Uniform Probability Research Articles

A homogenization-based model of the Gurson type for porous metals comprising randomly oriented spheroidal voids

In this work, we propose a new fully explicit isotropic, rate-independent, elasto-plastic model for porous materials comprising a random with uniform probability, isotropic distribution of randomly oriented spheroidal voids of the same shape. The proposed model is based on earlier homogenization estimates that use a linear comparison composite theory. The resulting expressions exhibit the simplicity of the well known Gurson model and, thus, its numerical implementation in a finite element code is straightforward. To assess the accuracy of the analytical model, we carry out detailed finite-strain, three-dimensional finite element (FE) simulations of representative volume elements (RVEs) with the corresponding microstructures. Proper minimal parameter calibration of the model leads to fairly accurate agreement of the analytical predictions with the corresponding FE average stresses and porosity evolution. We show, both analytically and numerically, that the initial aspect ratio of the voids has a significant effect on the homogenized yield surface of the porous material leading to extremely soft responses for flat oblate voids (e.g. aspect ratio less than 0.5) especially at large triaxialities. Finally, after numerical implementation of the model in a commercial finite element code (ABAQUS), we solve the industrially important problem of hole expansion and comment on the role of porous compressible plasticity versus classical incompressible plasticity.

Processes Towards Sedimentation around a Reed Island in a Shallow Lake

There are many studies on the hydromorphological impacts of emergent aquatic vegetation, but many of these focus on gravity-driven flows in riverine or tidal environments. However, an added effect of emergent vegetation in lakes is that it reduces the main external force (wind) significantly and in a spatially coherent way. We performed long Monte Carlo simulations using a 2D hydrodynamic model and a spectral wind wave model to study resuspension dynamics around a 100-m-wide reed island in southern Lake Fertő/Neusiedl. Wave-current interaction, computed in a post-processing step, was found to enhance maximum bed shear stresses only on the leeward side of the reed island, and even there to a small extent. We have found evidence that the present bed topography is close to an equilibrium where simulated combined wave-current shear stresses have a reasonably uniform exceedance probability over the critical shear stress of the bed sediment. We also found that an artificially flattened lakebed around the reed island would start evolving towards the present bed topography and grain size distribution (both of which were surveyed in the field). Despite the limitations of our modelling framework, our results illustrate the importance of how wind climate is translated to an uneven distribution of sediment entrainment around the reed island, explaining tendencies of sediment accumulation and sorting. Our results lead to a better understanding of the complicated processes involving interaction among wind, vegetation, circulation, wind waves, sediment and bathymetry.

Uniform chi-squared model probabilities in NMR crystallography

The UC model assigns likelihoods to candidate structures in NMR crystallography based on a hierarchical Bayesian framework.

The Overall Collection Efficiency of Catching‐Type Precipitation Gauges in Windy Conditions

AbstractThe wind‐induced bias of catching‐type precipitation measurement instruments is quantified using Computational Fluid Dynamics with embedded liquid (raindrops) and solid (snowflakes) particle tracking. The performance of six common commercial gauges having different outer geometry is compared under a range of Precipitation Intensity (PI) and wind speed conditions by means of the numerically calculated catch ratios. Validation of the simulated aerodynamic behavior and its effect on water drop trajectories is provided by previous wind tunnel experiments. The functional dependence of the overall collection efficiency on the PI is derived as a quantitative measure of the instrument performance under a wind climatology with a uniform probability density function. Instruments with aerodynamic design produce a less pronounced diversion of hydrometeor trajectories—at any given size—than those having more traditional geometry. For liquid precipitation measurements, chimney‐shaped instruments rank low, while inverted conical and Nipher shielded instruments are quite performant solutions. The investigated quasi‐cylindrical gauges have intermediate behavior depending on their detailed aerodynamic features. For solid precipitation, all instruments rank low at light to moderate PI, except the Nipher shielded gauge. Results allow selecting the appropriate instrument for the local precipitation climatology at the measurement site and can be used to apply suitable adjustments to the measured precipitation.

Uncertainty Cost Functions for Renewable Generation: A Simplified Approach using a Mixture of Uniform Probability Distribution

Photovoltaic energy, wind energy, and plug-in electric/hybrid vehicles are being considered as sources and loads, reflecting the increasing importance of renewable energy resources in new microgrids. However, the stochastic behavior of variables such as wind turbine speed, solar irradiation intensity and, plugin electric vehicle dynamics, introduces uncertainties that could affect the economic dispatch of electric power. This paper employs a mixture of uniform probability distribution (UPDs) techniques to characterize the variability of the available power from renewable energy sources. We propose a new analytical expression derived from the mixture of UPDs to calculate Uncertainty Cost Functions (UCFs), thereby assessing their impact on the economic dispatch of power. Finally, we performed Montecarlo simulations to validate our UCF methodology and its potential applicability in economic dispatch of power. The results demonstrate that our methodology accurately calculates the underestimated and overestimated costs of uncertainty power generation. This methodology holds the potential to optimize economic dispatch, thereby reducing costs and maximizing power generation from the generators.

