A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

This work studies how the Elo rating system can be applied to score-based sports, where it’s gaining popularity, and in particular for predicting the result at any point of a game, extending its statistical basis to stochastic processes. We derive some new theoretical results for this model and use them to implement Elo ratings for basketball and soccer leagues, where the assumptions of our model are tested and found to be mostly accurate. We showcase several metrics for comparing the performance of different ratings systems and determine whether adding a feature has a statistically significant impact. Finally, we propose an Elo model based in a discrete process for the score that allows us to obtain draw probabilities for soccer matches, and has a performance competitive with alternatives like SPI ratings.

The Work Ability Index (WAI) is the most widely used questionnaire for the self-assessment of working ability. Because of its different applications, shorter versions, and widespread use in healthcare activities, it is worthwhile assessing its characteristics. The WAI was distributed online among the workers of a healthcare company; the results were compared with data contained in the workers' personal health records and with absence registers. 340 out of 575 workers (59.1%) participated; 6.5% of them reported poor work ability. Exploratory factor analysis indicated that the one-factor version best described the characteristics of the WAI. The scores of the complete WAI, the shorter form without the list of diseases, and the minimal one-item version (WAS) had equal distribution and were significantly correlated. The WAI score was inversely related to age and significantly lower in women than in men, but it was higher in night workers than in colleagues due to the probable effect of selective factors. The WAI score was also correlated with absenteeism, but no differences were found between males and females in the average number of absences, suggesting that cultural or emotional factors influence the self-rating of the WAI. Workers tended to overreport illnesses in the online survey compared to data collected during occupational health checks. Musculoskeletal disorders were the most frequently reported illnesses (53%). Psychiatric illnesses affected 21% of workers and had the greatest impact on work ability. Multilevel ergonomic and human factor intervention seems to be needed to recover the working capacity of healthcare workers.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

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.

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.

With growing urbanisation the sustainability of cities has become increasingly important. Although cities have been using indicators for a long time it is only in the last decades that attempts have been made to collate indicators into indicator sets with the aim of reflecting the many different aspects that need to be covered to assess the sustainability of a city. The aim of this paper is to review how indicators for monitoring sustainable urban development have evolved over time and compare them to the indicators suggested by the UN Sustainable Development Goals (SDGs). The review reveals that previous indicator sets emphasised environmental sustainability, health and economic growth. It is also shown that indicator sets that pre-date the SDGs lacked dimensions such as gender equality and reduced inequalities. In all, the SDG indicators provide the possibility of a more balanced and integrated approach to urban sustainability monitoring. At the same time, a methodology is needed to facilitate the adaptation process of localising the SDGS, targets and indicators. Challenges of local application include their large number, their generic characteristics and the need to complement them with specific indicators that are more relevant at the city level.

This article systematically studied the A-optimal designs of a high-order mixture central polynomial model, which is an advancement of the research results for the A-optimal design of the most recent third-order mixture central polynomial model and a more accurate response surface model. This article is based on the simplex center design, obtaining measurement values at various design points, and verifying them through the A-optimal equivalence theorem. We also compare the A-efficiency of designs through examples, which can be applied to the A-optimal precise design of the fourth-order mixture model.

Shelter-in-place policies and the closure of non-essential workplaces intended to disrupt transmission of the SARS-COV-2 virus are effective approaches to combating COVID-19. They have, however, caused record levels of unemployment in the United States, raising questions of whether mitigation is more societally damaging than the disease. Here we use a coupled epidemiological-economic model to estimate the impact on employment of an unmitigated, business-as-usual approach to the pandemic. We compared unemployment between March-August 2020 in ten Californian socio-economic systems (SESs) to unemployment forecast by a model of industrial sector inter-dependencies subjected to unmitigated outbreaks of COVID-19. We found that economic losses are unavoidable because disease-driven losses propagate economically through SESs, amplifying losses to the disease. While model forecasts are generally lower than actual unemployment, jobs savings would come at the cost of greatly increased worker mortality. The costs would also be disproportionately greater among smaller and inland SESs.

Session-based recommendations which aim to predict subsequent user-item interaction based on historical user behavior during anonymous sessions can be challenging tasks. Two main challenges need to be addressed and improved: (1) How to analyze these sessions to accurately and completely capture users’ preferences, and (2) how to identify and eliminate any interference caused by noisy behavior. Existing methods have not adequately addressed these issues since they either neglected the valuable insight that can be gained from analyzing consecutive groups of items or failed to take these noisy data in sessions seriously and handled them properly, which can jointly impede recommendation systems from capturing users’ real intentions. To address these two problems, we designed a multi-order semantic denoising (MSD) model for session-based recommendations. Specifically, we grouped items of different lengths as varying multi-order semantic units to mine the user’s primary intention from multiple dimensions. Meanwhile, a novel denoising network was designed to alleviate the interference of noisy behavior and provide a more precise session representation. The result of extensive experiments on three real-world datasets demonstrated that the proposed MSD model exhibited improved performance compared with existing state-of-the-art methods in session-based recommendation.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

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.

