In this paper, we prove some random fixed point theorems for generalized random $\alpha-\psi-$contractive mappings in a Polish space and, as some applications, we show the existence of random solutions of second order random differential equation.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

Despite the growing capabilities of large language models, concerns exist about the biases they develop. In this paper, we propose a novel, automated mechanism for debiasing through specified dataset augmentation in the lens of bias producers that can be useful in a variety of industries, especially ones that are “restricted” and have limited data. We consider that bias can occur due to intrinsic model architecture and dataset quality. The two aspects are evaluated using two different metrics we created. We show that our dataset augmentation algorithm reduces bias as measured by our metrics.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

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.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

Sparse training (ST) aims to ameliorate deep learning by replacing fully connected artificial neural networks (ANNs) with sparse or ultra-sparse ones, such as brain networks are, therefore it might benefit to borrow brain-inspired learning paradigms from complex network intelligence theory. Here, we launch the ultra-sparse advantage challenge, whose goal is to offer evidence on the extent to which ultra-sparse (around 1% connection retained) topologies can achieve any leaning advantage against fully connected. Epitopological learning is a field of network science and complex network intelligence that studies how to implement learning on complex networks by changing the shape of their connectivity structure (epitopological plasticity). One way to implement Epitopological (epi- means new) Learning is via link prediction: predicting the likelihood of non-observed links to appear in the network. Cannistraci-Hebb learning theory inspired the CH3-L3 network automata rule for link prediction which is effective for general-purpose link prediction. Here, starting from CH3-L3 we propose Epitopological Sparse Meta-deep Learning (ESML) to apply Epitopological Learning to sparse training. In empirical experiments, we find that ESML learns ANNs with ultra-sparse hyperbolic (epi-)topology in which emerges a community layer organization that is meta-deep (meaning that each layer also has an internal depth due to power-law node hierarchy). Furthermore, we discover that ESML can in many cases automatically sparse the neurons during training (arriving even to 30% neurons left in hidden layers), this process of node dynamic removal is called percolation. Starting from this network science evidence, we design Cannistraci-Hebb training (CHT), a 4-step training methodology that puts ESML at its heart. We conduct experiments on 7 datasets and 5 network structures comparing CHT to dynamic sparse training SOTA algorithms and the fully connected counterparts. The results indicate that, with a mere 1% of links retained during training, CHT surpasses fully connected networks on VGG16, GoogLeNet, ResNet50, and ResNet152. This key finding is an evidence for ultra-sparse advantage and signs a milestone in deep learning. CHT acts akin to a gradient-free oracle that adopts CH3-L3-based epitopological learning to guide the placement of new links in the ultra-sparse network topology to facilitate sparse-weight gradient learning, and this in turn reduces the convergence time of ultra-sparse training. Finally, CHT offers the first examples of parsimony dynamic sparse training because, in many datasets, it can retain network performance by percolating and significantly reducing the node network size. Our code is available at: https://github.com/biomedical-cybernetics/Cannistraci-Hebb-training.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

Dynamic sparse training is an effective strategy to alleviate the training and inference demands of artificial neural networks. However, current sparse training methods face a challenge in achieving high levels of sparsity while maintaining performance comparable to that of their fully connected counterparts. The Cannistraci-Hebb training (CHT) method produces an ultra-sparse advantage compared to fully connected training in various tasks by using a gradient-free link regrowth method, which relies solely on the network topology. However, its rigid selection based on link prediction scores may lead to epitopological local minima, especially at the beginning of the training process when the network topology might be noisy and unreliable. In this article, we introduce the Cannistraci-Hebb training soft rule (CHTs), which applies a flexible approach to both the removal and regrowth of links during training, fostering a balance between exploring and exploiting network topology. Additionally, we investigate the network topology initialization using several approaches, including the bipartite scale-free and bipartite small-world network models. Empirical results show that CHTs can surpass the performance of fully connected networks with MLP architecture by using only 1% of the connections (99% sparsity) on the MNIST, EMNIST, and Fashion MNIST datasets and can provide remarkable results with only 0.1% of the links (99.9% sparsity). In some MLPs for image classification tasks, CHTs can reduce the active neuron network size to 20% of the original nodes (neurons), demonstrating a remarkable ability to generalize better than fully connected architectures, reducing the entire model size. This represents a relevant result for dynamic sparse training. Finally, we present evidence from larger network models such as Transformers, with 10% of the connections (90% sparsity), where CHTs outperform other prevalent dynamic sparse training methods in machine translation tasks.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

In this paper, we propose a partial differential equation model based on phase-field for sentiment analysis in the field of hotel comment texts. The comment texts are converted into word vectors using the Word2Vec tool, and then we utilize the multifractal detrended fluctuation analysis (MF-DFA) model to extract the generalized Hurst exponent of the word vector time series to achieve dimensionality reduction of the word vector data. The dimensionality reduced data is represented in a two-dimensional computational domain, and the modified Allen-Cahn (AC) function is used to evolve the phase values of the data to obtain a stable nonlinear boundary, thereby achieving automatic classification of hotel comment texts. The experimental results show that the proposed method can effectively classify positive and negative samples and achieve excellent results in classification indicators. We compared our proposed classifier with traditional machine learning models and the results indicate that our method possesses a better performance.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barabási-Albert (BA), Erdös-Rényi (ER) and Watts-Strogatz (WS) types. Both, walkers and nodes can be either susceptible (S) or infected and infectious (I) representing their states of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with transmission of the disease via vectors (mosquitos). Infected walkers may die during the time span of their infection introducing an additional compartment D of dead walkers. Infected nodes never die and always recover from their infection after a random finite time. This assumption is based on the observation that infectious vectors (mosquitos) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers R M , R 0 with and without mortality, respectively, and prove that R M < R 0 . For R M , R 0 > 1 the healthy state is unstable whereas for zero mortality a stable endemic equilibrium exists (independent of the initial conditions) which we obtained explicitly. We observe that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, among many others.

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: ’invertible games’ and ‘cyclical games'. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances these expressions can be simplified. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: ‘Tit-for-Tat' and ’Win-Stay, Lose-Switch'.

Keywords: olfactory rehabilitation; chronic pain; fMRI;

RNA sequencing techniques, like bulk RNA-seq and Single Cell (sc) RNA-seq, are critical tools for the biologist looking to analyze the genetic activity/transcriptome of a tissue or cell during an experimental procedure. Platforms like Illumina's next-generation sequencing (NGS) are used to produce the raw data for this experimental procedure. This raw FASTQ data must then be prepared via a complex series of data manipulations by bioinformaticians. This process currently takes place on an unwieldy textual user interface like a terminal/command line that requires the user to install and import multiple program packages, preventing the untrained biologist from initiating data analysis. Open-source platforms like Galaxy have produced a more user-friendly pipeline, yet the visual interface remains cluttered and highly technical, remaining uninviting for the natural scientist. To address this, SeqMate is a user-friendly tool that allows for one-click analytics by utilizing the power of a large language model (LLM) to automate both data preparation and analysis (differential expression, trajectory analysis, etc). Furthermore, by utilizing the power of generative AI, SeqMate is also capable of analyzing such findings and producing written reports of upregulated/downregulated/user-prompted genes with sources cited from known repositories like PubMed, PDB, and Uniprot.

