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Unmanned aerial vehicles (UAVs) have become widespread, raising concerns about security and privacy, making real-time detection of "low, slow, and small" UAVs crucial. Traditional detection systems, such as those based on radio frequency and radar, have limitations. This paper addresses challenges like low detection accuracy, high false alarm rates, and susceptibility to interference by proposing a novel detection method combining background difference and the lightweight Fast-YOLOv7 network(F-YOLOv7). The method first identifies potential UAV targets through background difference preprocessing, then optimizes model parameters with the Faster module to enhance speed and accuracy. Experiments on the DUT Anti-UAV dataset achieved a detection accuracy of 98.8%, outperforming the original YOLOv7 model’s 86.71%. This approach meets the real-time and precise detection requirements for low-altitude UAVs. [ABSTRACT FROM AUTHOR]

Serverless computing has attracted many researchers with features such as scalability and optimization of operating costs, no need to manage infrastructures, and build programs at a higher speed. Serverless computing can be used for real-time machine learning (ML) prediction using serverless inference functions. Deploying an ML serverless inference function involves building a compute resource, deploying an ML model, network infrastructure, and permissions to call the inference function. However, the subject of machine learning inference (MLI) has challenges such as resource management, delay and response time, large and complex models, and security and privacy, not many studies have been conducted in this field. This comprehensive literature review article examines the recent developments in MLI in serverless computing environments. The mechanisms presented in the taxonomy can be summarized in four categories: service level objective SLO-aware, acceleration-aware, framework-aware, and latency-aware. In each category, different methods and algorithms used to optimize inference in serverless environments have been examined along with their advantages and disadvantages. We show that acceleration-aware methods focus on the optimal use of computing resources, and framework-aware methods play an important role in improving system efficiency and scalability by examining different frameworks for inference in serverless environments. Also, SLO-aware and Latency-aware methods, considering time limits and service level agreement, help provide quality and reliable inference in serverless environments. Finally, this article presents a vision of future challenges and opportunities in this field and provides solutions for future research in the field of MLI in serverless. [ABSTRACT FROM AUTHOR]

Zero-inflated regression models are generally accepted for modeling data with inflated amounts of zeros. The principle used in constructing the distribution for these models has been extended to modeling certain types of data with inflation at the upper bound of the support. An excellent example of this is the zero and κ-inflated truncated Poisson regression model which utilizes the Poisson distribution. However, the equi-dispersion nature of the Poisson distribution makes the model less suitable for data that are under-dispersed and over-dispersed. Models based on exponentiated exponential geometric distribution (EEGD) are presented as alternatives for modeling any count data with an upper bound, irrespective of the nature of dispersion. The models are obtained by truncating the EEGD at the top and inflating at either or both zero and κ. A simulation study is conducted to examine the performances of the models under certain conditions. The result shows that the closer the dispersion parameter c is from the equi-dispersion line, the better the estimates for over-dispersed data, while the farther the dispersion parameter from the equi-dispersed line, the better the estimates for an under-dispersed model. The application of the models is illustrated using data from the Behavioral Risk Factor Surveillance System 2011. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology utilizing physics-informed neural network (PINN) as a junction condition for a 1D network model of blood flow in total cavopulmonary connection generated by the Fontan procedure. The technique integrates a 3D mesh generation process based on the parameterization of the junction geometry, along with a sophisticated physically regularized neural network architecture. Synthetic datasets are produced using 3D steady Stokes simulations within fixed boundaries. We use a physically informed feedforward neural network that utilizes a physically regularized loss function, which incorporates the principle of mass conservation. Our PINN achieves a tolerance of 6% on the test set. We develop a 1D-PINN multiscale model based on a previously developed method for multiscale 1D–3D simulations. Comparison with 1D–3D Stokes based model and 3D Navier–Stokes based model verifies the 1D-PINN model. In the first and second comparison, the maximum deviations of the averaged pressures and flows do not exceed 1.48% and 12.26%, respectively. [ABSTRACT FROM AUTHOR]

