the subway station collectively influence ride-hailing demand. The results are helpful for TNCs to allocate network ride-hailing resources reasonably and effectively.

We firstly present two popular space discretization models of the Nonlinear Schrödinger Equation in dark solitons motion : the Direct-Discrete model and the Ablowitz-Ladik model. Applying the midpoint scheme to the space discretization models, we get two time-space discretization models: the Crank-Nicolson method and the New-Difference method. Secondly, we demonstrate that the solutions of the two space discretization models converge to the solution of the Nonlinear Schrödinger Equation. Also, we prove that the convergence order of the two time-space discretization models are O(h2+τ2) in discrete L2-norm error estimates. Finally, the numerical experiments agree well with the proven theoretical results.

We evaluated the growth of four genetic groups, two pure (pacu and tambaqui) and two hybrids (tambacu and paqui) of Serrasalmidae fish fed with different feeding programs. Over the five months, 30 animals from each genetic group that were evaluated in three cages with 10 animals from each genetic group per cage. A different feeding program was used for each cage, consisting of three commercial diets containing 24, 28, or 32% crude protein (CP) in different combinations. A logistic model or an exponential were used to fit the growth curves. The evaluation time did not allow the adjustment of the logistic model for the tambaqui and paqui groups, as well as for the animals fed the food program with the highest initial protein intake. Pure pacu proved to be an early performing group, while tambacu hybrid reached a higher final weight without slowing down growth.

The development of plant-based meat analogues has become a significant challenge for the food industry in recent years due to the increasing demand for sustainable and healthier proteins in the context of a global protein transition. Plant-based meat analogues imitate the visual, textural, and chemical properties of traditional meat products and are required to closely resemble meat to appeal to consumers. In addition, consumers demand natural, clean-label, and nutritional and healthy products. To address these challenges, the food industry must develop highly healthy, nutritious, and E-number-free meat analogue products. Understanding the functionality of each ingredient and its role in the food matrix is crucial to being a key player in the innovation of the meat analogues market. This review provides updated information on the primary ingredients utilized for the development of plant-based burger meat alternatives and their functionality. The key components of meat analogue burgers are outlined, including plant proteins, binding agents, fats and oils, flavorings, colorings, preservatives, fortificants, and clean-label considerations.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

In current transportation hubs, it is a common phenomenon that passengers travel with necessary wheeled-luggage or suitcases. Due to the fact that most luggage occupies certain space within dense passenger crowds with giant mass inertia, its abnormal motions, such as drifting, frequently trig unavoidable local disturbances and turbulence in surrounding pedestrian flows, further increasing security risk. While, current researches primarily concentrate on examining the impact of luggage on crowd evacuation efficiency through scenario-based experiments and analyzing the spatial characteristics of crowd distribution in surveillance videos. There still lacks of the dynamic disturbance mechanisms and crowd stability associated with the combined motion of passengers and luggage. Therefore, this study considers the luggage-laden passenger as a deformable particle, the resulting disturbance on surrounding non-luggage passengers is analyzed and quantified into a nonlinear pressure term. Subsequently, the disturbance propagation model of passenger-luggage is developed by adapting the classical Aw-Rascle traffic flow model with incorporation of the pressure term. Simulation experiments of disturbances caused by luggage drifting and retrograding validate that the proposed propagation model aligns with real-world situations in transportation hubs. Quantitively, when luggage-laden passenger drifted left, the disturbing force of left side crowd can reach a peak of 238N in the passenger density of 3.0 p/m2, and the maximum difference between the left and right sides disturbing force can reach 153N. Furthermore, it is recommended that the proposed model can be applied to crowd flow analysis and risk assessment.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attack and packet loss. Firstly, the stochastic characteristics of DoS attack and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of systems. Then, by constructing a general common Lyapunov functional and combining with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through a numerical example.

The abilities of quantitative description of noise are restricted due to its origin and only the statistical and spectral analysis methods can be applied while an exact time evolution cannot be defined or predicted. It emphasizes the challenges faced in many applications including communication systems where noise can play, on one hand, a vital role impacting signal-to-noise ratio but possessing, on the other hand, unique properties such as infinite entropy (infinite information capacity), exponentially decaying correlation function and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criteria, on which the main idea of the study is based on, is the Central Limit Theorem which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. The study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.) whose output signals are analyzed according to criteria that encompass the probability density functions of a chaotic signal itself and its envelope and phase, statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. The analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates Gaussian distribution. It allows generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

With the development of organizational biology and forced from the EU Cosmetic Regulation (EU/1223/2009) with the complete ban of animal testing for cosmetic purposes, 3D skin models have been widely developed due to their similar physiological structure and metabolic function to native human tissue. 3D skin models for in vitro cosmetic evaluation are still promising alternative methods for evaluating phototoxicity, corrosivity and irritation. These models have been used for early screening and later validation of toxicity and efficacy evaluation by many well-known cosmetic companies. 3D skin models have become an important tool in cosmetic evaluation research. This article reviews the development of 3D skin models and their application in cosmetic evaluation. An outlook on the current application and future technological development directions in the cosmetic field is also presented.

