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Energetic particles of galactic and solar origin charge the metal free-falling test masses (TMs) of the interferometers for gravitational wave detection in space. The deposited charge couples with stray electric fields thus generating spurious Coulomb forces between the TMs and the electrode housing that limit the interferometer sensitivity. Long-term and short-term galactic cosmic-ray variations are strongly energy-dependent and the TM charging varies with particle energy distribution. We propose three different approaches involving Monte Carlo simulations and machine learning models in comparison to particle transport with the Parker equation to study the recurrent modulation of energy spectra of galactic particles ascribable to the passage of high-speed solar wind streams. The transit of interplanetary counterparts of coronal mass ejections modifies the effects of high-speed streams. This work aims at better understanding the energy-dependence of galactic cosmic-ray short-term variations for the Laser Interferometer Space Antenna (LISA), the first interferometer for gravitational wave detection in space, starting from lessons learned with LISA Pathfinder. The outcomes of our models will be used to assess the TM charging during the time LISA will remain in orbit around the Sun. [ABSTRACT FROM AUTHOR]

To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain several parameters which have to be chosen carefully to match the experimental data and to validate the effectiveness of the model. In the present paper the calibration of these parameters is described by nonlinear SDE-constrained optimization problems. In the optimize-before-discretize setting a rigorous analysis is carried out to ensure the existence of optimal solutions and to derive necessary first-order optimality conditions. For the numerical solution a Monte–Carlo method is applied using parallelization strategies to compensate for the high computational time. In the numerical examples an Ornstein–Uhlenbeck and a stochastic Prandtl–Tomlinson bath model are considered. [ABSTRACT FROM AUTHOR]

Expert judgments are widespread in many fields, and the way in which they are collected and the procedure by which they are aggregated are considered crucial steps. From a statistical perspective, expert judgments are subjective data and must be gathered and treated as carefully and scientifically as possible. In the elicitation phase, a multitude of experts is preferable to a single expert, and techniques based on anonymity and iterations, such as Delphi, offer many advantages in terms of reducing distortions, which are mainly related to cognitive biases. There are two approaches to the aggregation of the judgments given by a panel of experts, referred to as behavioural (implying an interaction between the experts) and mathematical (involving non-interacting participants and the aggregation of the judgments using a mathematical formula). Both have advantages and disadvantages, and with the mathematical approach, the main problem concerns the subjective choice of an appropriate formula for both normalization and aggregation. We propose a new method for aggregating and processing subjective data collected using the Delphi method, with the aim of obtaining robust rankings of the outputs. This method makes it possible to normalize and aggregate the opinions of a panel of experts, while modelling different sources of uncertainty. We use an uncertainty analysis approach that allows the contemporaneous use of different aggregation and normalization functions, so that the result does not depend on the choice of a specific mathematical formula, thereby solving the problem of choice. Furthermore, we can also model the uncertainty related to the weighting system, which reflects the different expertise of the participants as well as expert opinion accuracy. By combining the Delphi method with the robust ranking procedure, we offer a new protocol covering the elicitation, the aggregation and the processing of subjective data used in the construction of Delphi-based future scenarios. The method is very flexible and can be applied to the aggregation and processing of any subjective judgments, i.e. also those outside the context of futures studies. Finally, we show the validity, reproducibility and potential of the method through its application with regard to the future of Italian families. [ABSTRACT FROM AUTHOR]

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the '90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure. [ABSTRACT FROM AUTHOR]

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton's equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation. [ABSTRACT FROM AUTHOR]

Adaptive rejection sampling requires that users provide points that span the distribution’s mode. If these points are far from the mode, it significantly increases computational costs. This paper introduces a simple, automated approach for selecting initial points that uses numerical optimization to quickly bracket the mode. When an initial point is given that resides in a high-density area, the method often requires just four function evaluations to draw a sample—just one more than the sampler’s minimum. This feature makes it well-suited for Gibbs sampling, where the previous round’s draw can serve as the starting point. [ABSTRACT FROM AUTHOR]

The paper deals with Monte Carlo modeling of spatiotemporal signals of wide-angle lidars for probing atmospheric clouds. Using computational experiments, we study the features of lidar signals for monostatic and bistatic sensing schemes which make it possible to analyze the optical and microphysical properties of the cloud environment. When probing thin cloud layers, the lidar signal looks like an expanding and attenuating light ring. It is shown that for a bistatic scheme a second ring, which appears for a short time inside the main one, is characteristic of the lidar signal. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to use the residual strength theory to study the probability of a domino effect accident occurring following the explosion of a spherical tank. We build a novel domino effect accident probability model, using Monte Carlo methods to simulate the ejection of debris. At the same time, the velocity and velocity distribution of fragments ejecting from the upper and lower parts of the explosive spherical tank are obtained. Finally, the relationship between the volume of the exploding spherical tank and the target, the crater Angle (ψ0 and ϕ0) of debris impacting the target, the probability of target destruction and the risk of domino effect accidents are considered. The results show that the maximum speed of debris from the lower part of a spherical tank exceeds that from its upper part, and the hazard associated with the debris from the lower part cannot be ignored. With the same target volume and spacing, the probability of a domino effect accident caused by projectile debris from the upper half of an exploding spherical tank is higher than that from the lower half. As theψ0 value increases, the probability of target failure gradually decreases, and as the ϕ0 value decreases, the probability of target failure also gradually decreases. Moreover, with changes in ψ0 and ϕ0, the probabilities of destruction and the occurrence of a domino effect accident significantly change. The results of this paper can provide guidance for the risk assessment of oil and gas storage tanks. [ABSTRACT FROM AUTHOR]