Serverless computing is one of the latest technologies that has received much attention from researchers and companies in recent years since it provides dynamic scalability and a clear economic model. Serverless computing enables users to pay only for the time they use resources. This approach has several benefits, including optimizing costs and resource utilization; however, cold starts are a concern and challenge. Various studies have been conducted in the academic and industrial sectors to deal with this problem, which poses a significant research challenge. This paper comprehensively reviews recent cold start research in serverless computing. Hence, this paper presents a detailed taxonomy of several serverless computing strategies for dealing with cold start latency. We have considered two main approaches in the proposed classification: Optimizing Loading Times (OLT) and Optimizing Resource Usage (ORU), each including several subsets. The subsets of the primary approach OLT are divided into container-based and checkpoint-based. Also, the primary approach ORU is divided into machine learning (ML)-based, optimization-based, and heuristic-based approaches. After analyzing current methods, we have categorized and investigated them according to their characteristics and commonalities. Additionally, we examine potential challenges and directions for future research. [ABSTRACT FROM AUTHOR]

Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified. [ABSTRACT FROM AUTHOR]

In this paper, we consider random variables and stochastic processes from the space F ψ (Ω) and study approximation problems for such processes. The method of series decomposition of a stochastic process from F ψ (Ω) is used to find an approximating process called a model. The rate of convergence of the model to the process in the uniform norm is investigated. We develop an approach for estimating the cut-off level of the model under given accuracy and reliability of the simulation. [ABSTRACT FROM AUTHOR]

The phase-field surfactant model is popular to study the dynamics of surfactant-laden phase separation in a binary mixture. In this work, we numerically investigate the H - 1 -gradient flow based phase-field surfactant mathematical model using an energy dissipation-preserving numerical method. The proposed method adapts a Lagrange multiplier method. The present method not only preserves the unconditional stability, but also satisfies the original energy dissipation law, which is different from the modified energy dissipation laws estimated by the scalar auxiliary variable and invariant energy quadratization methods. An effective scheme is introduced to solve the weakly coupled discrete equations. In one time cycle, we only need to calculate four linear, fully decoupled discrete equations with constant coefficients and compute two nonlinear algebraic equations using Newton's iteration. The computational experiments indicate that the proposed method is accurate and satisfies the original energy stability. Moreover, the long-time behaviors of surfactant-laden phase separation can also be well simulated. [ABSTRACT FROM AUTHOR]

This study develops a mathematical model of embodied cognition integrated with personalized learning within an interactive Virtual Reality (VR) environment, employing nonlinear systems theory to optimize educational outcomes. The study mathematically formulates the interactions between learners’ cognitive states, bodily actions, and environmental inputs by applying state-space models and multi-modal data analysis. The framework incorporates real-time affective feedback and dynamic adjustment mechanisms, improving mental performance and reducing cognitive load. A randomized controlled trial validates the model, demonstrating significant enhancements in learning satisfaction and knowledge retention. This research provides a novel quantitative basis for integrating nonlinear mathematical methods into the design and optimization of personalized learning systems in VR.

Consider a source detection problem for a diffusion system at its stationary status, which is stated as the inverse source problem for an elliptic equation from the measurement of the solution specified only in part of the domain. For this linear ill-posed problem, we propose to reconstruct the interior source applying neural network algorithm, which projects the problem into a finite-dimensional space by approximating both the unknown source and the corresponding solution in terms of two neural networks. By minimizing a novel loss function consisting of PDE-fit and data-fit terms but without the boundary condition fit, the modified deep Galerkin method (MDGM) is applied to solve this problem numerically. Based on the stability result for the analytic extension of the solution, we strictly estimate the generalization error caused by the MDGM algorithm employing the property of conditional stability and the regularity of the solution. Numerical experiments show that we can obtain satisfactory reconstructions even in higher-dimensional cases, and validate the effectiveness of the proposed algorithm for different model configurations. Moreover, our algorithm is stable with respect to noisy inversion input data for the noise in various structures. [ABSTRACT FROM AUTHOR]

Many researchers have tried to predict the impact of the COVID-19 outbreak on morbidity, in order to help policy-makers find optimal isolation policies. However, despite the development and use of many models and sophisticated tools, these forecasting attempts have largely failed. We present a model that considers the severity of the disease and the heterogeneity of contacts between the population in complex space–time dynamics. Using mathematical and computational methods, the applied tool was developed to analyze and manage the COVID-19 pandemic (from an epidemiological point of view), with a particular focus on population heterogeneity in terms of age, susceptibility, and symptom severity. We show improved strategies to prevent an epidemic outbreak. We evaluated the model in three countries, obtaining an average mean square error of 0.067 over a full month of the basic reproduction number (R0). The goal of this study is to create a theoretical framework for crisis management that integrates accumulated epidemiological considerations. An applied result is an open-source program for predicting the outcome of an isolation strategy for future researchers and developers who can use and extend our model. [ABSTRACT FROM AUTHOR]

