Article
Statistics & Probability
Yuguang Ipsen, Ross A. Maller, Soudabeh Shemehsavar
Summary: In this study, the large-sample distribution of the number of species in a version of Kingman's Poisson-Dirichlet model was derived. It introduced a two-parameter version of the Dickman distribution, expanding on the existing single-parameter version, thereby enriching the range of distributions available for modeling purposes.
ADVANCES IN APPLIED PROBABILITY
(2021)
Article
Genetics & Heredity
John Wakeley, Wai-Tong (Louis) Fan, Evan Koch, Shamil Sunyaev
Summary: Recurrent mutation can produce multiple copies of the same allele in a population. However, most analyses assume that all observed copies trace back to a single mutation. This study develops a sampling theory for the number of latent mutations in the ancestry of a rare variant and applies it to explain differences in site-frequency spectra across mutation rates in the human genome.
Article
Statistics & Probability
Poly H. Da Silva, Arash Jamshidpey, Peter McCullagh, Simon Tavare
Summary: Fisher (1943) argued that the expected value of the sample variance of species found in large samples is asymptotically 0 log 2, contradicting the value 0 log n obtained from the Ewens Sampling Formula (ESF). To reconcile this contradiction, it is assumed that the population's species frequency spectrum is determined by the ESF and samples are sequentially drawn from this population. An explicit formula is derived for the expected value of p samples of arbitrary size, which converges to 0 log 2 for large equally-sized samples. Limit theorems are obtained for the sample variance of p samples of size n under different limiting regimes. The behavior of the number of species present in all samples is also examined, and Fisher's log-series distribution is revisited as the limiting distribution of the number of specimens observed in a large sample.
Article
Mathematics
Siddhartha Sahi, Jasper Stokman
Summary: This study explores elementary identities and duality properties of three types of non-symmetric interpolation Macdonald polynomials, as well as their applications to binomial formulas.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Statistics & Probability
Peter McCullagh
Summary: This article demonstrates that the standard repeated-sampling interpretation of variance in a finite-dimensional parametric model is ambiguous and open to misinterpretation. Three different operational interpretations are provided, all of which can be numerically different and consistent with repeated sampling from the same population with a fixed parameter. Only one of these interpretations aligns with the standard large-sample calculation based on inverse Fisher information, while the others do not. This variation in interpretations helps to resolve the apparent contradiction between Fisherian variance and the inverse-information variance obtained from the Ewens model.
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
(2023)
Article
Statistics & Probability
Bao-Anh Dang, K. Krishnamoorthy
Summary: The paper addresses the issues of constructing CIs, PIs, and TIs in negative binomial sampling, proposing various methods and evaluating them. The statistical intervals are illustrated using two examples with real data, demonstrating their application and effectiveness.
STATISTICAL PAPERS
(2022)
Article
Statistics & Probability
Han L. Gan, Nathan Ross
Summary: The paper presents a general theorem for bounding the error in the approximation of a random measure of interest and applies it to the finite Wright-Fisher model. The analysis is based on a new development of Stein's method for the Dirichlet process.
ANNALS OF APPLIED PROBABILITY
(2021)
Article
Statistics & Probability
Charalambos A. Charalambides
Summary: The concept of Bernoulli trials is extended to include chain-composite successes or failures, with a focus on the stochastic model and distribution of such sequences. The study explores the joint distributions of different types of successes or failures, providing a multivariate extension of existing distributions.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2021)
Article
Mathematics
Simona Grusea, Anthony Labarre
Summary: The paper explores the prefix exchange distance of a permutation and obtains expressions for the mean and variance using a probabilistic approach. It also proves the asymptotic normality of the distribution of this distance for a random permutation satisfying the Ewens sampling formula. Similar results in the uniform setting are derived as simple corollaries.
DISCRETE MATHEMATICS
(2021)
Article
Ergonomics
A. S. M. Mohaiminul Islam, Mohammadali Shirazi, Dominique Lord
Summary: Crash data often have characteristics such as high dispersion, numerous zero observations, and long tail, which cannot be properly modeled by the traditional Negative Binomial (NB) model. The Negative Binomial-Lindley (NB-L) model has been proposed as an alternative, and research studies have shown its superior performance in analyzing such data. Additionally, crash data are often collected from different subpopulations, and finite mixture models can be used to capture population heterogeneity. The Finite mixture NB-L model (FMNB-L) is introduced to analyze crash data from heterogeneous subpopulations with many zero observations and a long tail, and it has been found to provide a significantly better fit compared to other models.