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss further possible utilizations in other fields of data processing.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

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

This paper aims to demonstrate how the detection of communities for epidemiological networks can be used to reduce the dimensionality of optimal control problems. A range of planted partition stochastic blockmodels are generated, where the underlying communities in the model vary in detectability. A high-performance computing workflow is then used to simulate and estimate reduced model dynamics for the networks, which in turn is used to find optimal control solutions.

With the rapid growth of large language models (LLMs), there is increasing demand for memory and computation in LLMs. Recent efforts on post-training pruning of LLMs aim to reduce the model size and computation requirements, yet the performance is still sub-optimal. In this paper, we present a plug-and-play solution for post-training pruning of LLMs. The proposed solution has two innovative components: 1) Relative Importance and Activations (RIA), a new pruning metric that jointly considers the weight and activations efficiently on LLMs; and 2) Channel Permutation, a new approach to maximally preserve important weights under N:M sparsity. The two proposed components can be readily combined to further enhance the N:M semi-structured pruning of LLMs. Our empirical experiments show that RIA alone can already surpass all existing post-training pruning methods on prevalent LLMs, e.g., LLaMA ranging from 7B to 65B. Furthermore, N:M semi-structured pruning with channel permutation can even outperform the original LLaMA2-70B on zero-shot tasks, together with practical speed-up on specific hardware. Our code is available at: https://github.com/biomedical-cybernetics/Relative-importance-and-activation-pruning

The aim of the study was to examine the long-term prognostic value of changes in cardio-ankle vascular index (CAVI) within a year after coronary artery bypass grafting (CABG). Methods. Patients with coronary artery disease (n = 251) in whom cardio-ankle vascular index (CAVI) was assessed using the VaSera VS-1000 device before and in a year after CABG. Groups with improved CAVI (CAVI decreased from pathological value to normal or the index remained within normal values) or worsened CAVI (persistent pathological index value or an increase in CAVI to pathological values or an increase of 1 unit or more) were identified. The groups were compared for the following events at 10-year follow-up: death from all causes, myocardial infarction, stroke/transient ischemic attack, and the combined endpoint. Results. A year after CABG surgery, 45% of patients showed positive dynamics or stable normal CAVI values. Death from all causes was significantly more common in the group with CAVI progression - 32 (27.6%) than in the group with CAVI improvement - 14 (14.8%; p = 0.029). Patients with CAVI progression were more likely to have MACE (death, MI, stroke/TIA) in 49 (42.2%) cases, compared with patients with CAVI improvement - in 23 (24.5%; p=0.008). Negative dynamics of CAVI (p = 0.024), number of shunts (p = 0.006), and the presence of carotid stenosis more than 30% (p = 0.051) were independent predictors of death from all causes at 10-year follow-up after CABG. The presence of carotid stenosis more than 30% (p = 0.002) and the group with negative dynamics of CAVI after a year (p = 0.008) were independent predictors of the development of the combined endpoint during long-term follow-up. Conclusions. Patients with negative dynamics of CAVI one year after CABG were more likely to experience death from all causes and combined endpoint in the long-term follow-up than patients with normal CAVI. In further studies, it is advisable to evaluate the dynamics of CAVI and, based on this, identify the most effective interventions to improve the prognosis of patients after CABG.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Background and Objectives: Knee osteoarthritis (KOA) is a degenerative disease that is targeting continuously people of different ages, but especially the elderly population, the number of which tends to increase continuously at the global level. Apart from age, excess weight can influence the evolution of the disease, with obesity being associated with a weak inflammation stage, and an imbalance between pro-inflammatory and anti-inflammatory cytokines. The present work aimed to identify specific biomarkers alike ACRP-30, IL-10, TNF-α, and IL-6 in synovial fluid and correlate them with patients’ clinical data. Materials and Methods: 24 subjects with KOA and over 50 years of age are involved in the present study. All patients performed a supine X-ray at the target knee. Ultrasound was performed using an ESAOTE MyLab Omega (ESAOTE Spa, Italy) ultrasound device and a 6-19 MHz linear array transducer. Results: The obtained results highlighted a significant correlation between age and adiponectin level (p=0.0451, r=-0.412). Also, the IL-10 values are lower in cases where the intensity of the pain is more pronounced (p=0.0405, r=-0.421). In addition, analyzing the data by gender, it was observed that in the case of males, stiffness is more related to age (p=0.0079, r=0.7993), compared to women (p=0.0203, r=0.6223). In the case of women, the progression of the disease tends to increase more intensively total WOMAC score’s values (p=0.00031, r=0.8342), compared with men (p=0.0289, r=7013). Regarding interleukins and BMI, significant correlations were observed only in the case of men. Conclusions: A significant correlation between age and adiponectin, and adiponectin and IL-6, suggests that advanced age may contribute to adiponectin reduction. Comparing men with women, it was observed that men's age is more related to rigidity, and IL-6 and IL-10 are directly correlated to BMI and women seem to be more sensitive to pain and stiffness.

The endeavor to decode the brain's intricate architecture and its multifaceted functions has propelled scientists into the domain of complex differential equations, aiming to construct a computational framework capable of representing its uncountable intricacies. This article delves into the sophisticated and daunting task of modeling the brain, a system of seemingly uncountable coupled differential equations, each symbolizing the vast array of interconnected neural pathways and processes. We discuss the current limitations of computational resources and the significant challenges faced in accurately capturing the non-linear, high-dimensional, and plastic nature of neural dynamics. Despite these challenges, we explore the progressive strides in computational neuroscience that lay the groundwork for partial models, offering insights into the brain's localized circuits and broader network interactions. These models serve as pivotal stepping stones towards a more comprehensive understanding, which is incrementally built upon by interdisciplinary approaches, leveraging advancements in neuroimaging, data analysis, and theoretical biology. Looking ahead, the article speculates on the potential paradigm shifts that could arise from breakthroughs in computational technology, such as quantum computing, that may one day enable the simulation of the brain in its entirety. The article ultimately paints a picture of cautious optimism, where each incremental discovery is a valuable piece of the grand puzzle, bringing us closer to the epochal goal of comprehensively modeling the human brain.

Interaction of an electromagnetic field with matter in a laser cavity without the assumption of a fixed direction of the transverse electric field, described by the two-level Maxwell-Bloch equations, is studied. By using a perturbative nonlinear analysis, performed near the laser threshold, we report on the derivation of the laser (3+1)D vectorial complex cubic-quintic complex Ginzburg-Landau equation. Furthermore, we study the modulational instability of the plane waves both theoretically using the linear stability analysis, and numerically, using direct simulations via the split-step Fourier method. The linear theory predicts instability for any amplitude of the primary waves. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold of the amplitude of perturbations. The system understudy shows a deep dependence on the laser cavity parameters, for which there appear wave patterns in accordance with the predictions from the gain spectrum.