Several technologies have been introduced into neurorehabilitation programs to en-hance traditional treatment of individuals with Spinal Cord Injury (SCI). Their effec-tiveness has been widely investigated but their adoption has not been properly quanti-fied. The aim of this study is to assess the distribution of conventional (Treatment As Usual – TAU) and technology-aided (Treatment With Technologies – TWT) treatments, conveniently grouped based on different therapeutic goals, in a selected SCI unit. Data from 104 individuals collected in 29 months were collected in a custom database and categorized according to both the conventional American Impairment Scale classifica-tion and a newly developed multifactor (MF) clustering approach, that considers addi-tional sources of information (the lesion level, the level of independence in the activi-ties of daily living and the hospitalization duration). Results indicated an average technology adoption of about 30%. Moreover, the MF clusters were less overlapped and the differences in TWT adoption were more pronounced than in AIS-based clus-tering. MF clustering was capable of grouping individuals based both on neurological features and functional abilities. In particular, individuals with motor complete inju-ries were grouped together, whereas individuals with sensorimotor incomplete SCI were collected separately based on the lesion level. Analyzing TWT adoption, we found that in case of motor complete SCI, TWT for muscle tone control and modulation were mainly selected while the other types of TWT were seldom adopted. Even for in-dividuals with incomplete SCI the most frequent rehabilitation goal was muscle tone modulation, regardless of the AIS level, and technologies to improve walking ability and balance control were mainly used for individuals with thoracic or lumbar lesions. Analyzing TAU distribution, we found that the highest adoption of muscle tone mod-ulation strategies was reported in case of individuals with motor complete SCI, i.e. in cases when almost no gait training was pursued. In case of cervical motor incomplete SCI, compared to thoracic and lumbar incomplete SCI, there was a greater focus on muscle tone control and force recruitment in addition to walking, than on balance training.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

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 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.

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.

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.

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.

Transition metal dichalcogenides (TMDs) monolayers exhibit unique valleytronics properties due to the dependency of the coupled valley and spin state at the hexagonal corner of the first Brillouin zone. Precisely controlling valley spin-polarization via manipulating the electron population enables its application in valley-based memory or quantum technologies. This study uncovered the uncompensated spins of the antiferromagnetic oxide (NiO) serving as the ferromagnetic (FM) order to induce valley spin-polarization in molybdenum disulfide (MoS₂) monolayers via the magnetic proximity effect (MPE). A spin-resolved photoluminescence spectroscopy (SR-PL) was employed to observe MoS₂, where the spin-polarized trions appear to be responsible for the MPE, leading to a valley magnetism. Results indicate that local FM order from the uncompensated surface of NiO could successfully induce significant valley spin-polarization in MoS₂ with the depolarization temperature approximately at 100 K, which is relatively high compared to related literature. This study reveals new perspectives and potential of AFM materials in the field of exchange-coupled van der Waals heterostructures.

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.

(1) Background: Chronic musculoskeletal pain (CMP) in adolescents can negatively affect physical, psychological and social functioning, resulting in functional disability. This study aims to evaluate the effectiveness of an outpatient rehabilitation program based on graded exposure in vivo (EP) compared with care as usual (CAU) in a RCT. The aim of the interventions (EP and CAU) is to improve functional ability in adolescents with CMP, CAU is interdisciplinary outpatient rehabilitation care, based on graded activity. (2) Methods: A pragmatic multicenter randomized clinical trial with a 12-month follow-up was used. Adolescents (12-21 years) with musculoskeletal pain were invited to participate. Primary outcome was functional disability (Functional Disability Inventory). Most important secondary measures: perceived harmfulness, pain catastrophizing and intensity. Data analysis was performed by intention-to-treat linear mixed model analysis. (3) Results: Sixty adolescents were randomized to EP or CAU and data of 53 adolescents (93% female) could be analyzed (25 EP, 28 CAU). Mean age was 16.0 years (SD=1.87). Adolescents in EP showed a clinically relevant and statistically significant decrease in functional disability (estimated mean difference at least -8.81,p-values≤0.01) compared with CAU at all time points. Significant differences in favor of EP were found for perceived harmfulness at all time points (p-values≤0.002), for pain catastrophizing (PCS) at 2 months follow-up (p-value=0.039) and for pain intensity at 4 and 10 months follow-up (p-values≤0.028). (4) Conclusion: The effectiveness of the trial is in favor of the EP and leads to a significant and clinically relevant decrease in functional disability compared to usual care.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

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.

For many engineering applications it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches length scale parameter have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modelling as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

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.

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.

Poplars (Populus spp.) are of significant ecological and economic importance. Long-term breeding efforts were aimed mainly at obtaining fast-growing and productive plants and less considered resistance to pests. This study aimed to identify the patterns of susceptibility to Saperda carcharias (Linnaeus, 1758) (Coleoptera: Cerambycidae) among Populus hybrids and pure species, considering crossing combinations and some other traits. In our research, 35 clones of poplar species and hybrids of the Ukrainian and foreign selection from the Aigeiros, Tacamahaca, and Leucoides sections were tested in 2021 and 2023 in the plantation created in 2014 in Eastern Ukraine. S. carcharias preferred infesting clones with earlier foliage development, larger diameters, and height increments. Specifically, hybrids with American maternal lineage showed the highest susceptibility, whereas those with European maternal lineage or Asian origin displayed lower infestation levels or resistance, respectively. This variability suggests a complex relationship between genetic background and pest resistance, underlining the need for a deeper understanding of the factors influencing susceptibility to S. carcharias. Selecting native species clones or creating mixed clone plantations could enhance the resilience of poplar plantations to pest threats.