We infer the parameters of fractional discrete Wu Baleanu time series by using machine learning architectures based on recurrent neural networks. Our results shed light on how clearly one can determine that a given trajectory comes from a specific fractional discrete dynamical system by estimating the fractional exponent and the growth parameter μ . With this example, we also show how machine learning methods can be incorporated into the study of fractional dynamical systems. [ABSTRACT FROM AUTHOR]

We study the trade-off between two risks for scoring rules used in sports competitions containing multiple contests: (1) the threat of early clinch when the title is clinched before the last contest(s) of the competition take place; and (2) the danger of winning the competition without finishing first in any contest. Four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules. The current scheme seems to be a reasonable compromise close to the Pareto frontier. Our results contribute to the issue of choosing an optimal set of point values. [ABSTRACT FROM AUTHOR]

We design a multi-step predictor-corrector scheme for backward stochastic differential equations (BSDEs). This scheme tries its best to retain the simplicity and improve its convergence rate as much as possible. We investigate the stability and rigorously deduce the error estimates of this scheme. Numerical experiments are compared with the scheme given by Gobet et al. (Math Comput, 85(299): 1359-1391, 2016a) and are given to illustrate that the multi-step predictor-corrector scheme is an efficient probabilistic numerical method. [ABSTRACT FROM AUTHOR]

Diarrhea is one of the most common infectious diseases that affect people of all ages and is a serious public health concern around the world. The main causes of diarrhea include food quality, water, indoor meteorological, and outdoor meteorological conditions. In this study, a dew computing-assisted smart monitoring framework is developed to evaluate the relationship among the health, indoor meteorological, and food factors of an individual to predict the cause of diarrhea with the scale of severity. Smart sensors are utilized at the physical layer to collect the targeted parameters of health, indoor meteorological, and food of the individual. The captured events are classified at the cyber layer by utilizing the Probabilistic Weighted-Naïve Bayes (PW-NB) classification approach for quantifying abnormal health events. Furthermore, a Multi-scale Gated Recurrent Unit (M-GRU) is suggested to obtain the scale of severity by analyzing the correlation between irregular health, food, and environmental events. In this manner, the proposed model M-GRU has achieved a high precision value of ( 93.26 % ), whereas, LSTM, RNN, SVM achieved the precision value of ( 89.13 % ), ( 90.43 % ), ( 88.23 % ), respectively. In addition, the precision value of the PW-NB is ( 97.15 % ), which is also higher as compared to KNN ( 93.25 % ) and DT ( 96.91 % ). The outcome of the proposed solutions is shown the higher Precision values on dew computing and cloud computing. Moreover, a comparative analysis defines the prediction effectiveness of the proposed solution over several other decision-making solutions with regards to event classification, severity determination, monitoring stability, and prediction efficiency. [ABSTRACT FROM AUTHOR]

The quark-gluon plasma is written by the non-Abelian gauge theory. The dynamics of the gauge SU(2) are given by the Hamiltonian function, which contains the quadratic part of the field strength tensor Fμva{\rm{F}}_{\mu v}^{\rm{a}} expressed in Minkowski space. The homogeneous Yang-Mills equations are solved on lattice Nd considering classical approximation, which exhibits chaotic dynamics. We research the time-dependent entropy-energy relation, which can be shown by the energy spectrum of Kolmogorov-Sinai entropy and the spectra of the statistical complexity.