Multidimensional uniform semiclassical instanton thermal rate theory

Instanton-based rate theory is a powerful tool that is used to explore tunneling in many-dimensional systems. Yet, it diverges at the so-called “crossover temperature.” Using the uniform semiclassical transmission probability of Kemble [Phys. Rev. 48, 549 (1935)], we showed recently that in one dimension, one might derive a uniform semiclassical instanton rate theory, which has no divergence. In this paper, we generalize this uniform theory to many-dimensional systems. The resulting theory uses the same input as in the previous instanton theory, yet does not suffer from the divergence. The application of the uniform theory to dissipative systems is considered and used to revise Wolynes’ well-known analytical expression for the rate [P. G. Wolynes, Phys. Rev. Lett. 47, 968 (1981)] so that it does not diverge at the “crossover temperature.”

Equitable Top-k Results for Long Tail Data

For datasets exhibiting long tail phenomenon, we identify a fairness concern in existing top-k algorithms, that return a "fixed" set of k results for a given query. This causes a handful of popular records (products, items, etc) getting overexposed and always be returned to the user query, whereas, there exists a long tail of niche records that may be equally desirable (have similar utility). To alleviate this, we propose θ-Equiv-top-k-MMSP inside existing top-k algorithms - instead of returning a fixed top-k set, it generates all (or many) top-k sets that are equivalent in utility and creates a probability distribution over those sets. The end user will be returned one of these sets during the query time proportional to its associated probability, such that, after many draws from many end users, each record will have as equal exposure as possible (governed by uniform selection probability). θ-Equiv-top-k-MMSP is formalized with two sub-problems. (a) θ-Equiv-top-k-Sets to produce a set S of sets, each set has k records, where the sets are equivalent in utility with the top-k set; (b) MaxMinFair to produce a probability distribution over S, that is, PDF(S), such that the records in S have uniform selection probability. We formally study the hardness of θ-Equiv-top-k-MMSP. We present multiple algorithmic results - (a) An exact solution for θ-Equiv-top-k-Sets, and MaxMinFair. (b) We design highly scalable algorithms that solve θ-Equiv-top-k-Sets through a random walk and is backed by probability theory, as well as a greedy solution designed for MaxMinFair. (c) We finally present an adaptive random walk based algorithm that solves θ-Equiv-top-k-Sets and MaxMinFair at the same time. We empirically study how θ-Equiv-top-k-MMSP can alleviate a equitable exposure concerns that group fairness suffers from. We run extensive experiments using 6 datasets and design intuitive baseline algorithms that corroborate our theoretical analysis.

Reconstruction Guided Meta-Learning for Few Shot Open Set Recognition.

In many applications, we are constrained to learn classifiers from very limited data (few-shot classification). The task becomes even more challenging if it is also required to identify samples from unknown categories (open-set classification). Learning a good abstraction for a class with very few samples is extremely difficult, especially under open-set settings. As a result, open-set recognition has received limited attention in the few-shot setting. However, it is a critical task in many applications like environmental monitoring, where the number of labeled examples for each class is limited. Existing few-shot open-set recognition (FSOSR) methods rely on thresholding schemes, with some considering uniform probability for open-class samples. However, this approach is often inaccurate, especially for fine-grained categorization, and makes them highly sensitive to the choice of a threshold. To address these concerns, we propose Reconstructing Exemplar-based Few-shot Open-set ClaSsifier (ReFOCS). By using a novel exemplar reconstruction-based meta-learning strategy ReFOCS streamlines FSOSR eliminating the need for a carefully tuned threshold by learning to be self-aware of the openness of a sample. The exemplars, act as class representatives and can be either provided in the training dataset or estimated in the feature domain. By testing on a wide variety of datasets, we show ReFOCS to outperform multiple state-of-the-art methods.

