Uniform Probability Distribution Research Articles

Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

In this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.

Canonical Typicality for Other Ensembles than Micro-canonical

AbstractWe generalize Lévy’s lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix $$\rho $$ ρ on a separable Hilbert space $${\mathcal {H}}$$ H , $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) is the most spread-out probability measure on the unit sphere of $${\mathcal {H}}$$ H that has density matrix $$\rho $$ ρ and thus forms the natural generalization of the uniform distribution. We prove concentration-of-measure whenever the largest eigenvalue $$\Vert \rho \Vert $$ ‖ ρ ‖ of $$\rho $$ ρ is small. We use this fact to generalize and improve well-known and important typicality results of quantum statistical mechanics to GAP measures, namely canonical typicality and dynamical typicality. Canonical typicality is the statement that for “most” pure states $$\psi $$ ψ of a given ensemble, the reduced density matrix of a sufficiently small subsystem is very close to a $$\psi $$ ψ -independent matrix. Dynamical typicality is the statement that for any observable and any unitary time evolution, for “most” pure states $$\psi $$ ψ from a given ensemble the (coarse-grained) Born distribution of that observable in the time-evolved state $$\psi _t$$ ψ t is very close to a $$\psi $$ ψ -independent distribution. So far, canonical typicality and dynamical typicality were known for the uniform distribution on finite-dimensional spheres, corresponding to the micro-canonical ensemble, and for rather special mean-value ensembles. Our result shows that these typicality results hold also for $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) , provided the density matrix $$\rho $$ ρ has small eigenvalues. Since certain GAP measures are quantum analogs of the canonical ensemble of classical mechanics, our results can also be regarded as a version of equivalence of ensembles.

Stochastic characterization of navigation strategies in an automated variant of the Barnes maze.

Animals can use a repertoire of strategies to navigate in an environment, and it remains an intriguing question how these strategies are selected based on the nature and familiarity of environments. To investigate this question, we developed a fully automated variant of the Barnes maze, characterized by 24 vestibules distributed along the periphery of a circular arena, and monitored the trajectories of mice over 15 days as they learned to navigate towards a goal vestibule from a random start vestibule. We show that the patterns of vestibule visits can be reproduced by the combination of three stochastic processes reminiscent of random, serial, and spatial strategies. The processes randomly selected vestibules based on either uniform (random) or biased (serial and spatial) probability distributions. They closely matched experimental data across a range of statistical distributions characterizing the length, distribution, step size, direction, and stereotypy of vestibule sequences, revealing a shift from random to spatial and serial strategies over time, with a strategy switch occurring approximately every six vestibule visits. Our study provides a novel apparatus and analysis toolset for tracking the repertoire of navigation strategies and demonstrates that a set of stochastic processes can largely account for exploration patterns in the Barnes maze.

FAST: Filter-Adapted Spatio-Temporal Sampling for Real-Time Rendering

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and spatial denoising is an integral part of the real-time graphics pipeline. The main insight presented in this paper is that we can optimize the samples used in stochastic sampling such that the post-processing error is minimized. The core of our method is an analytical loss function which measures post-filtering error for a class of integrands --- multidimensional Heaviside functions. These integrands are an approximation of the discontinuous functions commonly found in rendering. Our analysis applies to arbitrary spatial and spatiotemporal filters, scalar and vector sample values, and uniform and non-uniform probability distributions. We show that the spectrum of Monte Carlo noise resulting from our sampling method is adapted to the shape of the filter, resulting in less noisy final images. We demonstrate improvements over state-of-the-art sampling methods in three representative rendering tasks: ambient occlusion, volumetric ray-marching, and color image dithering. Common use noise textures, and noise generation code is available at https://github.com/electronicarts/fastnoise.

