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The timely delivery of status update packets is essential for many real-time Internet of Things (IoT) applications. For monitoring and control, a key performance measure of interest is the Age of Information (AoI). We study the AoI for a status update system with two independent sources and a single server, where a status update packet of a source renders earlier status update packets irrelevant. As new updates might arrive during the service of a status update packet, we study various preemptive update mechanisms. In preemptive scenarios, the packet being served is updated, which affects the remaining service time. Using an effective service time approach, we find explicit expressions for the Laplace-Stieltjes transform of the time average age of information, and of the peak age of information.

The Gumbel-max trick is a method to draw a sample from a categorical distribution, given by its unnormalized (log-)probabilities. Over the past years, the machine learning community has proposed several extensions of this trick to facilitate, e.g., drawing multiple samples, sampling from structured domains, or gradient estimation for error backpropagation in neural network optimization. The goal of this survey article is to present background about the Gumbel-max trick, and to provide a structured overview of its extensions to ease algorithm selection. Moreover, it presents a comprehensive outline of (machine learning) literature in which Gumbel-based algorithms have been leveraged, reviews commonly-made design choices, and sketches a future perspective., Comment: Accepted as a survey article in IEEE TPAMI

This study investigates the dynamics of three discrete independent events occurring randomly and repeatedly within the interval [0,T]. Each event spans a predetermined fraction γ of the total interval length T before concluding. Three independent continuous random variables represent the starting times of these events, uniformly distributed over the time interval [0,T]. By employing a geometric probability approach, we derive a rigorous closed-form expression for the probability of the joint occurrence of these three events, taking into account various values of the fraction γ. Additionally, we determine the expected value of the intersection duration of the three events within the time interval [0,T]. Furthermore, we provide a comprehensive solution for evaluating the expected number of trials required for the simultaneous occurrence of these events. Numerous numerical examples support the theoretical analysis presented in this paper, further validating our findings.

In contrast to their seemingly simple and shared structure of independence and stationarity, L\'evy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes. Inspired by the recent paper of Ghourchian, Amini, and Gohari (2018), we characterize their compressibility by studying the entropy of their double discretization (both in time and amplitude) in the regime of vanishing discretization steps. For a L\'evy process with absolutely continuous marginals, this reduces to understanding the asymptotics of the differential entropy of its marginals at small times, for which we obtain a new local central limit theorem. We generalize known results for stable processes to the non-stable case, with a special focus on L\'evy processes that are locally self-similar, and conceptualize a new compressibility hierarchy of L\'evy processes, captured by their Blumenthal-Getoor index., Comment: 34 pages, 1 figure

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the conditional mean in the case of finite-variance input signals and additive Gaussian noise. The main result is a new lower bound in terms of the differential entropies of the input signal and the noisy observation. The main results are also extended to the vector Gaussian channel and to the natural exponential family. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. Two applications of the lower bound in the remote-source coding and CEO problem are discussed., Partially presented at the 2021 IEEE Information Theory Workshop, Japan

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in the asymptotic regime., Comment: This work has been accepted for publication in the IEEE Transactions on Signal Processing. Copyright may be transferred without notice, after which this version may no longer be accessible

The paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the excitation function in the form of the sum of the inertial and velocity forces of sea waves, taking into account relative wave–structure kinematics. Moreover, the wind acting on the exciting side causes similar effects. The second source is the subsoil–structure interaction problem, modelled by a system of springs and dashpots that yields stochastic non-linearity of the dynamic system. The matrix equations of structural motion in FEM terms are set up. The perturbation method is adopted to determine the mechanical response of the system, making it possible to determine response spectra of the first and the second approximations for displacements and internal forces of the platform. The paper is the continuation of research detailed in the paper [1]. It is assumed, that the fluctuation parts of the dynamic loading forces are in line with the direction of sea wave propagation. Sea current and lift forces effects are neglected in this study. A numerical example refers to structural data of the Baltic drilling platform in the stationary configuration, i.e. when three legs support the deck above the seawater level.