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations to date that have been fully carried out are discussed in two main situations: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh-Jeans radiation, and second where only these radiation fields exist within a cavity. The emphasis here will be on the first more difficult situation where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in clasical statistical mechanics involving probabilistic notions of phase space occupation, the calculations to date for both particles and fields or for fields alone, follow the caloric entropy method where the notions of heat flow, adiabatic surfaces, and isothermal conditions, are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have been successfully utilized.

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.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

The evolutionary success of land plants largely relies on their ability to cope with constant environmental fluctuations, which negatively impact their reproductive fitness and trigger adaptational responses to biotic and abiotic stresses. In this challenging scenario, comprehensive research efforts so far aimed at depicting the roles of well-known phytohormones, mainly auxins, along with brassinosteroids, jasmonates, and abscisic acid, although the signaling networks coordinating the crosstalk among them remains vaguely understood. Accordingly, this review focuses on the Arabidopsis Amidase Signature (AS) superfamily members, highlighting the hitherto relatively underappreciated functions of AMIDASE1 (AMI1) and FATTY ACID AMIDE HYDROLASE (FAAH), as crucial coordinators of the growth-defense response trade-off by modulating auxin and ABA homeostasis.

In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.

In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.

Background: Telemedicine (interconsultation between primary and hospital care teams) has been operating in the counties of Central Catalonia Bages, Moianès and Berguedà since 2011 in the specialties of teledermatology, teleulcers, teleeyelids and teleaudiometries. For the period until the end of 2019, a total of 52,198 visits have been recorded. Objective: To analyse the differential costs between telemedicine and usual care in a semi-urban environment. Methodology: A cost-minimization evaluation, including direct and indirect costs from a societal perspective, distinguishing healthcare and user’s costs, within a three-month period. Results: Telemedicine saved € 780,397 over the period analysed. A differential cost favourable to telemedicine of about € 15/visit has been observed, the patient being the largest beneficiary of this saving (by 85%) in terms of shorter waiting times and travel costs. From the healthcare system perspective, moving the time spent in a hospital care consultation to primary care is efficient in terms of the total time devoted per patient. In social terms and in this context, telemedicine is more efficient than usual care. Conclusion: Users’ saving of time in terms of consultation and travel is the main driver of interconsultation between primary and hospital care savings in a semi-urban context. The telemedicine service is also economically favourable for the healthcare system, enabling it to provide a more agile service, which also benefits the healthcare professionals.

The exact, non perturbative, response theory developed within the field of nonequilibrium molecular dynamics, also known as TTCF (Transient Time Correlation Function) applies to quite general dynamical systems. Its key element is called dissipation function, because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time independent external perturbations, and then it has been extended to time dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated withe.g. linear response theory. The present work includes time dependent stochastic perturbations, in the theory, using the Karhunen-Loeve theorem. This leads to three different investigations of a given process. One in which a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigations, one averages over both initial conditions and stochastic coefficients. We conclude illustrating the applicability of the resulting exact response theory with simple examples.

This study investigates the stochastic dynamics of hepatitis B virus (HBV) infection using a newly proposed stochastic model. Contrary to deterministic models that fail to encapsulate the inherent randomness and fluctuations in biological processes, our stochastic model provides a more realistic representation of HBV infection dynamics. It incorporates random variability, thereby acknowledging the changes in viral and cellular populations and uncertainties in parameters such as infection rates and immune responses. We examine the solution's existence, uniqueness, and positivity for the proposed model, followed by a comprehensive stability analysis. We provide the necessary and sufficient conditions for local and global stability, offering deep insight into the infection dynamics. Furthermore, we utilize numerical simulations to corroborate our theoretical results. This research provides a robust tool for understanding the complex behavior of HBV dynamics, contributing significantly to the ongoing quest for more effective HBV control and prevention strategies.

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.

An exploding demand for processing capabilities related to the emergence of the IoT, AI and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path, but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations; four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the SC framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications.

The paper presents the author’ original modification of the residual method in order to construct an efficient tool for assessing the condition of photovoltaic cells, in particular – panels made of amorphous cells which are characterized by significant random operation parameter changes. The solution constructed has been verified through experiments, which show the usefulness of the proposed methodology as it allows to minimize the risk of obtaining false diagnostic information in the process of assessing the condition of photovoltaic panels.

Functional connectivity (FC) is a potential candidate that can increase the performance of brain-computer interfaces (BCIs) in the elderly because of its compensatory role in neural circuits. However, it is difficult to decode FC by current machine learning techniques because of a lack of its physiological understanding. To investigate the suitability of FC in BCI for the elderly, we propose the decoding of lower- and higher-order FCs using a convolutional neural network (CNN) in six cognitive-motor tasks. The layer-wise relevance propagation (LRP) method describes how age-related changes in FCs impact BCI applications for the elderly compared to younger adults. Seventeen younger (24.5±2.7 years) and twelve older (72.5±3.2 years) adults were recruited to perform tasks related to hand-force control with or without mental calculation. CNN yielded a six-class classification accuracy of 75.3% in the elderly, exceeding the 70.7% accuracy for the younger adults. In the elderly, the proposed method increases the classification accuracy by 88.3% compared to the filter-bank common spatial pattern (FBCSP). LRP results revealed that both lower- and higher-order FCs were dominantly overactivated in the prefrontal lobe depending on task type. These findings suggest a promising application of multi-order FC with deep learning on BCI systems for the elderly.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described.

