Statistical Properties Research Articles

Toward the Bayesian brain: a generative model of information transmission by vestibular sensory neurons

The relative accessibility and simplicity of vestibular sensing and vestibular-driven control of head and eye movements has made the vestibular system an attractive subject to experimenters and theoreticians interested in developing realistic quantitative models of how brains gather and interpret sense data and use it to guide behavior. Head stabilization and eye counter-rotation driven by vestibular sensory input in response to rotational perturbations represent natural, ecologically important behaviors that can be reproduced in the laboratory and analyzed using relatively simple mathematical models. Models drawn from dynamical systems and control theory have previously been used to analyze the behavior of vestibular sensory neurons. In the Bayesian framework, which is becoming widely used in cognitive science, vestibular sense data must be modeled as random samples drawn from probability distributions whose parameters are kinematic state variables of the head. We show that Exwald distributions are accurate models of spontaneous interspike interval distributions in spike trains recoded from chinchilla semicircular canal afferent neurons. Each interval in an Exwald distribution is the sum of an interval drawn from an Exponential distribution and a Wald or Inverse Gaussian distribution. We show that this abstract model can be realized using simple physical mechanisms and re-parameterized in terms of the relevant kinematic state variables of the head. This model predicts and explains statistical and dynamical properties of semicircular canal afferent neurons in a novel way. It provides an empirical foundation for realistic Bayesian models of neural computation in the brain that underlie the perception of head motion and the control of head and eye movements.

Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems

Abstract We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles, respectively. We derive analytic results for the fluctuations in the number of particles exiting the boundaries of the finite confining box. The statistical properties of this quantity crucially depend on how the system is prepared initially. Two common types of averages employed to understand the impact of initial conditions in stochastic systems are annealed and quenched averages. It is well known that for an infinitely extended system, these different initial conditions produce quantitatively different fluctuations, even in the infinite time limit. We demonstrate explicitly that in finite systems, annealed and quenched fluctuations become equal beyond a system-size dependent timescale, $t \sim L^2$. For diffusing particles, the fluctuations exhibit a $\sqrt{t}$ growth at short times and decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D$, where $D$ is the diffusion constant. Meanwhile, for run-and-tumble particles, the fluctuations grow linearly at short times and then decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D_{\text{eff}}$, where $D_{\text{eff}}$ represents the effective diffusive constant for run-and-tumble particles. To study the effect of confinement in detail, we also analyze two different setups (i) with one reflecting boundary and (ii) with both boundaries open.

The introduction of coinage in Europe did not change pre-existing monetary patterns

IntroductionThis paper investigates whether the introduction of coinage in Europe fundamentally changed pre-existing monetary circulation patterns. By analysing the statistical properties of bronze money before and after the advent of coinage (c. 1500–27 BCE), it challenges the prevailing assumption that coinage revolutionized the use and exchange of money. The research engages with longstanding academic debates between competing theories, which posit that money is either market-driven or state-imposed.MethodsUsing a combination of archaeological data and quantitative analysis, the study examines large datasets of pre-coinage money and early coinage, focusing on weight-based regulation and the log-normal distribution of mass values as key indicators of monetary behaviour.ResultsThe findings reveal that pre-coinage bronze money, consisting of weighed metal fragments, circulated in a manner similar to early coinage. Both forms of money complied with weight-based systems and exhibited log-normal distribution patterns, reflecting structured economic behaviours. The analysis suggests that the introduction of coinage did not lead to a fundamental transformation in how money circulated but rather continued pre-existing patterns.DiscussionThese results challenge the assumption that state-issued coinage marked a watershed moment in the history of monetary economies. The paper proposes that the beginning of coinage introduced a minor technological improvement rather than a revolutionary change in monetary circulation, offering a new perspective on the continuity between pre-coinage and coinage-based economies in ancient Europe.