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with remarkable efficiency. [ABSTRACT FROM AUTHOR]

Simplices are the fundamental domain when integrating over convex polytopes. The aim of this work is to establish a novel framework of Monte Carlo integration over simplices, throughout from sampling to variance reduction. Namely, we develop a uniform sampling method on the standard simplex consisting of two independent procedures and construct theories on change of measure on each of the two independent elements in the developed sampling technique with a view towards variance reduction by importance sampling. We provide illustrative figures and numerical results to support our theoretical findings and demonstrate the strong potential of the developed framework for effective implementation and acceleration of Monte Carlo integration over simplices. [ABSTRACT FROM AUTHOR]

Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and physics. In this paper, we present novel simulation methods based on subordination with a generalised inverse Gaussian (GIG) process and using a generalised shot-noise representation that involves random thinning of infinite series of decreasing jump sizes. Compared with our previous work on GIG processes, we provide tighter bounds for the construction of rejection sampling ratios, leading to improved acceptance probabilities in simulation. Furthermore, we derive methods for the adaptive determination of the number of points required in the associated random series using concentration inequalities. Residual small jumps are then approximated using an appropriately scaled Brownian motion term with drift. Finally the rejection sampling steps are made significantly more computationally efficient through the use of squeezing functions based on lower and upper bounds on the Lévy density. Experimental results are presented illustrating the strong performance under various parameter settings and comparing the marginal distribution of the GH paths with exact simulations of GH random variates. The new simulation methodology is made available to researchers through the publication of a Python code repository. [ABSTRACT FROM AUTHOR]

Astrophysical very high energy (VHE) gamma-rays (with energies >30 GeV) are believed to result almost exclusively from the interactions of populations of highly relativistic particles with ambient matter or photon fields. The study of these VHE photons therefore allows us to examine the processes of particle acceleration in the Universe, and the extreme environments in which they occur. Gamma-rays are also highly directional, making them useful for studying the origin, acceleration, propagation, and composition of cosmic rays. This study uses the Monte Carlo method to simulate the process of extensive air showers being initiated when primary incident γ -rays with energies ranging from 10 GeV to 5 TeV interact with the atmosphere. The ultimate goal is to investigate and analyze the properties and lateral density distributions of Cherenkov light at different altitudes. The simulation considers various energies and zenith angles. The results show that a hump in the lateral density distribution of Cherenkov light is a distinctive feature of a γ -initiated shower, with the hump becoming less prominent at higher energy levels and altitudes. These significant findings not only facilitate better fitting of experimental data obtained from actual extensive air showers but also assist with estimating readings from detectors, thus advancing our understanding of these processes. [ABSTRACT FROM AUTHOR]

The paper considers the NP-hard problem of calculation the reliability of a network, which elements are subject to accidental failures. As network reliability, we mean the probabilistic connectivity of a random graph with unreliable edges. To evaluate the reliability of a network, a parallel Monte Carlo method is used, improved by checking the connectivity of a particular graph realization simultaneously with the generation of this realization. Based of multi-agent simulation, we study the scalability of this algorithm and tune the parameters for an execution using high-performance supercomputers. [ABSTRACT FROM AUTHOR]

A brief review of methods in design of experiments and criteria to determine space-filling properties of a set of samples is given. Subsequently, the so-called curse of dimensionality in sampling is reviewed and used as motivation for the proposal of an adaptation to the strata creation process in Latin hypercube sampling based on the idea of nested same-sized hypervolumes. The proposed approach places samples closer to design space boundaries, where in higher dimensions the majority of the design space volume is located. The same idea is introduced for Monte Carlo considering an affordable number of samples as an a-posteriori transformation. Both ideas are studied on different algorithms and compared using different distance-based space-filling criteria. The proposed new sampling approach then enables more efficient sampling for optimization especially for high-dimensional problems, i.e. for problems with a high number of design variables. [ABSTRACT FROM AUTHOR]