The assortment of low-cost 3D printers for “in-practice” use, e.g., for clear aligner therapies, is ever increasing. To address concerns about the accuracy of orthodontic models produced on such printers when cost efficient modes of 3D printing are employed, this study examined the effect of print model body type and print angulation on accuracy. Six printing-configuration groups were included: 2 model types (solid or hollow shell) combined with 3 print angles (0°, 70°, or 90°) with 10 models/group; all models were printed with 100-µm layer thickness using a digital light processing-based 3-dimensional printer. Eleven selected structures and distances were measured on the printed models with a digital microscope and compared to the same measures on a digitized master model. The clinically-acceptability range was set at ±0.25 mm difference from the master model for single tooth measurements (intra-tooth) and ±0.5 mm for cross-arch measurements (inter-tooth). For individual measurements across all models, 98% fell within clinical acceptability. For mean measurements within each model group, only canine height for the shell-0° model had a mean difference (0.26 mm ± 0.03) outside the clinically acceptable range for intra-tooth measurements. Standard deviations for all intra-tooth measurements were within 0.07 mm. While none of the mean inter-tooth measurements exceeded the acceptability range, the standard deviations were larger (0.04 to 0.30 mm). Accuracy of orthodontic models for clear aligner therapies was not impacted beyond the clinically acceptable range when altering model body type and print angulation to improve efficiency of 3D printing. These findings suggest greater flexibility of the practitioner to alter print settings to address time and cost efficiency in various clinical scenarios and still maintain clinically acceptable model accuracy.

Tendons transmit forces from muscles to bones through joints. Typically, tendons and muscles work together to innovate a particular type of motion. Therefore, in order for the tendons to find attachment to the bones, they are naturally adapted as much thinner strands than the muscles that they serve. Thus, they are often subjected to much higher stresses than the muscles that they actually serve in any given action. As a result, tendons are susceptible to injuries that may lead to a permanent dysfunction in joint mobility due to the fact that the scar tissue that forms after healing does not often have the same mechanical properties of the original tissue. It is, therefore, very important to understand the mechanical response of tendons. This paper examines the performances of two viscoelastic standard nonlinear models in modelling the elastic and plastic behaviour of the tendon in the light of a well-known hyperelastic Yeoh model. The use of the Yeoh model is more for validating the performances of the viscoelastic models within the elastic region rather than for comparison purposes. Yeoh model’s selection was based on its superior performance in modelling the elastic phase of soft tissue as reported in previous studies combined with its simplicity. The results show that the two standard nonlinear solid models perform extremely well both in fitting accuracies and in correlating stress results. The most promising result is the fact that the two standard nonlinear models can model tendon behaviour in the nonlinear plastic region. It is also noted that the two standard nonlinear models are physically insightful since their optimisation parameters can be easily interpreted in terms of tendon elasticity and viscoelastic parameters.

As Artificial Intelligence (AI) technology, particularly Machine Learning algorithms, becomes increasingly ubiquitous, our abilities to understand and interpret AI and machine learning algorithms are becoming increasingly desirable. Visualization has been used as a common tool to view and understand complex machine learning processes. In this paper, we will focus on developing a general framework for the visualization of machine learning models as a scalar valued multi-dimensional function to help users understand how the models behave over different viewing spaces. We first give a formal definition of the visualization problem. Interpolation-based morphing and subspace sampling techniques are applied to generate various renderings through projections and cross-sections of the model space as 3D surfaces or heatmap images. This method will be applied to two real-world datasets and applications: the diagnosis of Alzheimer's Disease (AD) using a human brain networks dataset and a real-world benchmark dataset for predicting home credit default risks. The visualizations show that different machine learning algorithms can behave quite differently under different conditions.

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.

Predicting human trajectories poses a significant challenge due to the complex interplay of pedestrian behavior, which is influenced by environmental layout and interpersonal dynamics. This complexity is further compounded by variations in scene density. To address this, we introduce a novel dataset from the Festival of Lights in Lyon 2022, characterized by a wide range of densities (0.2-2.2 ped/m2). Our analysis demonstrates that density-based classification of data can significantly enhance the accuracy of predictive algorithms. We propose an innovative two-stage processing approach, surpassing current state-of-the-art methods in performance. Additionally, we utilize a collision-based error metric to better account for collisions in trajectory predictions. Our findings indicate that the effectiveness of this error metric is density-dependent, offering prediction insights. This study not only advances our understanding of human trajectory prediction in dense environments but also presents a methodological framework for integrating density considerations into predictive modeling, thereby improving algorithmic performance and collision avoidance.

The multiphase motors due to their reliability find new areas of application in the industry and transportation. Developing of any system with multiphase motors at first requires elaborate model of the system, define control mode and controllers. The model of control system for the six-phase drive is based on its conventional d-q mathematical model and indirect field-oriented control. Simulink model of six-phase drive with indirect field-oriented control and simulated with two types PID and PID fuzzy controllers. The simulation results, reflecting step response and provided speed reference law as well as load application at constant speed, are presented and analyzed. Fuzzy controller with 49 rules is considered and applied. Six-phase electric drive with field-oriented control at well-tuned PID controller has good step response specifications: settling time 0.13 s at starting without load, step response has no overshoot, small about 1 % short time decrease of speed at load of 5 Nm application. The system employing PID fuzzy controller shows slightly better results in response to torque application: the decrease in speed 1 % is eliminated in shorter time. Simulation results indicate the robustness of both systems with six-phase drive to disturbance and provide high quality transient specifications at determined reference speed.

Electricity price forecasting has become a crucial element for both private and public decision-making. This importance has been growing since the wave of deregulation and liberalization of energy sector worldwide late 1990s. Given these facts, this paper tries to come up with a precise and flexible forecasting model for the wholesale electricity price for the Italian power market on an hourly basis. We utilize artificial intelligence models such as neural networks and bagged regression trees that are rarely used to forecast electricity prices. After model calibration, our final model is bagged regression trees with exogenous variables. The selected model outperformed neural network and bagged regression with single price used in this paper, it also outperformed other statistical and non-statistical models used in other studies. We also confirm some theoretical specifications of the model. As a policy implication, this model might be used by energy traders, transmission system operators and energy regulators for an enhanced decision-making process.