The Effects of Manufacturing Errors on the Performance of Acoustic Metamaterial Lenses Operating in the MHz Regime

This article explores the use of acoustical metamaterials to design lenses in the megahertz frequency range of relevance to applications in nondestructive testing and medical imaging. In particular, the effect of manufacturing errors on their focusing performance is quantified. A rapid method for including manufacturing errors is described and this is used to perform Monte Carlo simulations of wave pressure fields from lenses with manufacturing errors. In this process, the required time delay distribution for a target focal length is calculated and the acoustical lenses with a chosen unit cell type are designed. Manufacturing errors of the unit cells are then added, considering their statistical properties and a large number of realizations. As an example, an acoustical lens with a focal length of 76 mm at a frequency of 1 MHz is designed using three different unit cell types: steel cross unit cell, resin circular void unit cell, and silicone–resin layered unit cell. Finally, the resulting acoustic pressure fields are computed using a Huygens’ principle model to assess the effects of manufacturing errors on lens performance, i.e., the focal length and the size of the focal spot. It is shown that the performance of lenses consisting of silicone–resin layered units is less affected by the manufacturing errors than for lenses constructed with the other unit cells. This study paves the way for selecting a suitable combination of metamaterial unit cell and manufacturing method to enable acceptable lens imaging performance.

EFFECTS OF LOCALIZED NON-GAUSSIAN ROUGHNESS ON HIGH PRESSURE TURBINE AERO-THERMAL PERFORMANCE: CONVECTIVE HEAT TRANSFER, SKIN-FRICTION AND THE REYNOLDS' ANALOGY

Abstract Compressible direct numerical simulations are conducted to investigate how surface roughness affects the aero-thermal performance of a high pressure turbine vane operating at an exit Reynolds number of 0.59 × 106 and exit Mach number of 0.92. The roughness under investigation here was synthesized with non- Gaussian statistical properties and an amplitude that varies over its chord length — representative of what truly occurs on an in-service vane. Particular attention is directed towards how sys- tematically changing the axial extent of leading edge roughness affects convective heat transfer (Nusselt and Stanton numbers) and aerodynamic drag (skin-friction coefficient) on the pressure and suction surfaces. The results of this investigation demonstrate that moving the larger amplitude roughness further along the suc- tion surface can cause major changes in the blade boundary-layer state. In fact, towards the trailing-edge of one of the rough vanes investigated here, the local skin-friction coefficient increases by a factor of twenty-three (2, 300%) compared to smooth-vane lev- els, whereas the local Stanton number increases by a factor six (600%). The disproportionate rise of drag compared to heat transfer is explored in further detail by quantifying the Reynolds' analogy and by calculating the fractional contributions of pres- sure drag and viscous drag to the total drag force. The effect of varying the inlet turbulence intensity and integral length-scale for a fixed roughness topography is also investigated, along with the Reynolds-number scaling of heat transfer and drag.

A Novel Two‐Stage Reliability Analysis Method Combining Improved Cross‐Entropy Adaptive Sampling and Relevant Vector Machine

ABSTRACTThe computational burden becomes unbearable when reliability analysis involves time‐consuming finite element analysis, especially for rare events. Therefore, reducing the number of performance function calls is the only way to improve computing efficiency. This paper proposes a novel reliability analysis method that combines relevant vector machine (RVM) and improved cross‐entropy adaptive sampling (iCE). In this method, RVM is employed to approximate the limit state surface and iCE is performed based on the constructed RVM. To guarantee the precision of RVM, the first level samples and the last level samples of iCE are used as candidate samples and the last level samples are regenerated along with the RVM updates. To prevent unnecessary updates of RVM, the proposed method considers the positions of the samples in the current design of experiment. In addition, based on the statistical properties of RVM and iCE, an error‐based stopping criterion is proposed. The accuracy and efficiency of the proposed method were validated through four benchmark examples. Finally, the proposed method is applied to engineering problems which are working in extreme environment.