In soft real-time systems, tasks may occasionally miss their deadlines. This possibility has triggered research on probabilistic timing analysis for the execution time of a single program and probabilistic response time analysis of concurrently executed tasks. Under fixed-priority preemptive uniprocessor scheduling, it was shown that the classical critical instant theorem (for deriving the worst-case schedulability or response time) by Liu and Layland (in JACM 1973) can be applied to analyze the worst-case deadline failure probability (WCDFP) and the worst-case response time exceedance probability (WCRTEP). In this work, we present a counterexample for this result, showing that the WCDFP and WCRTEP derived by the classical critical instant theorem is unsound. We further provide two sound methods: one is to account for one additional carry-in job of a higher-priority task and another is to sample and inflate the execution time of certain jobs without adding one additional carry-in job. We show that these two methods do not dominate each other and, in the evaluation, apply them to two well-known approaches based on direct convolution and Chernoff bounds.

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.

In probabilistic analysis, random variables with unknown distributions are often appeared when dealing with practical engineering problem. A Hermite normal transformation model has been proposed to conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions. Recently, linear moments (L-moments) are widely used due to the advantages of stability and insensitivity. In this paper, the complete expressions of the inverse transformation of L-moments Hermite (L-Hermite) model have been proposed. The criteria are proposed to derive the complete inverse transformation of performance function and the complete expressions of the inverse transformation of L-Hermite model are formulated. Moreover, a first-order reliability method for structural reliability analysis based on the proposed inverse transformation of L-Hermite model is then developed using the first four L-moments of random variables. Through the numerical examples, the proposed method is found to be efficient for normal transformations since the results of the proposed L-Hermite are in close agreement with the results of Rosenblatt transformation. Additionally, the reliability index obtained by the proposed method using the first four L-moments of random variables provides a close result to the reliability index obtained by first-order reliability method with known probability density functions in structural reliability assessment.

It has been shown in literature that East Asians are more inclined to process context information than individuals in Western cultures. Using a context memory task that requires studying object images in social contexts (i.e., rating objects in an imagined social or experiential scenario), our recent study revealed an age-invariant advantage for Chinese young and older participants compared to their Canadian counterparts in memory for encoding contexts. To examine whether this cultural difference also occurred during encoding, this follow-up report analyzed encoding performance and its relationship to subsequent memory based on the same data from the same task of the same sample. The results revealed that at encoding, Chinese participants provided higher ratings of objects, took longer to rate, and reported more vivid imagery of encoding contexts relative to their Canadian counterparts. Furthermore, only Chinese participants rated objects with recognized context at retrieval higher and slower relative to those with misrecognized context. For Chinese participants, primarily older adults, slower ratings were only related to better context memory but not item memory. Importantly, Chinese participants’ context memory advantage disappeared after controlling for encoding differences. Taken together, these results suggest that Chinese participants’ memory advantage for social contexts may have its origin in the construction of elaborative and meaningful object-context associations at encoding.

U ovom diplomskom radu proučavamo jednostavne simetrične slučajne šetnje i uočavamo neke naizgled neočekivane rezultate. Kroz primjere uviđamo da neki naizgled neočekivani rezultati imaju veću vjerojatnost nego što smo pretpostavili. Pokazuje se da posjeti ishodištu nisu toliko učestali te da je vjerojatnost da se čestica vratila u ishodište u nekom trenutku jednaka vjerojatnosti da se do tog trenutka uopće nije vratila. Pokazujemo da intiucija zavarava te da prethodni dio šetnje ne utječe na nastavak (kockarova propast). Proučavamo slučajne varijable koje imaju arkus sinusovu distribuciju te pratimo svojstva iste. To nam pokazuje neke zanimljive rezultate koji su iznenađujući. Pokazuje se da ne očekujemo veliki broj promjena vodstva u igri i da postoji velika vjerojatnost da jedna strana provede većinu vremena u vodstvu. Nalazimo dobru aproksimaciju za vjerojatnost u kojoj točki će slučajna šetnja završiti pomoću centralnog graničnog teorema. Preko simulacija i grafova izrađenih simulacija bolje shvaćamo ponašanja jednostavnih simetričnih slučajnih šetnji i uspoređujemo s očekivanim rezultatima. In this paper, we study simple symmetrical random walks and observe some seemingly unexpected results. Through some examples, we see that some seemingly unexpected results have a higher probability than we assumed. It is shown that the visits to the origin are not so frequent and that the probability that the particle has returned to the origin at some point in time is equal to the probability that it has not returned at all until that moment. We show that intuition is deceiving and that the previous part of the walk does not a ect the continuation (gambler’s ruin). We study random variables that have an arcsine distribution and monitor its properties. This shows us some interesting results that are surprising. It turns out that we don’t expect a lot of lead changes in the game and that there is a big chance one side spends most of the time in the lead. An interesting result is that if we fix that our walk ends at the origin, the distribution of spending time in the positive quadrant ceases to be an arcsine distribution and becomes unfornm. We find a good approximation for the probability at which point the random walk will end using the central limit theorem. Using simulations and graphs of the created simulations, we better understand the behavior of simple symmetric random walks and compare them with the expected results.

