Extensive Simulations Research Articles

Federated Learning of Generalized Linear Causal Networks.

Causal discovery, the inference of causal relations among variables from data, is a fundamental problem of science. Nowadays, due to an increased awareness of data privacy concerns, there has been a shift towards distributed data collection, processing and storage. To meet the pressing need for distributed causal discovery, we propose a novel federated DAG learning method called distributed annealing on regularized likelihood score (DARLS) to learn a causal graph from data stored on multiple clients. DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by distributed optimization. This distributed optimization relies on multiple rounds of communication between local clients and a central server to estimate the graphical structure. We establish its convergence to the solution obtained by an oracle with access to all the data. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such finite-sample oracle guarantees. To establish the consistency of DARLS, we also derive new identifiability results for causal graphs parameterized by generalized linear models, which could be of independent interest. Through extensive simulation studies and a real-world application, we show that DARLS outperforms existing federated learning methods and is comparable to oracle methods on pooled data, demonstrating its great advantages in estimating causal networks from distributed data.

Representing Noisy Image Without Denoising.

A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in training phase (i.e., data augmentation) or 2) pre-processing the noisy image by learning to solve the inverse problem (i.e., image denoising). However, such methods generally exhibit inefficient process and unstable result, limiting their practical applications. In this paper, we explore a non-learning paradigm that aims to derive robust representation directly from noisy images, without the denoising as pre-processing. Here, the noise-robust representation is designed as Fractional-order Moments in Radon space (FMR), with also beneficial properties of orthogonality and rotation invariance. Unlike earlier integer-order methods, our work is a more generic design taking such classical methods as special cases, and the introduced fractional-order parameter offers time-frequency analysis capability that is not available in classical methods. Formally, both implicit and explicit paths for constructing the FMR are discussed in detail. Extensive simulation experiments and robust visual applications are provided to demonstrate the uniqueness and usefulness of our FMR, especially for noise robustness, rotation invariance, and time-frequency discriminability.

Inference for depending competing risks from Marshall–Olikin bivariate Kies distribution under generalized progressive hybrid censoring

This paper explores inferences for a competing risk model with dependent causes of failure. When the lifetimes of competing risks are modelled by a Marshall–Olikin bivariate Kies distribution, classical and Bayesian estimations are studied under generalized progressive hybrid censoring. The existence and uniqueness results for maximum likelihood estimators of unknown parameters are established, whereas approximate confidence intervals are constructed using the observed Fisher information matrix. In addition, Bayes estimates are explored based on a flexible Gamma-Dirichlet prior information. Furthermore, when there is a priori order information on competing risk parameters being available, traditional classical likelihood and Bayesian estimates are also established under restricted parameter case. The behavior of the proposed estimators is evaluated through extensive simulation studies, and a real data study is presented for illustrative purposes.

Global Inference and Test for Eigensystems of Imaging Data Over Complicated Domains

A nonparametric approach for analyzing eigensystems of image data over a complex domain is novelly developed. The proposed estimators, which are based on bivariate splines, have both oracle efficiency of O p ( n − 1 / 2 ) , meaning they are asymptotically indistinguishable from estimators computed with true trajectories, and computational efficiency with more convenient spectrum decomposition forms. Under mild conditions, we derive consistency and weak convergence of our proposed estimators, which can be used to construct confidence intervals and simultaneous confidence corridors for any individual eigenvalue and eigenfunction, as well as design uniform inference procedures for eigensystems with a diverging number of components. In addition, we extend our method to two-sample test problems. Extensive simulation results provide strong support for the asymptotic theory, and the procedures are applied to two potential seawater temperature data sets to demonstrate its validity.

Efficient deep reinforcement learning based task scheduler in multi cloud environment