Inverse Transformation to Generate Neutrosophic Random Variables Following Weibull and Geometric Distributions

In practical applications, we encounter many systems that cannot be studied directly, and the reason for this is due to the nature of the system or to the high cost. Therefore, we resort to the simulation process, which depends on conducting the study on systems similar to real systems, and then projecting these results, if they are appropriate, onto the system. The real system. The simulation process depends on generating a series of random numbers that follow a uniform probability distribution in the field [0, 1], then converting these random numbers into random variables that follow the probability distribution in which the system to be simulated operates. One of the most important conversion methods is the conversion method. The opposite. This method is used for probability distributions in which we can obtain a function inverse of its cumulative distribution function. In two previous researches, we used this method to generate neutrosophic random variables that follow a uniform distribution in the field [a, b] and the exponential distribution. In this research, we present a valuable study to clarify how to use this method. The method for generating neutrosophic random variables follows the Weibull distribution and the geometric distribution, based on what was presented in the classic study and in the research on neutrosophic random number generation.

Generation and Storage of Random Voltage Values via Ring Oscillators Comprising Feedback Field-Effect Transistors.

In this study, we demonstrate the generation and storage of random voltage values using a ring oscillator consisting of feedback field-effect transistors (FBFETs). This innovative approach utilizes the logic-in-memory function of FBFETs to extract continuous output voltages from oscillatory cycles. The ring oscillator exhibited uniform probability distributions of 51.6% for logic 0 and 48.4% for logic 1. The generation of analog voltages provides binary random variables that are stored for over 5000 s. This demonstrates the potential of the ring oscillator in advanced physical functions and true random number generator technologies.

Appearance debiased gaze estimation via stochastic subject-wise adversarial learning

Recently, appearance-based gaze estimation has been attracting attention in computer vision, and remarkable improvements have been achieved using various deep learning techniques. Despite such progress, most methods aim to infer gaze vectors from images directly, which causes overfitting to person-specific appearance factors. In this paper, we address these challenges and propose a novel framework: Stochastic subject-wise Adversarial gaZE learning (SAZE), which trains a network to generalize the appearance of subjects. We design a Face generalization Network (Fgen-Net) using a face-to-gaze encoder and face identity classifier and a proposed adversarial loss. The proposed loss generalizes face appearance factors so that the identity classifier inferences a uniform probability distribution. In addition, the Fgen-Net is trained by a learning mechanism that optimizes the network by reselecting a subset of subjects at every training step to avoid overfitting. Our experimental results verify the robustness of the method in that it yields state-of-the-art performance, achieving 3.89°and 4.42°on the MPIIFaceGaze and EyeDiap datasets, respectively. Furthermore, we demonstrate the positive generalization effect by conducting further experiments using face images involving different styles generated from the generative model.

Simplified Approach for Wind Uncertainty Cost Functions using a Mixture of Uniform Probability Distribution

Wind energy generation is an individual source of energy considered in renewable energy resources. It is completely dependent on the natural process of air blown in the area or past forecasting of air blown data. It is considered an uncertain source of energy and less reliable in the context of real-time energy provisions. To make this wind energy more reliable and consistent, we are introducing a simplified approach for wind uncertainty cost functions based on uniform probability distributions and its evaluation for usage. We have developed analytical mathematics cost functions based on several assumptions and they are constructed using Weibull and Rayleigh probability distributions. The proposed method produces the required results to make this energy reliable and consistent with the distribution networks. Computing time and complexity are less as compared to the other methods to minimize the uncertainty of wind energy.

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.

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.

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.

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.

Private Sampling with Identifiable Cheaters

In this paper we study verifiable sampling from probability distributions in the context of multi-party computation. This has various applications in randomized algorithms performed collaboratively by parties not trusting each other. One example is differentially private machine learning where noise should be drawn, typically from a Laplace or Gaussian distribution, and it is desirable that no party can bias this process. In particular, we propose algorithms to draw random numbers from uniform, Laplace, Gaussian and arbitrary probability distributions, and to verify honest execution of the protocols through zero-knowledge proofs. We propose protocols that result in one party knowing the drawn number and protocols that deliver the drawn random number as a shared secret.

N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium

We consider how a mechanism of final-offer arbitration may be applied to a negotiation between N players attempting to split a unit of wealth. The game model is defined where the arbitrator chooses a fair split from a Dirichlet distribution. For the case of a uniform probability distribution the equilibrium strategy is found as a function of the Harmonic numbers.