This letter focuses on the analysis of a diffusion-based molecular communication (MC) system where the received signal is approximated as a Poisson random variable. Concentration shift keying (CSK) is used as the modulation technique for encoding information in the system. In particular, this work aims to study the performance of the MC system in terms of reliable information exchange for the channel with finite-state memory, which introduces intersymbol interference (ISI). The main objective is the derivation of analytical expressions for the upper and the lower bound of the constrained channel capacity for a range of values of the modulated symbols, i.e., for a number of different sets of amplitude levels of CSK modulation, and for various levels of ISI. In addition, the numerical evaluation of the derived expressions is presented. Results allow discussing the relationship between ISI level and achievable channel capacity. Moreover, numerical outcomes highlight how the estimation of the bounds is not affected by the presence of ISI in the case of binary CSK modulation, as the bounds remain quite tight.

Робота присвячена теоретичному аналiзу коректного застосування моделi неперервної нормально розподiленої випадкової величини при обґрунтуваннi так званих формул перенесення похибок в задачi статистичного опрацювання експериментальних даних. Звернута увага на роль обмеження iнтервалу розсiяння значень випадкової величини, пiдданої нелiнiйним прямим g(X) перетворенням елементарними функцiями X2; aX та cos X, i оберненими до них g-1(X) = √X, arccos X, loga X. Дослiджено закономiрностi статистичного усереднення даних, одержаних шляхом розкладу функцiй перетворення в ряд Тейлора. Для пiдтвердження правомiрностi одержаних результатiв використано метод оптимiзацiї квадратичного функцiонала., The work is devoted to the theoretical analysis of the correct application of the model of a continuous normally distributed random variable in the substantiation of the so-called error transfer formulas in the problem of a statistical processing of experimental data. Attention is paid to the role of limiting the scattering interval of values of a random variable subjected to nonlinear direct g(X) transformation by elementary functions X2; aX and cos X, as well as the inverse g-1(X) = √X, arccos X, loga X to them. The regularities of the statistical averaging of the data obtained by the disorder of the Taylor transform functions are studied. To confirm the validity of the obtained results, the method of quadratic functional optimization is used.

The one–sample log–rank test is the method of choice for single–arm Phase II trials with time–to–event endpoint. It allows to compare the survival of patients to a reference survival curve that typically represents the expected survival under standard of care. The one–sample log–rank test, however, assumes that the reference survival curve is known. This ignores that the reference curve is commonly estimated from historic data and thus prone to sampling error. Ignoring sampling variability of the reference curve results in type I error rate inflation. We study this inflation in type I error rate analytically and by simulation. Moreover we derive the actual distribution of the one–sample log–rank test statistic, when the sampling variability of the reference curve is taken into account. In particular, we provide a consistent estimate of the factor by which the true variance of the one-sample log–rank statistic is underestimated when reference curve sampling variability is ignored. Our results are further substantiated by a case study using a real world data example in which we demonstrate how to estimate the error rate inflation in the planning stage of a trial., Finanziert durch den Open-Access-Publikationsfonds der Westfälischen Wilhelms-Universität Münster (WWU Münster)

In this paper, the concept of a neutrosophic stable random variable is introduced. Two definitions of a neutrosophic random variable are presented. We introduced both the neutrosophic probability distribution function and the neutrosophic probability density function, and the convolution with the neutrosophic concept. In addition, we proved some properties of a neutrosophic stable random variable, and three examples are discussed.

A disciplinary profile of a country is defined as the versor whose components are the numbers of articles produced in a given discipline divided the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject area, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals [1980-1988] and [1992-2017], the fall of the Berlin Wall being the watershed. We analyse the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized $n_d$-dimensional Heisenberg model. The set of network interactions of the Heisenberg model have been inferred and to it they have been applied two clusterization methods, hierarchical clustering and principal component analysis. On a geopolitical plane this allow to obtain a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to deeper historical analysis. In order to obtain the optimal set of pairwise interactions we used a Pseudo-Likelihood approach. We analytically computed the Pseudo-Likelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving a $n_d$-dimensional Heisenberg model.