This paper proposes an approximate solution based on two-dimensional shifted Legendre polynomials, together with its operational matrices of integration and stochastic integration for solving stochastic Burgers' equations with a space-uniform white noise and with variable coefficients. The aforementioned operational matrices transform the problem under consideration into a system of algebraic equations. The error analysis in the L 2 norm for the proposed method is discussed in detail. The transformation is done by taking into account the initial and boundary conditions. Hence, the proposed method is very simple for solving such problems. Numerical examples discussed confirm the efficiency and accuracy of the proposed method. A simulation study was carried out. An algorithm was developed and implemented on Maple software. [ABSTRACT FROM AUTHOR]

Many studies have considered mixed Poisson distributions as alternatives for fitting count data with overdispersion. However, in some cases, the data have an abundance of zeros and ones which makes modelling using distributions with no consideration to the inflated values less desirable. This study aims to introduce a new distribution for count data with inflated values at zero and one, known as zero–one-inflated Poisson–Lindley distribution. The statistical properties of the proposed distribution are discussed. Furthermore, the maximum likelihood and method of moments for the parameters of the proposed distribution are developed. A simulation study is conducted to investigate the performance of the zero–one-inflated Poisson–Lindley distribution in describing overdispersed data with excess zeros and ones by changing the proportion of zeros and ones in the data. It is found that the fitting of the zero–one-inflated Poisson–Lindley distribution always gives a larger log-likelihood value than the fitting of the zero–one-inflated Poisson distribution. The results from the applications of the real datasets with an overdispersed property as well as a large number of ones and zeros conclude that the proposed distribution provides the best fit compared to other contending distributions in the study. [ABSTRACT FROM AUTHOR]

The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used in handball and other sports, are shown to be incentive incompatible in the sense that a team can be strictly better off by not exerting full effort in a game. Historical examples are presented when a team was ex ante disinterested in winning by a high margin. We propose a family of incentive compatible designs. Their main characteristics are compared to the original format via simulations. Carrying over half of the points scored in the previous round turns out to be a promising policy. [ABSTRACT FROM AUTHOR]

The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ⁢ ([ 0 , T ]) . [ABSTRACT FROM AUTHOR]

This paper conducts a computational analysis of several specifications of the affine term structure model (ATSM) to explore the tradeoff between estimation when parameter restrictions are imposed and computational burdens are simplified and estimation in the absence of parameter restrictions and the economic implications of the findings are able to be generalized. We measure the effects of this tradeoff using distance measures constructed from histograms containing data corresponding to important components of the state space model formulation for the ATSM generated from simulation analyses. In estimating each specification, we optimize the log-likelihood function for the underlying state space model using the Kalman filter (KF). We find that the introduction of parameter restrictions bolsters the variability in its computation by introducing complex parameter dependencies (e.g., higher order exponents, exponentiation, logarithms, logarithms of higher order exponents) that are difficult to interpret. For conditional moments, the introduction of parameter restrictions reduces the complexity of the parameter dependencies and this reduces the variability in its computation. Finally, we connect these insights obtained from the simulation analyses to the application of the KF using market data and perform consistency tests on each state space model to demonstrate the accuracy of the application of the KF. Suggestions for future research are provided. [ABSTRACT FROM AUTHOR]

Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution of such problems can be non trivial, both from a mathematical and a geometrical standpoint. Indeed 3D-1D coupling requires to operate in non standard function spaces, and, also, simulation geometries can be complex for the presence of multiple intersecting domains. Recently, a PDE-constrained optimization based formulation has been proposed for such problems, proving a well posed mathematical formulation and allowing for the use of non conforming meshes for the discrete problem. Here an unconstrained optimization formulation of the problem is derived and an efficient gradient based solver is proposed for such formulation, along with a suitable preconditioner to speed up the iterative solver. Some numerical tests on quite complex configurations are discussed to show the viability of the method. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for the accurate estimation of the derivative (aka. sensitivity) of expectations of functions involving an indicator function by modifying a (stochastic) algorithmic differentiation, replacing the derivative of the indicator function with a suitable operator. We show that we can split this operator into a conditional expectation operator and the density. This allows using different or improved numerical approximation methods for these operators, e.g. regression. The method is an improvement of the approach presented in C.P. Fries [Automatic backward differentiation for American Monte-Carlo algorithms (conditional expectation). Risk, April, 2018; Stochastic automatic differentiation: Automatic differentiation for Monte-Carlo simulations, Quant. Finance 19(6) (2019), pp. 1043–1059]. The finite difference approximation of a partial derivative of a Monte-Carlo integral of a discontinuous function is known to exhibit a high Monte-Carlo error. The issue is evident since the Monte-Carlo approximation of a discontinuous function is just a finite sum of discontinuous functions and as such, not even differentiable. The algorithmic differentiation of a discontinuous function is problematic. A natural approach is to replace the discontinuity by continuous functions. This is equivalent to replacing a path-wise automatic differentiation by a (local) finite difference approximation. The decoupling of the integration of the Dirac delta and the remaining conditional expectation introduced here results in an improvement in terms of variance reduction and implementation design. [ABSTRACT FROM AUTHOR]

