Unique Probability Research Articles

Intentional learning establishes multiple attentional sets that simultaneously guide attention.

One of the key human cognitive capabilities is to extract regularities from the environment to guide behavior. An attentional set for a target feature can be established through statistical learning of probabilistic target associations; however, whether an array of attentional sets of predictive target features can be established during intentional learning, and how they might guide attention, is not known yet. To address these questions, we had human observers perform a visual search task where we instructed them to try to use color to find their target shape. We structured the task with a fine-grained statistical regularity such that the target shapes appeared in different colors with five unique probabilities (i.e., 33%, 26%, 19%, 12%, and 5%) while we recorded their electroencephalogram. Observers rapidly learned these regularities, evidenced by being faster to report targets that appeared in higher probability colors. These effects were not due to unequal sample sizes or simple feature priming. More importantly, equivalent speeding across a set of high-probability colors suggests that the brain was driving attention to multiple targets simultaneously. Our electrophysiological results showed larger amplitude N2 posterior contralateral component, indexing perceptual attention, and late positive complex (LPC) component, indexing postperceptual processes, for targets paired with high-probability colors. These electrophysiological data suggest that the learned attentional sets change both perceptual selection and how postperceptual decisions are made. In sum, we show that multiple attentional sets can be established during intentional learning that accompanies general task acquisition and that these attentional sets can simultaneously guide attention by enhancing both perceptual attention and postperceptual processes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials

We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori–Zwanzig approach, we represent the system by a class of Markovian dynamics. Under a general set of conditions on the nonlinearities, we study the large-time asymptotics of the multi-particle Markovian GLEs. We show that the system is always exponentially attractive toward the unique invariant Gibbs probability measure. The proof relies on a novel construction of Lyapunov functions. We then establish the validity of the small-mass approximation for the solutions by an appropriate equation on any finite-time window. Important examples of singular potentials in our results include the Lennard–Jones and Coulomb functions.

Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process

In this paper, we explore and analyze a stochastic epidemiological model with vaccination and two mean-reverting Ornstein-Uhlenbeck processes to describe the dynamics of HBV transmission. Our study begins by deriving a sufficient condition for the extinction of hepatitis B. Additionally, we determine the presence of a stationary distribution using the Markov process stability theory. Next, we utilize algebraic equation theory and the associated Fokker-Planck equation to derive an explicit expression for the unique probability density function. To validate our theoretical findings, we conduct several numerical simulations using hepatitis B data provided by the World Health Organization (WHO). The results of these simulations support and complement our analytical approach.

Paradox? What paradox?

AbstractThis article is a response to the preceding paper by Huang, who considers a recent result of Willink (Measurement: Sensors, 24:100416, 2022) and who describes the result as a paradox. The result implied that a set of information or a “state of knowledge” about a measurand cannot be identified with a unique probability distribution for the measurand, contrary to what seems suggested in the literature surrounding the revision of the Guide to the Expression of Uncertainty in Measurement. The result is restated and viewed in the context of CIPM Recommendation INC-1, which was foundational in the original development of the Guide. It is argued that the result is a proof, not a paradox, and that it will only appear paradoxical to those who have adopted an incorrect premise about probability. The idea of having “information” about the true value of a measurand is discussed and contrasted with the idea of having “belief” about it. The material supports the view that the analysis of measurement uncertainty is to be based on classical statistical principles.

Optimal Weak Order and Approximation of the Invariant Measure with a Fully-Discrete Euler Scheme for Semilinear Stochastic Parabolic Equations with Additive Noise

In this paper, we consider the ergodic semilinear stochastic partial differential equation driven by additive noise and the long-time behavior of its full discretization realized by a spectral Galerkin method in spatial direction and an Euler scheme in the temporal direction, which admits a unique invariant probability measure. Under the condition that the nonlinearity is once differentiable, the optimal convergence orders of the numerical invariant measures are obtained based on the time-independent weak error, but not relying on the associated Kolmogorov equation. More precisely, the obtained convergence orders are O(λN−γ) in space and O(τγ) in time, where γ∈(0,1] from the assumption ∥Aγ−12Q12∥L2 is used to characterize the spatial correlation of the noise process. Finally, numerical examples confirm the theoretical findings.

Optogenetic inhibition of the caudal substantia nigra inflates behavioral responding to uncertain threat and safety.