We study the high-dimensional identification systems under the presence of statistical uncertainties. The task is to design mappings for enrollment and identification purposes. The identification mapping compresses users' information then stores the index in the corresponding position in a database. The identification mapping combines the information in the database and the observation which originates randomly from an enrolled user to produce an estimate of the underlying user index. We study two scenarios. Users' data are generated from the same unknown distribution while the observation channel is also subjected to uncertainty. Each user's data are generated iid from the distribution corresponding to its own state, while the observation channel is known. We provide an achievable compression-identification trade-off for the first and second settings considering both discrete and continuous cases. In the discrete scenario, the described regions are also the correspondingly complete characterizations. QC 20180907. QC 20200318 QC 20211024

The optimization of the sampling scheme is particularly important in order to achieve sustainability in quality management. This paper discusses the problem of optimizing the design of metrological sampling scheme when the mean is a random variable. Assuming that the prior distribution of product means is known, a Bayesian posterior probability is calculated by using the likelihood function with decision variables to measure the sampling risk, and the expected cost of the sampling scheme is calculated based on the protection of producer and user risk in combination with the Taguchi quality loss function. The influence of model parameters on the selection of the optimal sampling scheme is investigated through sensitivity analysis. The model constructed in this paper solves the problem of sampling design in the case of food processing enterprises, quantifies the quality loss of products in the sampling process, facilitates sustainable quality management of enterprises, and has important theoretical significance and application value for sustainable business management of food processing enterprises.

International audience; With its aim to reduce the amount of sensed data and to improve the energy efficiency, compressive sensing (CS) is recently witnessing a growing research interest in remote-sensing applications. The Fourier transform domain plays a significant role as a signal-processing tool and the sparsity domain for the CS-reconstruction methods. A generalized expression for the error in the reconstruction of nonuniformly sampled, approximately sparse, or nonsparse, noisy signals in the Fourier domain is presented in this letter. This expression holds for a wide range of practically important nonuniform signal-sampling strategies, covering the uniform and completely random sampling as the special cases. Additive noise and noise-folding effects are included in the analysis. Statistical examples and two real-world examples validate the presented theory.

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.

International audience; The term “machine learning” especially refers to algorithms that derive mappings, i.e., input–output transforms, by using numerical data that provide information about considered transforms. These transforms appear in many problems related to classification/clustering, regression, system identification, system inversion, and input signal restoration/separation. We here analyze the connections between all these problems in the classical and quantum frameworks. We then focus on their most challenging versions, involving quantum data and/or quantum processing means, and unsupervised, i.e., blind, learning. We consider the general single-preparation quantum information processing (SIPQIP) framework that we have recently proposed. It involves methods that can work with a single instance of each (unknown) state, whereas usual methods are quite cumbersome because they have to very accurately create many copies of each (known) state. In our previous papers, we applied the SIPQIP approach to only one task [blind quantum process tomography (BQPT)], but it opens the way to a large range of other types of methods. In this article, we, therefore, propose various new SIPQIP methods that efficiently perform tasks related to system identification (blind Hamiltonian parameter estimation (BHPE), blind quantum channel identification/estimation, and blind phase estimation), system inversion and state estimation (blind quantum source separation (BQSS), blind quantum entangled state restoration (BQSR), and blind quantum channel equalization), and classification. Numerical tests show that our SIPQIP framework, moreover, yields much more accurate estimation than the usual multiple-preparation approach. Our methods are especially useful in a quantum computer, which we propose to more briefly call a “quamputer”: BQPT and BHPE simplify the characterization of quamputer gates; BQSS and BQSR yield quantum gates that may be used to compensate for the nonidealities that alter states stored in quantum registers and open the way to very general self-adaptive quantum gates.

We consider a network of agents, each with its own private cost consisting of a sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and can only communicate with its neighbors. The challenging aspect of our study is that the smooth part of the private cost function is given as an expected value and agents only have access to this part of the problem formulation via a heavy-tailed stochastic oracle. To tackle such sampling-based optimization problems, we propose a stochastic extension of the triangular pre-conditioned primal-dual algorithm. We demonstrate almost sure convergence of the scheme and validate the performance of the method via numerical experiments.