Theoretically, the conditional expectation of a square-integrable random variable Y given a d-dimensional random vector X can be obtained by minimizing the mean squared distance between Y and f(X) over all Borel measurable functions f : R d → R . However, in many applications this minimization problem cannot be solved exactly, and instead, a numerical method which computes an approximate minimum over a suitable subfamily of Borel functions has to be used. The quality of the result depends on the adequacy of the subfamily and the performance of the numerical method. In this paper, we derive an expected value representation of the minimal mean squared distance which in many applications can efficiently be approximated with a standard Monte Carlo average. This enables us to provide guarantees for the accuracy of any numerical approximation of a given conditional expectation. We illustrate the method by assessing the quality of approximate conditional expectations obtained by linear, polynomial and neural network regression in different concrete examples. [ABSTRACT FROM AUTHOR]

The aim of the work underpinning this paper has been to track the evolution of tail risk in banks' NPL portfolios present under normal and worst conditions (before and during the pandemic of COVID-19), and to estimate the impact of sector concentration risk on amounts of economic capital. Results further allowed for analysis of different sectors with a view to determining which is riskiest. The study makes use of a multi-factor structural model, given that each sector is affected by a different systematic risk factor, with the assets of borrowers from the same sector thus correlated markedly, even as correlations between sectors are low. The research has in fact sought the further development of methodology proposed by Düllmann and Masschelein in 2006—in the direction of improved accuracy of economic-capital estimates, thanks to alternate means of mapping out the sectoral factor correlation matrix. The empirical analysis was based on individual data from Prudential Reporting under the National Bank of Poland, as well as market data. Results reveal an increase in tail risk through the 2015–2017 period, as followed by the onset of a decline. Where the paper's second aim is concerned, there is found to be support for the idea that economic capital may be increased where sector concentration in the portfolio of a bank is accounted for. Tail risk is found to be concentrated in the sectors of construction and real estate, with accommodation and food services becoming more volatile during the pandemic. A channel for risk transfer between the financial and corporate sectors is thus found to exist. Thanks to the work done we have a better understanding of the impact of sectoral concentration of individual banks' lending activities on level of risk, with the possibility of this gaining application as stress tests are conducted, and as supervisory recommendations from Poland's Financial Supervision Authority are formulated. [ABSTRACT FROM AUTHOR]

The interaction between light and materials is key to physically-based realistic rendering. However, it is also complex to analyze, especially when the materials contain a large number of details and thus exhibit "glinty" visual effects. Recent methods of producing glinty appearance are expected to be important in next-generation computer graphics. We provide here a comprehensive survey on recent glinty appearance rendering. We start with a definition of glinty appearance based on microfacet theory, and then summarize research works in terms of representation and practical rendering. We have implemented typical methods using our unified platform and compare them in terms of visual effects, rendering speed, and memory consumption. Finally, we briefly discuss limitations and future research directions. We hope our analysis, implementations, and comparisons will provide insight for readers hoping to choose suitable methods for applications, or carry out research. [ABSTRACT FROM AUTHOR]

We introduce a model in the context of ecology that can be used to describe the distribution and abundance of individuals when data from field work is extremely limited (for example, in the case of endangered species). Our procedure is based on an intuitive understanding of the physical properties of phenomena. The idea is that individuals have the tendency to be attracted (or repulsed) to certain properties of the environment. At the same time, they are spread in such a way that if there is no reason for them to be in some specific locations, then they are uniformly distributed throughout the region. Our model draws from quantum mechanics, by using quantum Hamiltonians in the context of classical statistical mechanics. The equilibrium between the spreading and the attractive (or repulsive) forces determines the behavior of the species that we model, and this is expressed in terms of a global control problem of an energy operator which is the sum of a kinetic term (spreading) and a potential (attraction or repulsion). We focus on the full probability measure and a global control of the model (instead of looking at conditional measures that generate a global measure). Furthermore, we propose a numerical solution to this global control problem that overcomes the well-known major difficulty of Gibbs sampling (annealing) which is the fact that a global control is hardly reachable when the number of variables is large (the algorithms get stuck in non-optimal states). [ABSTRACT FROM AUTHOR]

This paper deals with Monte Carlo simulation of optical phenomena which appear in lidar sensing of atmospheric clouds and water media. By numerical experiments we study peculiarities of laser pulse propagation when light forms expanding ring structures due to multiple scattering. [ABSTRACT FROM AUTHOR]