Defensive responding is adaptive when it approximates the current threat but maladaptive when it exceeds the current threat. Here we asked if the substantia nigra, a region consistently implicated in reward, is necessary to show appropriate levels of defensive responding in Pavlovian fear discrimination. Rats received bilateral transduction of the caudal substantia nigra with halorhodopsin or a control fluorophore and bilateral ferrule implants. Rats then behaviorally discriminated cues predicting unique foot shock probabilities (danger, p = 1; uncertainty, p = .25; and safety, p = 0). Green-light illumination (532 nm) during cue presentation inflated defensive responding of halorhodopsin rats-measured by suppression of reward seeking-to uncertainty and safety beyond control levels. Green-light illumination outside of cue presentation had no impact on halorhodopsin or control rat responding. The results reveal caudal substantia nigra cue activity is necessary to inhibit defensive responding to nonthreatening and uncertain threat cues. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Prospective validation of a unique pretest probability score for preoperative deep vein thrombosis

Abstract Background Venous thromboembolism is a crucial perioperative complication. We developed a pretest probability score (KAGOSHIMA DVT score) for predicting deep vein thrombosis (DVT) before surgery. The purpose of our study was to validate KAGOSHIMA DVT score prospectively. Methods KAGOSHIMA DVT score was assigned 2 points to D-dimer ≥ 1.5 μg/mL and 1 point each to age ≥ 60 years, female, ongoing glucocorticoid therapy, cancer with high risk of DVT and prolonged immobility. KAGOSHIMA DVT score of 3 points or higher was defined as intermediate group, 5 or higher as high group. We included a total of 4051 patients planned surgery under general anesthesia between May 2022 and February 2023. 452 patients were performed whole leg ultrasonography suspected DVT using a cutoff point of D-dimer ≥ 1μg/ml, KAGOSHIMA DVT score of 3 points or higher. We excluded aneurysm, pregnancy, ongoing anticoagulant therapy, and other thrombosis. We validated 253 patients of the presence of DVT. Results DVT was detected in 93/253 (36.8%) patients, 64/200 (32%) in the intermediate probability group, and 29/53 (54.7%) in the high group, respectively. The prevalence of DVT increased with each increase in KAGOSHIMA DVT score. D-dimer ≥ 1.5 μg/mL (92% vs 100%, p=0.033), age ≥ 60 years (86.5% vs 96.2%, p=0.048), female (53% vs 96.2%, p<0.001), glucocorticoids (6.5% vs 22.6%, p=0.001), active cancer with high risk of DVT (23% vs 64.2%, p<0.001), and prolonged immobility (4.5% vs 22.6%, p<0.001) were significantly higher in the high probability group than the intermediate group. The number of whole-leg ultrasonography decreased from 461 to 253(54.7%) during the same period. In the intermediate group, the detection rate of DVT was a significantly higher in the prospective study than in the retrospective study (21.4% vs 32%, p=0.012). In the high probability group, there was no significant difference (48.2% vs 54.7%, p=0.49). Conclusion KAGOSHIMA DVT score stratified perioperative DVT probability and was useful to detect DVT prospectively.rate of DVT

Contracting on average iterated function systems by metric change

We study contraction conditions for an iterated function system (IFS) of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space, which turn the IFS into one which is contracting on average. For the particular case of a system of C 1-diffeomorphisms of the circle which is proximal and does not have a probability measure simultaneously invariant by every map, we derive an equivalent metric which contracts on average and conclude that it carries a unique stationary probability measure. Here we strongly use local contraction properties established by Malicet in 2017, which then imply that the IFS has a negative random Lyapunov exponent and generalizes a result by Baxendale.

Simulation Analysis of Dynamic Damage Probability Modelling for Laser Systems

The paper proposes a method that analyses the dynamic damage probability of laser systems to address the shortcomings of the quantitative model for the damage probability of laser systems. Firstly, the far-field energy density distribution model is constructed according to the power spectrum inversion method. Then, the instantaneous on-target spot power density distribution is equivalently portrayed based on the combination of the far-field power density and the missile target characteristics. Next, the instantaneous on-target spot is combined with the tracking and aiming error to obtain the probability distribution of the energy density of the long-period on-target spot. Finally, the temperature probability distribution is obtained by analyzing the relation between the target energy density and the temperature of the inner wall of the warhead. Consequently, the damage probability was calculated. The simulation shows that there is a unique maximum damage probability when the target is flying in a straight line and the laser system strikes the missile sideways. The method can provide support for the shooting timing of high-energy laser systems.