In this study, we aimed to identify the features of indeterminate choroidal melanocytic lesions visualized on optical coherence tomography angiography (OCTA) and to identify predictors of growth. We retrospectively evaluated 86 patients with indeterminate lesions treated at our cen-tre from 2016 to 2021. Clinical management involved active surveillance followed by brachy-therapy if growth was detected. The lesions were classified into two groups according to wheth-er they grew (small melanomas) or remained stable (choroidal nevi). Growth was detected in 19 (22.1%) lesions. All patients underwent OCTA at baseline. These images were compared to iden-tify possible predictors of growth. Significant between-group differences were observed in thickness (p=0.00), greatest basal diameter (p=0.00), number of risk factors (p=0.00), symptoms (p=0.001; relative risk [RR]: 4.3), orange pigment (p=0.00; RR: 6.02), and ultrasonographic hol-lowness (Kappa sign); p=0.000; RR: 5.3). The melanomas had significantly more vessels with a diameter ≥ 76.3 µm (p=0.02; RR: 2.46). The time to growth in these lesions was significantly shorter (p=0.05) than in lesions with smaller vessels. These findings show that vessel diameter quantified by OCTA can differentiate between choroidal nevi and small melanomas, especially when considered together with clinical risk factors.

Graves' disease (GD) is an autoimmune disorder in which Thyrotropin Receptor Antibodies (TRAb) continuously stimulate thyroid receptors, leading to excessive production of thyroid hormones. TRAb also affect the orbital tissues, causing Graves' ophthalmopathy. Treatment to control Graves' disease consists of antithyroid drugs, radioiodine and thyroidectomy, and through such treatments, TRAb is reduced and the disease is alleviated. The mechanism by which TRAb, which play a critical role in the pathogenesis of Graves’ disease, decreases after GD treatment is still unknown. This paper presents a theoretical mechanism of how GD patients maintain a vicious cycle and how GD treatment can reduce the TRAb levels and breaks the cycle using stress-based ideas.

Complexity science studies physical phenomena that cannot be explained by the mere analysis of the single units of a system but requires to account for their interactions. A feature of complexity in connected systems is the emergence of mesoscale patterns in a geometric space, such as groupings in bird flocks. These patterns are formed by groups of points that tend to separate from each other, creating mesoscale structures. When multidimensional data or complex networks are embedded in a geometric space, some mesoscale patterns can appear respectively as clusters or communities, and their geometric separability is a feature according to which the performance of an algorithm for network embedding can be evaluated. Here, we introduce a framework for the definition and measure of the geometric separability (linear and nonlinear) of mesoscale patterns by solving the travelling salesman problem (TSP), and we offer experimental evidence on embedding and visualization of multidimensional data or complex networks, which are generated artificially or are derived from real complex systems. For the first time in literature the TSP’s solution is used to define a criterion of nonlinear separability of points in a geometric space, hence redefining the separability problem in terms of the travelling salesman problem is an innovation which impacts both computer science and complexity theory.

Image restoration plays a vital role in image processing and pattern recognition in producing better recognition accuracy. It was observed that, most of the traditional restoration algorithms were meant for removing a single type of noise and efforts have been made towards the use of partial differential equation model (PDE), to restore different types of images such as super-resolution, bleeding through and deblurring. This research work deployed hybridized shock filter, shock diffusion of higher order PDE to remove degraded images that have been affected by atmospheric turbulence and water smear images. Degraded images of different types were acquired from various sources. The degraded images were subjected to shock filter algorithm, shock diffusion of higher order PDE. The shock filter was combined with PDE, likewise the shock diffusion was also combined with PDE, and the three algorithms were also combined to test the efficiency of the hybridized method on different degraded images. The result was validated using Mean Square Error, Structural Similarity Index Measure (SSIM), Peak-to-Noise-Signal -Ratio (PNSR) and universal quality index (UQI). From the result, it was observed that the combination of many image restoration algorithms does not give better results whereas, the combination of two of the algorithms has really proved effective.

Background: Pediatric mallet finger injuries lack specific treatment guidelines, necessitating an exploration of effective techniques. Our aim was to evaluate the outcomes of the extension block technique in adolescent mallet finger management. Methods: A comprehensive retrospective analysis was conducted involving 36 adolescents who underwent surgery between 2014 and 2022. Ishiguro’s extension block pinning technique was the primary method employed. Treatment outcomes were evaluated using Crawford's criteria, and complications were also assessed. Results: Bone union was achieved in all cases with a mean union time of 42 days (range: 30-92 days). According to Crawford's criteria, 27 cases (75%) were classified as excellent, 5 cases (14%) as good, and 4 cases (11%) as fair. Minimal complications were observed, including three cases (8%) of superficial infections, one case (3%) of dermal necrosis, and another rare instance (3%) of osteomyelitis. No cases of poor outcomes or significant long-term complications were noted. The average follow-up period was 8.6 months (range: 2-42 months). Conclusions: Ishiguro’s extension block technique is a promising surgical option for adolescent mallet fingers. Its adoption could enhance pediatric orthopedic care, offering a valuable child-friendly treatment alternative.

Nucleation is a fundamental and general process at the initial stage of first order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding on nanoscales are still required. Here we focus on homogeneous bubble nucleation, in which evaluation of the size dependence of bubble free energy is the key issue. We propose application of a formula in stochastic thermodynamics, the Jarzynski’s equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of bubble nucleation. As a test case, we performed a series of MD simulations with Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during bubble growth as the Jarzynski’s ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions.

Microwave technology has a potential application in the extraction of zinc from sulphide ores, knowledge of the dielectric properties of these ores plays a major role in the microwave design and simulation for any process. The dielectric properties of zinc sulfide concentrate for two different apparent densities—1.54 and 1.63 g/cm³—have been measured by using the resonance cavity perturbation technique at 915 and 2450 MHz during the roasting process for the temperature ranging from room temperature to 850 °C. The variations of dielectric constant, the dielectric loss factor, the dielectric loss tangent and the penetration depth with the temperature, frequency and apparent density have been investigated numerically. The results indicate that the dielectric constant increases as the temperature increases and temperature has a pivotal effect on the dielectric constant, while the dielectric loss factor has a complicated change and all of the temperature, frequency and apparent density have a significant impact to dielectric loss factor. Zinc sulfide concentrate is high loss material from 450 to 800 °C on the basis of theoretical analyses of dielectric loss tangent and penetration depth, its ability of absorbing microwave energy would be enhanced by increasing the apparent density as well. The experimental results also have proved that zinc sulfide concentrate is easy to be heated by microwave energy from 450 to 800 °C. In addition, the experimental date of dielectric constant and loss factor can be fitted perfectly by Boltzmann model and Gauss model, respectively.