Bayesian Risk Assessment Technique for Economic Stress-Strength Models

This paper explores two areas of risk assessment modelling in economics and business: the Stress-Strength model and Bayesian techniques. The model assumes that the probability of stress exceeding strength is a measure of risk. The interpretation of stress and strength largely depends on the particular event or phenomenon being modelled. The use of the Stress-Strength model is demonstrated through the Gaussian assumption of probability distributions for random model parameters, particularly in assessing the risk of not achieving a required margin value. The concept of the capability function, representing the difference between strength and stress, is introduced in the modelling process. The probability distribution for the capability function is initially determined based on the Gaussian distribution of the random variables used in the model, allowing for evaluating the risk metric. The Bayesian approach is then applied to generalise the problem statement when dealing with unknown parameters of probability distributions for the Stress and Strength models. The uncertainty of these parameters is modelled through uniform probability distributions, and equations for calculating prior and posterior estimates are consistently obtained. Since multidimensional integrals are involved in these calculations, and solutions cannot be obtained in closed analytical form, Monte Carlo simulation is used to solve this computation problem.

Substitution box generator with enhanced cryptographic properties and minimal computation time

With the widespread use of digital devices and the internet, implementing advanced security systems is essential to protect confidential information from cyberattacks and unauthorized access. The substitution box (S-box) is an integral part of security systems that confuses confidential data. Randomized or optimized S-box generators are commonly used in these systems. The former aims to generate highly key-dependent dynamical S-boxes, while the latter generates static S-boxes with optimal cryptographic properties. However, the process of generating S-boxes is computationally expensive, which limits the attainable encryption throughput. This highlights the need to develop new S-box generators that can offer optimal security with minimal computational overhead. We utilized the high resistance of elliptic curves against modern cryptanalysis to propose a novel S-box generator capable of generating both randomized and optimized S-boxes in minimal computation time. The proposed generator has three phases. In the first phase, it generates points on an elliptic curve, converts their coordinates into binary form, and merges them. The second phase diffuses the binary sequences to calculate indices for swapping operations. In the final phase, swapping operations are applied to the initial S-box, resulting in a randomized S-box. For optimizing the S-box, a simplified version of the generator is introduced by omitting swapping operations that reduce nonlinearity in the resulting S-box. The dynamic behavior of the proposed generator is analyzed by proving necessary conditions for outputting distinct S-boxes and ensuring that the resultant S-boxes have a uniform probability distribution. Rigorous security analysis reveals that our generator can output S-boxes with strong cryptographic properties. A detailed comparison indicates that our method is at least 10 times faster than the fastest available randomized generator, while maintaining comparable cryptographic properties. Furthermore, the proposed generator achieves higher nonlinearity of 108 compared to the best available optimized S-box generator with minimal computation time. Our theoretical and computational analyses suggest that our S-box generator is a promising candidate for practical applications that can effectively address the modern security threats and computational time demands. Specifically, we demonstrate the application of our S-box generator by integrating it into an image encryption scheme.

Some New Results Involving Past Tsallis Entropy of Order Statistics.

This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events. In addition, we investigate how to find a bound for the new dynamic information measure related to the lifetime unit under various conditions and whether it is monotonic with respect to the time when the device is idle. By exploring these properties and also investigating the monotonic behavior of the new dynamic information measure, we contribute to a broader understanding of order statistics and related entropy quantities.

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees.

Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (stimulated emission depletion (STED)) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

Does the Best System Need the Past Hypothesis?

AbstractMany philosophers sympathetic with Humeanism about laws have thought that the fundamental laws will include not only the traditional dynamical equations, but also two additional principles: the Past Hypothesis (PH) and the Statistical Postulate (SP). PH says that the universe began in a particular very-low-entropy macrostate M(0), and SP posits a uniform probability distribution over the microstates compatible with M(0). This view is arguably vindicated by the orthodox Humean Best System Account (BSA). However, I argue that recent developments of the BSA render the Past Hypothesis otiose. In particular, Pragmatic Humeanism does not support the idea that PH is a law.

Aging decreases the precision of visual working memory

ABSTRACT Objectives As individuals age, cognitive abilities such as working memory (WM), decline. In the current study, we investigated the effect of age on WM, and elucidated sources of errors. Method A total of 102 healthy individuals, aged 18 to 71, participated in this research. We designed and administered a face-based visual WM task, collecting responses via a graded scale in a delayed match-to-sample reproduction task. Results The error of participants increased significantly as they aged. Our analysis revealed a significant age-related rise in the standard deviation of error distribution. However, there was no significant change in uniform probability with age. Conclusion We found that WM performance declines through the lifespan. Investigating the sources of error, we found that the precision of WM decreased monotonously with age. The results also indicated that the probability of guessing the response as a measure of random response is not affected by age.