ACCIDENT ANALYSIS AND PREVENTION
(2022)
Article
Entomology
Rafael Carlesso Aita, Daniela T. Pezzini, Eric C. Burkness, Christina D. DiFonzo, Deborah L. Finke, Thomas E. Hunt, Janet J. Knodel, Christian H. Krupke, Lia Marchi-Werle, Brian McCornack, Andrew P. Michel, Christopher R. Philips, Nicholas J. Seiter, Adam J. Varenhorst, Robert J. Wright, William D. Hutchison, Robert L. Koch
Summary: Stink bugs pose an increasing threat to soybean production in the Midwest region of the United States, requiring a more efficient sampling plan for management. Through field sampling and development of a binomial sequential sampling plan, the optimal threshold values and action thresholds for this region were identified.
JOURNAL OF ECONOMIC ENTOMOLOGY
(2021)
Article
Chemistry, Analytical
Bo Svensmark
Summary: The Theory of Sampling by Pierre Gy is a comprehensive theory that explains sampling errors and how to obtain a representative sample. While Gy's formula for predicting the Fundamental Sampling Error (FSE) may be challenging to use in practice, an extended formula derived from Gy's definition of constitutional heterogeneity provides an exact method for estimating FSE for various particulate materials. This extended formula allows for accurate prediction of FSE for complex materials with multiple particle classes.
ANALYTICA CHIMICA ACTA
(2021)
Article
Mathematics
Emanuele Dolera, Stefano Favaro
Summary: The paper examines the relationship between the Ewens-Pitman sampling model (EP-SM) and the negative Binomial compound Poisson sampling model (NB-CPSM), presenting a new proof regarding the asymptotic behavior of the number of blocks in random partitions and discussing the properties that analogous compound Poisson representations may hold for the EP-SM as a noteworthy special case.
Article
Automation & Control Systems
Miaofen Li, Tianyang Wang, Fulei Chu, Qinkai Han, Zhaoye Qin, Ming J. Zuo
Summary: A novel time-frequency analysis method, SBCT, was developed to accurately handle multicomponent signals with close-spaced frequencies and high levels of background noise.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2021)
Article
Mathematics
Rehan Ahmad Khan Sherwani, Sadia Iqbal, Shumaila Abbas, Muhammad Aslam, Ali Hussein AL-Marshadi
Summary: This research introduces the neutrosophic negative binomial distribution to address issues related to interval-valued data under the negative binomial distribution, including derivations of various properties of the proposed distribution and discussions on its applications in real data scenarios.
JOURNAL OF MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Xiaoyu Shi, Jian Zhang, Xia Jiang, Juan Chen, Wei Hao, Bo Wang
Summary: This study presents a novel framework using offline reinforcement learning to improve energy consumption in road transportation. By leveraging real-world human driving trajectories, the proposed method achieves significant improvements in energy consumption. The offline learning approach demonstrates generalizability across different scenarios.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Junhyuk Woo, Soon Ho Kim, Hyeongmo Kim, Kyungreem Han
Summary: Reservoir computing (RC) is a new machine-learning framework that uses an abstract neural network model to process information from complex dynamical systems. This study investigates the neuronal and network dynamics of liquid state machines (LSMs) using numerical simulations and classification tasks. The findings suggest that the computational performance of LSMs is closely related to the dynamic range, with a larger dynamic range resulting in higher performance.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Yuwei Yang, Zhuoxuan Li, Jun Chen, Zhiyuan Liu, Jinde Cao
Summary: This paper proposes an extreme learning machine (ELM) algorithm based on residual correction and Tent chaos sequence (TRELM-DROP) for accurate prediction of traffic flow. The algorithm reduces the impact of randomness in traffic flow through the Tent chaos strategy and residual correction method, and avoids weight optimization using the iterative method. A DROP strategy is introduced to improve the algorithm's ability to predict traffic flow under varying conditions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Chengwei Dong, Min Yang, Lian Jia, Zirun Li
Summary: This work presents a novel three-dimensional system with multiple types of coexisting attractors, and investigates its dynamics using various methods. The mechanism of chaos emergence is explored, and the periodic orbits in the system are studied using the variational method. A symbolic coding method is successfully established to classify the short cycles. The flexibility and validity of the system are demonstrated through analogous circuit implementation. Various chaos-based applications are also presented to show the system's feasibility.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Viorel Badescu
Summary: This article discusses the maximum work extraction from confined particles energy, considering both reversible and irreversible processes. The results vary for different types of particles and conditions. The concept of exergy cannot be defined for particles that undergo spontaneous creation and annihilation. It is also noted that the Carnot efficiency is not applicable to the conversion of confined thermal radiation into work.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