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with “single-user” or sequential decoding can yield better achievable rates. For instance, the compute–forward problem examines the scenario of recovering $L \le K$ linear combinations of transmitted codewords over a $K$ -user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute–forward over a $K$ -user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.

International audience; This paper proposes an extension of the well-known concept of Granger causality, called GB-Granger causality. GB-Granger causality is designed to relate the internal structure of bilinear state-space systems and statistical properties of their output processes. That is, if such a system generates two processes, where one does not GB-Granger cause the other, then it can be interpreted as the interconnection of two subsystems: one that sends information to the other, which does not send information back. This result is an extension of earlier obtained results [1] on the relationship between Granger-causality and the internal structure of linear time-invariant state-space representations.

An output signal from a multi-section wireless relay communication system is equal to the product of the signal envelopes from individual sections. In this paper, a three-sections relay system is considered in the presence of Nakagami-m fading at each section. First, random variable (RV) is formed as the product of three Nakagami-m RVs. For such product, the moments are determined in the closed forms. The first moment is the mean of the signal; the second moment is the average power of the signal, and the third moment is skewness. Then, the Amount of Fading (AoF) is calculated. AoF is a measure of the severity effect of fading in a particular channel model. Besides, all system performance are shown graphically and the parameters influence has been analyzed and discussed.

Operative parameters of La Fuenfría Hospital such as: hospitalized patients; daily admissions and discharges were studies for the hospital as a whole, and for each hospital’s service unit (henceforth called ‘services’). Conventional statistical analyzes and fractal dimension analyzes were performed on daily In-Patient series. The sequence of daily admissions and patients staying on each service were found to be a kind of random series known as random walks (Rw), sequences where what happens next, depends on what happens now plus a random variable. Rw analyzed with parametric or nonparametric statistics may simulate cycles and drifts which resemble seasonal variations or fake trends which reduce the Hospital’s efficiency. Globally, inpatients Rw s in LFH, were found to be determined by the time elapsed between daily discharges and admissions. The factors determining LFH R were found to be the difference between daily admissions and discharges. The discharges are replaced by admissions with some random delay and the random difference determines LFH Rw s. These findings show that if the daily difference between admissions and discharges is minimized, the number of inpatients would fluctuate less and the number of unoccupied beds would be reduced, thus optimizing the Hospital service.

A novel generalized Gamma-Laguerre polynomial chaos expansion is proposed to account for the effect of random variations in lower-bounded design parameters on antenna performance. After fitting a shifted generalized Gamma distribution to data sets of such random variables, a predistorted polynomial chaos expansion is generated based on a set of orthogonal generalized Laguerre polynomials. The new statistical methodology is applied to assess the random change in resonance frequency when bending a wearable antenna around different parts of the human body, such as a leg, an arm and a head. For different data sets, an excellent statistical fit is found to both the estimated probability density function of the bending radius and the resulting statistical distribution of the resonance frequency, while requiring up to 480 times fewer sample evaluations.

The current study deals with imputation of item non-response in probability proportional to size (PPS) sampling. A new imputation procedure is proposed by using the known co-variance between the study variable and the auxiliary variable in the case of quantitative sensitive study variable by considering the non-response in a randomization mechanism on the second call. An empirical study is conducted at the optimum values ofkogandnogfor the relative comparisons of ratio, difference, and proposed estimators, respectively, with the Hansen-Hurwitz estimator.

We estimate Growth-at-Risk (GaR) statistics for the US economy using daily regressors. We show that the relative importance, in terms of forecasting power, of financial and real variables is time varying. Indeed, the optimal forecasting weights of these types of variables were clearly different during the Global Financial Crisis and the recent Covid-19 crisis, which reflects the dissimilar nature of the two crises. We introduce the LASSO and the Elastic Net into the family of mixed data sampling models used to estimate GaR and show that these methods outperform past candidates explored in the literature. The role of the VXO and ADS indicators was found to be very relevant, especially in out-of-sample exercises and during crisis episodes. Overall, our results show that daily information for both real and financial variables is key for producing accurate point and tail risk nowcasts and forecasts of economic activity.