This paper presents an approach to the Timoshenko beam theory (TBT) using the finite difference method (FDM). The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. The model developed in this paper consisted of formulating differential equations with finite differences and introducing additional points at the beam’s ends and at positions of discontinuity (concentrated loads or moments, supports, hinges, springs, brutal change of stiffness, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends. Moreover, grid points with variable spacing were considered, the grid being uniform within beam segments. First-order, second-order, and vibration analyses of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis, vibration analysis). Finally, a direct time integration method (DTIM) was presented; the FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

Here, I present an alternate solution for the dark matter problem. I show that the stars of a galaxy’s arm attract each other with a force other than gravity, producing a chain of stars. We already have an abundance of data (ring and multiring galaxies) as proof for the existence of this strong stars’ chain. This attraction force does not end at the galaxy’s boundaries but gets deeper into the cosmos, and it may explain the dark-energy problem. This attraction force affects only stars and seems to have no effect on planets. I also offer a novel timeline order for the well-known galaxies using Hubble classification. I nominate entangled particles for the role that causes this phenomenon.

Real assets in the energy market are subject to ecological uncertainty due to the penetration of renewables. We illustrate this point by analysing electrolysers, a class of assets which recently became the subject of a large interest, as they lead to the production of the desirable green hydrogen and green ammonia. The latter has the advantage of being easily stored and has huge potential in decarbonising both the fertilizer and shipping industries. We consider the optimization of green ammonia production with different types of electricity procurement in the context of stochastic power and ammonia markets, a necessary assumption to translate the features of renewable, hence intermittent, electricity. We emphasise the importance of using stochastic prices to effectively model the volatile nature of the price dynamics, illustrating the project risks that can be mitigated by hedging activities. This study shows the pivotal role of flexibility when dealing with fluctuating renewable production and volatile electricity prices to maximise profits and better manage risks.

Dealing with randomness is a crucial aspect that cost-effectiveness analysis (CEA) tools need to address, but existing stochastic CEA tools have rarely examined risk and return from the perspective of global benefits. This paper proposes a stochastic CEA tool that supports medical decision-making from the perspective of global benefits of risk and return, the risk-adjusted incremental cost-effectiveness ratio (ICER). The tool has a traditional form of ICER but uses the risk-adjusted expected cost. Theoretically, we prove that the tool can provide marginal medical decisions that promote the risk-return level on global benefits within any intervention structure and can also serve as a discriminating condition for the optimal intervention structure. Numerical simulations within a framework of mean-variance support the conclusions in this paper.

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

Partial differential representation of self-similarity feature has been derived from notion of the homogenous function in general sense. This representation allows consideration of stochastic self-similar systems. As well as the partial differential representation allows consideration of Stochastic Partial Differential Equation.

This paper presents an approach to the Euler-Bernoulli beam theory (EBBT) using the finite difference method (FDM). The EBBT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally, the finite difference approximations are derived based on fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection curve; the FOPH is made for the fourth and third derivative of the deflection curve while the SOPH is made for its second and first derivative. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, the FOPH was made for all of the derivatives of the deflection curve, and additional points were introduced at the beam’s ends and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. First-order analysis, second-order analysis, and vibration analysis of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis). Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid. Further research will be needed to investigate polynomial refinements (higher-order polynomials such as fifth-order, sixth-order…) of the deflection curve; the polynomial refinements aimed to increase the accuracy, whereby non-centered finite difference approximations at beam’s ends and positions of discontinuity would be used.

As a model for economic and ecological systems, replicator dynamics represents a basic form of agent competition for finite resources. Here, we investigate the effects of stochastic resetting in this kind of processes. Random reset events abruptly lead individual resources to a small value from which dynamics must start anew. Numerical results show that resource distribution over the population of competing agents develops highly nonuniform profiles, exhibiting clustering and fluctuations with anomalous dependence on the population size. This non-standard statistical behavior jeopardizes an analytical treatment based on mean-field assumptions. We propose alternative simplified analytical approaches which provide a stylized description of entropy evolution for the clustered distribution of resources and explain the unusually slow decrease of fluctuations.

Intratumoral heterogeneity can exist along multiple axes: Cancer Stem Cells (CSCs)/non-CSCs, drug-sensitive/drug-tolerant states and a spectrum of epithelial-hybrid-mesenchymal phenotypes. Further, these diverse cell-states can switch reversibly among one another, thereby posing a major challenge to therapeutic efficacy. Therefore, understanding the origins of phenotypic plasticity and heterogeneity remains an active area of investigation. While genomic components (mutations, chromosomal instability) driving heterogeneity have been well-studied, recent reports highlight the role of non-genetic mechanisms in enabling both phenotypic plasticity and heterogeneity. Here, we discuss various processes underlying phenotypic plasticity such as stochastic gene expression, chromatin reprogramming, asymmetric cell division and the presence of multiple “attractors”. These processes can facilitate a dynamically evolving cell population such that a subpopulation of (drug-tolerant) cells can survive lethal drug exposure and recapitulate population heterogeneity on drug withdrawal, leading to relapse. These drug-tolerant cells can be both pre-existing and also induced by the drug itself through cell-state reprogramming. The dynamics of cell-state transitions both in absence and presence of the drug can be quantified through mathematical models. Such a dynamical systems approach to elucidating patterns of intratumoral heterogeneity by integrating longitudinal experimental data with mathematical models can help design effective combinatorial and/or sequential therapies for better clinical outcomes.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

In this paper, we consider the problem that the maximal order consider the groups that consisting of transformations we called NG-Transformation on a nonempty set A has no bijection as its element. We find the order of these groups not greater that (n-1)!. In addition, we will prove our result by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.