Primary biliary cholangitis (PBC) is a cholestatic liver disease characterized by immune-mediated injury to small bile ducts. Although PBC is an autoimmune disease, the results of traditional immunosuppressive therapy are disappointing. Nearly 40% of PBC patients do not respond to the first-line drug UDCA. Without appropriate intervention, PBC patients would eventually progress to liver cirrhosis and even death. There is an urgent need to develop new therapies. The gut-liver axis emphasizes the interconnection between the gut and the liver, and there is increasing evidence that gut microbiota and bile acids play an important role in cholestatic diseases. Dysbiosis of gut microbiota, imbalance of bile acids, and immune-mediated bile duct injury constitute the triad of pathophysiology in PBC. Understanding the gut microbiota-bile acid network and corresponding immune functions in PBC provides a new perspective for its treatment strategies. Therefore, we summarize the latest advancements in research of gut microbiota and bile acids in PBC and, for the first time, explore the potential of immune factors related to them as novel immunotherapy targets. This article discusses potential therapeutic approaches focusing on regulating gut microbiota, maintaining bile acid homeostasis, their interactions, and related immune factors.

Weak signal spectral detection is a serious problem in many applications, especially the target possesses certain frequency band and under low signal-to-noise ratio (SNR). A kind of novel technique based on pre-whitening scale-transformation symmetric bistable parallel stochastic resonance (SR) is proposed to solve the problem. Firstly, the pre-whitening can ensure the even distribution of the receiving signal to fit the requirement of SR processing. Secondly, the scale- transformation can help to utilize the weak signal improvement property especially under low frequency band more effectively. Thirdly, the symmetric bistable parallel SR can try to reduce the variance of the clutter and additive noise fluently. Fourthly, by subtracting the steady state re-sponse of the selected symmetric bistable SR system from the parallel SR output, the weak signal spectral detection objective can be realized successfully. Simulation results based on the real sea clutter radar data guarantee the effectiveness and applicability of the proposed symmetric bistable PSR processing approach.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

In this study, a cholera infection model with the bilinear infection rate is developed by considering the perturbation of the infection rate by the mean-reverting process. First of all, we give the existence of a globally unique positive solution for a stochastic system at arbitrary initial value. On this basis, the sufficient condition for the model to have an ergodic stationary distribution is given by constructing proper Lyapunov functions and tight sets. This indicates in a biological sense the long-term persistence of cholera infection. Furthermore, after transforming the stochastic model to an relevant linearised system, an accurate expression for the probability density function of the stochastic model around a quasi-endemic equilibrium is derived. Subsequently, the sufficient condition to make the disease extinct is also derived. Eventually, the theoretical findings are shown by numerical simulations. Numerical simulations show that the impact of regression speed and fluctuation intensity on stochastic systems.

The real systems are often complex, nonlinear, and noisy in various areas including mathematics, natural science, and social science. We present the symplectic entropy (SymEn) measure as well as an analysis method based on SymEn to estimate the nonlinearity of the complex system by analyzing the given time series. The SymEn estimation is a kind of entropy based on symplectic principal component analysis (SPCA) which represent organized but unpredictable behaviors of systems. The key to SPCA is to preserve the global submanifold geometrical properties of the systems through symplectic transform in the phase space, which is a kind of the measure-preserving transforms. The capability of preserving the global geometrical characteristics makes the SymEn a test statistic to detect the nonlinear characteristics in several typical chaotic time series and the stochastic characteristic in the Gaussian white noise. The results are in agreement with findings in the approximate entropy (ApEn), the sample entropy (SampEn) and the fuzzy entropy (FuzzyEn). Moreover, the SymEn method is also used to analyze the nonlinearities of the real signals (including the EEG signals for ASD and healthy subjects, and the sound and vibration signals for the mechanical systems). The results indicate that the SymEn estimation can be taken as a measure for describing the nonlinear characteristics in the data collected from the natural complex systems.

Partial Differential Equations (PDEs) constitute a fundamental framework for modeling various physical phenomena across diverse fields such as physics, engineering, and finance. Solving PDEs accurately and efficiently remains a significant challenge, particularly when dealing with complex systems or high-dimensional data. In this paper, we present a novel approach based on deep learning techniques to investigate the effective factors in solving PDEs. Our methodology leverages the expressive power of deep neural networks to learn and represent the underlying relationships between input parameters and the solutions of PDEs. By incorporating domain knowledge into the network architecture and training process, our approach aims to provide insights into the key factors influencing the solution of PDEs. We demonstrate the effectiveness of our method through numerical experiments on various PDEs, showcasing its capability to identify important features and improve predictive accuracy. Our findings suggest that deep learning techniques offer a promising avenue for understanding and analyzing the complex dynamics inherent in PDEs, paving the way for enhanced computational methods in scientific and engineering applications.

Abstract. This paper proposes a Second Order Terminal Sliding Mode (2TSM) approach to the trajectory tracking of Differential Drive Mobile Robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the inner most loop, tracks the robot’s velocity quantities; while a kinematic controller, at the outer most loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated and finite time convergence is guaranteed by the second order TSM manifold which involves higher order derivatives of the state variables, resulting in inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.

The paper presents the problem of damage detection in steel girders. Static displacements at the selected point of the structure play the role of measured variables. Structural response signal decomposition is performed according to the Mallat pyramid algorithm, which is used to perform the discrete wavelet transform (DWT). This procedure allows us to quite well determine the location of structural damage. The geometry and the placement of any defective part of the structure may have a random character. It can be assumed that the random processes occurring in the broadly understood structure mechanics are Gaussian in nature. The first four probabilistic moments are estimated using three approaches independent: semi-analytical (SAM), perturbative (SPT), and Monte-Carlo simulations (MCS). The semi-analytical random approach seems to be the most optimal due to the necessary computation time. The incorporation of the mathematical stochastic apparatus into the classical (deterministic) analysis of the statics of the structure makes it possible to estimate the reliability measures of the analyzed girder.

In this paper, we succeed to discover the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear FPDEs.

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast forward to Constantino Tsallis’ illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino’s collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis’ enduring inspiration, Eroglu, Boghosian, Borges and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude.