This work conducts a probabilistic inquiry on how the variability of the parameter defining soil deformability affects the settlement of the foundation located on the soil. The analysis addresses the random foundation model to relevantly estimate the probability of allowable deflection exceedance. The constitutive model parameter is based either on a single random variable or a random field. The computations incorporate direct Monte Carlo sampling and the variance reduction techniques, i.e. Stratified Sampling and Latin Hypercube Sampling. The work focuses on soil parameter modelling by random fields defined by various correlation functions. One of the analytical means is the application of a non-homogeneous function capable of reflecting the soil strata. The probabilistic methods proposed in the paper are tested on a standard example of a foundation strip featuring load eccentricity. It is proved that the modelling mode of the soil—a single variable or a random field—substantially affects the results, i.e. foundation settlements. It was detected that incorporating random fields in soil analysis allows for a valid reliability assessment of a foundation in respect to Serviceability Limit State. The relevantly adjusted correlation functions of random fields allow for a realistic subsoil analysis even in the case of a limited in situ measurement database. [ABSTRACT FROM AUTHOR]

In systems engineering, requirements derivation is an important step to achieve a successful product design. This process consists of obtaining technical specifications that meet the client's needs. Some applications, however, do not have a clear relationship between these two. Therefore, we contribute with a requirements derivation method by studying the trade-off between product performance and specification demand. We apply this method to the RoboCup Small Size League, a robot competition that promotes research in artificial intelligence and robot systems. In this work, we focus in the goal interception task. The development of a team for this competition requires a hardware project to build the robots and a software project to make game decisions. In this context, we derive requirements both for the robot's parameters (maximum velocity, maximum acceleration, robot's bandwidth, robot's phase margin) and for the perception system's parameters (information update frequency, information delay). During this study's development, we model the robots and game dynamics to determine the influence of the system's parameters in the task and evaluate the goalkeeper's performance by using Monte Carlo methods to estimate the goalkeeper's performance. Moreover, we observe that the performance estimation depends not only on the system's parameters but also on the Monte Carlo sampling model and the selected game strategy. Lastly, realistic ranges for the design parameters are obtained using the proposed methods. [ABSTRACT FROM AUTHOR]

Participating media are frequent in real-world scenes, whether they contain milk, fruit juice, oil, or muddy water in a river or the ocean. Incoming light interacts with these participating media in complex ways: refraction at boundaries and scattering and absorption inside volumes. The radiative transfer equation is the key to solving this problem. There are several categories of rendering methods which are all based on this equation, but using different solutions. In this paper, we introduce these groups, which include volume density estimation based approaches, virtual point/ray/beam lights, point based approaches, Monte Carlo based approaches, acceleration techniques, accurate single scattering methods, neural network based methods, and spatially-correlated participating media related methods. As well as discussing these methods, we consider the challenges and open problems in this research area. [ABSTRACT FROM AUTHOR]

In this paper novel simulation methods are provided for the generalised inverse Gaussian (GIG) Lévy process. Such processes are intractable for simulation except in certain special edge cases, since the Lévy density associated with the GIG process is expressed as an integral involving certain Bessel functions, known as the Jaeger integral in diffusive transport applications. We here show for the first time how to solve the problem indirectly, using generalised shot-noise methods to simulate the underlying point processes and constructing an auxiliary variables approach that avoids any direct calculation of the integrals involved. The resulting augmented bivariate process is still intractable and so we propose a novel thinning method based on upper bounds on the intractable integrand. Moreover, our approach leads to lower and upper bounds on the Jaeger integral itself, which may be compared with other approximation methods. The shot noise method involves a truncated infinite series of decreasing random variables, and as such is approximate, although the series are found to be rapidly convergent in most cases. We note that the GIG process is the required Brownian motion subordinator for the generalised hyperbolic (GH) Lévy process and so our simulation approach will straightforwardly extend also to the simulation of these intractable processes. Our new methods will find application in forward simulation of processes of GIG and GH type, in financial and engineering data, for example, as well as inference for states and parameters of stochastic processes driven by GIG and GH Lévy processes. [ABSTRACT FROM AUTHOR]

When problems of analysis, synthesis, and filtration for systems of the jump-diffusion type are solved statistically, it is necessary to simulate an inhomogeneous Poisson point process. To this end, sometimes the algorithm relying on the ordinariness of the process is used. In this paper, a modification of this algorithm, using a cost-effective method for simulating random variables, is constructed. The statistical adequacy of the method developed is checked on test problems. [ABSTRACT FROM AUTHOR]

Bioprocess development and optimization are still cost- and time-intensive due to the enormous number of experiments involved. In this study, the recently introduced model-assisted Design of Experiments (mDoE) concept (Möller et al. in Bioproc Biosyst Eng 42(5):867, https://doi.org/10.1007/s00449-019-02089-7, 2019) was extended and implemented into a software ("mDoE-toolbox") to significantly reduce the number of required cultivations. The application of the toolbox is exemplary shown in two case studies with Saccharomyces cerevisiae. In the first case study, a fed-batch process was optimized with respect to the pH value and linearly rising feeding rates of glucose and nitrogen source. Using the mDoE-toolbox, the biomass concentration was increased by 30% compared to previously performed experiments. The second case study was the whole-cell biocatalysis of ethyl acetoacetate (EAA) to (S)-ethyl-3-hydroxybutyrate (E3HB), for which the feeding rates of glucose, nitrogen source, and EAA were optimized. An increase of 80% compared to a previously performed experiment with similar initial conditions was achieved for the E3HB concentration. [ABSTRACT FROM AUTHOR]