Funder: NIHR Cambridge Biomedical Research Centre, Clustering genetic variants based on their associations with different traits can provide insight into their underlying biological mechanisms. Existing clustering approaches typically group variants based on the similarity of their association estimates for various traits. We present a new procedure for clustering variants based on their proportional associations with different traits, which is more reflective of the underlying mechanisms to which they relate. The method is based on a mixture model approach for directional clustering and includes a noise cluster that provides robustness to outliers. The procedure performs well across a range of simulation scenarios. In an applied setting, clustering genetic variants associated with body mass index generates groups reflective of distinct biological pathways. Mendelian randomization analyses support that the clusters vary in their effect on coronary heart disease, including one cluster that represents elevated body mass index with a favourable metabolic profile and reduced coronary heart disease risk. Analysis of the biological pathways underlying this cluster identifies inflammation as potentially explaining differences in the effects of increased body mass index on coronary heart disease.

Infinitely divisible random variables have distributions that can be written as sums of countably many independent and identical distributions, i.e. a random variable $X$ is infinitely divisible if X= ∑_(i=1)^n X_i =X_1+X_2+⋯+X_n for any n, where the X_i are independent and identically distributed. In terms of moment generating functions – functions with special properties that are unique to each distribution – X will have the property M_X (θ)=(M_(X_i ) (θ) )^n These kind of random variables are interesting to explore due to their broad application to many fields and concepts. In this thesis, I will look at an infinitely divisible bivariate gamma distribution studied in the 1969 paper “A Class of Infinitely Divisible Bivariate Gamma Distributions" by R. C. Griffiths. Throughout this paper, Griffiths obtains his conclusions by working with the moment generating function of the bivariate gamma, but does not mention how the moment generating function might arise from random variables. I will thus construct this bivariate gamma distribution through joint Poisson and gamma random variables. I will then extend this construction method to create two different infinitely divisible multivariate gamma distributions and an infinitely divisible negative binomial distribution.

This paper considers a feedback-based projected gradient method for optimizing systems modeled as algebraic maps. The focus is on a setup where the gradient is corrupted by random errors that follow a sub-Weibull distribution, and where the measurements of the output -- which replace the input-output map of the system in the algorithmic updates -- may not be available at each iteration. The sub-Weibull error model is particularly well-suited in frameworks where the cost of the problem is learned via Gaussian Process (GP) regression (from functional evaluations) concurrently with the execution of the algorithm; however, it also naturally models setups where nonparametric methods and neural networks are utilized to estimate the cost. Using the sub-Weibull model, and with Bernoulli random variables modeling missing measurements of the system output, we show that the online algorithm generates points that are within a bounded error from the optimal solutions. In particular, we provide error bounds in expectation and in high probability. Numerical results are presented in the context of a demand response problem in smart power grids., Version of the IEEE Control Systems Letters (L-CSS) paper with one typo corrected

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2021-2022, Tutor: M. Mercè Claramunt Bielsa, The aim of this research is to study the implementation of segmentation in bonus-malus systems that base its analysis in the random variable number of claims. To this end, the theoretical framework proposed by Norberg for the construction of this a posteriori pricing method, for both not segmented and segmented case, is presented. This formulation has allowed the computation of the relative pure premiums and the premiums when unitary claim amount is assumed under different examples and scenarios. Then the different paths of premiums for certain insureds from simulated datasets are assessed. It is also evaluated this framework to surcharge premiums.

We characterize the reachability probabilities in stochastic directed graphs by means of reinforcement learning methods. In particular, we show that the dynamics of the transition probabilities in a stochastic digraph can be modeled via a difference inclusion, which, in turn, can be interpreted as a Markov decision process. Using the latter framework, we offer a methodology to design reward functions to provide upper and lower bounds on the reachability probabilities of a set of nodes for stochastic digraphs. The effectiveness of the proposed technique is demonstrated by application to the diffusion of epidemic diseases over time-varying contact networks generated by the proximity patterns of mobile agents., Comment: in IEEE Transactions on Automatic Control, 2023