Healthcare leaders are faced with many financial challenges in the contemporary environment, leading to many bankruptcies in recent years. What is not well understood are the specific conditions that lead to organizational economic failure. Ideally, hospital leaders could examine the literature for guidance to predict bankruptcy before it occurs. However, existing regression methods have proven inadequate, especially when the finance variables follow a nonnormal frequency pattern. Furthermore, the regression approach encounters difficulties due to multicollinearity and nonnormality issues. Therefore, an alternate stochastic approach for predicting the probability of hospital bankruptcy is warranted. This new method includes computing and interpreting the correlations between the hospital’s revenue and expenses for bivariate lognormal data, calculating the risk of bankruptcy due to the mismatch between revenues and expenses, determining the likelihood of a hospital’s expense exceeding the state’s median expense level, and evaluating a hospital’s financial memory level. Ultimately in our research, we demonstrate a novel approach to anticipate hospital bankruptcy, which can be particularly useful for health policy analysts and hospital leaders in making informed financial decisions and proactively managing risks to ensure the sustainability and stability of their institutions.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U-procedure verses the R-procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of (c+id). All the sample phases forms a group G_R. Taking G_R as the sampling potential, combined with the dynamic phase group G_U，we establish a unified model of U-procedure and R-procedure for the evolution of wavefunction. Based on the Born rule, the probability of a sample is given by the squared magnitude of （c+id）. Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike. The measurement problem widely exists in dynamic analysis, higher cognition, and large data modeling. Thus, the work reported here has a wide range of applications. Keywords: The measurement problem; U-R procedures; the Yes/No type measurement; stochastic sampling; sample phase; Born probability.

It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered as a displacement along a certain fault surface. Usually, when describing the source, the geometry of the fault surface is simplified to a flat rectangular area. The displacement vector is assumed to be constant. In this paper, we propose a model of an earthquake source in the form of a displacement with a constant vector along a stochastic surface. A number of standard assumptions were made when modeling. We take into account only the elastic properties of the medium. We consider the Earth’s crust as a half-space and assume that the medium is homogeneous and isotropic. For the mathematical description of the earthquake source, we use the classical force equivalent of displacement along the fault. This is the distribution of double pairs of forces. The field of displacements under the action of body forces is found through a combination of Mindlin nuclei of strain. The paper presents solutions for strike-slip fault. To obtain a stochastic fault surface, we propose to introduce a random deformation of a rectangular flat surface. The paper presents the results of a computational experiment comparing the levels and regions of relative deformations of the Earth’s crust in the case of displacement along a flat rupture surface and along a stochastic one. In the case of a stochastic surface, the regions of relative deformations become asymmetric. The developed model will help to indirectly take into account various mechanical properties of the Earth’s crust when modeling deformations caused by earthquakes.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

Due to the increased use of memristors, and its many applications, the use of emulators has grown in parallel to avoid some of the difficulties presented by real devices such as variability and reliability. In this paper, we present a memristive emulator designed using a Switched Capacitor (SC), this is, an analog component/ block and a control part or block implemented using stochastic computing (SCo) and therefore fully digital. Our design is thus a mixed signal circuit. Memristor equations are implemented using stochastic computing to generate the control signals necessary to work with the controllable resistor implemented as switched capacitor.

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

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

In recent years, the field of deep learning achieved considerable success in pattern recognition, image segmentation and may other classification fields. There are a lot of studies and practical applications of deep learning on images, video or text classification. In this study, we suggest a method for changing the architecture of the most performing CNN models with the aim of designing new models to be used as stand-alone networks or as a component of an ensemble. We propose to replace each activation layer of a CNN (usually a ReLu layer) by a different activation function stochastically drawn from a set of activation functions: in this way the resulting CNN has a different set of activation function layers.

Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search.

In this paper we introduce the Adomian decomposition method for a class of first order fuzzy dynamic equations on arbitrary time scales for existence of solutions. The results are provided with suitable numerical examples.

Autism spectrum disorder (ASD) is characterized by diverse patterns of social interaction, communication, and behavior. This study explores the application of clustering and stochastic migration models to visualize and understand the social and neural connectivity patterns associated with autism. The clustering model, with its strong internal connections and limited external connections, mirrors the tight-knit social groups and communication barriers often observed in individuals with autism. In contrast, the stochastic model, characterized by more dispersed connections and greater adaptability, represents the variability and flexibility seen in social interactions across typical individuals. By comparing these models, we can gain deeper insights into the unique challenges and strengths of individuals with autism, highlighting the importance of personalized interventions. Additionally, these models provide a visual framework for understanding the differences in brain connectivity patterns observed in autism, with implications for both behavioral and neural correlates. This study underscores the value of computational models in advancing our understanding of autism and guiding effective support strategies.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Analyzing the records of Advanced LIGO and Virgo gravitational observatories, we found a specific time-domain asymmetry inherent only to the signals of their gravitational detectors. Experiments with different periodic signals, Gaussian and non-Gaussian noises, made it possible to conclude that the noise of gravitational detectors is an unusual mixture of signals. We also developed a specialized Pearson correlation analyzer to recognize the gravitational-wave events. It turned out that the LIGO detectors’ output signals include a significant (– 6 dB) component, which has the properties of records of reliably recognized gravitational waves. It allows us to argue that the gravitational background noise is largely due to the processes of merging astronomical objects. Since the specific signal is registered by the detectors continuously, we can consider the sub-kilohertz band gravitational oscillations field as detected. Our analysis method also allows us to estimate the contribution of the gravitational background component to the total signal energy. With its help, it will be possible not only to provide the radio-frequency estimation of the magnitude of gravitational disturbances but also, possibly, to construct a map of the gravitational noise of the sky.