Classical a posteriori error analysis for differential equations quantifies the error in a Quantity of Interest which is represented as a bounded linear functional of the solution. In this work we consider a posteriori error estimates of a quantity of interest that cannot be represented in this fashion, namely the time at which a threshold is crossed for the first time. We derive two representations for such errors and use an adjoint-based a posteriori approach to estimate unknown terms that appear in our representation. The first representation is based on linearizations using Taylor's Theorem. The second representation is obtained by implementing standard root-finding techniques. We provide several examples which demonstrate the accuracy of the methods. We then embed these error estimates within a framework to provide error bounds on a cumulative distribution function when the parameters of the differential equations are uncertain. [ABSTRACT FROM AUTHOR]

Scientific interest in studying justifiability towards morally debatable behaviors across nations is considerable, but the statistical assessment of the issue has not been very rigorous so far. In fact, many authors measure the related constructs computing composite indicators of justifiability as unweighed averages of perceived justifiability towards morally debatable behaviors. Other than not allowing for different weights, another drawback is that even if the items have different variability, no transformation like the z score is typically applied before computing the average. Another major shortcoming of the available justifiability indexes is the lack of robustness analysis of the results, making their message weak. The aim of this paper is to design very general composite indicators of justifiability towards dishonest-illegal and personal-sexual behaviors without the shortcomings of the other indicators. The indexes are computed for a data set from the European Values Study covering 47 countries and regions. The results show that Sweden, Netherlands and Finland are the most permissive countries towards personal-sexual behaviors followed by other Western and Scandinavian countries, whereas the strictest countries are Kosovo and Turkey. The most permissive countries towards dishonest-illegal behaviors are all ex-communist countries with Belarus and Slovak Republic being the most permissive countries whereas the strictest ones are Northern Cyprus and Turkey. [ABSTRACT FROM AUTHOR]

We model shallow-water waves using a one-dimensional Korteweg–de Vries equation with the wave generation parameterized by random wave amplitudes for a predefined sea state. These wave amplitudes define the high-dimensional stochastic input vector for which we estimate the short-term wave crest exceedance probability at a reference point. For this high-dimensional and complex problem, most reliability methods fail, while Monte Carlo methods become impractical due to the slow convergence rate. Therefore, first within offshore applications, we employ the dimensionality reduction method called Active-Subspace Analysis. This method identifies a low-dimensional subspace of the input space that is most significant to the input–output variability. We exploit this to efficiently train a Gaussian process (i.e., a kriging model) that models the maximum 10-min crest elevation at the reference point, and to thereby efficiently estimate the short-term wave crest exceedance probability function. The active low-dimensional subspace for the Korteweg–de Vries model also exposes the expected incident wave groups associated with extreme waves and loads. Our results show the advantages and the effectiveness of the active-subspace analysis against the Monte Carlo implementation for offshore applications. [ABSTRACT FROM AUTHOR]

Purpose: A major challenge for accurate quantitative SPECT imaging of some radionuclides is the inadequacy of simple energy window-based scatter estimation methods, widely available on clinic systems. A deep learning approach for SPECT/CT scatter estimation is investigated as an alternative to computationally expensive Monte Carlo (MC) methods for challenging SPECT radionuclides, such as 90Y. Methods: A deep convolutional neural network (DCNN) was trained to separately estimate each scatter projection from the measured 90Y bremsstrahlung SPECT emission projection and CT attenuation projection that form the network inputs. The 13-layer deep architecture consisted of separate paths for the emission and attenuation projection that are concatenated before the final convolution steps. The training label consisted of MC-generated "true" scatter projections in phantoms (MC is needed only for training) with the mean square difference relative to the model output serving as the loss function. The test data set included a simulated sphere phantom with a lung insert, measurements of a liver phantom, and patients after 90Y radioembolization. OS-EM SPECT reconstruction without scatter correction (NO-SC), with the true scatter (TRUE-SC) (available for simulated data only), with the DCNN estimated scatter (DCNN-SC), and with a previously developed MC scatter model (MC-SC) were compared, including with 90Y PET when available. Results: The contrast recovery (CR) vs. noise and lung insert residual error vs. noise curves for images reconstructed with DCNN-SC and MC-SC estimates were similar. At the same noise level of 10% (across multiple realizations), the average sphere CR was 24%, 52%, 55%, and 67% for NO-SC, MC-SC, DCNN-SC, and TRUE-SC, respectively. For the liver phantom, the average CR for liver inserts were 32%, 73%, and 65% for NO-SC, MC-SC, and DCNN-SC, respectively while the corresponding values for average contrast-to-noise ratio (visibility index) in low-concentration extra-hepatic inserts were 2, 19, and 61, respectively. In patients, there was high concordance between lesion-to-liver uptake ratios for SPECT reconstruction with DCNN-SC (median 4.8, range 0.02–13.8) compared with MC-SC (median 4.0, range 0.13–12.1; CCC = 0.98) and with 90Y PET (median 4.9, range 0.02–11.2; CCC = 0.96) while the concordance with NO-SC was poor (median 2.8, range 0.3–7.2; CCC = 0.59). The trained DCNN took ~ 40 s (using a single i5 processor on a desktop computer) to generate the scatter estimates for all 128 views in a patient scan, compared to ~ 80 min for the MC scatter model using 12 processors. Conclusions: For diverse 90Y test data that included patient studies, we demonstrated comparable performance between images reconstructed with deep learning and MC-based scatter estimates using metrics relevant for dosimetry and for safety. This approach that can be generalized to other radionuclides by changing the training data is well suited for real-time clinical use because of the high speed, orders of magnitude faster than MC, while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