Predicting the Future Appearances of Lost Children for Information Forensics with Adaptive Discriminator-Based FLM GAN

This article proposes an adaptive discriminator-based GAN (generative adversarial network) model architecture with different scaling and augmentation policies to investigate and identify the cases of lost children even after several years (as human facial morphology changes after specific years). Uniform probability distribution with combined random and auto augmentation techniques to generate the future appearance of lost children’s faces are analyzed. X-flip and rotation are applied periodically during the pixel blitting to improve pixel-level accuracy. With an anisotropic scaling, the images were generated by the generator. Bilinear interpolation was carried out during up-sampling by setting the padding reflection during geometric transformation. The four nearest data points used to estimate such interpolation at a new point during Bilinear interpolation. The color transformation applied with the Luma flip on the rotation matrices spread log-normally for saturation. The luma-flip components use brightness and color information of each pixel as chrominance. The various scaling and modifications, combined with the StyleGan ADA architecture, were implemented using NVIDIA V100 GPU. The FLM method yields a BRISQUE score of between 10 and 30. The article uses MSE, RMSE, PSNR, and SSMIM parameters to compare with the state-of-the-art models. Using the Universal Quality Index (UQI), FLM model-generated output maintains a high quality. The proposed model obtains ERGAS (12 k–23 k), SCC (0.001–0.005), RASE (1 k–4 k), SAM (0.2–0.5), and VIFP (0.02–0.09) overall scores.

Efficient Data-Driven Machine Learning Models for Cardiovascular Diseases Risk Prediction.

Cardiovascular diseases (CVDs) are now the leading cause of death, as the quality of life and human habits have changed significantly. CVDs are accompanied by various complications, including all pathological changes involving the heart and/or blood vessels. The list of pathological changes includes hypertension, coronary heart disease, heart failure, angina, myocardial infarction and stroke. Hence, prevention and early diagnosis could limit the onset or progression of the disease. Nowadays, machine learning (ML) techniques have gained a significant role in disease prediction and are an essential tool in medicine. In this study, a supervised ML-based methodology is presented through which we aim to design efficient prediction models for CVD manifestation, highlighting the SMOTE technique's superiority. Detailed analysis and understanding of risk factors are shown to explore their importance and contribution to CVD prediction. These factors are fed as input features to a plethora of ML models, which are trained and tested to identify the most appropriate for our objective under a binary classification problem with a uniform class probability distribution. Various ML models were evaluated after the use or non-use of Synthetic Minority Oversampling Technique (SMOTE), and comparing them in terms of Accuracy, Recall, Precision and an Area Under the Curve (AUC). The experiment results showed that the Stacking ensemble model after SMOTE with 10-fold cross-validation prevailed over the other ones achieving an Accuracy of 87.8%, Recall of 88.3%, Precision of 88% and an AUC equal to 98.2%.

The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution

The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution

Stochastic dynamic programming solution to transmission scheduling: Multi sensor-multi process with wireless noisy channel

We investigate sensor scheduling for remote estimation when multiple smart sensors monitor multiple stochastic dynamical systems. The sensors transmit their measurements to a remote estimator through a noisy wireless communication channel. Such a remote estimator can receive multiple packets simultaneously sent by local sensors. Sensors transmit their measurements if their Signal Interference and Noise Ratio (SINR) is above a threshold. We compute the optimal policy for sensor scheduling by minimizing expected error covariance subject to total signal transmissions from all sensors. We model this problem as Markov Decision Process (MDP) with discounted cost per stage in the finite time horizon framework, then we employ stochastic Dynamic Programming as the optimization method. A novel algorithm based on sampling and machine learning techniques is proposed as the approximation. At each phase of the DP algorithm, samples are collected using a uniform probability distribution. The data is used to feed Neural Network (NN) and Random Forest (RF) models for cost function and policy approximation. The results of the proposed framework are supported by simulation examples comparing RF and NN as Approximate DP (ADP). Note that this idea builds a bridge among the recent advances in the area of data science, Machine Learning, and the ADP.