In this study, we investigated the features of co-infection with SARS-CoV-2 and nonpathogenic strain LEV8 of coxsackievirus A7 or enterovirus A71 for Vero E6 cells and Syrian hamsters. The investigation of co-infection with SARS-СoV-2 and LEV-8 or EV-A71 in the cell model was shown that a competitive inhibitory effect for these viruses were especially significant against SARS-CoV-2. Pre-infection with enteroviruses in animals caused more than a 100-fold decrease in the levels of SARS-CoV-2 virus replication in the respiratory tracts and more rapid clearance of the lower respiratory tract from infectious SARS-CoV-2. Co-infection with SARS-CoV-2 and LEV-8 or EV-A71 also reduced the severity of clinical manifestations of the SARS-CoV-2 infection for animals. Additionally, the histological data illustrated that co-infection with nonpathogenic coxsackievirus decreased the level of pathological changes by SARS-CoV-2 in the lungs. Research into the chemokine/cytokine profile demonstrated that the studied enteroviruses efficiently triggered this part of antiviral immune response, which can be associated with significant inhibition of SARS-CoV-2 infection. These results demonstrate that there exists a strong viral interference between the studied nonpathogenic strain of coxsackievirus A7 or enteroviruses A71 and SARS-CoV-2 pathogenic for humans in vitro and in vivo.

Molnupiravir, a prodrug known for its broad antiviral activity, demonstrated efficacy in animal models of Covid-19, prompting clinical trials where initial results indicated a significant effect against the disease. However, subsequent clinical studies did not confirm these findings, leading to the rejection of molnupiravir for permanent market authorization in many countries. This report critically assessed 19 studies published in 17 reports that investigated the efficacy of molnupiravir in animal models of Covid-19 with the purpose of determining how well the design of these models informed human studies. We found that the administered doses of molnupiravir in most studies involving animal Covid-19 models were disproportionately higher than the dose rec-ommended for human use. Specifically, when adjusted for body surface area, half of the doses of molnupiravir used in the animal studies were more than twice as high as the human dose. Addi-tionally, the drug was frequently given prophylactically or shortly after SARS-CoV-2 inoculation in these models, in contrast to clinical trials where such timing is not consistently achieved. Furthermore, the recommended five-day treatment duration for humans was exceeded in several animal studies. Collectively, we suggest that these design elements in the reported animal studies contributed to a bias favoring molnupiravir, and thus inflated expectations for its efficacy against Covid-19. Addressing these elements may offer avenues to enhance the clinical efficacy of mol-nupiravir for treatment of Covid-19 that include dose increment, early treatment, and admin-istration by inhalation along with use of molnupiravir in antiviral combination therapy.

The paper examines the impact of inward remittances flows on per capita GDP growth in Bangladesh during 1976-2012. We find that the growth effect of remittances is negative at first but becomes positive at a later stage, an evidence of a non-linear. Unproductive use of remittances was rampant in the beginning when they were received by migrant families but better social and economic investments led to more productive utilisation of remittances receipts at later periods. This was the possible mechanism behind the U-shaped relationship. Unlike what is suggested in the literature that the effect of remittances is more pronounced in a less financially developed economy, our evidence do not show that the effect of remittances on per capita GDP growth in Bangladesh is conditional on the level of financial development.

This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which provides powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Despite advancements, Italy’s 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

The pursuit of Artificial Intelligence (AI) that emulates human cognitive processes is a cornerstone of ethical AI development, ensuring that emerging technologies can integrate seamlessly into societal frameworks requiring nuanced understanding and decision-making. Zero-Shot Instance Retrieval (ZSIR) stands at the forefront of this endeavour, potentially providing a robust platform for AI systems, particularly large visual language models, to demonstrate and refine cognition-aligned learning without the need for direct experience. In this paper, we critically evaluate current cognition alignment methodologies within traditional zero-shot learning paradigms, using visual attributes and word embedding generated by large AI models. We propose a unified similarity function that quantifies the cognitive alignment level, bridging the gap between AI processes and human-like understanding. Through extensive experimentation, our findings illustrate that this similarity function can effectively mirror the visual-semantic gap, steering the model towards enhanced performance in zero-shot instance retrieval. This work not only benchmarks the cognition alignment of AI, but also sets a new precedent for the development of visual language models attuned to the complexities of human cognition.}

The speed-density or flow-density relationship is a fundamental aspect of traffic flow theory. Single-regime models often face challenges in consistently fitting empirical data under diverse traffic conditions. This paper addresses the inaccuracies of single-regime models, attributing them not only to their functional forms but also to data dispersion and sample selection bias. To mitigate these issues, the data is segmented into day and night periods, leading to the creation of separate models for each. Calibration results, conducted on data from two freeways, Tehran-Karaj and Tehran-Qom, reveal distinct challenges, with the former exhibiting high dispersion and the latter showing low dispersion. Surprisingly, single-regime models demonstrate notable effectiveness when applied to distinct day and night data. Further analysis, categorizing data into day and night, results in reduced errors (20-60% improvement in R-Square), emphasizing the potential for enhanced accuracy by considering distinct regimes. Overall, the study underscores the significance of regime-specific considerations for accurate traffic flow modeling. Upon thorough evaluation, the study highlights the superiority of the neural network Multi-layer Perceptron (MLP) over traditional models. The research discusses the implications of incorporating day and night parameters into the models, emphasizing their potential for accuracy enhancement.

