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result(s) for
"probability distribution"
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Probability Distributions Describing Qubit-State Superpositions
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.
Journal Article
INFERENCE FROM LARGE SETS OF RADIOCARBON DATES: SOFTWARE AND METHODS
The last decade has seen the development of a range of new statistical and computational techniques for analysing large collections of radiocarbon (14C) dates, often but not exclusively to make inferences about human population change in the past. Here we introduce rcarbon, an open-source software package for the R statistical computing language which implements many of these techniques and looks to foster transparent future study of their strengths and weaknesses. In this paper, we review the key assumptions, limitations and potentials behind statistical analyses of summed probability distribution of 14C dates, including Monte-Carlo simulation-based tests, permutation tests, and spatial analyses. Supplementary material provides a fully reproducible analysis with further details not covered in the main paper.
Journal Article
Distributionally Robust Convex Optimization
Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.
Journal Article
Exponential distribution optimizer (EDO): a novel math-inspired algorithm for global optimization and engineering problems
Numerous optimization problems can be addressed using metaheuristics instead of deterministic and heuristic approaches. This study proposes a novel population-based metaheuristic algorithm called the Exponential Distribution Optimizer (EDO). The main inspiration for EDO comes from mathematics based on the exponential probability distribution model. At the outset, we initialize a population of random solutions representing multiple exponential distribution models. The positions in each solution represent the exponential random variables. The proposed algorithm includes two methodologies for exploitation and exploration strategies. For the exploitation stage, the algorithm utilizes three main concepts, memoryless property, guiding solution and the exponential variance among the exponential random variables to update the current solutions. To simulate the memoryless property, we assume that the original population contains only the winners that obtain good fitness. We construct another matrix known as memoryless to retain the newly generated solutions regardless of their fitness compared to their corresponding winners in the original population. As a result, the memoryless matrix stores two types of solutions: winners and losers. According to the memoryless property, we disregard and do not memorize the previous history of these solutions because past failures are independent and have no influence on the future. The losers can thus contribute to updating the new solutions next time. We select two solutions from the original population derived from the exponential distributions to update the new solution throughout the exploration phase. Furthermore, EDO is tested against classical test functions in addition to the Congress on Evolutionary Computation (CEC) 2014, CEC 2017, CEC 2020 and CEC 2022 benchmarks, as well as six engineering design problems. EDO is compared with the winners of CEC 2014, CEC 2017 and CEC 2020, which are L-SHADE, LSHADE−cnEpSin and AGSK, respectively. EDO reveals exciting results and can be a robust tool for CEC competitions. Statistical analysis demonstrates the superiority of the proposed EDO at a 95% confidence interval.
Journal Article
CMIP6 Model-Projected Hydroclimatic and Drought Changes and Their Causes in the Twenty-First Century
Drought is projected to become more severe and widespread as global warming continues in the twenty-first century, but hydroclimatic changes and their drivers are not well examined in the latest projections from phase 6 of the Coupled Model Intercomparison Project (CMIP6). Here, precipitation (P), evapotranspiration (E), soil moisture (SM), and runoff (R) from 25 CMIP6 models, together with self-calibrated Palmer drought severity index with Penman—Monteith potential evapotranspiration (scPDSIpm), are analyzed to quantify hydroclimatic and drought changes in the twenty-first century and the underlying causes. Results confirm consistent drying in these hydroclimatic metrics across most of the Americas (including the Amazon), Europe and the Mediterranean region, southern Africa, and Australia, although the drying magnitude differs, with the drying being more severe and widespread in surface SM than in total SM. Global drought frequency based on surface SM and scPDSIpm increases by ~25%–100% (50%–200%) under the SSP2-4.5 (SSP5-8.5) scenario in the twenty-first century together with large increases in drought duration and areas, which result from a decrease in the mean and flattening of the probability distribution functions of SM and scPDSIpm, while the R-based drought changes are relatively small. Changes in both P and E contribute to the SM change, whereas scPDSIpm decreases result from ubiquitous PET increases and P decreases over subtropical areas. The R changes are determined primarily by P changes, while the PET change explains most of the E increase. Intermodel spreads in surface SM and R changes are large, leading to large uncertainties in the drought projections.
Journal Article
Fréchet analysis of variance for random objects
Fréchet mean and variance provide a way of obtaining a mean and variance for metric space-valued random variables, and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and operations. Examples of such data objects include covariance matrices, graph Laplacians of networks and univariate probability distribution functions. We derive a central limit theorem for the Fréchet variance under mild regularity conditions, using empirical process theory, and also provide a consistent estimator of the asymptotic variance. These results lead to a test for comparing k populations of metric space-valued data objects in terms of Fréchet means and variances. We examine the finite-sample performance of this novel inference procedure through simulation studies on several special cases that include probability distributions and graph Laplacians, leading to a test for comparing populations of networks. The proposed approach has good finite-sample performance in simulations for different kinds of random objects. We illustrate the proposed methods by analysing data on mortality profiles of various countries and resting-state functional magnetic resonance imaging data.
Journal Article
Genome sequence of Gossypium herbaceum and genome updates of Gossypium arboreum and Gossypium hirsutum provide insights into cotton A-genome evolution
Upon assembling the first
Gossypium herbaceum
(A
1
) genome and substantially improving the existing
Gossypium arboreum
(A
2
) and
Gossypium hirsutum
((AD)
1
) genomes, we showed that all existing A-genomes may have originated from a common ancestor, referred to here as A
0
, which was more phylogenetically related to A
1
than A
2
. Further, allotetraploid formation was shown to have preceded the speciation of A
1
and A
2
. Both A-genomes evolved independently, with no ancestor–progeny relationship. Gaussian probability density function analysis indicates that several long-terminal-repeat bursts that occurred from 5.7 million years ago to less than 0.61 million years ago contributed compellingly to A-genome size expansion, speciation and evolution. Abundant species-specific structural variations in genic regions changed the expression of many important genes, which may have led to fiber cell improvement in (AD)
1
. Our findings resolve existing controversial concepts surrounding A-genome origins and provide valuable genomic resources for cotton genetic improvement.
Assembly of the first
Gossypium herbaceum
genome and improved
Gossypium arboreum
and
Gossypium hirsutum
genomes provide insights into the phylogenetic relationships and origin history of cotton A-genomes.
Journal Article
Confined active Brownian particles: theoretical description of propulsion-induced accumulation
The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.
Journal Article