This paper presents an approach to the Kirchhoff-Love plate theory (KLPT) using the finite difference method (FDM). The KLPT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally in the case of KLPT, the finite difference approximations are derived based on the fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection surface. The FOPH is made for the fourth and third derivative of the deflection surface while the SOPH is made for its second and first derivative; this leads to a 13-point stencil for the governing equation. In addition, the boundary conditions and not the governing equations are applied at the plate edges. In this paper, the FOPH was made for all of the derivatives of the deflection surface; this led to a 25-point stencil for the governing equation. Furthermore, additional nodes were introduced at plate edges and at positions of discontinuity (continuous supports/hinges, incorporated beams, stiffeners, brutal change of stiffness, etc.), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at the plate edges and to satisfy the boundary and continuity conditions. First-order analysis, second-order analysis, buckling analysis, and vibration analysis of plates were conducted with this model. Moreover, plates of varying thickness and plates with stiffeners were analyzed. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. In first-order, second-order, buckling, and vibration analyses of rectangular plates, the results obtained in this paper were in good agreement with those of well-established methods, and the accuracy was increased through a grid refinement.

This paper presents an exact solution to the Timoshenko beam theory (TBT) for first-order analysis, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory (EBBT) neglects shear deformations. Thus, the Euler–Bernoulli beam is a special case of the Timoshenko beam. The moment-curvature relationship is one of the governing equations of the EBBT, and closed-form expressions of efforts and deformations are available in the literature. However, neither an equivalent to the moment-curvature relationship of EBBT nor closed-form expressions of efforts and deformations can be found in the TBT. In this paper, a moment-shear force-curvature relationship, the equivalent in TBT of the moment-curvature relationship of EBBT, was presented. Based on this relationship, first-order and second-order analyses were conducted, and closed-form expressions of efforts and deformations were derived for various load cases. Furthermore, beam stability was analyzed and buckling loads were calculated. Finally, first-order and second-order element stiffness matrices were determined.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

In a recent paper we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work we have kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that indeed a second order analysis will suffice, and higher order terms can be neglected.

In this paper we present a successful implementation of the Hindmarsh–Rose model within a SC environment. The merits of the proposed approach are design simplicity, due to stochastic computing, and the ease of implementation. Simulation results showed that the approximation achieved is equivalent to introducing a noise source into the original model. A study for the level of noise introduced, according to the number of bits in the stochastic sequence, has been performed. Additionally, we demonstrate that such an approach, even though it is noisy, it reproduces the behaviour of biological systems, which are intrinsically noisy. It is also demonstrated that a speedup of x2 compared to biological systems is easily achievable, with a very small number of gates, thus paving the road for the in silico implementation of large neuron networks.

Semantic segmentation is a very popular topic in modern computer vision and it has applications to many fields. Researchers proposed a variety of architectures over time, but the most common ones exploit an encoder-decoder structure that aims to capture the semantics of the image and it low level features. The encoder uses convolutional layers, in general with a stride larger than one, to extract the features, while the decoder recreates the image by upsampling an using skip connections with the first layers. In this work, we use DeepLab as architecture to test the effectiveness of creating an ensemble of networks by randomly changing the activation functions inside the network multiple times. We also use different backbone networks in our DeepLab to validate our findings. We manage to reach a dice coefficient of 0.888, and a mean Intersection over Union (mIoU) of 0.825, in the competitive Kvasir-SEG dataset. Results in skin detection also confirm the performance of the proposed ensemble, which is ranked first with respect to other state-of-the-art approaches (including HardNet) in a large set of testing datasets. The developed code will be available at https://github.com/LorisNanni.

Water is essential to all life-forms including various ecological, geological, hydrological, and climatic processes/activities. With changing climate, associated El Nino/Southern Oscillation (ENSO) events appear to stimulate highly uncertain patterns of precipitation (P) and evapotranspiration (EV) processes across the globe. Changes in P and EV patterns are highly sensitive to temperature variation and thus also affecting natural streamflow processes. This paper presents a novel suite of stochastic modelling approaches for associating streamflow sequences with climatic trends. The present work is built upon a stochastic modelling framework HMM_GP that integrates a Hidden Markov Model with a Generalised Pareto distribution for simulating synthetic flow sequences. The GP distribution within HMM_GP model is aimed to improve the model's efficiency in effectively simulating extreme events. This paper further investigated the potentials of Generalised Extreme Value Distribution (EVD) coupled with an HMM model within a regression-based scheme for associating impacts of precipitation and evapotranspiration processes on streamflow. The statistical characteristic of the pioneering modelling schematic has been thoroughly assessed for their suitability to generate/predict synthetic river flows sequences for a set of future climatic projections. The new modelling schematic can be adapted for a range of applications in the area of hydrology, agriculture and climate change.