Background: Clinical trails have revealed that patients with depression generally accompanied with learning and memory impairment, which critically impact on individual’s health and development. Danggui-Shaoyao-San (DSS), a famous Chinese complex prescription, significantly overcame depression and relieved cognitive disorder based on previous research and publication. However, its effectsand potential mechanism against chronic restraint stress (CRS) remained unknown. Methods: CRS animal model was established and mice were divided to six groups while they were oral administrated with Danggui-Shaoyao-San at doses of 1.25, 2.5 and 5 g/kg for 14 days. Emotional and cognitive performances were detected by behavior tests, meanwhile neural plasticity and its molecular mechanism were examined by Dil staining, western blot and immunofluorescence. Results: DSS treatment dose-dependently improved locomotion ability in open filed test, overcame depression behavior in forced swimming test and elevated plus maze test, enhanced learning and memory ability in Morris water maze test. CRS decreased number of total spines and mushroom spines, while DSS treatment dose-dependently restored these by Dil staining. Expression of BDNF and GluR1 were significantly down-regulated in CRS group, which were significantly normalized by DSS. Conclusions: DSS treatment dose-dependently reversed CRS-induced cognitive impairments by inducing structural remodeling of neurons.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

Currently there are fewer depth models applied to pepper picking detection, while the existing generalized neural networks have problems such as large model parameters, long training time, and low model accuracy.In order to solve the above problems, this paper proposes a Yolo-chili target detection algorithm for chili pepper detection. First, the classical target detection algorithm yolov5 is used as a benchmark model, and an adaptive spatial feature pyramid structure combining the attention mechanism and the idea of multi-scale prediction is introduced to improve the model's detection effect on occluded peppers and small target peppers. Secondly, a three-channel attention mechanism module is introduced to improve the algorithm's long-distance recognition ability and reduce the interference of redundant testers. Finally, the quantized pruning method is used to reduce the model parameters and realize the lightweight processing of the model. Applying the method to the homemade chili pepper dataset, the AP value of chili pepper reaches 93.11%; the accuracy rate is 93.51% and the recall rate is 92.55%.The experimental results show that yolo-chili is able to achieve accurate and real-time pepper detection under complex orchards.

The article is devoted to the new results of the author, which add his previously published ones, of studying hidden rules and symmetries in structures of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes. The author uses the existence of different alphabets of n-plets in DNA: the alphabet of 4 nucleotides, the alphabet of 16 douplets, the alphabet of 64 triplets, etc. Each of such DNA alphabets of n-plets can serve for constructing a text as a chain of these n-plets. Using this possibility, the author represents any long DNA nucleotide sequence as a bunch of many so-called n-texts, each of which is written on the basis of one of these alphabets of n-plets. Each of such n-texts has its individual percents of different n-plets in its genomic DNA. But it turns out that in such multi-alphabetical or multilayer presentation of each of many genomic DNA, analyzed by the author, universal rules of probabilities and symmetry exist in interrelations of its different n-texts regarding their percents of n-plets. In this study, the tensor product of matrices and vectors is used as an effective analytical tool borrowed from the arsenal of quantum mechanics. Some additions to the topic of algebra-holographic principles in genetics are also presented. Taking into account the described genomic rules of probability, the author puts also forward a concept of the important role of stochastic resonances in genetic informatics.

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

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

Apple replant disease (ARD) is a complex issue caused by various fungal, oomycetes pathogens and parasites which can differ in their abundance between sites within a geographic region. Knowledge of the specific etiology of ARD at a particular site is required in order to develop commercially viable soil management strategies to combat specific/individual components of the disease. In this study we analyzed the soil from six ARD sites for the presence of fungal, bacterial and oomycetes communities and plant parasitic nematodes. Five fungal, and 17 bacterial classes were differentially represented in the microbiomes from different locations. Mortierellomycetes was the most abundant fungal taxa represented followed by Sordariomycetes. Mortierella exigua a fungal endophyte was the most abundant fungal amplicon sequence variant (ASV) in the core microbiome. Proteobacteria was the most prevalent phylum identified in orchard soils. Several potential phytopathogenic fungi involved in ARD and endophytes including Fusarium oxysporum, F. solani, Nectria ramulariae, Ilyonectria robusta and Nectriaceae were identfied in the orchard soil. Pythium attrantheridium (Globisporangium attrantheridium), P. monospermum and P. ultimum (Globisporangium ultimum) were the most abundant oomycete taxa identified in these soil samples. Six different groups of plant-parasitic nematodes were found across the six orchards soil. Root-lesion nematodes, Pratylenchus spp., which are commonly associated with ARD, were identified in all orchards soil at population densities ranging from 12 to 33/100 cm3 soil. This research contributes valuable understanding of the ARD complex as the apple industry needs alternative approaches to combat the disease.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

An information-theoretic data mining method is employed to analyze categorical spatiotemporal Geographic Information System land use data. Reconstructability Analysis (RA) is a maximum-entropy-based data modeling methodology that works exclusively with discrete data such as those in the National Land Cover Database (NLCD). The NLCD are organized into a spatial (raster) grid, and are available in consistent format for every five years from 2001 to 2021. An NLCD tool reports how much change occurred for each category of land use; for the study area examined the most dynamic class is Evergreen Forest (EFO), so the presence or absence of EFO in 2021 was chosen as the dependent variable that our data modeling attempts to predict. RA predicts the outcome with approximately 80% accuracy using a sparse set of cells from a spacetime data cube consisting of neighboring lagged-time cells. When the predicting cells are all Shrubs &amp; Grasses there is a high probability for a 2021 state of EFO, while when the predicting cells are all EFO, there is a high probability that the 2021 state will be not-EFO. These findings are interpreted as detecting forest clear-cut cycles that show up in the data, and explain why this class is so dynamic. This study introduces a new approach to analyzing GIS categorical data and expands the range of applications that this entropy-based methodology can successfully model.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

This paper describes the first results of an Image Recognition Based Location (IRBL) for mobile application focusing on the procedure to generate a Database of range images (RGB-D). In an indoor environment, to estimate the camera position and orientation, a prior spatial knowledge of the surrounding is needed. In order to achieve this objective a complete 3D survey of two different environment (Bangbae metro station of Seoul and E.T.R.I. building in Daejeon – Republic of Korea) was performed using LiDAR (Light Detection And Ranging) instrument and the obtained scans were processed in order to obtain a spatial model of the environments. From this, two databases of reference images were generated using a specific software realized by the Geomatics group of Politecnico di Torino (ScanToRGBDImage). This tool allow to generate synthetically different RGB-D images) centered in the each scan position in the environment. Later, the external parameters (X, Y, Z, ω, φ, κ) and the range information extracted from the DB images retrieved, are used as reference information for pose estimation of a set of acquired mobile pictures in the IRBL procedure. In this paper the survey operations, the approach for generating the RGB-D images and the IRB strategy are reported. Finally the analysis of the results and the validation test are described.

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.