Task scheduling problem (TSP) is huge challenge in cloud computing paradigm as number of tasks comes to cloud application platform vary from time to time and all the tasks consists of variable length, runtime capacities. All these tasks may generated from various heterogeneous resources which comes onto cloud console directly effects the performance of cloud paradigm with increase in makespan, energy consumption, resource costs. Traditional task scheduling algorithms cannot handle these type of complex workloads in cloud paradigm. Many authors developed Task Scheduling algorithms by using metaheuristic techniques, hybrid approaches but all these algorithms give near optimal solutions but still TSP is a highly challenging and dynamic scenario as it resembles NP hard problem. Therefore, to tackle the TSP in cloud computing paradigm and schedule the tasks in an effective way in cloud paradigm, we formulated Adaptive Task scheduler which segments all the tasks comes to cloud console as sub tasks and fed these to the scheduler which is modeled by Improved Asynchronous Advantage Actor Critic Algorithm(IA3C) to generate schedules. This scheduling process is carried out in two stages. In first stage, all incoming tasks are segmented as sub tasks. After segmentation, all these sub tasks according to their size, execution time, communication time are grouped together and fed to the (ATSIA3C) scheduler. In the second stage, it checks for the above said constraints and disperse them onto the corresponding suitable processing capacity VMs resided in datacenters. Proposed ATSIA3C is simulated on Cloudsim. Extensive simulations are conducted using both fabricated worklogs and as well as realtime supercomputing worklogs. Our proposed mechanism evaluated over baseline algorithms i.e. RATS-HM, AINN-BPSO, MOABCQ. From results it is evident that our proposed ATSIA3C outperforms existing task schedulers by improving makespan by 70.49%. Resource cost is improved by 77.42%. Energy Consumption is improved over compared algorithms 74.24% in multi cloud environment by proposed ATSIA3C.

Iterative site percolation on triangular lattice

The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation cluster, we obtain coarse-grained configurations by merging adjacent clusters that share the same color. It is shown that the process can be infinitely iterated in the infinite-lattice limit, leading to an iterative site percolation model. We conjecture from the self-matching argument that percolation clusters remain fractal for any finite generation, which can even take any positive real number by a generalized process. Extensive simulations are performed, and, from the generation-dependent fractal dimension, a continuous family of previously unknown universalities is revealed. Published by the American Physical Society 2024

A High-Resolution and Robust Microwave Correlation Imaging Method Based on URRF Using MC-AAMPE Algorithm

This manuscript presents a novel framework for high-resolution and robust microwave correlation imaging. In order to generate a more diverse random radiation field distribution, the unified random radiation field (URRF) model is proposed. The URRF model can accurately characterize the joint random modulation in the signals’ phase, amplitude, and frequency. Furthermore, we build a parametric imaging model based on URRF which clearly describes the relationship between the image to be reconstructed and the signals by the URRF model. By using this imaging model, the reconstruction of an image is converted into solving a multi-parameter optimization problem with multiple constraints. To solve this optimization problem with high efficiency and accuracy, the model-constrained adaptive alternating multiple parameter estimation (MC-AAMPE) algorithm is proposed. This algorithm decomposes the high-dimensional multi-parameter optimization problem into several sub-optimization problems. The renewing solutions to these sub-optimization problems make the multi-parameter optimization converge to the image of the target and the parameters of clutter and noise, which are all unknown before the solution. In comparison with the existing methods, the proposed scheme generates images with higher resolution and is more robust under noise conditions. Extensive simulation experiments confirmed the effectiveness and robustness of the proposed method.

Explosive percolation in finite dimensions

Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [], we demonstrated that the correct critical behaviors of EP in infinite dimensions (complete graph) can be accurately extracted using the event-based method, with finite-size scaling behaviors still described by the standard finite-size scaling theory. We perform an extensive simulation of EPs on hypercubic lattices ranging from dimensions d=2 to 6, and find that the critical behaviors consistently obey the standard finite-size scaling theory. Consequently, we obtain a high-precision determination of the percolation thresholds and critical exponents, revealing that EPs governed by the product and sum rules belong to different universality classes. Remarkably, despite the mean of the dynamic pseudocritical point TL deviating from the infinite-lattice criticality by a distance determined by the d-dependent correlation-length exponent, TL follows a normal (Gaussian) distribution across all dimensions, with a standard deviation proportional to 1/V, where V denotes the system volume. A theoretical argument associated with the central-limit theorem is further proposed to understand the probability distribution of TL. These findings offer a comprehensive understanding of critical behaviors in EPs across various dimensions, revealing a different dimension-dependence compared to standard bond percolation. Published by the American Physical Society 2024

An effective and small sample-size valid confidence interval for isotonic dose-response curves by inverting a partial likelihood ratio test