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

We discuss methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D and 3D channels are brought up. Power series for the permeability derived for small values of amplitude are employed to calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. The technique developed for critical phenomena is applied then for relaxation phenomena. The concept of time-translation invariance is discussed, its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the timetranslation symmetry complete (or partial) restoration. We estimate typical time extent, amplitude and direction for such restorative process. The new technique is based on explicit introduction of origin in time. After some transformations we come to the exponential and generalized, exponential-type solution with explicit finite time scale, which was only implicit in initial parametrization with polynomial approximation. The concept of crash as a relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is put forward. COVID-19 related mini-crash in the time series for Shanghai Composite is discussed as an illustration.

When dealing with limited sample sizes or missing values in time series data, achieving high accuracy in forecasting becomes challenging. This challenge is particularly common in wind energy forecasting, where many wind farms lack complete data. In this paper, we employ the widely-used ARIMA (Autoregressive Integrated Moving Average) model for time series forecasting. To address the difficulties posed by limited sample sizes and missing values, we adopt a unique approach by utilizing multiple ARIMA models for different datasets. A key distinction from other multiple models methods for time series forecasting lies in each model within our approach using its own dataset, making the fusion process more intricate. To overcome this, we incorporate neural networks and two techniques for model fusion: direct fusion with a learning mechanism and compensation for missing data through training. For each ARIMA model, we introduce a noise estimation method to circumvent the white noise assumptions inherent in ARIMA models. Finally, we apply these methods to wind energy prediction, and our experimental results showcase a significant enhancement in forecasting accuracy.

Time evolution of the quantum correlation of the hybrid qubit-qutrit system in multilocal and global dephasing under the effect of a classical noises environment is presented. We considered the qutrit in z direction and the qubit x direction. In addition, our system presents two configurations: the different and the common environment and our discussion involves three types of noises: A Static Noise (SN), Random Telegraph Noise (RTN) and Ornstein- Uhlenbeck noise (OU). By using the density matrix approach to determine the evolution of the state of the system, the found that the static noise is fatal for the quantum entanglement, the quantum correlation and for RTN and OU noises the quantum entanglement, the quantum correlation decreases monotonically with a sufficiently long time. Therefore, we can say that, entanglement and the quantum correlation are more robust to the noise precisely those Random telegraph noise and Ornstein-Uhlenbeck noise.

Previously, we described a 19-base pair double-stranded RNA with 3'-trinucleotide overhangs, acting as immunostimulatory RNA (isRNA). This molecule demonstrated notable antiproliferative effects on cancer cells, inhibited tumor growth, and elicited immunostimulatory and antiviral responses by inducing cytokine and interferon production. Within this study, we compared the efficiency of lung fibrosis development, initiated in mice by BLM or LPS using different schemes of induction. Then we compared the effect of isRNA used in a preventive or therapeutic regimen on the development of fibrosis in selected BLM- and LPS-induced mouse models and showed that isRNA can be used in pathological conditions accompanied by the development of inflammation and the risk of fibrosis formation, without adverse side effects. Prophylactic regimen of isRNA application is beneficial for prevention of the development of pulmonary fibrosis.

Count data analysis presents unique challenges due to its discrete nature, often exhibiting excessive zeros and overdispersion. To address these complexities, count models, such as Poisson regression and Negative Binomial regression, have been developed, enabling modeling and prediction of count-based phenomena. Additionally, it’s important to notice that zero inflation, a phenomenon commonly observed in count data, requires specialized techniques for robust analysis. This article provides an overview of count data and count models, explores zero inflation, introduces Likelihood Ratio Tests, and explains how the Vuong Test can be used as a model selection criteria. Furthermore, we created a Vuong Test implementation from scratch using the Python programming language. This implementation enhances the accessibility and applicability of the Vuong Test in real-world scenarios, providing a valuable contribution to the academic community, since Python didn’t have an implementation of this statistical test.

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by . Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

This paper is aimed at studying the temporal evolution of the surface displacements occurred over the past few years in the ocean-reclaimed platforms of the Shanghai megacity (China), which are mainly ascribable to consolidation processes of large dredger fills and alluvial deposits. With respect to previous analyses carried out over the same area, this work provides a joint multi-platform differential interferometry synthetic aperture radar (DInSAR) analysis, based on the application of the advanced Small BAseline Subset (SBAS) algorithm. This led us to retrieve long-term deformation time-series that are helpful for a better understanding of the on-going deformation phenomena. To this aim, we have exploited two sequences of SAR data collected by the ASAR/ENVISAT and by the COSMO-SkyMed (CSK) sensors, respectively, spanning the whole time period from 2007 to 2016. Unfortunately, the large time gap (of about three years) existing between the available ASAR/ENVISAT and CSK datasets gave rise to additional difficulties for their combination. Nevertheless, this problem has been faced by benefiting from the knowledge of a time-dependent model describing the temporal evolution of the expected deformations affecting the Shanghai ocean-reclaimed platforms.

A review of quantitative risk assessment (QRA) models of L. monocytogenes in produce was carried out, with the objective of appraising and contrasting the effectiveness of the control strategies placed along the food chains. Despite nine of the thirteen QRA models recovered focused on fresh or RTE leafy greens, none of them represented important factors or sources of contamination in the primary production, such as type of cultivation, water, fertilisers or irrigation method/practices. Cross-contamination at processing and during consumer’s handling was modelled using transfer rates, which were shown to moderately drive the final risk of listeriosis; highlighting therefore the importance of accurately representing the transfer coefficient parameters. Many QRA models coincided in the fact that temperature fluctuations at retail or temperature abuse at home were key factors contributing to increasing the risk of listeriosis. In addition to a primary module that could help assess current on-farm practices and potential control measures, future QRA models for minimally-processed produce should also contain a refined sanitisation module able to estimate the effectiveness of various sanitisers as a function of type, concentration and exposure time. Finally, L. monocytogenes growth in the products down the supply chain should be estimated by using realistic time-temperature trajectories, and validated microbial kinetic parameters, both of them currently available in the literature.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