Stochastic Risk Assessment Framework of Deep Shale Reservoirs by a Deep Learning Method and Random Field Theory

Risk assessment of deep shale reservoirs is very important for subsurface energy development. However, due to complex geological environments and physicochemical interactions, shale reservoir fabric parameters exhibit variability. Moreover, the actual investigation and testing information is very limited, which is a typical small-sample problem. In this paper, the heterogeneity and statistical characteristics of deep shale reservoirs are clarified by the measured mechanical parameters. A deep learning method for deep shale reservoirs with limited survey data information is proposed. The variability of deep shale reservoirs is characterized by random field theory. A variable stiffness method and stochastic analysis method are developed to evaluate the risk of deep shale reservoirs. The detailed workflow of the stochastic risk assessment framework is presented. The frequency distribution and failure risk of deep shale reservoirs are calculated and analyzed. The risk assessment of deep shale reservoirs under different model parameters is discussed. The results show that a stochastic risk assessment framework of deep shale reservoirs, using a deep learning method and random field theory, is scientifically reasonable. The scatter plots of the elasticity modulus (EM), cohesive force (CF), and Poisson ratio (PR) distribute along the 45-degree line. The different distributed variables of EM, CF, and PR have a positive correlation. The statistical properties of the measurement data and deep learning data are approximately the same. The principal stress of deep shale follows the normal distribution with significance level 0.1. Under positive copula conditions, the maximum failure probability is 5.99%. Under negative copula conditions, the maximum failure probability is 4.58%. Different copula functions under positive and negative copula conditions have different failure probabilities. For the exponential correlation structure, the minimum failure probability is 3.46%, while the maximum failure probability is 6.19%. The mean failure probability of the EM, CF, and PR of deep shale reservoirs is 4.85%. Different random field-related structures and parameters have different influences on the failure risk.

Numerical investigation of bubble dynamics in ageing foams using a phase-field model

A novel numerical method for simulating liquid foam decay has been developed. This method is based on a phase-field model and captures gas pressure inside the bubbles. It employs an algorithm that includes the spontaneous rupture of foam separating films and coalescence of bubbles. We found that the microstructure evolution in liquid foam in the dry foam limit is predicted. The numerical results demonstrate that the foam ageing dynamics are mapped for the decay process due to successive coalescence events. Moreover, the method is well suited for large-scale microstructure simulations. This allows the investigation of statistical properties of foams, based on the structures’ characteristics at the bubble scale. In summary, the method is effective to gain insight into the impact of fundamental factors controlling the evolution and dynamics of decaying liquid foam.

Structural Analysis of Latticed Steel Transmission Towers Subjected to Nondeterministic Wind Loads

Lattice steel towers are commonly used to support overhead power transmission lines. However, the dynamic behavior of these structures is often overlooked in current design practices. Given that many accidents involving these towers occur even at basic wind speeds lower than those specified in the project, it is likely that dynamic actions play a significant role in these failures. This study proposes a method to accurately simulate the interaction between transmission line cables and towers under non-deterministic wind loads to assess displacements and forces in the steel towers. The study examines a transmission line system consisting of towers, conductors, shield wires, and insulators, featuring a central suspension tower of 32.86 m in height, flanked by two end towers with 450 m spans. Finite element modeling was developed to account for the dynamic characteristics of the wind. Wind loads were modeled as a random process based on their statistical properties. The results revealed significant differences in displacement and force values when comparing the results provided by static and dynamic analyses. The structural design of a base leg member indicated potential failure at higher wind velocities, highlighting the importance of considering the wind dynamic effects in the design.