A dose-response curve is essential for determining the safe dosage of a drug and is widely used in bioassay and in phase 1 clinical trials. It is generally accepted that the probability of death or the probability of dose-limiting toxicity is a non-decreasing function of the dose. This paper proposes and develops an effective point-wise confidence interval for an isotonic dose-response curve, a problem without a satisfactory solution so far. We show that one subset of the observations informs the lower limit while the other subset informs the upper limit. A partial likelihood ratio test using these subsets of observations is fully investigated. The resulting confidence interval is compared to three existing methods (Morris, Meyer, and Oron) in an extensive simulation study. The new method produces tight intervals while maintaining coverage. It is therefore preferred when maintaining an actual coverage probability is crucial as often in a regulatory environment. The new method extends to one-way ANOVA of a continuous response variable in a straightforward way. An R function is provided.

Advancements in UAV Path Planning: A Deep Reinforcement Learning Approach with Soft Actor-Critic for Enhanced Navigation

This paper tackles the intricate challenge of autonomous navigation for Unmanned Aerial Vehicles (UAVs) through dynamically changing environments. We focus on a sophisticated Deep Reinforcement Learning (DRL) approach using the Soft Actor-Critic (SAC) algorithm, optimized for UAV path planning within a continuous action space. This methodology leverages environmental image data to enhance the precision of flight maneuvers and effective obstacle avoidance. Our approach, validated through extensive simulations in Gazebo and field tests, demonstrates the algorithm’s efficacy in enabling UAVs to adeptly navigate obstacles using depth maps. The study further explores the robustness of the SAC algorithm by comparing it with traditional DRL methods, emphasizing its superior performance in real-world applications. This research contributes significantly to advancing UAV technology, particularly in autonomous motion planning, by integrating cutting-edge machine learning techniques. The video link is: https://www.youtube.com/watch?v=Nd_aMzejNXY .

A genetic algorithm approach for flexible power point tracking in partial shading conditions

A novel Flexible Power Point Tracking (FPPT) algorithm based on Genetic Algorithms (GAs) is presented in this study. The algorithm is designed to effectively handle fluctuating solar irradiation levels and partial shading scenarios. The main objective is to enhance power output and tracking accuracy under dynamic environmental conditions, based on extensive simulations. The results showed superior performance for power output, tracking accuracy, and convergence speed than traditional techniques. Its adaptability to changing environmental conditions renders it suitable for real-time implementation, thereby contributing to efficient power generation in PV systems. Simulations demonstrate the efficacy of the algorithm in maximizing power extraction and meeting grid-code requirements under dynamic conditions. The comparative analyses underscore the superiority of the GA-based FPPT algorithm, highlighting its potential to significantly improve power point tracking in photovoltaic systems. This shows significance of adaptive algorithms in modern PV systems, particularly for reducing the effects of partial shading on energy yield. More research is required on the refinement of the algorithm's performance for long-term reliability and scalability in larger PV installations fostering advancements in photovoltaic power point tracking toward sustainable energy systems.

Insight into a new perspective on the complex propagation processes in networks: dynamic link equations

Abstract The control of epidemic spread in complex networks is a significant research challenge within network science, extensively explored by numerous scholars. A central issue in epidemic transmission within complex networks is the transmission mechanism, which can be categorized into simple and complex transmission. While simple transmission has been thoroughly investigated and its theory is relatively well-established, complex transmission remains a subject of numerous unresolved inquiries. Notably, the higher-order structure of the network exerts a crucial influence in complex transmission processes, impacting transmission speed, scale, and path by reinforcing the mechanism. However, the lack of sophisticated dynamic analysis tools has restricted the measurement of propagation influence to low-dimensional node levels. In this study, we propose a set of closed dynamic higher-order structure equations to gain deeper insights into complex propagation processes in networks, shifting the focus from the node level to the higher-order level. This novel approach opens up new avenues for analyzing higher-order interactions in dynamic networks. Application of the proposed higher-order dynamic equations to a complex SIR epidemiological model on two real and synthetic networks, along with extensive numerical simulations, demonstrates the efficacy of our approach. Our findings enhance understanding of the interplay between complex propagation mechanisms and higher-order structures, and establish a comprehensive suite of complex dynamic analysis tools that can be extended to higher-order forms, facilitating a deeper comprehension of propagation rules and mechanisms in complex processes. This work provides a vital theoretical foundation for predicting, analyzing, and controlling complex propagation processes.