Natural language Processing (NLP) has significantly transformed in the last decade, especially in the field of Language Modeling. Large Language Models (LLMs) have achieved SOTA performances on Natural Language Understanding (NLU) and Natural Language Generation (NLG) tasks by learning language representation in self-supervised ways. This paper provides a comprehensive survey to capture the progression of advances in Language Models. In this paper, we examine the different aspects of Language Models, which started with a few million parameters but have reached the size of a trillion in a very short time. We also look at how these LLMs transitioned from task-specific to task-independent to task-and-language-independent architectures. This paper extensively discusses different pre-training objectives, benchmarks, and transfer learning methods used in LLMs. It also examines different fine-tuning and In-Context learning techniques used in downstream tasks. It also explores how LLMs can perform well across many domains and datasets if sufficiently trained on a large and diverse dataset. Next, it discusses how, over time, the availability of cheap computational power and large datasets have improved LLM’s capabilities and raised new challenges. As part of our study, we also inspect LLMs from the lens of scalability to see how their performance is affected by the model’s depth, width, and data size. Lastly, we provide an empirical comparison of existing trends and techniques and a comprehensive analysis of where the field of LLM currently stand.

Responding to changing value creation processes in the sheet metal working sec-tor, where the complexity and interchangeability of products challenge traditional dif-ferentiation strategies, this empirical analysis explores integrating service-oriented and data-driven business models as new paths to ensure competitiveness, especially for small and medium-sized enterprises (SMEs). This study aims to capture the current state and challenges associated with the implementation of these business models in this sector. The research was conducted through semi-structured interviews with SMEs in the industry. The findings indicate that service-oriented and data-driven business models are not yet widely adopted and that manufacturing companies re-quire support in their implementation. Fields of action were identified for the industry. These are "Creating awareness and understanding", "Recognizing added value", "In-creasing company maturity" and "Understanding the change process". Cooperation between science and industry is essential in tackling these fields of action to ensure the successful integration of such business models in manufacturing companies. This pa-per identifies challenges in the fields of action that companies must address through a structured approach promoting awareness, recognizing value, improving organiza-tional maturity, and understanding the change process to successfully implement ser-vice-oriented and data-driven business models.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Continuation methods are presented that are capable of treating frequency-domain flutter equations including multiple nonlinearities represented by describing functions. A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence. Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors give a compact view of the nonlinear behavior throughout the flight regime. A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented. These processes are economical enough to be a routine part of aircraft design and certification.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

Herein, we examined the effects of weather parameters and individual clinicodemographic risk factors on hemorrhagic stroke (HS) incidence, severity on admission, and disability at discharge in a harsh desert climate. In a retrospective design we studied patients admitted to a stroke unit in Arab Emirates in 2016-2019. With a distributed lag nonlinear model we explored immediate and delayed effects of weather on stroke incidence. Supervised machine learning was used to build models predictive of scores in NIHSS and mRS scales. We assessed model performance by calculating ROC AUC, F1 scores, specificity, and sensitivity. HS risk increased after a significant change in any weather parameter. The risk was reduced below baseline after 1-week adjustment to environmental changes. Climate input from the previous 3 days yielded reliable classification models. Humidex was a better predictor of severity than air temperature, whereas body mass index, age, and time of day at stroke onset were the strongest clinical predictors. Weather parameters before admission were stronger predictors of disease severity than individual clinical factors. We addressed limitations of previous studies by analyzing a full set of climate parameters: ambient temperature, relative humidity, humidex, atmospheric pressure, and wind speed. Predictive models may help to optimize patient management and develop preventative strategies.

Crash prediction of the sharp horizontal curve segment (SHCS) of a freeway is an important tool in analyzing safety of SHCSs and in building a crash prediction model (CPM). The design and crash report data of 88 SHCSs from different institutions were surveyed and three negative binomial (NB) regression models and three generalized negative binomial (GNB) regression models were built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The study demonstrates the effective use of the GNB model in analyzing the interactive influence of explanatory variables and in predicting freeway basic segments. Traffic volume, highway horizontal radius, and curve length have been formulated as explanatory variables. Subsequently, we performed statistical analysis to determine the model parameters and conducted sensitivity analysis. Among the six models, the result of model 6, which considered interactive influence, is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 SHCSs with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than models 1 and 3.

Effective agricultural management in maize production operations starts with the early quantification of seedlings. Accurately determining plant presence allows growers to optimize planting density, allocate resources, and detect potential growth issues early on. This study presents an in-depth analysis of multiple object detection models used by drones to count maize seedlings, while concurrently investigating the influence of planting density, flight altitude, and plant growth stage. The findings of this study demonstrate that one-stage models are able to more accurately detect maize seedlings than two-stage models. In particular, YOLOv8n exhibits outstanding performance, achieving an F1-score of over 0.92 under various density conditions and maintaining a stable performance, especially under densities below 105,000 plants/ha. Additionally, planting density and growth stage were observed to significantly affect detection accuracy, with performance declining as density and growth stage increased. Image resolution and detection were impacted by flight altitude, with lower flights producing higher-quality results. Ultimately, YOLOv8n displays optimal performance under various conditions, providing crucial data to support intelligent decision-making. This research offers valuable insights into the application of object detection technology and provides a basis for the future development of precision agriculture.