The EX-Lindley distribution with applications to renewable energy sources data

This study introduces a novel extension of the X-Lindley model, called the EX-Lindley model. The EX-Lindley model is a mixture model that combines the characteristics of the gamma model with the weighted Lindley model. The EX-Lindley model is analyzed to determine various statistical properties, including ordinary moments, inverse moments, moment generating function, incomplete moments, conditional moments, mean deviation, Lorenz, mean residual life, mean inactivity time, order statistics, and extropy. The maximum likelihood method is employed to estimate model parameters using complete data. Moreover, the simulation study is used to compare and evaluate the attributes of the estimations for this generalized model. Finally, two examples of datasets on renewable energy sources are utilized to show the importance of the new model compared to some well-known statistical models.

Sustained EEG responses to rapidly unfolding stochastic sounds reflect Bayesian inferred reliability tracking.

How does the brain track and process rapidly changing sensory information? Current computational accounts suggest that our sensations and decisions arise from the intricate interplay between bottom-up sensory signals and constantly changing expectations regarding the statistics of the surrounding world. A significant focus of recent research is determining which statistical properties are tracked by the brain as it monitors the rapid progression of sensory information? Here, by combining EEG (three experiments N≥22 each) and computational modelling, we examined how the brain processes rapid and stochastic sound sequences that simulate key aspects of dynamic sensory environments. Passively listening participants were exposed to structured tone-pip arrangements that contained transitions between a range of stochastic patterns. Predictions were guided by a Bayesian predictive inference model. We demonstrate that listeners automatically track the statistics of unfolding sounds, even when these are irrelevant to behaviour. Transitions between sequence patterns drove an increase of the sustained EEG response. This was observed to a range of distributional statistics, and even in situations where behavioural detection of these transitions was at floor. These observations suggest that the modulation of the EEG sustained response reflects a process of belief updating within the brain. By establishing a connection between the outputs of the computational model and the observed brain responses, we demonstrate that the dynamics of these transition-related responses align with the tracking of "precision" - the confidence or reliability assigned to a predicted sensory signal - shedding light on the intricate interplay between the brain's statistical tracking mechanisms and its response dynamics.

New Transformed Versions of the Lindley-G family with Discrete Transformer: Properties and Applications

In this research paper, two new discrete distributions have been developed by considering Poisson and Geometric distribution as baseline distributions in the Lindley-G family. Some statistical and mathematical properties such as moments, index of dispersion, hazard and reliability functions are explored. The maximum likelihood method has been used to estimate unknown parameters in the proposed distribution. The performance of the MLE have been assessed through simulation study. The applicability of the proposed distribution over some competing distributions have been studied using a real-life data set.. KEYWORDS :Lindley-G family, Hazard rate function, Index of dispersion, Discrete baseline distribution.

A Comprehensive Analysis of Factors Affecting GNSS Observation Noise

Observation noise is one of the most significant error sources in the Global Navigation Satellite System (GNSS). It can be influenced by various factors. Analyzing these factors is crucial for developing a stochastic model for GNSS navigation and positioning. This process ensures that the statistical properties of the observational data are accurately characterized, leading to more reliable and precise positioning results. Previous research has predominantly focused on code type and PPP techniques, often limited by the inability to separately assess observation types across different frequency bands due to ionospheric delay. If based on short baseline, these studies were generally constrained by limited experimental data. This study provides a detailed analysis of the affecting factor on observation noise, including elevation, SNR (signal-to-noise ratio), different receiver and antenna type, different GNSS system, and different frequency bands etc. In addition, environmental effects on observation noise are investigated by comparison between short baseline and zero baseline.

Enhanced Conditional GAN for High-Quality Synthetic Tabular Data Generation in Mobile-Based Cardiovascular Healthcare.