Deployment of the deep neural networks (DNNs) on resource-constrained devices is a challenging task due to their limited memory and computational power. In most cases, the pruning techniques do not prune the DNNs to full extent and redundancy still exists in these models. Considering this, a mixed filter pruning approach based on principal component analysis (PCA) and geometric median is presented. First, a pre-trained model is analyzed by using PCA to identify the important filters for every layer. These important filters are then used to reconstruct the network with a fewer number of layers and a fewer number of filters per layer. A new network with optimized structure is constructed and trained on the data. Secondly, the trained model is then analyzed using geometric median as a base. The redundant filters are identified and removed which results in further compression of the network. Finally, the pruned model is fine tuned to regain the accuracy. Experiments on CIFAR-10, CIFAR-100 and ILSVRC 2017 datasets show that the proposed mixed pruning approach is feasible and can compress the network to greater extent without any significant loss to accuracy. With VGG-16 on CIFAR-10, the number of operations and parameters are reduced to 18.56× and 3.33×, respectively, with almost 1% loss in the accuracy. The compression rate for AlexNet on CIFAR-10 dataset is 2.61× and 4.85× in terms of number of operations and number of parameters, respectively, with a gain of 1.2% in the accuracy. On CIFAR-100, VGG-19 is compressed by 16.02 X in terms of number of operations and 36× in terms of number of parameters with a 2.6% loss of accuracy. Similarly, the compression rate for VGG-19 network on ILSVRC 2017 dataset is 1.87× and 2.4× for operations and parameters with 0.5% loss in accuracy.

Objective Different visual stimuli are classically used for triggering visual evoked potentials comprising well-defined components linked to the content of the displayed image. These evoked components result from the average of ongoing EEG signals in which additive and oscillatory mechanisms contribute to the component morphology. The evoked related potentials often resulted from a mixed situation (power variation and phase-locking) making basic and clinical interpretations difficult. Besides, the grand average methodology produced artificial constructs that do not reflect individual peculiarities. This motivated new approaches based on single-trial analysis as recently used in the brain-computer interface field. Approach We hypothesize that EEG signals may include specific information about the visual features of the displayed image and that such distinctive traits can be identified by state-of-the-art classification algorithms based on Riemannian geometry. The same classification algorithms are also applied to the dipole sources estimated by sLORETA. Main results and significance We show that our classification pipeline can effectively discriminate between the display of different visual items (Checkerboard versus 3D navigational image) in single EEG trials throughout multiple subjects. The present methodology reaches a single-trial classification accuracy of about 84% and 93% for inter-subject and intra-subject classification respectively using surface EEG. Interestingly, we note that the classification algorithms trained on sLORETA sources estimation fail to generalize among multiple subjects (63%), which may be due to either the average head model used by sLORETA or the subsequent spatial filtering failing to extract discriminative information, but reach an intra-subject classification accuracy of 82%.

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in this asymptotic regime. IEEE

This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.

In this thesis, we provide a self contained introduction to the theory of random matrices and matrix models. Our analysis has a chronological order and it begins with the study of nuclear energy levels and ensemble averaging which yields the famous Wigner surmise. Then, the standard Gaussian theory of the orthogonal, unitary and symplectic ensemble is derived from symmetry arguments of the corresponding physical system, which is then followed by the explicit calculation of Wigner's semicircle distribution. Moreover, interactions are introduced to the free theory which leads to the topological expansion, a diagrammatic way of evaluating certain expectation values. Also, it is shown that there exists a duality between the resulting graphs and the quantization of a two dimensional surface through mapping as well as a method for solving a specific family of potentials. Finally, the numerical confirmation for some observables is carried out using the Hamburger moment problem, and the derivation of critical points for some theories.

Preventive and modelling approaches to address the COVID-19 pandemic have been primarily based on the age or occupation, and often disregard the importance of heterogeneity in population contact structure and individual connectivity. To address this gap, we developed models based on Erdős-Rényi and a power law degree distribution that first incorporate the role of heterogeneity and connectivity and then can be expanded to make assumptions about demographic characteristics. Results demonstrate that variations in the number of connections of individuals within a population modify the impact of public health interventions such as lockdown or vaccination approaches. We conclude that the most effective strategy will vary depending on the underlying contact structure of individuals within a population and on timing of the interventions.Author summaryThe best strategy for public health interventions, such as lockdown or vaccination, depends on the contact structure of the population and the timing of the intervention. In general, for heterogeneous contact structures that mimic the COVID-19 spread, which is characterized by the presence of super spreaders, vaccinating the most connected individuals first was the most effective strategy to prevent infections and deaths, especially when coupled to serological tests. Models considering heterogeneity in human interactions need be used to identify the best potential vaccine prioritization strategies.