A contribution to the investigation of acoustic interferences in aircraft distributed propulsion

The objective of this work is to better understand the acoustic interferences created by distributed propulsion engines based on an approach that combines RANS simulation results for the aerodynamic prediction and analytical models to calculate acoustics. A multi-propeller configuration without wing is considered for this investigation. The propeller geometry and the operating conditions are realistic for a regional transport airplane. In the first part of the paper, the results obtained by two different and independent prediction methods are compared. One method is well-established and serves as validation for the second, low-order method, which is better suited for design-to-noise applications since it requires less details as input and is computationally faster by several orders of magnitude. The good agreement between both methods, obtained for a single propeller as well as for the distributed propeller configuration, is exploited in the second part of the paper to investigate the role of acoustic interferences. Taking acoustic interferences into account drastically affects the directivity of the tonal emission. Compared to the results obtained by considering the propellers as if they were uncorrelated, the far-field sound pressure levels can be significantly lower at the radiation nodes or amplified up to the theoretical limit of 9 dB calculated for eight propellers. The directivity patterns depend on the relative initial angular positions of the propellers. When these positions are randomly varied according to the uniform probability density distribution model, the mean result (expectation) is the same as if the propellers were considered as uncorrelated. Finally, the results show that the probability that the acoustic level is lower than the mean value is higher than 50% because of the positive skewness of the probability distribution of the resulting pressure amplitude. Even though the propeller–propeller and propeller–wing interactions were not considered, the essence of the findings is expected to remain valid for more complex configurations because those interactions are rotor phase-locked.

Uniform probability in cosmology

Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.

R] Inferential Statistics IV: Uniform and (Standard) Normal Probability (Density) Functions

R] Inferential Statistics IV: Uniform and (Standard) Normal Probability (Density) Functions

Effect of porosity and pore size distribution on elastic modulus of foams

In this study, we investigate the impact of pore distribution and size on the mechanical response of elastic porous materials. Two-dimensional porous media with convex porosity are considered (e.g., foams and sponges). These structures are numerically generated by subtracting randomly dispersed circular holes from a solid square domain. The in-plane position vector of pore centers is given by a uniform probability density function (PDF). The pore diameters are, instead, drawn from a non-uniform two-parameter continuous probability distribution. The influence of the void ratio, i.e., the volume fraction of voids, and the parameters of the diameter PDF are studied over a wide range of values, including the percolation threshold, where the effective elastic modulus of the material abruptly drops to zero. This transition takes place at a critical value of the void ratio, which turns out to be unaffected by the parameters of the pore size distribution. Our results demonstrate that the elastic response of these structures is primarily governed by the void ratio, with the correlation length playing a secondary role. While the pore size distribution may affect the correlation length, it has a minimal impact on the foam’s overall behavior.

Influence of manufacturing uncertainty treatment on neutronics uncertainty analysis for lattice physics parameters in PWR-UO2 fuel assembly

ABSTRACT This study discussed the practical perspective on the neutronics uncertainty analysis related to manufacturing uncertainties by identifying discrepancies in analysis results due to manufacturing uncertainty treatment. First, the probability density function given for manufacturing uncertainties was focused on. The random sampling-based uncertainty analysis was performed with the normal and uniform probability distributions, using data from Phase I of the OECD/NEA/NSC LWR-UAM benchmark for PWR-UO2 fuel assembly. The results showed that the uncertainty of lattice physics parameters was smaller with the normal distribution, which is explained that broader sampling results were given by the uniform distribution. Then, the influence of manufacturing uncertainty treatment was investigated under the simple assumption, with or without the correlations between the manufacturing uncertainties, considering the total mass of fuel materials and the diameter of fuel rods. With such correlations, the uncertainty analysis results generally became small since the manufacturing uncertainties were modified to be small by calculating the covariance matrix for the manufacturing parameters. Consequently, clarification of the correlation data in the manufacturing process or introduction of a conservative assumption for the correlation condition related to manufacturing parameters is necessary for the appropriate neutronics uncertainty analysis.

Computing the quantumguesswork: a quadratic assignment problem

The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on standard semi-definite programming techniques and therefore lead to approximated results. In contrast, we show that computing the quantum guesswork of qubit ensembles with uniform probability distribution corresponds to solving a quadratic assignment problem and we provide an algorithm that, upon the input of any qubit ensemble over a discrete ring, after finitely many steps outputs the exact closed-form expression of its guesswork. While in general the complexity of our guesswork-computing algorithm is factorial in the number of states, our main result consists of showing a more-than-quadratic speedup for symmetric ensembles, a scenario corresponding to the three-dimensional analog of the maximization version of the turbine-balancing problem. To find such symmetries, we provide an algorithm that, upon the input of any point set over a discrete ring, after finitely many steps outputs its exact symmetries. The complexity of our symmetries-finding algorithm is polynomial in the number of points. As examples, we compute the guesswork of regular and quasi-regular sets of qubit states.