The generation of synthetic tabular data has emerged as a critical task in various fields, particularly in healthcare, where data privacy concerns limit the availability of real datasets for research and analysis. This paper presents an enhanced Conditional Generative Adversarial Network (GAN) architecture designed for generating high-quality synthetic tabular data, with a focus on cardiovascular disease datasets that encompass mixed data types and complex feature relationships. The proposed architecture employs specialized sub-networks to process continuous and categorical variables separately, leveraging metadata such as Gaussian Mixture Model (GMM) parameters for continuous attributes and embedding layers for categorical features. By integrating these specialized pathways, the generator produces synthetic samples that closely mimic the statistical properties of the real data. Comprehensive experiments were conducted to compare the proposed architecture with two established models: Conditional Tabular GAN (CTGAN) and Tabular Variational AutoEncoder (TVAE). The evaluation utilized metrics such as the Kolmogorov-Smirnov (KS) test for continuous variables, the Jaccard coefficient for categorical variables, and pairwise correlation analyses. Results indicate that the proposed approach attains a mean KS statistic of 0.3900, demonstrating strong overall performance that outperforms CTGAN (0.4803) and is comparable to TVAE (0.3858). Notably, our approach shows lowest KS statistics for key continuous features, such as total cholesterol (KS = 0.0779), weight (KS = 0.0861), and diastolic blood pressure (KS = 0.0957), indicating its effectiveness in closely replicating real data distributions. Additionally, it achieved a Jaccard coefficient of 1.00 for eight out of eleven categorical variables, effectively preserving categorical distributions. These findings indicate that the proposed architecture captures both distributions and dependencies, providing a robust solution in supporting mobile personalized cardiovascular disease prevention systems.

Estimating the causal effect of dexamethasone versus hydrocortisone on the neutrophil- lymphocyte ratio in critically ill COVID-19 patients from Tygerberg Hospital ICU using TMLE method

BackgroundCausal inference from observational studies is an area of interest to researchers, advancing rapidly over the years and with it, the methods for causal effect estimation. Among them, Targeted Maximum Likelihood estimation (TMLE) possesses arguably the most outstanding statistical properties, and with no outright treatment for COVID-19, there was an opportunity to estimate the causal effect of dexamethasone versus hydrocortisone upon the neutrophil-lymphocyte ratio (NLR), a vital indicator for disease progression among critically ill COVID-19 patients.MethodsTMLE variations were used in the analysis. Super Learner (SL), Bayesian Additive Regression Trees (BART) and parametric regression (PAR) were implemented to estimate the average treatment effect (ATE).ResultsThe study had 168 participants, 128 on dexamethasone and 40 on hydrocortisone. The mean causal difference in NLR on day 5; ATE [95% CI]: from SL-TMLE was − 0.309 [-3.800, 3.182] BART-TMLE 0.246 [-3.399, 3.891] and PAR-TMLE 1.245 [-1.882, 4372]. The ATE of dexamethasone versus hydrocortisone on NLR was not statistically significant since the confidence interval included zero.ConclusionThe effect of dexamethasone is not significantly different from that of hydrocortisone on NLR in critically ill COVID-19 patients admitted to ICU. This implies that the difference in effect on NLR between the two drugs is due to random chance. TMLE remains an outstanding approach for causal analysis of observational studies with the ability to be augmented with multiple prediction approaches.

Model Selection for Ordinary Differential Equations: A Statistical Testing Approach.

Ordinary differential equations(ODEs) are foundational tools in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different understandings of nuances in internal mechanisms or abstraction levels, presents a model selection challenge. This study introduces a testing-based approach for ODE model selection amidst statistical noise. Rooted in the model misspecification framework, we adapt classical statistical paradigms (Vuong and Hotelling) to the ODE context, allowing for the comparison and ranking of diverse causal explanations without the constraints of nested models. Our simulation studies numerically investigate the statistical properties of the test, demonstrating its attainment of the nominal size and power across various settings. Real-world data examples further underscore the algorithm's applicability in practice. To foster accessibility and encourage real-world applications, we provide a user-friendly Python implementation of our model selection algorithm, bridging theoretical advancements with hands-on tools for the scientificcommunity.