Modified Cox Models: A Simulation Study on Different Survival Distributions, Censoring Rates, and Sample Sizes

The classical Cox model is the most popular procedure for studying right-censored data in survival analysis. However, it is based on the fundamental assumption of proportional hazards (PH). Modified Cox models, stratified and extended, have been widely employed as solutions when the PH assumption is violated. Nevertheless, prior comparisons of the modified Cox models did not employ comprehensive Monte-Carlo simulations to carry out a comparative analysis between the two models. In this paper, we conducted extensive Monte-Carlo simulation to compare the performance of the stratified and extended Cox models under varying censoring rates, sample sizes, and survival distributions. Our results suggest that the models’ performance at varying censoring rates and sample sizes is robust to the distribution of survival times. Thus, their performance under Weibull survival times was comparable to that of exponential survival times. Furthermore, we found that the extended Cox model outperformed other models under every combination of censoring, sample size and survival distribution.

A novel asymmetric extension of power XLindley distribution: properties, inference and applications to engineering data

It is impossible to overstate the importance of using trigonometric functions appropriately in distribution theory. The main contribution of the research is to construct a flexible trigonometric extension of the power XLindley distribution. More specifically, we build an innovative two-parameter lifetime distribution known as the sine power XLindley distribution (SPXLD) using characteristics from the sine-generated family of distributions. As the main motivational fact, it provides an attractive alternative to the power Lindley, power XLindley, weighted Lindley, and extended power Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic and platkurtic nature. In contrast to the increasing, decreasing, and reversed-j-shaped hazard rate function, the density exhibits asymmetric shapes with varying peakedness levels. Several significant characteristics are illustrated, including moments, the quantile function, the probability density function in series representation, the stress-strength reliability, and incomplete moments. To analyze the behavior of the suggested distribution, sixteen estimation techniques are applied, such as the maximum likelihood, percentiles, some methods of minimum distances, some methods based on minimum and maximum spacing distances, and the Kolmogorov method. After that, an extensive simulation study and the examination of two survival real datasets are used to show the viability, usefulness, and adaptability of the SPXLD. Relevant goodness of fit criteria demonstrates that the SPXLD fits several current distributions.

Enhanced electric vehicle battery management system employing bat algorithm with chaotic diversification strategies

AbstractAs the demand for electric vehicles (EV) continues to increase, the need for effective charging and switching of battery systems becomes more important. This article presents a method using the Bat Algorithm (BA) improved by chaotic diversification as well as social education to optimize the power source replacement and the electric vehicle charging procedure. The plan is intended to solve the issues of payment delay and battery management failure. The algorithm searches for better positions by combining chaotic diversity, while social learning supports the coordination of battery stations. Thanks to extensive simulation and real‐world testing, our approach shows significant improvements in optimization and a reduced payback period. The results show that the suggested approach outperforms the current algorithms in terms of rotation speed and good solution. This research supports the development of efficient transportation by providing practical solutions to increase the efficiency of electric vehicle transfer and payment and ultimately encourage greater effort.

A Bayesian complex-valued latent variable model applied to functional magnetic resonance imaging

Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.

Two-Stage Distributed Robust Optimization Scheduling Considering Demand Response and Direct Purchase of Electricity by Large Consumers

The integration of large-scale wind power into power systems has exacerbated the challenges associated with peak load regulation. Concurrently, the ongoing advancement of electricity marketization reforms highlights the need to assess the impact of direct electricity procurement by large consumers on enhancing the flexibility of power systems. In this context, this paper introduces a Distributed Robust Optimal Scheduling (DROS) model, which addresses the uncertainties of wind power generation and direct electricity purchases by large consumers. Firstly, to mitigate the effects of wind power uncertainty on the power system, a first-order Markov chain model with interval characteristics is introduced. This approach effectively captures the temporal and variability aspects of wind power prediction errors. Secondly, building upon the day-ahead scenarios generated by the Markov chain, the model then formulates a data-driven optimization framework that spans from day-ahead to intra-day scheduling. In the day-ahead phase, the model leverages the price elasticity of the demand matrix to guide consumer behavior, with the primary objective of maximizing the total revenue of the wind farm. A robust scheduling strategy is developed, yielding an hourly scheduling plan for the day-ahead phase. This plan dynamically adjusts tariffs in the intra-day phase based on deviations in wind power output, thereby encouraging flexible user responses to the inherent uncertainty in wind power generation. Ultimately, the efficacy of the proposed DROS method is validated through extensive numerical simulations, demonstrating its potential to enhance the robustness and flexibility of power systems in the presence of significant wind power integration and market-driven direct electricity purchases.