P. M. Centres, D. J. Perez-Morelo, R. Guzman, L. Reinaudi, M. C. Gimenez
Summary: In this study, a phenomenological investigation of epidemic spread was conducted using a model of agent diffusion over a square region based on the SIR model. Two possible contagion mechanisms were considered, and it was observed that the number of secondary infections produced by an individual during its infectious period depended on various factors.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zuan Jin, Minghui Ma, Shidong Liang, Hongguang Yao
Summary: This study proposes a differential variable speed limit (DVSL) control strategy considering lane assignment, which sets dynamic speed limits for each lane to attract vehicle lane-changing behaviors before the bottleneck and reduce the impact of traffic capacity drop. Experimental results show that the proposed DVSL control strategy can alleviate traffic congestion and improve efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Matthew Dicks, Andrew Paskaramoorthy, Tim Gebbie
Summary: In this study, we investigate the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event-driven agent-based financial market model. The results show that the agents with smaller state spaces converge faster and are able to intuitively learn to trade using spread and volume states. The introduction of the learning agent has a robust impact on the moments of the model, except for the Hurst exponent, which decreases, and it can increase the micro-price volatility as trading volumes increase.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zhouzhou Yao, Xianyu Wu, Yang Yang, Ning Li
Summary: This paper developed a cooperative lane-changing decision system based on digital technology and indirect reciprocity. By introducing image scoring and a Q-learning based reinforcement learning algorithm, drivers can continuously evaluate gains and adjust their strategies. The study shows that this decision system can improve driver cooperation and traffic efficiency, achieving over 50% cooperation probability under any connected vehicles penetration and traffic density, and reaching 100% cooperation probability under high penetration and medium to high traffic density.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Josephine Nanyondo, Henry Kasumba
Summary: This paper presents a multi-class Aw-Rascle (AR) model with area occupancy expressed in terms of vehicle class proportions. The qualitative properties of the proposed equilibrium velocity and the stability conditions of the model are established. The numerical results show the effect of proportional densities on the flow of vehicle classes, indicating the realism of the proposed model.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Oliver Smirnov
Summary: This study proposes a new method for simultaneously estimating the parameters of the 2D Ising model. The method solves a constrained optimization problem, where the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. Monte Carlo simulations were conducted using models of different shapes and sizes to evaluate the performance of the method with and without the Hamiltonian constraint. The results demonstrate that the proposed estimation method yields lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Przemyslaw Chelminiak
Summary: The study investigates the first-passage properties of a non-linear diffusion equation with diffusivity dependent on the concentration/probability density through a power-law relationship. The survival probability and first-passage time distribution are determined based on the power-law exponent, and both exact and approximate expressions are derived, along with their asymptotic representations. The results pertain to diffusing particles that are either freely or harmonically trapped. The mean first-passage time is finite for the harmonically trapped particle, while it is divergent for the freely diffusing particle.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Hidemaro Suwa
Summary: The choice of transition kernel is crucial for the performance of the Markov chain Monte Carlo method. A one-parameter rejection control transition kernel is proposed, and it is shown that the rejection process plays a significant role in determining the sampling efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Xudong Wang, Yao Chen
Summary: This article investigates the joint influence of expanding medium and constant force on particle diffusion. By starting from the Langevin picture and introducing the effect of external force in two different ways, two models with different force terms are obtained. Detailed analysis and derivation yield the Fokker-Planck equations and moments for the two models. The sustained force behaves as a decoupled force, while the intermittent force changes the diffusion behavior with specific effects depending on the expanding rate of the medium.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