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

Although researchers have proposed various indentation size effect (ISE) models, these models often involve different form and number of parameters that can make our wonder which is the best in existed ISE models. Three types of ISE test data, namely, normal ISE, reverse ISE and transition of normal to reverse ISE, are used to evaluate the sixteen ISE models. The comparatively study indicates that H-J, N-G-Fs, N-G-H, N-G-A and N-G-Qs models can accurately predict the normal ISE. The reason for this is that the friction stress that is not related to dislocation activities or the indentation size effect of plastic zone has been introduced into these models. Therefore, these two factors should be considered in future ISE models. The sixteen ISE models are originally proposed to describe the normal ISE of different materials. However, to our surprise, some of these models are able to capture the reverse ISE and the transition of normal to reverse ISE of different materials. The determination coefficients (DC) of the sixteen ISE models are also determined for different materials. For reverse ISE, the highest DC value for NiCSi, TC4 and PED Ni are given by the EXP, N-G-Fs and N-G-A models, respectively. For the transition of normal to reverse ISE, the N-G-YC, N-G-Fs, and N-G-H models produce the maximum DC for ZrO2, Cu and Y2O3-ZrO2, respectively. Moreover, the mean DC of the N-G-Fs model is the maximum among the sixteen ISE models, followed by the N-G-H model, but they cannot accurately predict the reverse ISE. Therefore, the N-G-Fs and N-G-H models should be further modified to accurately predict the reverse ISE.

The advent of deep learning (DL) has revolutionized medical imaging, offering unprecedented avenues for accurate disease classification and diagnosis. DL models have shown remarkable promise for classifying brain tumor from Magnetic Resonance Imaging (MRI) scans. However, despite their impressive performance, the opaque nature of DL models poses challenges in understanding their decision-making processes, particularly crucial in medical contexts where interpretability is essential. This paper explores the intersection of medical image analysis and DL interpretability, aiming to elucidate the decision-making rationale of DL models in brain tumor classification. Leveraging state-of-the-art DL frameworks with transfer learning, we conduct a comprehensive evaluation encompassing both classification accuracy and interpretability. Using state-of-the-art DL frameworks with transfer learning, we conduct a thorough evaluation covering both classification accuracy and interpretability. We employ adaptive path-based techniques to understand the underlying decision-making mechanisms of these models. Grad-CAM and Grad-CAM++ highlight critical image regions where the tumors are located.

A hallmark of Alzheimer’s disease (AD) are the proteinaceous aggregates formed by the amyloid-beta peptide (Aβ) that is deposited inside the brain as amyloid plaques. The accumulation of aggregated Aβ may initiate or enhance pathologic processes in AD. According to the amyloid hypothesis any agent that has the capability to inhibit Aβ aggregation and/or destroy amyloid plaques represents a potential disease modifying drug. In 2023, a humanized IgG1 monoclonal antibody (lecanemab) against the Aβ soluble protofibrils was approved by US FDA for AD therapy thus providing compelling support to the amyloid hypothesis. To acquire a deeper insight on the in vivo Aβ aggregation, various animal models, including aged herbivores and carnivores, non-human primates, transgenic rodents, fish and worms are widely exploited. This review is based on the recent data obtained using transgenic animal AD models and presents experimental verification of the critical role in Aβ aggregation seeding of the interactions between zinc ions, Aβ with the isomerized Asp7 (isoD7- Aβ) and the α4β2 nicotinic acetylcholine receptor.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

The massive amount of human biological, imaging and clinical data produced by multiple and diverse sources, necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels as well as their orchestration and links are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof of concept study cases. Personalized simulations over the actual anatomy of a patient have been carried out. The hypermodel has also applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin based clinical decision support system and the core of future in silico trial platforms, although additional retrospective adaptation and validation is necessary.

Background: Health insurance (HI) run by government is providing health care service to large population. Due to poor accountability, participation and sustainability, cooperative health insurance is becoming more popular and effective in low and middle income and some high-income countries too. In Nepal, there are public and cooperative HI is in practice. The aim of this study is to compare the effectiveness of public (government) and cooperative HI in relation to benefit packages, population coverage, inclusiveness, health care utilization, and promptness for treatment in these two health insurance models in Nepal. Method: This is an institution based concurrent mixed study consists of qualitative and quantitative variables from public and cooperative groups. We included all public HI operated by government hospitals and cooperatives groups those purchased hospital service in contract. Two separate study tools were applied to access the effectiveness of insurance models. The key questions were asked for the representatives of government and private health insurance. The numeric information consisted of in quantitative data and subjective response was included in qualitative approach. Descriptive statistics and Mean Whitney U test was applied in numeric data and qualitative information were analyzed by inductive approach Results: The study revealed that new enrolment was not increased, health care utilization rate was increased and the benefit package was almost same in both groups. The overall inclusiveness was higher for the government HI, but enrolment from the religious minority, proportion of negotiated amount during treatment were significantly higher (p<0.05). During illness, the response time to reach hospital was significantly faster in cooperative health insurance than government health insurance. Qualitative findings showed that level of participation, accountability, transparency and recording system was better in cooperative health insurance than public. Conclusion: Cooperative HI could be more sustainable and accountable to the community for all; low, middle and high-income countries.

This paper studies the duration patterns of unemployment spells for immigrants and the determinants of unemployment’s completion into one of a number of studied labour market states in Finland. We estimate a duration model for unemployment with competing risks of its terminating into employment, labour market training or economic inactivity. Taking into account the wide period of observation and opportunities to analyse processes of labour market integration during various periods of economic development in Finland, in combination with the individualistic character of the labour careers of immigrants, this research is beneficial owing to the many various findings concerning labour market integration of immigrants. The approach undertaken in this research has a dualistic “descriptive-dynamic” character under which integration is understood as a never-ending process, which is conditioned by a time period of long-term existence and a context of solitary action. We find that transitions out of unemployment spells have a cyclical character; after every new “cycle” in unemployment, the probability of terminating unemployment decreases further. We also find that ascriptive factors make sense in the process of job-placement of immigrants from unemployment. Therefore, the gender, education and age of immigrants, as well as the effect of the period in which first unemployment occurred, potentially predict transitions out of unemployment and further labour market integration of immigrants.