This study purposes the use of plug-in electric vehicles for demand side management (DSM) considering uncertainties in demand as well as uncertainties due to mobility of PEV to mitigate peak demand. The solution also seeks to reduce electric cost in addition to reducing the effects of greenhouse gases. In recent years DSM using distributed storage system such as battery energy management system (BESS) and plugged-in electric vehicles (PEV) have become very prevalent with most implementations resorting to deterministic load forecast. These methods do not consider the potential growth in demand making their solutions less robust. In this study we propose a real-time density demand forecast and stochastic optimization for robust operation of PEV for a building. This method accounts for demand uncertainties in addition to uncertainties in mobile energy storage as found in PEV, making the resulting solution robust as compared to the deterministic case. A case study on a real site in South Korea is used for verification and testing. The proposed study is verified and tested against existing algorithms. The result verifies the effectiveness of the proposed approach

A Demand-side management technique are deployed along with battery energy-storage systems (BESSs) to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

The genetic code evolved by parallel tracks of chaotic and ordered processes. Liquid-liquid phase separation (hydrogels), a chaotic process, constructs diverse membraneless compartments within cells, resulting in regulated hydration and sequestration and concentration of reaction components. Hydrogels relate to chaotic amyloid fiber production. We propose that polyglycine and related hydrogels (i.e. GADV; G is glycine), phase separations, membraneless droplets and amyloid accretions organized protocell domains to drive the earliest evolution of the genetic code and the pre-life to cellular life transition. By contrast, evolution of tRNA, tRNAomes, aminoacyl-tRNA synthetases and translation systems followed highly ordered and systematic pathways, described by well-defined mechanisms and rules. The pathway of evolution of aminoacyl-tRNA synthetases, which tracked evolution of the genetic code, is clarified. Hydrogels and amyloids form a chaotic component, therefore, that complemented otherwise systematic processes. We describe with detail a pre-life world in which hydrogels and amyloids provided the selections of the first life.

Purpose: Perceptual learning and production practice are basic mechanisms that children depend on to acquire adult levels of speech accuracy. In this study, we examined perceptual learning and production practice as they contributed to changes in speech accuracy in three- and four-year-old children. Our primary focus was manipulating the order of perceptual learning and baseline production practice to better understand when and how these learning mechanisms interact. Method: Sixty-five typically-developing children between the ages of three and four were included in the study. Children were asked to produce CVCCVC nonwords like /bozjəm/ and /tʌvtʃəp/ that were described as the names of make-believe animals. All children completed two separate experimental blocks: a baseline block in which participants heard each nonword once and repeated it, and a test block in which the perceptual input frequency of each nonword varied between 1 and 10. Half of the participants completed a baseline-test order; half completed a test-baseline order. Results: Greater accuracy was observed for nonwords produced in the second experimental block, reflecting a production practice effect. Perceptual learning resulted in greater accuracy during the test for nonwords that participants heard 3 or more times. However, perceptual learning did not carry over to baseline productions in the test-baseline design, suggesting that it reflects a kind of temporary priming. Finally, a post hoc analysis suggested that the size of the production practice effect depended on the age of acquisition of the consonants that comprised the nonwords. Conclusions: The study provides new details about how perceptual learning and production practice interact with each other and with phonological aspects of the nonwords, resulting in complex effects on speech accuracy and learning of form-referent pairs. These findings may ultimately help speech-language pathologists maximize their clients’ improvement in therapy.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

This study explores the potential trajectories of human civilization influenced by the development and competition of advanced artificial intelligence (AI) systems. Using a system of stochastic partial differential equations (SPDEs), we model the probability density function representing the state of civilization in a phase space defined by prosperity and knowledge. The model incorporates diffusion, growth, saturation, and drift terms, alongside stochastic noise to reflect the uncertainties and random fluctuations in AI impacts.The simulation results are visualized in a probability density graph, revealing the likelihood of various outcomes ranging from extinction and regression, to prosperity and technological advancement. The analysis highlights the balanced prospects of human future, with significant probabilities in both positive and negative directions. Positive scenarios suggest potential for increased prosperity and knowledge, emphasizing the importance of effective AI management and international cooperation. Conversely, the notable risks of regression and extinction underline the need for strategic interventions to mitigate adverse impacts. Our findings stress the stochastic nature of future developments and the critical role of adaptive and flexible policies in steering human civilization towards favorable outcomes. This study provides a simple yet comprehensive framework for understanding the complex dynamics at play and underscores the importance of proactive strategies in the age of AI.

The container relocation problem (CRP) is one of the important topics in container terminals, which aims to find the optimal sequence of movements to minimize the total number of relocations needed to retrieve all the containers within a bay according to a given specific layout and retrieval order. However, determining such an order may be difficult due to uncertainty. Various CRP solution methods proposed so far show a common pitfall concerning the complexity of the solving process, whose scale grows exponentially with the number of containers. Considering the retrieval operation process of the inbound containers in a bay consists of several operation rounds, this paper focuses on the real-time operation scenario of each round to minimize the actual number of relocations during the pick-up process, i.e., starting from the initial layout of the bay, we minimize the sum of the incremental number of blocking containers due to the layout change and the number of reallocated containers unrelated to the target container. We present a heuristic algorithm (called SPFH) based on the three rules (LL, MSS, and FSS), considering the adjustment of the pick-up order of containers. Numerical experiments on a set of instances generated from the literature are performed. The proposed methodology excels in both execution efficiency and solution quality and is capable of solving instances that were impossible to solve before. This also makes our methods appealing for being applied in practice. The source codes are available at https://github.com/zhou-sf/rt-scrp.