Prediction of centrifugal pump performance parameters based on a multilayer hybrid model

The present paper presents a multilayer hybrid model for sensorless measurement of pump operating status, with the objective of enabling safe and stable operations while reducing energy losses. The model takes easily measurable variables such as rotational frequency and valve opening as input features to predict the performance parameters of the centrifugal pump. By integrating just-in-time learning (JITL) with Gaussian process regression (GPR) and leveraging the unique probability features of GPR, a just-in-time-learning GPR (JGPR) is developed to extract valuable feature information. The JGPR sequentially predicts the flow rate, coefficient for dynamic head, and shaft power. The predicted values are extended to other input features, which can accurately capture the characteristics of the centrifugal pump and effectively replace the process of acquiring process parameters through sensors. Finally, the mechanism model is integrated into the multilayer JGPR model to calculate the performance parameters of centrifugal pump. The validation results indicate a strong agreement between predicted and experimental results, with predicted meeting performance parameters all engineering requirements. Compared to a single model, the multilayer hybrid model significantly improves the reliability of predictions, demonstrating the feasibility of using this approach to predict performance parameters. This research provides valuable insights into the measurement of sensorless pump operating states, enabling safe and efficient operation in complex conditions.

Modeling and dynamic analysis of a stochastic mutualism model with distributed delays

A stochastic two-species mutualism model that incorporates nonlinear perturbations and distributed delays is proposed and analyzed in this paper, in where saturation effects and distributed delays with weak kernel are contained in the interspecies mutualism term. We first investigate that a nonlinear stochastic mutualism model possesses a unique global positive solution regarding arbitrarily given initial value. Therewith the sufficient conditions for two-species extinction and the existence of a unique stationary distribution (USD) are obtained. Whereafter, it is derived that the stationary solution near the quasi-positive equilibrium adheres a unique probability density function with the aid of tackling Fokker–Planck (FP) equation corresponding to the linearized system and applying the theory of algebraic equations we have developed. At last, several numerical examples are presented to validate the validity of our theoretical findings.

Distributional Censored and Uncensored Validation Testing under a Modified Test Statistic with Risk Analysis and Assessment

This paper introduces and studies a unique probability distribution. The maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson–Darling estimation methods all take into account a number of financial risk indicators, including the value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These four approaches were used in a simulation study and an application to insurance claims data for the actuarial evaluation. The well-known Nikulin–Rao–Robson statistic is taken into consideration for distributional validation under the whole set of data. Three complete actual datasets and a simulation study are used to evaluate the Nikulin–Rao–Robson test statistic. An updated version of the Nikulin–Rao–Robson statistic is taken into consideration for censored distributional validation. Three censored actual datasets and a thorough simulation analysis are used to evaluate the novel Nikulin–Rao–Robson test statistic.

Statistical learning speeds visual search: More efficient selection, or faster response?

Learning statistical regularities of target objects speeds visual search performance. However, we do not yet know whether this statistical learning effect is driven by biasing attentional selection at the early perceptual stage of processing, as theories of attention propose, or by improving the decision-making efficiency at a late response-related stage. Leveraging the high-temporal resolution of the event-related potential (ERP) technique, we had 16 human observers perform a visual search task where we inserted a fine-grained statistical regularity that the target shapes appeared in different colors with six unique probabilities. Observers unintentionally learned these regularities such that they were faster to report targets that appeared in more likely target colors. The observers' ERPs showed that this learning effect resulted in subjects making faster decisions about the target presence, and not by preferentially shifting attention to more rapidly select likely target colors, as is often assumed by the attentional selection account, supporting a post-selection account for statistical learning of the probabilistic regularities of target features. These results provide fundamental insights into the attentional control mechanisms of statistical learning. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

On the spectral theory of groups of automorphisms of S-adic nilmanifolds

AbstractLet $S=\{p_1, \ldots , p_r,\infty \}$ for prime integers $p_1, \ldots , p_r.$ Let X be an S-adic compact nilmanifold, equipped with the unique translation-invariant probability measure $\mu .$ We characterize the countable groups $\Gamma $ of automorphisms of X for which the Koopman representation $\kappa $ on $L^2(X,\mu )$ has a spectral gap. More specifically, let Y be the maximal quotient solenoid of X (thus, Y is a finite-dimensional, connected, compact abelian group). We show that $\kappa $ does not have a spectral gap if and only if there exists a $\Gamma $ -invariant proper subsolenoid of Y on which $\Gamma $ acts as a virtually abelian group,

Probabilistic causal bipolar abstract argumentation: an approach based on credal networks

The Bipolar Argumentation Framework approach is an extension of the Argumentation Framework. A Bipolar Argumentation Framework considers a support interaction between arguments, besides the attack interaction. As in the Argumentation Framework, some researches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a Bipolar Argumentation Framework under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real application domains there is a need for aggregating probability values from different sources so it is not suitable to aggregate such probability values in a unique probability distribution. To tackle this challenge, we use credal networks theory for modelling the uncertainty of the degree of belief of arguments in a BAF. We also propose an algorithm for calculating the degree of uncertainty of the extensions inferred by a given argumentation semantics. Moreover, we introduce the idea of modelling the support relation as a causal relation. We formally show that the introduced approach is sound and complete w.r.t the credal networks theory.