Domain generalization via geometric adaptation over augmented data

This article addresses the challenge of adapting deep learning models trained on specific datasets to effectively generalize to similar-class dataset with different underlying distributions. We introduce a novel deep representation learning method that takes into account both statistical and geometric properties of features for domain generalization. Our approach utilizes Fourier augmentation and Nyström estimation to evaluate the similarity between graphs derived from original and augmented data features. Furthermore, we employ a contrastive loss function to maintain proximity among samples belonging to the same class while ensuring separation between samples from different classes in the feature space. By minimizing these loss functions, our method aims to enhance model generalizability across diverse domains. Comprehensive experiments conducted on real-world benchmark datasets, including PACS, Office-Home, VLCS, Digits-DG and UTKFace, demonstrate the effectiveness of the proposed method. The results consistently indicate superior performance compared to other approaches under various conditions, underscoring its robustness in achieving improved generalization across domains.

Integrating clustering and sequential analysis for improving the spectral density estimation and dependency structure of time series

Time series models (TSMs) are used to forecast events based on verified historical data that are widely applied to describe natural and social phenomena. The spectral density function (SDF) of the TSM has the benefit to determine trends, periodic patterns and behavior of observable events and is used in degree of memory (DOM) which is used to identify independent and dependent structures. Therefore, paying attention to the estimator of SDF (SDE) is the cornerstone and desired goal in the statistical properties of TSMs. This paper gives a novel perspective for improving the SDE then dependency structure of TSMs by integrating clustering and sequential analysis. The accuracy of the lag window estimator (LWE) and periodogram estimator (PE), which are commonly used as SDEs in practice, is examined both with and without integrating the new proposed technique in order to figure out the efficacy of the new technique. Several circumstances, including independent and dependent data structures, TSMs with long and short DOMs, different numbers of clusters, and different dataset sizes, are used to carry out the investigation. The main findings indicate that: (i) The SDEs (PE and LWE) perform better when combined with the new proposed technique than when used alone. (ii) Using the new technique in conjunction with the SDEs results in absolutely perfect estimators for independent processes. (iii) High efficiency estimators for short memory TSMs arise when the new proposed technique is combined with the SDEs in the dependent processes; however, high efficiency in long memory TSMs (LMTSMs) is not guaranteed. (iv) Using the new technique, the correlation estimator behavior between SDEs and frequencies improves significantly with increasing DOM values of LMTSMs. (v) By applying the new technique for LMTSMs, the DOM estimator provides results indicating significant dependence. This study demonstrates that there are other efficient ways to improve the estimator than estimate techniques.

Effect of random roughness on Stokes flow

Microscopic irregularity (roughness) of bounding surfaces affects macroscopic dynamics of fluid flows. Its effect on bulk flow is usually quantified empirically by means of a roughness coefficient. A new approach, which treats rough surfaces (e.g. parallel plates) as random fields whose statistical properties can be inferred from measurements, is presented. The mapping of a random flow domain onto its deterministic counterpart, and the subsequent stochastic averaging of the transformed Stokes equations, yield expressions for the effective viscosity and roughness coefficient in terms of the statistical characteristics of the irregular geometry of the boundaries. The analytical nature of the solutions allows one to handle surface roughness characterized by short correlation lengths, a challenging feature for numerical stochastic simulations.

Quasi-2D crystals as an electrode material for high energy storage devices

The high value of the specific surface area in quasi-2D crystals, with the possibility of a large variation of their properties due to external factors, allows us to consider them as electrode materials for supercapacitors. In order to describe the specific physical properties of such crystals due to the different types of chemical bonds in them, a model is proposed. The electronic spectrum obtained has the structure (discrete levels) + (two-dimensional bands) or (mini-bands) + (two-dimensional bands). A significant relationship between the geometrical, spectral and statistical properties of the quasi-2D crystals has been found by studying the energy density of the accumulation W within the microscopic model. Contrary to existing models, the proposed model shows that under certain conditions there are two or more optimal crystal sizes where the experimentally observed maximum energy density W is realised. The model and its qualitative conclusions should be considered as the result of a microscopic approach to the problem.