On sequences of convex records in the plane

Abstract Convex records have an appealing purely geometric definition. In a sequence of d-dimensional data points, the nth point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e. two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number ⟨ R n ⟩ of convex records up to time n to the mean number ⟨ N n ⟩ of vertices in the convex hull of the first n points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of Nn and Rn grow proportionally to each other, resulting in the finite limit Fano factors FN and FR . We also consider planar random walks, i.e. sequences of points with iid increments. For both the Pearson walk in the continuum and the Pólya walk on a lattice, we characterise the growth of the mean number ⟨ R n ⟩ of convex records and demonstrate that the ratio R n / ⟨ R n ⟩ keeps fluctuating with a universal limit distribution.

Copula Approximate Bayesian Computation Using Distribution Random Forests

Ongoing modern computational advancements continue to make it easier to collect increasingly large and complex datasets, which can often only be realistically analyzed using models defined by intractable likelihood functions. This Stats invited feature article introduces and provides an extensive simulation study of a new approximate Bayesian computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, that unifies and extends previous ABC methods proposed separately. This framework, copulaABCdrf, aims to accurately estimate and describe the possibly skewed and high-dimensional posterior distribution by a novel multivariate copula-based meta-t distribution based on univariate marginal posterior distributions that can be accurately estimated by distribution random forests (drf), while performing automatic summary statistics (covariates) selection, based on robustly estimated copula dependence parameters. The copulaABCdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of the ABC framework is illustrated and compared with previous standard ABC methods through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. This paper also proposes and studies a new solution to the simulation cost problem in ABC involving the posterior estimation of parameters from datasets simulated from the given model that are smaller compared to the potentially large size of the dataset being analyzed. This proposal is motivated by the fact that, for many models defined by intractable likelihoods, such as the network models when they are applied to analyze massive networks, the repeated simulation of large datasets (networks) for posterior-based parameter estimation can be too computationally costly and vastly slow down or prohibit the use of standard ABC methods. The copulaABCdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks of sizes ranging between 28,000 and 65.6 million nodes (between 3 million and 1.8 billion edges), including a large multilayer network with weighted directed edges. The results of the simulation studies show that, in settings where the true posterior distribution is not highly multimodal, copulaABCdrf usually produced similar point estimates from the posterior distribution for low-dimensional parametric models as previous ABC methods, but the copula-based method can produce more accurate estimates from the posterior distribution for high-dimensional models, and, in both dimensionality cases, usually produced more accurate estimates of univariate marginal posterior distributions of parameters. Also, posterior estimation accuracy was usually improved when pre-selecting the important summary statistics using drf compared to ABC employing no pre-selection of the subset of important summaries. For all ABC methods studied, accurate estimation of a highly multimodal posterior distribution was challenging. In light of the results of all the simulation studies, this article concludes by discussing how the copulaABCdrf framework can be improved for future research.

Mathematical model of dating apps’ influence on sexually transmitted diseases spread

Sexually transmitted diseases (STDs) are a group of pathogens infecting new hosts through sexual interactions. Due to its social and economic burden, multiple models have been proposed to study the spreading of pathogens. In parallel, in the ever-evolving landscape of digital social interactions, the pervasive utilization of dating apps has become a prominent facet of modern society. Despite the surge in popularity and the profound impact on relationship formation, a crucial gap in the literature persists regarding the potential ramifications of dating apps usage on the dynamics of STDs. In this paper, we address this gap by presenting a novel mathematical framework - an extended Susceptible-Infected-Susceptible (SIS) epidemiological model to elucidate the intricate interplay between dating apps engagement and the propagation of STDs. Namely, as dating apps are designed to make users revisit them and have mainly casual sexual interactions with other users, they increase the number of causal partners, which increases the overall spread of STDS. Using extensive simulation, based on real-world data, explore the effect of dating apps adoption and control on the STD spread. We show that an increased adoption of dating apps can result in an STD outbreak if not handled appropriately.