We formulate algebraically solutions to the isotropic Heisenberg ferromagnet, which is an integrable geometric curve flow. The derivation is based on correspondences between this Heisenberg ferromagnet and the nonlinear Schrödinger equation. The existence of solutions to the Cauchy problems of the isotropic Heisenberg ferromagnet with periodic boundary conditions follows from the correspondence. We then obtain a geometric framework of algorithms to solve the periodic Cauchy problem numerically for the Heisenberg ferromagnet. Analytical and experimental results will be presented. [ABSTRACT FROM AUTHOR]

The paper presents some of our recent results in the field of computer emulation for supporting and enhancing the educational processes. The ATmega 328P micro-controller emulator has been developed as a set of emuStudio emulation platform extension modules (plug-ins). The platform is used at the Department of Computers and Informatics as a studying and teaching support tool. Within the Assembler course, currently, the Intel 8080 architecture and language is briefly described as a preliminary preparation material for the study of Intel x86 architecture, and the Intel 8080 emuStudio emulator module is used here. The aim of this work is to explore the possibility to enrich the course by introducing a more up-to-date and relevant technology and the ATmega is the heart of Arduino – a popular hardware and software prototyping platform. We consider the options to make the process of studying the assembly language principles more attractive for students and using the ATmega AVR architecture, which is broadly deployed in embedded systems, seems to be one of them.

The concept of the statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allow us to understand this driven dynamical system by the probability distribution in phase space to make distinguish among the regular, random and structural complexity on finite simulation. We present the dependence of the kicked top and kicked rotor model through the strength excitation in the framework of statistical complexity.

In this paper, Generalized Mittag-Leffler function method (GMLFM) and Sumudu transform method (STM) are applied to study and solve the fractional order smoking model, where the derivatives are defined in the Caputo fractional sense. The disease free equilibrium (DFE) and stability of equilibrium point are studied. Lyapunov exponents and Poincare map of the model are drawn to ensure the stability of the model. The obtained results show that the proposed methods are very effective and convenient. In addition, the model is presented by its signal flow graph and simulated using Matlab/Simulink.

A new approach to achieve fault diagnosis and prognosis of bearing based on hidden Markov model (HMM) with multi-features is proposed. Firstly, the time domain, frequency domain, and wavelet packet decomposition are utilized to extract the condition features of bearing vibration signals, and the PCA method is merged into multi-features to reduce their dimensionality. Then the low-dimensional features are processed to obtain the scalar probabilities of each bearing condition, which are multiplied to generate the observed values of HMM. The results reveal that the established approach can well diagnose fault conditions and achieve the remaining life estimation of bearing.

Heterogeneous systems providing diverse computational capabilities have unlocked a new pathway in multicore processors. The versatility in applications and their ever-increasing performance demands have brought a paradigm shift to the heterogeneous systems. We use a deep neural network (DNN) based model to maximize performance under power constraints in heterogeneous systems. The dynamic power management technique is implemented in three stages. In the first stage, the core statistics and workload characteristics are collected for the DNN training at the later stage. This step dynamically estimates workload change for the current epoch using dynamic voltage frequency scaling (DVFS) based heuristic algorithm. In the second stage, DNN is trained through collected data points. The third stage uses the trained DNN model to identify a suitable voltage-frequency values to maximize performance under power capping. The power manager controls power-consumption at both per-core and per-chip levels. Our DNN prediction model is trained to address both core types (Large and Small) thus, improving the accuracy of the model. Simulations indicate that the proposed approach can achieve an overall 10.63% reduction in power-consumption and 5.5–6.8% improvement in power-savings when compared with the existing approaches. Besides, the proposed DNN model-based approach is able to maintain power capping with 95.81% accuracy with performance degradation of only 5.38% for a quad-core architecture. [ABSTRACT FROM AUTHOR]

In this work we propose a mathematical model to simulate Chikungunya spread; the spread model is implemented in a C++ cellular automata code defined on unstructured triangular grids and space visualizations are performed with Python. In order to simulate the time space spread of the Chikungunya diseases we include assumptions such as: heterogeneous human and vector densities, population mobility, geographically localized points of infection using geographical information systems, changes in the probabilities of infection, extrinsic incubation and mosquito death rate due to environmental variables. Numerical experiments reproduce the qualitative behavior of diseases spread and provide an insight to develop strategies to prevent the diseases spread.