The problem of generating sequences of uniformly distributed pseudorandom numbers is considered. A simple visual test for estimating the randomness of numbers in a sequence is used. The test shows that the most popular modern random number generators, such as the Mersenne Twister, linear congruential sequence, and others, yield unsatisfactory results. Accordingly, the generation of good generators remains an open problem, and results of computing stochastic processes (molecular dynamics method, etc.) have to be treated with caution. [ABSTRACT FROM AUTHOR]

In this work, computer modeling of the surface phase transition in semi-infinite antiferromagnetic systems under the influence of external magnetic field is carried out. Cases of different values for the surface exchange integral and exchange integral for interaction between surface spins and the first subsurface layer are considered. For the surface phase transition, as for the bulk transition, the Néel temperature decreases with increasing magnetic-field intensity according to the quadratic law. The rate of decrease in the transition temperature is determined by the ratio of exchange integrals on the surface and in the bulk. For each ratio of the exchange integrals, there is a magnetic-field intensity limit above which the surface of the system does not transit into the antiferromagnetic phase. The limiting value of the magnetic field for the surface transition is no lower than the same value for the bulk. There is an interval of the magnetic-field intensity in which the antiferromagnetic ordering of spins is possible only in a thin surface layer. A tricritical point on the system phase diagram is present at the same value of the ratio of the exchange integrals for all magnetic-field-intensity values. The tricritical temperature also decreases in accordance with quadratic law with increasing magnetic-field intensity. [ABSTRACT FROM AUTHOR]

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão et al. (??2019) and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed. [ABSTRACT FROM AUTHOR]

Modern precision agriculture equipment enables site-specific management by allowing different treatments for different parts of a field. This ability to subdivide the field calls for identifying management zones. A compromise between treating a field uniformly and treating every plant individually is needed, as the former does not maximize yields and the latter is often impractical. This work presents an algorithm for inferring the yield productivity zones (YPZ) for a field based on yield data from multiple years. The algorithm uses a hidden Markov random field model (HMRF) to find regions of the field which likely correspond to the same underlying yield distribution (i.e., productivity zones). These regions are modeled to be the same every year, but their distributions (i.e., yield characteristics) are allowed to vary with time to account for year-to-year variability (from e.g., weather effects, differing crops or crop varieties). The zone assignments and distributions are estimated using stochastic expectation maximization (SEM) and the maximizer of the posterior marginals (MPM). The underlying assumption of the model and algorithm is that the yields corresponding to a given YPZ will behave similarly and therefore derive from the same probability distribution. YPZs are useful inputs for determining management zones. An advantage of this method is that it is able to run with only the yield data which are automatically collected during harvest. Also, this method requires no crop specific calibration or configuration or normalization of the data by year. [ABSTRACT FROM AUTHOR]

We address the numerical solution of stochastic differential equations with multiplicative noise (SDEs) by means of balanced schemes. In particular, we study the design of balanced schemes that achieve the first order of weak convergence without involve the simulation of multiple stochastic integrals. We start by using the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak schemes based on the addition of stabilizing functions to the drift terms. Then, we consider multidimensional linear SDEs. In this case, we propose to find appropriate stabilizing weights through an optimization procedure. Finally, we illustrate the potential of the new methodology by solving the stochastic Duffing-Van Der Pol equation, which is a classical test non-linear SDE. Numerical experiments show a good performance of the numerical methods introduced in this paper. [ABSTRACT FROM AUTHOR]

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are the Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use. Finally, five numerical examples (including the estimation of the parameters of a chaotic system, a localization problem in wireless sensor networks and a spectral analysis application) are provided in order to demonstrate the performance of the described approaches. [ABSTRACT FROM AUTHOR]