Complex atypical endometrial hyperplasia (CAH) carries a high probability of cancer. Intraoperative evaluation of endometrial cancer in cases of CAH has not been reliable. The safety and sensitivity of sentinel lymph node (SLN) sampling has been validated. We aim to evaluate the efficacy and safety of SLN sampling in CAH managed by the da Vinci robotic platform. A total of 113 patients with a preoperative diagnosis of CAH were included in this retrospective cohort study. All underwent a robot assisted total laparoscopic hysterectomy and bilateral salpingo-oophorectomy with 69 patients undergoing SLN sampling. Statistical analysis calculated the probability of cancer, SLN map rate, and surgical complications. Predictors of cancer were evaluated. Forty-seven percent of the entire cohort were diagnosed with endometrial cancer. Median age was 63 years in the SLN cohort (N = 69) and 61 in the No SLN cohort (N = 44) (p= 0.363).  Median BMI was 34 Kg/m2 in the SLN cohort and 40 in the No SLN cohort (p= 0.004). Bilateral SLN map was 92.8% and unilateral SLN map rate was 7.2%. There were no grade 3-4 complications in the SLN cohort, and 4 grade 3-4 complications in the No SLN group (p=0.021). A preoperative diagnosis of CAH bordering on or cannot rule out cancer was the only predictor of cancer.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

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.

We describe a family of paraxial and quasi-monochromatic optical wave packets with finite energy and smoothly shaped amplitude in space and time that develops a singularity in the intensity when spatiotemporally focused by imparting a converging spherical wave front and a negative temporal chirp. This singular behavior upon ideal focusing is manifested in actual focusing with finite apertures and in media with high-order dispersion in an "exploding" behavior featuring indefinitely increasing concentration of the energy when opening the aperture radius, thus exercising a continuous control on the focal intensity and spatial and temporal resolution. These wave packets offer a new way of focusing that outperforms what can be achieved with standard Gaussian wave packets in terms of focal intensity and resolution, and new possibilities in applications where energy concentration and its control are crucial.

A new low-pass filter (LPF) circuit with independent adjustment of various, incl. digitally controlled, pole frequency resistors, pole quality factor and transmission coefficient. The proposed low-pass filter is based on the use of the properties of a multi-differential operational amplifier that performs the functions of a signal adder. The peculiarity of the filter is that it has three inputs, with respect to which different transmission coefficients are implemented, incl. inverting (-1) and non-inverting (+1). To check these properties of a low-pass filter in the Micro-Cap environment, computer simulation of a specific circuit was performed on a multi-differential operational amplifier AD 8130. Mathematical expressions are given for the main parameters of the proposed low-pass filter, which allow parametric synthesis of elements of a specific circuit under given restrictions on the used element base.

Some peptide-based drugs including oxytocin, vasopressin, ziconotide, pramlintide, nesiritide, and octreotide, contain one intramolecular disulfide bonds. A novel and reusable monodispersed silica nanosphere-supported Pt(IV) complex (SiO2@TPEA@Pt(IV)) was synthesized via a four-step procedure and used for formation of intramolecular disulfide bonds in peptides. TEM and chemical mapping results for the Pt(II) intermediates and for SiO2@TPEA@Pt(IV) show that the silica nanospheres possess a monodisperse spherical structure and contain uniformly distributed Si, O, C, N, Cl, and Pt. The valence state of Pt on the silica nanospheres was characterized by XPS. The Pt(IV) loaded on SiO2@TPEA@Pt(IV) was 0.15 mmol/g, as determined by UV-vis spectrometry. Formation of intramolecular disulfides in six dithiol-containing peptides of variable lengths by use of SiO2@TPEA@Pt(IV) was investigated and the relative oxidation yields were determined by HPLC. In addition, peptide 1 (Ac-CPFC-NH2) was utilized to study the reusability of SiO2@TPEA@Pt(IV). No significant decrease in the relative oxidation yield was observed after ten reaction cycles. Moreover, the structure of SiO2@TPEA@Pt(IV) after being used ten cycles was determined to be similar to its initial one, demonstrating the cycling stability of the complex.

The Vacuum Energy Parameter (VEP) of standard cosmology denotes the fraction of the critical density attributed to the accelerated expansion of the Universe. Astrophysical evidence sets the numerical range of VEP at 0.692 +, - 0.012, yet the root cause of these values is currently unknown. Drawing from the stochastic interpretation of early-Universe cosmology, we develop here a derivation of the VEP based on classical diffusion theory and the Langevin equation. Predictions are shown to be in reasonable agreement with observations.

Tumid Lupus Erythematosus has been the subject of heated debate as to its correct nosographic classification. In particular, its definition has changed over time, depending on the different studies performed. In this review we address the initial definition of TLE, the changes that have taken place in the understanding and placement within the classification of Lupus Erythematosus (LE), and focus on clinical, histopathological, immunophenotypical and differential diagnosis aspects.

The conventional well placement was done manually by using a numerical reservoir simulator, and it required a lengthy trial-and-error process. It required great experience and expertise to manipulate the variables and uncertainties that lie on the reservoir to determine the best placement of the well. In addition, the traditional gradient-based methods such as Line-search and Trust-region were not viable in terms of maximum results obtained. Gradient-based methods were too dependent on the surface gradient of the solution and may only converge to local optima instead of global optima. Complex reservoirs have rough surfaces with high uncertainties, which hinders the traditional gradient-based method from converging to global optima. Thus, genetic algorithms were utilized to automate the manual trial-and-error process and to overcome the limitations of the traditional gradient-based method. The objectives of this study were to analyse the effect of different initial well placement distributions, the number of random solution sizes, and the crossover rate on cumulative oil production. A synthetic reservoir model built using CMG Builder was used as the testing platform for the optimization problems. Well-placement parameterization and optimization set-up were carried out using the CMG CMOST optimization tool. The integration of CMG IMEX and CMOST optimized cumulative oil production based on the objectives of the study. The results obtained showed that the higher number of random solutions used resulted in higher cumulative oil production, with more generations needed to reach the optimum solution. It can be concluded that the larger number of random solutions used increased the probability of reaching the optimum solution, but will take more generations.

Hepatocellular carcinoma (HCC) development is associated with altered modifications in DNA methylation, changing transcriptional regulation. Emerging evidence indicates that DNA methyltransferase 1 (DNMT1) plays a key role in carcinogenesis process. This study aimed to investigate how pirfenidone (PFD) modifies this pathway and the effect generated by the association between c-Myc expression and DNMT1 activation. Rats F344 were used for HCC development using 50 mg/kg of diethylnitrosamine (DEN) and 25 mg/kg of 2-aminofluorene (2-AAF). HCC/PFD group received simultaneous doses of 300 mg/kg of PFD. All treatments lasted 12 weeks. On the other hand, HepG2 cells were used to evaluate the effects of PFD in restoring DNA methylation in the presence of the inhibitor 5-Aza. Histopathological, biochemical, immunohistochemical, and western blot analysis were carried out and our findings showed that PFD treatment reduced the amount and size of tumors along with decreased Glipican-3, β-catenin, and c-Myc expression in nuclear fractions. Also, this treatment improved lipid metabolism by modulating PPARγ and SREBP1 signaling. Interestingly, PFD augmented DNMT1 and DNMT3a protein expression, which restores global methylation, both in our in vivo and in vitro models. In conclusion, our results suggest that PFD could slow down HCC development by controlling DNA methylation.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