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective simulations in realistic DFMs. [ABSTRACT FROM AUTHOR]

A three-dimensional mathematical model of the diffusion of impurities from a short-term source taking into account meteorological conditions is presented. The model includes the system of equations of hydrothermodynamics describing regional atmospheric processes. The transfer of multicomponent gas impurities is calculated taking into account microphysical processes, precipitation, and fog. Initial information for model initialization is aerological information in the form of actual or forecast fields of meteorological parameters and characteristics of sources of impurities. A numerical analysis of the diffusion of impurities in the near zone of a cosmodrome from short-term sources such as engines of launch vehicles was performed for various meteorological parameters, including wind in the atmosphere. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional, nonstationary numerical model of convective clouds is presented. Hydrothermodynamical, microphysical, and electrical processes are described in detail; results of studies of changes in thermodynamical, microstructural, and electrical parameters in time are given. The hydrothermodynamical block of the model consists of equations of motion that describe the wet convection in the Boussinesq approximation. The equations of the microphysical block describe the processes of nucleation, condensation, coagulation, sublimation, accretion, aggregation, and freezing of drops, deposition of cloud particles in the gravity field, their transport by air flows, and interaction of cloud particles under the influence of electric fields of clouds. Numerical experiments based on the model developed were carried out to study the formation of convective clouds for various stratifications of the atmosphere and the structure of the wind field in the atmosphere. Thermodynamical and microstructural parameters in the zone of a powerful convective cloud are determined. The system of equations of the model was solved by the methods of splitting in physical processes and component-wise splitting. [ABSTRACT FROM AUTHOR]

For solving the inverse Cauchy problem of a three-dimensional (3D) non-homogeneous sideways heat equation in a cuboid, we first transform it into a partial homogeneous boundary value problem, using a time-dependent two-dimensional (2D) homogenization technique. After a time step-by-step approach of the inverse Cauchy problem, it becomes an inverse Cauchy problem of the 3D modified Helmholtz equation. A sequence of 2D sine functions and a set of second-order ordinary differential equations are derived to determine the expansion coefficients, which can be solved in closed-form. In order to stably solve the inverse Cauchy problem, we simply introduce a spring-damping regularization technique to modify the coefficients, which results in a regularized 2D Fourier sine series solution of the unknown Dirichlet data on the top of the cuboid. The novel method can find the solution in the whole domain, which is quite accurate with small errors, even a large noise up to 20 % is imposed on the given data. The present method together with the analyses of regularization parameter and the stability of solution is novel and shows promise in the 3D sideways problems of the heat equation. [ABSTRACT FROM AUTHOR]

We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the time series making a difference between the regular, random and structural complexity on finite measurements. We interpreted the statistical complexity on snapshot attractor and determined it on the quasiperiodical forced pendulum.

In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model. [ABSTRACT FROM AUTHOR]

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm. [ABSTRACT FROM AUTHOR]

The smooth transition autoregressive (STAR)(k)–GARCH(l, m) model is a non-linear time series model that is able to account for changes in both regime and volatility respectively. The model can be widely applied to analyse the dynamic behaviour of data exhibiting these two phenomenons in areas such as finance, hydrology and climate change. The main aim of this paper is to perform a Bayesian analysis of STAR(k)–GARCH(l, m) models. The estimation procedure will include estimation of the mean and variance coefficient parameters, the parameters of the transition function, as well as the model orders (k, l, m). To achieve this aim, the joint posterior distribution of the model orders, coefficient and implicit parameters in the logistic STAR(k)–GARCH(l, m) model is presented. The conditional posterior distributions are then derived, followed by the design of a posterior simulator using a combination of MCMC algorithms which includes Metropolis–Hastings, Gibbs Sampler and Reversible Jump MCMC algorithms. Following this are extensive simulation studies and a case study presenting the methodology. [ABSTRACT FROM AUTHOR]