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

The widespread integration and growing dependence among currency, stock and commodity markets make these markets often very vulnerable to shocks and at risk of collapse at the same time. As a result, these trends threaten the sustainability of the entire financial system. In this study, we explore the spillovers and nonlinear dependences between the seven major foreign ex-change rates, crude oil and gold prices, a global stock price index, and oil and stock implied volatility indices as proxy variables for global risk factors by em-ploying directional spillover network approach. We also use multi-scale de-composition method and nonlinear causality test between these variables to capture multi-level relationships at short and long horizons. Major findings are summarized as follows. First, from the multi-scale decomposition analysis, we identify that Granger causality test results and the direction and strength of return spillovers change with the level of decomposition. Second, the results of nonlinear causality tests show variation in both the significance and direction of Granger causality relationships between the decomposed currency and other series at different timescales, especially for the decomposed oil, gold, and OVX series. Third, the measured directional spillover indices identify the EUR as the largest contributor of connectedness to the other series. The central role of the EUR is a net transmitter of connectedness to gold, oil, the GBP, JPY, and CHF.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

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.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Change Detection (CD) of aerial images refers to identifying and analyzing changes between two or more aerial images of the same location taken at different times. The CD is a highly challenging task due to the need to distinguish relevant changes, such as urban expansion, deforestation, or post-disaster damage assessment, from irrelevant ones, such as light conditions, shadows, and seasonal variations. Many CD papers have recently been published, where most of the papers that proposed a new model contained a comparison between their proposed and state-of-the-art (SOTA) models. While many recent studies propose new deep learning (DL) models for improving CD performance, their comparative analyses are often restricted, lacking comprehensive insights into the proposed models' real-world generalizability, robustness, and performance trade-offs across diverse change characteristics. This paper presents a novel generic framework to systematically benchmark and assess DL-based CD models through three parallel pipelines: 1) cross-testing models on diverse benchmark datasets to evaluate generalization, 2) robustness analysis against different image corruptions, and 3) multi-faceted contour-level analytics evaluating detection sensitivity to change size/complexity. The framework is applied to comparatively evaluate five state-of-the-art DL-based CD models - Changeformer, BIT, Tiny, SNUNet, and CSA-CDGAN. Extensive experiments unveil each model's strengths, limitations and biases, highlighting their relative proficiencies in generalizing across data distributions, resilience to noise corruption, and discriminative capabilities for changes of varying characteristics. The proposed benchmarking framework demonstrates significant potential for guiding the selection of suitable CD models tailored to specific application requirements by comprehensively evaluating their generalizability, robustness, and detection capabilities across diverse real-world scenarios. This systematic evaluation approach can drive future research into developing more robust and versatile CD solutions aligned with practical needs.

In this paper we introduce an ODE system to model the interaction between nature resources and human exploitation in a rich consumeristic society. In this model the rate of change of population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. As in our previous work \cite{BaCra_1}, we distinguish between renewable and non renewable resources, and we introduce a replenishment term for non renewable resources. We first get some information on the asymptotic behaviour of wealth and population, then we compute all the equilibria of the system and we study their stability when the parameter of exploitation of resources is small. Some numerical simulations confirm the theoretical results, and give suggestions for future research.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

As a rapidly expanding family of two-dimensional (2D) materials, MXenes have recently gained considerable attention due to their appealing properties. Here, by developing a solution-based coating method that enables transfer-free and layer-by-layer film coating, we investigate the layer-dependent nonlinear optical absorption of Ti₃C₂T_x films ‒ an important member of the MXene family. By using the Z-scan technique, we characterize the nonlinear absorption of the prepared MXene films consisting of different numbers of monolayers. The results show that there is a strong and layer-dependent nonlinear absorption behavior, transitioning from revisable saturable absorption (RSA) to saturable absorption (SA) as the layer number increases from 5 to 30. Notably, the nonlinear absorption coefficient β varies significantly within this range, changing from ~7.13 × 10² cm/GW to ~-2.69 × 10² cm/GW. We also characterize the power-dependent nonlinear absorption of the MXene films at various incident laser intensities, and a decreasing trend in β is observed for increasing laser intensity. These results reveal the intriguing layer-dependent nonlinear optical properties of 2D MXene films, highlighting their versatility and potential for implementing high-performance nonlinear photonic devices.

Soft tactile sensors based on piezoresistive materials have various large-area sensing applications. However, their accuracy is often affected by hysteresis, a phenomenon that poses a significant challenge during operation. This paper introduces a novel approach that employs a backpropagation (BP) neural network to address the hysteresis nonlinearity in conductive fibre-based tactile sensors. To assess the effectiveness of the proposed method, four sensor units with different layer configurations (1, 3, 6, and 12) were designed. These sensor units underwent force sequences to collect corresponding output resistances. A backpropagation network was trained using these force sequences, thereby correcting the resistance values. The training process exhibited excellent convergence, effectively adjusting the network's parameters to minimize the error between predicted and actual resistance values. As a result, the trained BP network accurately predicted the output resistances. Several validation experiments were conducted to highlight the primary contribution of this research. The proposed method reduced the maximum hysteresis error from 24.2% of the sensor's full-scale output to 13.5%. This improvement establishes the approach as a promising solution for enhancing the accuracy of soft tactile sensors based on piezoresistive materials. By effectively mitigating hysteresis nonlinearity, the capabilities of soft tactile sensors in various applications can be enhanced. These sensors become more reliable and more efficient tools for force measurement and control, particularly in the fields of soft robotics and wearable technology. Consequently, their widespread applications extend to robotics, medical devices, consumer electronics, and gaming. Notably, the complete elimination of hysteresis in tactile sensors may not be feasible. Nevertheless, the proposed method effectively modifies the hysteresis nonlinearity, leading to improved sensor output accuracy.