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis–Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving a complex differential model, which is then approximated on a sequence of increasingly accurate discretizations. The key point of this algorithm is to construct highly coupled Markov chains together with the standard multilevel Monte Carlo argument to obtain a better cost-tolerance complexity than a single-level MCMC algorithm. Our method extends the ideas of Dodwell et al., [SIAM/ASA J. Uncertain. Quantif., 3 (2015), pp. 1075–1108] to a wider range of proposal distributions. We present a thorough convergence analysis of the ML-MCMC method proposed, and show, in particular, that (i) under some mild conditions on the (independent) proposals and the family of posteriors, there exists a unique invariant probability measure for the coupled chains generated by our method, and (ii) that such coupled chains are uniformly ergodic. We also generalize the cost-tolerance theorem of Dodwell et al. to our wider class of ML-MCMC algorithms. Finally, we propose a self-tuning continuation-type ML-MCMC algorithm. The presented method is tested on an array of academic examples, where some of our theoretical results are numerically verified. These numerical experiments evidence how our extended ML-MCMC method is robust when targeting some pathological posteriors, for which some of the previously proposed ML-MCMC algorithms fail.

Environmental variability in a stochastic HIV infection model

In this paper, a stochastic HIV infection model with the Ornstein–Uhlenbeck process is established and studied. It is assumed that the death rate of healthy CD4+ T cells satisfies the Ornstein–Uhlenbeck process. First, we verify that the stochastic model has an unique global solution for any initial value. Then, using Markov semigroup technique, we obtain the sufficient criteria for the existence of a stable stationary distribution to the stochastic system, which reflects the strong persistence of all CD4+ T cells and HIV virus particles. Furthermore, it is deduced that the above global solution around the endemic equilibrium follows an unique probability density function by solving the corresponding Fokker–Planck equation and having to apply our developed algebraic equation theory. The necessary conditions for the exponential extinction of HIV infection are established for completeness. Finally, several numerical simulations are provided to validate our theories.

Fractional Probability Theory of Arbitrary Order

A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability density function (fractional PDF) is proposed. The basic properties of the fractional PDF are proven. The definition of the fractional cumulative distribution function (fractional CDF) is also suggested, and the basic properties of these functions are also proven. It is proven that the proposed fractional cumulative distribution functions generate unique probability spaces that are interpreted as spaces of a fractional probability theory of arbitrary order. Various examples of the distributions of the fractional probability of arbitrary order, which are defined on finite intervals of the real line, are suggested.

The composition of the choice set modulates probability weighting in risky decisions.

Probability distortion-the tendency to underweight larger probabilities and overweight smaller ones-is a robust empirical phenomenon and an important driver of suboptimal choices. We reveal a novel contextual effect on probability distortion that depends on the composition of the choice set. Probability distortion was larger in a magnitude-diverse choice set (in which participants encountered more unique magnitudes than probabilities) but declined, resulting in more veridical weighting, in a probability-diverse choice set(more unique probabilities than magnitudes). This effect was consistent in two, large, independent datasets (N = 481, N = 100) and held for a subset of lotteries that were identical in the two contexts. It also developed gradually as a function of exposure to the choice set, was independent of attentional biases to probability versus magnitude information, and was specific to probability weighting, leaving risk attitudes unaffected. The results highlight the importance of context when processing probabilistic information.

I-VITAL: Information aided visual tracking with adversarial learning

With the advent of convolutional neural networks (CNN), MDNet and the Siamese trackers posed tracking as supervised learning. They model an object’s presence using classification (foreground and background) and location using regression. For the first time, we have brought probability distribution into the CNN framework for tracking. We have selected “Information maximization Generative Adversarial Network (InfoGAN)” to couple the target and background classes with two unique Gaussian distributions. This paper highlights the use of InfoGAN in information extraction & feedback to improve the tracking framework. Specifically, the novel features proposed in this tracking framework are (i) Coupling of unique probability distributions to target and background classes and (ii) Unsupervised tracker status (success/ failure) identification and correction through information feedback. We demonstrated the efficacy of the proposed I-VITAL tracker in visual tracking with experimental comparisons on well-known data sets such as GOT10K, VOT2020, and OTB-2015. Compared with base works, the proposed tracker has improved performance in locating the object of interest.