This paper challenges the traditional seeding regime of round-robin tournaments that aims to create balanced groups. In particular, the design of the most prestigious European men's handball club competition is compared to two alternative formats with equally strong groups via simulations. We find that it is possible to increase the quality of all matches played together with raising the uncertainty of outcome, essentially without sacrificing fairness. Our results have useful implications for the governing bodies of major sports. [ABSTRACT FROM AUTHOR]

Both sequential Monte Carlo (SMC) methods (a.k.a. 'particle filters') and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish an $\mathbb{L}_r$ -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators. [ABSTRACT FROM AUTHOR]

The monotonicity-preserving (MP) scheme is an accurate shock-capturing scheme. However, its performance is still inefficient for resolving high-frequency waves. In this paper, to improve the resolution characteristics, an upwind compact interpolation is proposed as a substitute to the original one in the MP scheme, and the coefficients of that were analytically optimized to minimize the dispersion and dissipation errors. Moreover, it was found that the limiting part of the original MP scheme degenerates the accuracy in a high-wavenumber region due to unnecessarily activation. This limitation is improved by applying a new indicator and criterion. The results of the nonlinear wave (N-wave) propagation demonstrate that the proposed scheme guarantees the robustness at the sharp discontinuity. At the same time, the solutions of linear wave propagation prove the excellent resolution of the proposed scheme. We intensively evaluated the performance for the standard and long-time situations of the shock-entropy wave interaction problems. The results prove that the usefulness of proposed scheme is more pronounced in the flow fields involving both of shock and waves. [ABSTRACT FROM AUTHOR]

In the progressive Type-II censoring with random removal, choosing a distribution for removing the number of unfailed units which is independent from the lifetime distribution, may be a serious challenge and lead to an unreliable inference. Two approaches based on the time distance between consecutive failure times are proposed to determine the removal numbers. Then, the joint probability mass functions of random removals are derived where the underlying distribution of the lifetime data is assumed to be an exponential. Furthermore, The expected test time is investigated under these two approaches and is subsequently considered as an optimality criterion for identifying progressive Type-II censoring schemes. Some statistical inference results are also obtained by using Monte Carlo simulations. The empirical results indicate that the proposed methods work perfectly well in the sense that, reduce the expected total time on the test. Finally, a numerical example, based on a real data set, is presented and analysed to illustrate the proposed approaches. [ABSTRACT FROM AUTHOR]

We give an explicit representation for the transition law of a tempered stable Ornstein–Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation of increments from this process. Our results apply to general classes of both univariate and multivariate tempered stable distributions and contain a number of previously studied results as special cases. [ABSTRACT FROM AUTHOR]

Recent advances in GPUs opened a new opportunity in harnessing their computing power for general purpose computing. CUDA, an extension to C programming, is developed for programming NVIDIA GPUs. However, efficiently programming GPUs using CUDA is very tedious and error prone even for the expert programmers. Programmer has to optimize the resource occupancy and manage the data transfers between host and GPU, and across the memory system. This paper presents the basic architectural optimizations and explore their implementations in research and industry compilers. The focus of the presented review is on accelerating computational science applications such as the class of structured grid computation (SGC). It also discusses the mismatch between current compiler techniques and the requirements for implementing efficient iterative linear solvers. It explores the approaches used by computational scientists to program SGCs. Finally, a set of tools with the main optimization functionalities for an integrated library are proposed to ease the process of defining complex SGC data structure and optimizing solver code using intelligent high-level interface and domain specific annotations. [ABSTRACT FROM AUTHOR]

The dry spinning of fibers can be described by three-dimensional multi-phase flow models that contain key effects like solvent evaporation and fiber-air interaction. Since the direct numerical simulation of the three-dimensional models is in general not possible, dimensionally reduced models are deduced. We recently developed a one-two-dimensional fiber model and presented a problem-tailored numerical solution strategy in Wieland et al. (J Comput Phys 384:326–348, 2019). However, in view of industrial setups with multiple fibers spun simultaneously the numerical schemes must be accelerated to achieve feasible simulation times. The bottleneck builds the computation of the radial concentration and temperature profiles as well as their cross-sectionally averaged values. In this paper we address this issue and develop efficient numerical algorithms. [ABSTRACT FROM AUTHOR]