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles in Acta Numer. 24:259–328, 2015. 10.1017/S096249291500001X) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin equations with a strongly concave potential. We show that when appropriate contracting couplings for the numerical integrators are available, one can obtain a uniform-in-time estimate of the MLMC variance in contrast to the majority of the results in the MLMC literature. As a consequence, a root mean square error of O (ε) is achieved with O (ε - 2) complexity on par with Markov Chain Monte Carlo (MCMC) methods, which, however, can be computationally intensive when applied to large datasets. Finally, we present a multi-level version of the recently introduced stochastic gradient Langevin dynamics method (Welling and Teh, in: Proceedings of the 28th ICML, 2011) built for large datasets applications. We show that this is the first stochastic gradient MCMC method with complexity O (ε - 2 | log ε | 3) , in contrast to the complexity O (ε - 3) of currently available methods. Numerical experiments confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Taking 109 gymnosperm species in China as a case, the uncertainty and risk of losing habitat areas of gymnosperm species under future climate conditions were investigated via representative concentration pathways climate change scenarios, fuzzy set classifications and Monte Carlo techniques. Under nonrandom climate change scenarios, the richness of 109 species increased in the partial locations of northwestern and northeastern China and declined in the partial locations of eastern and central and southeastern China; the numbers of species that losing <20%, 20–40%, 40–60%, 60–80%, and over 80% of their current habitat areas were ~33–49, 36–40, 11–24, 7–9, and 2–8, respectively; ~99–105 species occupied over 80% of their total suitable areas and ~4–9 species occupied 60–80% their total suitable areas. Under random climate change scenarios, the number of species that losing various level of the habitat areas declined with enhancing probability; with a probabilities of over 0.6, the numbers of species that losing <20%, 20–40%, 40–60%, 60–80% and over 80% of their current habitat areas were ~19–28, 3–19, 0–3, 1–2, and 9–14, respectively, and the numbers of species that occupying ~20%, 20–40%, 40–60%, 60–80%, and over 80% of their total suitable areas were ~9–14, 4–11, 2–6, 1–3, and 34–45, respectively. Approximately 41% of 109 species will face extinction risks from climate change; the losing habitat areas in future climate condition will cause the varying of coniferous forest composition and the losing of ecosystem service related to the species; the uncertainty of losing distribution areas for species should not be ignored. [ABSTRACT FROM AUTHOR]

"Work-stealing" is one of the most common methods of parallel task balancing. In this method, each core (processor) has a buffer of its tasks—a double-ended queue called "deque". A core (processor) use one end of the deque to add new tasks or to take already available to execute them. The second end of the deque is accessible by other cores (processors), which have become empty and can intercept tasks—this is the mechanism of "work-stealing". Algorithms and techniques for the high-performance big data processing are becoming increasingly sought after not only for storing databases but also for the proper handling of big data from a variety of domains such as science and engineering. Models and algorithms of optimal control of large deques belong to this area of research. The goal of this work is to develop, analyze and compare the models and methods of control of work-stealing deques in limited shared memory. For the case of three deques, the following control methods will be discussed: 1. Each of the three deques is located in its separate memory area; 2. Three deques move one after another in a circle; 3. Combined method—two deques are located one after another, one separately. To solve the posed problems, controlled random walks and simulation modeling were used. [ABSTRACT FROM AUTHOR]

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow O (N - 1 / 2) convergence rates as a function of the number of sample paths N. This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely τ -leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature. [ABSTRACT FROM AUTHOR]

Model selection criteria are often used to find a "proper" model for the data under investigation when building models in cases in which the dependent or explained variables are assumed to be functions of several independent or explanatory variables. For this purpose, researchers have suggested using a large number of such criteria. These criteria have been shown to act differently, under the same or different conditions, when trying to select the "correct" number of explanatory variables to be included in a given model; this, unfortunately, leads to severe problems and confusion for researchers. In this paper, using Monte Carlo methods, we investigate the properties of four of the most common criteria under a number of realistic situations. These criteria are the adjusted coefficient of determination ( R 2 -adj), Akaike's information criterion (AIC), the Hannan–Quinn information criterion (HQC) and the Bayesian information criterion (BIC). The results from this investigation indicate that the HQC outperforms the BIC, the AIC and the R 2 -adj under specific circumstances. None of them perform satisfactorily, however, when the degree of multicollinearity is high, the sample sizes are small or when the fit of the model is poor (i.e., there is a low R 2) . In the presence of all these factors, the criteria perform very badly and are not very useful. In these cases, the criteria are often not able to select the true model. [ABSTRACT FROM AUTHOR]

We construct Monte Carlo methods for the L2-approximation in Hilbert spaces of multivariate functions sampling not more than n function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling n pieces of arbitrary linear information, including function values. [ABSTRACT FROM AUTHOR]