The relentless challenges posed by the COVID-19 pandemic have placed immense pressure on densely populated regions, such as Hong Kong, particularly in the context of an aging population. The burgeoning demand for healthcare services has necessitated the optimization of resource al-location within healthcare systems. This research presents an innovative analytical queueing model specifically tailored to address the intricate gridlock dynamics prevalent in healthcare systems, with a focused application in the challenging landscape of COVID-19 management. Hong Kong, like numerous other regions, has experienced a demo-graphic transition leading to heightened healthcare demands. Traditional methodologies for scrutinizing gridlock issues in healthcare settings, including simulation models, often prove suboptimal within the context of sophisticated optimization frameworks. This study, however, delves into analytical queueing models, offering a more efficient and effective approach. These models have been underexplored, primarily due to the intricacies involved in modeling gridlock propagation within restricted capacity, a critical concern magnified by the COVID-19 pandemic. The novel Queueing Model introduced in this research incorporates the maintenance of queue capacities and topological aspects as exogenous parameters, rendering it exceptionally adaptable for diverse gridlock-related applications. This adaptability is especially pertinent to healthcare management during the COVID-19 crisis. The model meticulously integrates the concept of gridlock, furnishing a comprehensive comprehension of its origins and repercussions. Validation of this model involves rigorous comparison with established methodologies, exact results, and simulation data, consistently high-lighting its versatility and precision. By applying the model to healthcare management, we scrutinize the dynamics of patient flow within a Hong Kong hospital, placing specific emphasis on the critical issue of bed blockage, further exacerbated by the COVID-19 pandemic. The model's gridlock decomposition unearths the nuanced impact of bed blockage on distinct hospital units, addressing the imperative requirement for quantifying in-patient bed blockage within healthcare systems during a pandemic.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.

A dioxomolybdenum catalyst [(MoO2Cl2-O-MoO2Cl2)(L)] (1) (with L (1S,2S)-N,N´-bis(2-pyridinecarboxamide)-1,2-cyclohexane) was prepared and used as catalyst for the desulfurization of a multicomponent model fuel containing the most refractory sulfur compounds in real fuels. This complex showed to have a high efficiency to oxidize the aromatic benzothiophene derivative compounds present in fuels, mainly using a biphasic 1:1 model fuel/MeOH system. This process conciliates catalytic oxidative and extractive desulfurization, occurring the oxidation of the sulfur compounds in the polar organic solvent. The oxidative catalytic performance of (1) showed to be influenced by the presence of water in the system. Using 50% aq. H2O2 it was possible to reuse the catalyst and the extraction solvent MeOH during ten consecutive cycles without loss of desulfurization efficiency.

Furthermore, the nasal congestion typical of rhinitis can contribute to upper airway obstruction and sleep-disordered breathing. A vicious circle is created between asthma and sleep-disordered breathing: uncontrolled asthma and sleep-disordered breathing can worsen each other. In children with genetic obesity, despite alterations in the immune system, fewer allergies are found compared to the general population. The causes of this reduced allergenicity are unclear but probably involve genetic, immunological, and environmental factors. Further studies are needed to understand the mechanisms. The study emphasizes the importance of jointly evaluating and managing allergies, obesity, and sleep-disordered breathing in children, considering their close interconnection.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

The present study explored whether exposure to complex childhood trauma (CCT) is reflected in the resting-state electroencephalography (EEG) temporal alpha power of complex trauma-exposed adolescents, given the association of temporal alpha with fear circuitry (learning and conditioning) in a sample of 25 adolescents and similar controls, ages 12-17 years. Both trauma and psychopathology were screened or assessed, and resting-state EEG was recorded, following a preregistered protocol for data collection. Temporal alpha power, corresponding to T5 and T6 electrode location (10-20 international system), was extracted from resting-state EEG in both eyes-open and eyes-closed conditions. We found that in the eyes-open condition, right, but not left, temporal alpha was significantly higher in adolescents exposed to CCT, relative to healthy controls, suggesting that childhood trauma exposure may have a measurable impact on alpha oscillatory patterns, specifically in the right temporal region. Our study highlights the importance of considering neural markers, such as temporal alpha power, in understanding the long-term consequences of CCT exposure in developmental samples, with possible important clinical implications in guiding neuroregulation interventions.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.

Capsule endoscopy, which uses a wireless camera to take images of the digestive tract, is emerging as an alternative to traditional colonoscopy. The diagnostic values of these images depend on the quality of revealed underlying tissue surfaces. In this paper, we consider the problem of enhancing the visibility of detail and shadowed tissue surfaces for capsule endoscopy images. Using concentric circles at each pixel for random walks combined with stochastic sampling, the proposed method enhances the details of vessel and tissue surfaces. The framework decomposes the image into two detail layers that contain shadowed tissue surfaces and detail features. The target pixel value is recalculated for the smooth layer using similarity of the target pixel to neighboring pixels by weighting against the total gradient variation and intensity differences. In order to evaluate the diagnostic image quality of the proposed method, we used clinical subjective evaluation with a rank order on selected KID image database and compared to state of the art enhancement methods. The result showed that the proposed method provides a better result in terms of diagnostic image quality and objective quality contrast metrics and structural similarity index.

Based on the dynamic strength variation mechanism of concrete under complex loading conditions, two approaches were devised: numerical testing and CT scanning, guided by the principle of minimizing energy dissipation. A methodology for calculating concrete's failure area and measuring its strength was developed. The analysis delves into the mechanisms behind failure patterns and variations in concrete specimen strength, focusing on crack initiation, development, and the resultant failure surface formed by crack propagation, along with the stress distribution in concrete specimens subjected to diverse loading conditions. Through evaluating the strength and computed failure area of concrete specimens, it is evident that the loading method influences both the strength and failure area of concrete specimens. In general, a larger failure area correlates with a higher measured strength.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The Marun-Keu complex plays a significant role in understanding the geological evolution of the Ural orogen; however, it remains poorly understood. This study aims to provide insights into the complex's age, protolith composition, rock formation conditions, and its position in the region's history. The zircons from the host granitic gneisses are characterized by magmatic cores with an age of 470 Ma and metamorphic rims with an age of approximately 370 Ma. We suggest that the metamorphic rims were formed during eclogite metamorphism and that the metagranitoids hosting the eclogites experienced eclogite metamorphism simultaneously with the basic and ultrabasic rocks that are common in this area. Heterogeneous zircons were also isolated from the selvage of a pegmatite vein, in which four domains are distinguished, two to three of which can be identified within single grains, as follows: 1) igneous cores with an age of approximately 470 Ma and the geochemical characteristics of zircon crystallized in basic rocks; 2) zircons recrystallized during eclogite metamorphism with geochemical characteristics intermediate between those of the magmatic cores and true eclogitic zircon; 3) pegmatitic zircon, exhibiting the most sharply differentiated REE spectra of all four domains, characterized by a prominent positive Ce anomaly and a weakly expressed negative Eu anomaly; and 4) eclogitic zircon, observed in the form of veins and rims, superimposed in relation to the other three domains. The age of the latter three domains is within the error range and is estimated to be approximately 370 Ma. This indicates that the processes of eclogite metamorphism and the formation of pegmatites occurred at approximately the same time in the studied area.