This paper presents the common methods and corresponding drawbacks concerning nonlinear analysis of fluxgate excitation circuits and emphasizes the importance of nonlinear analysis for these circuits. With regard to the nonlinearity of the excitation circuit, this paper proposes the use of the core-measured hysteresis curve for mathematical analysis and the use of a nonlinear model that considers the coupling effect of the core and winding and influence of the historical magnetic field on the core for simulation analysis. The feasibility of mathematical calculations and simulation for the nonlinear study of fluxgate excitation circuit is verified via experiments. The results demonstrate that, in this regard, the simulation is better than a mathematical calculation. The simulation and experimental results of the excitation current and voltage waveforms under different excitation circuit parameters and structures are essentially consistent with each other, thereby verifying the effectiveness of the nonlinear excitation analysis method.

With correct dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed incorrectly, a learning method may be used to find the correct parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown victrix (i.e., a regression form) tracking errors may be projected onto the known matrix to update the unknown victrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The modified approach is two magnitudes better than the methods in the prequels in terms of state error convergence.

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all-optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high-performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms, such as strong nonlinear optical absorption or an inadequate optical nonlinearity. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO’s optical properties and the fabrication technologies needed for its on-chip integration is provided. Next, the state-of-the-art GO nonlinear integrated photonic devices are reviewed, together with comparisons of the nonlinear optical performance of different integrated platforms incorporating GO. Finally, the challenges and perspectives of this field are discussed.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

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.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

A temperature-modulated pyroelectricity measurement system for a small single crystal is developed and applied to standard sample measurements performed on a thin single crystal of lithium niobate. The modulation measurement is based on the AC technique, in which the temperature of the sample is periodically oscillated, and the synchronized pyroelectric signal is extracted using a lock-in amplifier. Temperature modulation is applied by irradiating periodic light on the sample placed in the heat exchange gas. To apply this technique to the transparent reference sample, a commercially available black resin is coated on the sample’s surface to absorb the light energy and transmits it to the specimen. The experimental results are analyzed using a two-layer heat transfer model to verify the effect of the light-absorbing layer as well as the non-contact temperature modulation system.

We have investigated the canine of olive flounder in terms of the nonlinear optical signals of two-photon excitation autofluorescence (2PEF) and second harmonic generation (SHG), whereby two kinds of nonlinear microscope images of the canine were obtained using ~140 femtosecond pulses. For increasing excitation power of laser pulses, a photobleaching effect was found to be significant in the red and green ranges of autofluorescence, where a double-exponential decay of the intensity occurs within hundreds of second due to collagen fluorophores in the canine. In the blue range of autofluorescence, the photobleaching is suppressed due to an energy conversion of the incident laser pulse to SHG signal. As a result, the signal in blue range remains constant for long term exposure to laser. We have also found that the SHG intensity depends on the orienta-tion of linearly polarized excitation, and the optical anisotropy of SHG can be attributed to the collagen alignment of canines.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

Principle of memristor presented by Leon Chua and time reversal based non-linear elastic wave spectroscopy (TR-NEWS) which can be applied to acoustic tomography are reviewed. Correlation of acoustic or electromagnetic nonlinear waves and its time reversed wave can produce strong signal. Materials like transducer or biological skin can be assumed to be composed of a large number of small elastic unit: hysteretic elementary unit (HEU), and one can take a HEU as a memristor whose operation depends on time. Relation between TR-NEWS and solitonic wave in fluid, and relation between decomposition of time reversal operator (DORT) and chaotic oscillation are discussed.

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III are investigated under different shear deformations; large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still show elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

COVID-19 is the most severe health crisis of the 21st century. COVID-19 presents a threat to almost all countries world-wide. The restriction of human mobility is one of the strategies used to control the transmission of COVID-19. However, it has yet to be determined how effective this restriction is in controlling the rise in COVID-19 cases, particularly in major capital cities such as Jakarta, Indonesia. Using Facebook's mobility data, our study explores the impact of restricting human mobility on COVID-19 case control in Jakarta. Our main contribution is showing how the restriction of human mobility data can give important information about how COVID-19 spreads in different places. We proposed modifying a global regression model into a local regression model by accounting for the spatial and temporal interdependence of COVID-19 transmission across space and time. We applied Bayesian hierarchical Poisson spatiotemporal models with spatially varying regression coefficients. We estimated the regression parameters using an Integrated Nested Laplace Approximation. We found that the local regression model with spatially varying regression coefficients outperforms the global regression model based on DIC, WAIC, MPL, and R2 criteria for model selection. In Jakarta's 44 districts, the impact of human mobility varies significantly. The impacts of human mobility on the log relative risk of COVID-19 range from –4.445 to 2.353. The prevention strategy involving the restriction of human mobility may be beneficial in some districts but ineffective in others. Therefore, a cost-effective strategy had to be adopted.

As AI models become more and more common in business and even in our daily lives, it is important to understand what the carbon impact of these models is. Recent papers have shown that this impact can be quite great, i.e., the training of a single high-end model can result in emissions of more than 500t of CO2eq. In this paper we discuss the factors that influence the carbon footprint of AI models, explore what impact different decisions have, and show how the footprint can be reduced. We also examine the footprint of different models to give a guideline on how urgent action is for different organizations.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Our earlier work has tentatively shown that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. In this brief sequel we survey a similar scenario in which the Cabibbo angle arises from the nonlinear dynamics of charged-current interactions.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.