The suitable choice of the materials forming the wearing course of highly trafficked roads is a delicate task because of their direct interaction with vehicles. Furthermore, modern roads must be planned according to sustainable development goals, which is complex because some of these might be in conflict. Under this premise, this paper develops a multi-criteria decision support model based on the analytic hierarchy process and the technique for order of preference by similarity to ideal solution to facilitate the selection of wearing courses in European countries. Variables were modelled using either fuzzy logic or Monte Carlo methods, depending on their nature. The views of a panel of experts on the problem were collected and processed using the generalized reduced gradient algorithm and a distance-based aggregation approach. The results showed a clear preponderance by stone mastic asphalt over the remaining alternatives in different scenarios evaluated through sensitivity analysis. The research leading to these results was framed in the European FP7 Project “DURABROADS” (No. 605404). [ABSTRACT FROM AUTHOR]

A Cauchy problem for the time-dependent radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions describing Fresnel reflection and refraction at the interface of the media is considered. The unique solvability of the problem is proven, a Monte Carlo method for solving the initial-boundary value problem is developed, and computational experiments for different implementations of the algorithm are conducted. [ABSTRACT FROM AUTHOR]

The level of accessibility to basic services is an important issue because it is closely related to social inclusion and social capital, key aspects of societal well-being. There is a large and growing literature on access to health care in an era of dwindling public resources due to recent economic downturns. Health care is an essential service, but it is not the only basic service. The literature on access to basic services including, but not limited to, health care is relatively small. The paper aims at contributing to the literature by providing a new index to measure and monitor household accessibility to basic services. A study of Italian regions is presented. It is shown that northern regions have more accessible basic services than central, southern and island regions. A longitudinal comparison has been performed. The results are very worrying because show that policy makers have failed in reducing regional (and in particular north-south) disparities in basic service accessibility. Measuring and monitoring the level of accessibility is central for an adequate provision of basic services and for exploring how the delivery of basic services in the most problematic regions can be improved. [ABSTRACT FROM AUTHOR]

Temporally, precise correlations between simultaneously recorded neurons have been interpreted as signatures of cell assemblies, i.e., groups of neurons that form processing units. Evidence for this hypothesis was found on the level of pairwise correlations in simultaneous recordings of few neurons. Increasing the number of simultaneously recorded neurons increases the chances to detect cell assembly activity due to the larger sample size. Recent technological advances have enabled the recording of 100 or more neurons in parallel. However, these massively parallel spike train data require novel statistical tools to be analyzed for correlations, because they raise considerable combinatorial and multiple testing issues. Recently, various of such methods have started to develop. First approaches were based on population or pairwise measures of synchronization, and later led to methods for the detection of various types of higher-order synchronization and of spatio-temporal patterns. The latest techniques combine data mining with analysis of statistical significance. Here, we give a comparative overview of these methods, of their assumptions and of the types of correlations they can detect. [ABSTRACT FROM AUTHOR]

Despite the development of sophisticated techniques such as sequential Monte Carlo (Del Moral et al. in J R Stat Soc Ser B 68(3):411-436, 2006), importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions (Chopin and Ridgway in Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation, 32:64-87, 2017). This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic (de Figueiredo and Stolfi in Numer Algorithms 37(1-4):147-158, 2004). This work builds on the Moore rejection sampler (Sainudiin in Machine interval experiments, Cornell University, Ithaca, 2005; Sainudiin and York in Algorithms Mol Biol 4(1):1, 2009) to which we provide a comparison. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor expansion. In our study we deal with a nonlinear SDE. We approximate to numerical solution using Monte Carlo simulation for each method. Also exact solution is obtained from Ito's formula. To show the effectiveness of the numerical methods, approximation solutions are compared with exact solution for different sample paths. And finally the results of numerical experiments are supported with graphs and error tables. [ABSTRACT FROM AUTHOR]

Monte Carlo methods have become essential tools to solve complex Bayesian inference problems in different fields, such as computational statistics, machine learning, and statistical signal processing. In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky Markov Chain Monte Carlo (MCMC) algorithms, to sample efficiently from any bounded target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities, which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively from previously drawn samples. The algorithm's efficiency is ensured by a test that supervises the evolution of the set of support points. This extra stage controls the computational cost and the convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples of specific methods are provided. Although the novel algorithms are presented for univariate target densities, we show how they can be easily extended to the multivariate context by embedding them within a Gibbs-type sampler or the hit and run algorithm. The ergodicity is ensured and discussed. An overview of the related works in the literature is also provided, emphasizing that several well-known existing methods (like the adaptive rejection Metropolis sampling (ARMS) scheme) are encompassed by the new class of algorithms proposed here. Eight numerical examples (including the inference of the hyper-parameters of Gaussian processes, widely used in machine learning for signal processing applications) illustrate the efficiency of sticky schemes, both as stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs samplers in order to draw from multi-dimensional target distributions. [ABSTRACT FROM AUTHOR]