In the current era of emerging technologies and cutting-edge inventions, it is equally important to consider the ethical aspects of research and innovations to have an ethical space for the sustainable progress and safety of humanity. The field of nanotechnology research and innovation often faces criticism due to its potential adverse impacts on health, the environment, limited accessibility, high costs, and concerns about data privacy. Therefore, it is crucial to address and resolve these ethical issues systematically. In this regard, we present our findings and methods for exploring the application of the ethics technology assessment method by considering its relevance at different stages of innovation development. Specifically, the present work provides a conceptual framework for ethics technology assessment focused on evaluating a significant innovation in nanotechnology within the domain of food safety with specific reference to mycotoxin remediation. By leveraging the value-sensitive design approach, we described various strategies for analyzing the ethical implications of nanotechnology-based innovations in mycotoxin remediation. Through comprehensive ethics technology assessment, nanotechnology-based innovations can be guided toward becoming more value-oriented, thereby making substantial contributions to social progress.

Fibrodysplasia Ossificans Progressiva (FOP) is an enigmatic, ultra-rare genetic disorder characterized by progressive heterotopic ossification, wherein soft connective tissues undergo pathological transformation into bone structures. This incapacitating process severely limits patient mobility and poses formidable challenges for therapeutic intervention. Predominantly caused by missense mutations in the ACVR1 gene, the disorder has hitherto defied comprehensive mechanistic understanding and effective treatment paradigms. This write-up offers a comprehensive overview of the contemporary understanding of FOP's complex pathobiology, underscored by advances in molecular genetics and proteomic studies. We shed light on targeted therapy, spanning genetic therapeutics, enzymatic and transcriptional modulation, stem cell therapies, and innovative immunotherapies. We also focused on the intricate complexities surrounding clinical trial design for ultra-rare disorders like FOP, addressing fundamental statistical limitations, ethical conundrums, and methodological advancements essential for the success of interventional studies. We advocate for the adoption of a multi-disciplinary approach that converges bench-to-bedside research, clinical expertise, and ethical considerations to tackle the challenges of ultra-rare diseases like FOP and comparable ultra-rare diseases. Overall, this article serves a dual role: as a definitive scientific resource for ongoing and future FOP research and as a call to action for innovative solutions to address methodological and ethical challenges that impede progress in the broader field of medical research for ultra-rare conditions.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Lirianthe delavayi has valuable ornamental and medicinal value, is an important economic tree, and has a long history of cultivation. As important regulatory molecules, miRNAs are involved in important physiological processes, such as the plant stress response, organ morphogenesis, hormone secretion, and signaling. In this study, based on miRNA sequencing analysis of wild and cultivated Lirianthe delavayi, we explored the differences in posttranscriptional regulation during the cultivation of Lirianthe delavayi from the aspect of miRNA molecular regulation. The results revealed the following: 1. A total of 365 miRNAs were sequenced and identified, and their first bases had obvious uracil (U) base preferences. Among them, 242 miRNAs were classified into 32 miRNA families; 2. Analysis of miRNA expression differences revealed that 39 miRNAs had significant expression differences between wild and cultivated populations; 3. Bioinformatics target gene prediction and target gene enrichment analysis of significantly differentially expressed miRNAs revealed that the target genes were significantly enriched in plant‒pathogen interactions, sphingolipid metabolism, defense responses, and ADP binding. 4. The plant‒pathogen interaction pathway involves seven differentially expressed miRNAs and 30 miRNA‒target gene regulatory pairs, which are involved mainly in pathogen signature molecule recognition and binding, signal transduction, and the regulation of disease resistance molecules or gene expression; Ath-MIR169g-p3_2ss7AG19GA, ath-MIR169g-p5_2ss7AG19GA, and ath-miR408-3p_L-3 are expressed only in wild population, and it is hypothesized that the domestication process from wild to cultivation species may be accompanied by the loss of disease resistance-related miRNAs. This study provides a reference for exploring the posttranscriptional-level regulatory mechanisms of adaptive changes in Lirianthe delavayi from wild to cultivated.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

This study addresses the critical need for standardizing Building Information Modeling (BIM) Execution Plans (BEPs) in the Architecture, Engineering, Construction, and Operations (AECO) sector. By analyzing 36 BEP documents from international organizations, we identify key elements and propose a comprehensive framework aimed at enhancing digital transformation and collaboration in complex construction projects. This research employs scientometric analysis to map the evolution of BEP standards and integrates empirical data from industry surveys to validate the proposed framework. Our findings highlight the benefits of standardized BEPs in reducing inefficiencies and improving project outcomes, thereby providing a significant contribution to the field of BIM implementation.

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.

Human papillomavirus (HPV) uses the cellular trafficking machinery to reach the cell nucleus and initiate a successful infection. The HPV capsid consists of two proteins: L1 (the major capsid protein) and L2 (minor capsid protein), and L2 is known to be responsible for trafficking the viral genome to the nucleus. From previous studies, we know that many cellular proteins interact with L2 and are involved in the trafficking process at different stages of the infectious entry process. To further investigate how HPV-16 achieves successful viral entry, we have performed a mass spectrometry analysis to identify novel interacting proteins that associate with incoming HPV-16 virions. We show that HPV-16 pseudovirions interact with a group of cellular cargo proteins (COPI), and here we confirm that this is mediated by the direct binding of L2, but not L1, to the COPB1 subunit. We also show that the ability of L2 to interact with COPB1 is conserved in both low- and high-risk HPV types. Furthermore, we also show that the interaction is essential for successful infection entry of multiple HPV types, thereby identifying a novel constituent of the infectious entry pathway of the HPV.

The main sources of intrinsic noise in excitable cells at the microcircuit and network levels are the stochastic characteristics of ion channel gating and activation of the synaptic conductance. Studies using in vivo, in vitro, and in silico methods to examine the effects of synaptic background activity were not adequately investigated in non-neuronal excitatory cells, where neurotransmitter-based innervation also occurs. We created a mathematical model to replicate the background synaptic noise dynamics in a non-neuronal cell. We utilized the stochastic Ornstein-Uhlenbeck process to represent excitatory synaptic conductance, which was incorporated into a whole-cell model to produce spontaneous and evoked cellular electrical activities. The single-cell model includes many biophysically detailed ion channels represented by a set of ordinary differential equations in Hodgkin-Huxley and Markov formalisms. This paradigm effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) resembling in vitro-like electrical activity in the cells. The input resistance decreased by multiple factors, and the spontaneous action potential firing rate elevated. The potential to reach the action potential threshold is altered. Background synaptic activity can alter the input/output characteristics of non-neuronal excitatory cells. Suppressing these baseline activities would facilitate the discovery of new pharmaceutical targets for different clinical diseases.