Iterative Stochastic decoding is an alternative to standard fixed-point decoding of Low-density parity check codes (LDPC) to reduce inter-node routing. In this paper, we propose a Flexible Field-Programmable Gate Array (FPGA)-Based Stochastic decoding (SD) hardware architecture for LDPC codes in the Fifth-Generation (5G) New Radio (NR) Standard that supports decoding of set of various code rates. This decoder’s runtime flexibility is desirable to switch a better performing code rate automatically based on the channel conditions without the extra time needed for reprogramming of FPGA. An offline design method is implemented to generate the hardware description language (HDL) code description of the decoder for the required code-rate set, which is further synthesized and integrated into the Xilinx Kintex-7 series FPGA board to determine the hardware resource utilisation and processing throughput. The Synopsys design tools were employed during both the simulation and synthesis stages, in combination with TSMC 65-nm CMOS standard cell technology, to facilitate comparative analysis. Compared with state-of-the-art designs, the proposed architecture reduces hardware utilization by up to 26% and achieved energy efficiency by 52%.

The need to find the global minimum in multi-dimensional functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the optimization algorithm to search for the best solution in the solution space. In the context of this article, a novel approach to generating the initial solution distribution is presented which is applied to a genetic optimization algorithm. Using the k-means clustering algorithm, a distribution based on data similarity is created. This helps in generating initial estimates that may be more tailored to the problem. Additionally, the proposed method employs a rejection sampling algorithm to discard samples that do not yield better solution estimates in the optimization process. This allows the algorithm to focus on potentially optimal solutions, thus improving its performance. Finally, the article presents experimental results from the application of this approach to various optimization problems, providing the scientific community with a new method for addressing this significant problem.

Machinery parts gradually wear out over time due to regular usage. To improve machinery health and prevent critical issues, a reliable prognosis framework can be implemented by monitoring the behaviour of machinery parts and issuing warnings before they reach a critical state. To achieve this, vibration data from roller bearings experiencing various fault conditions have been collected. Different techniques from the literature were combined to analyze the distinct configurations in the vibration data sets and identify the main defects in roller bearings. The significant features extracted from this analysis were then used to create optimized stochastic model equations, separately regressing inner and outer race fault features to healthy bearing features under random conditions. These models can help engineers design more dependable systems, optimize their performance, and minimize the risk of failures and downtime.

In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the idle time of such systems. It is assumed that, at a time t the failure of a cold standby system is observed, but the actual time of the failure is a time before t. The idle time of the inactive cold standby system is measured as the time between the exact time of failure, which is a random variable, and time t. We use the idle times of the components of the system to obtain lower and upper bounds on the lifetime of the standby system to which they are assembled. We bring some examples to show that the results and the conditions imposed to get them are achievable.

A thermal load dispatch problem minimizes the number of objectives viz operating cost and emission of gaseous pollutants together while allocating the power demand among the committed generating units subject to physical and technological system constraints. A stochastic thermal load dispatch problem is undertaken while taking into consideration, the uncertainties, errors in data measurements and nature of load demand which is random. Owing to uncertain load demand, variance due to mismatch of power demand termed as risk, is considered as another conflicting objective to be minimized. Generally multiobjective problems generate a set of non-inferior solutions are generated and supplied to a decision maker to select the best solution from the set of non-inferior solutions. This paper proposes opposition-based greedy heuristic search (OGHS) method to generate a set of non-inferior solutions. Opposition-based learning is applied to generate initial population to select good candidates. Migration to maintain diversity in the set of feasible solutions is also based on opposition-based learning. Mutation strategy is implemented by perturbing the genes heuristically in parallel and better one solution is sought for each member. Feasible solutions are achieved heuristically by modifying the generation-schedules in such a manner that violation of operating generation limits are avoided. The OGHS method is simple to implement and provides global solutions derived from the randomness of the population generated without tuning of parameters. Decision maker exploits fuzzy membership functions to decide the final decision. Validity of the method has been demonstrated by analysing systems in different scenarios consisting of six generators and forty generators.

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

Dams design and their operation cause strong environmental alteration and therefore a long-term debate is ongoing for the scale of these projects. At the same time, the concept of Environmental Flow Assessment (EFA) is a crucial element of modified ecosystems featuring large infrastructure such as dams and reservoirs for mitigating potential environmental degradation while they operate. Nowadays, integrated scientific frameworks are required to quantify the risks caused by large infrastructure. Through the use of stochastic analysis, it is possible to quantify these uncertainties, and present a solution that incorporates long-term persistence and environmental sustainability into a balanced reservoir simulation model. In this work, an attempt is made to determine a benchmark reservoir size incorporating hydrological and ecological criteria though stochastic analysis. The primary goal is to ensure the best possible conditions for the ecosystem, and then secondarily to allow a steady supply of water for other uses. Using a synthetic timeseries based on historical inputs, it is possible to determine and preserve essential statistical characteristics of a river’s streamflow, and use these to detect the optimal reservoir capacity that maximizes environmental and local water demand reliability.