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach., Comment: preprint of a correction to the article with the same name, published with PLOS ONE, and currently under review

Testing is recommended for all close contacts of confirmed COVID-19 patients. However, existing pooled testing methods are oblivious to the circumstances of contagion provided by contact tracing. Here, we build upon a well-known semi-adaptive pooled testing method, Dorfman's method with imperfect tests, and derive a simple pooled testing method based on dynamic programming that is specifically designed to use information provided by contact tracing. Experiments using a variety of reproduction numbers and dispersion levels, including those estimated in the context of the COVID-19 pandemic, show that the pools found using our method result in a significantly lower number of tests than those found using Dorfman's method. Our method provides the greatest competitive advantage when the number of contacts of an infected individual is small, or the distribution of secondary infections is highly overdispersed. Moreover, it maintains this competitive advantage under imperfect contact tracing and significant levels of dilution., PLoS Computational Biology, 18 (3), ISSN:1553-734X, ISSN:1553-7358

When dealing with customers, original equipment manufacturers (OEMs) classify vehicular usage by resorting to simplified, often colloquial, descriptions that allow for a rough understanding of the operating conditions and the user’s needs. In this way, the information retrieved from the customers is exploited to guide their choices in terms of vehicle design and configuration, based on the characteristics of the transport application, labeled using intuitive metrics. However, a common problem in this context is the absence of any formal connection to lower levels of representation that might effectively be used to assess vehicular energy performance in simulation, or for design optimization using mathematical algorithms. Indeed, both processes require more accurate modeling of the surroundings, including exhaustive information about the local road, weather, and traffic conditions. Therefore, starting with a detailed statistical description of the environment, this paper proposes a method for mathematical classification of transport missions and applications within the theoretical framework of the operating cycle (OC). The approach discussed in the paper combines a collection of statistical models structured hierarchically, called a stochastic operating cycle (sOC), with a bird’s-eye view description of the operating environment. The latter postulates the existence of different classes, which are representative of the usage and whose definition is based on simple metrics and thresholds expressed mathematically in terms of statistical measures. Algebraic expressions, called operating classes in the paper, are derived analytically for all the stochastic models presented. This establishes a connection between the two levels of representation, enabling to simulate longitudinal vehicle dynamics in virtual environments generated based on the characteristics of the intended application, using log data collected from vehicles and/or information provided by customers. Additionally, the relationships between the two descriptions are formalized using elementary probability operators, allowing for an intuitive characterization of a transport operation. An example is adduced to illustrate a possible application of the proposed method, using six sOCs parametrized from log data collected during real-world missions. The proposed approach may facilitate the interaction between OEMs, customers, and road operators, allowing for planning of maintenance, and optimization of transport missions, components, and configurations using standard procedures and routines.

The ordinary linear regression method is limited to bivariate data because it is based on the Cartesian representation y = f(x). Using the chain rule, we transform the method to the parametric representation (x(t), y(t)) and obtain a linear regression framework in which the weighted average is used as a parameter for a multivariate linear relation for a set of linearly related variable vectors (LRVVs). We confirm the proposed approach by a Monte Carlo simulation, where the minimum coefficient of variation for error (CVE) provides the optimal weights when forming a weighted average of LRVVs. Then, we describe a parametric linear regression (PLR) algorithm in which the Moore-Penrose pseudoinverse is used to estimate measurement error regression (MER) parameters individually for the given variable vectors. We demonstrate that MER parameters from the PLR and nonlinear ODRPACK methods are quite similar for a wide range of reliability ratios, but ODRPACK is formulated only for bivariate data. We identify scale invariant quantities for the PLR and weighted orthogonal regression (WOR) methods and their correspondences with the partitioned residual effects between the variable vectors. Thus, the specification of an error model for the data is essential for MER and we discuss the use of Monte Carlo methods for estimating the distributions and confidence intervals for MER slope and correlation coefficient. We distinguish between elementary covariance for the y = f(x) representation and covariance vector for the (x(t), y(t)) representation. We also discuss the multivariate generalization of the Pearson correlation as the contraction between Cartesian polyad alignment tensors for the LRVVs and weighted average. Finally, we demonstrate the use of multidimensional PLR in estimating the MER parameters for replicate RNA-Seq data and quadratic regression for estimating the parameters of the conical dispersion of read count data about the MER line.

The paper considers the problem of constructing an equation of linear stochastic dependence between 2 random variables. As the above equation, it is proposed to use the bisector of the angle formed by the lines of direct and reverse regressions. Рассматривается задача построения уравнения линейной стохастической зависимости между двумя случайными величинами. В качестве упомянутого уравнения предлагается использовать биссектрису угла, образованного линиями прямой и обратной регрессий.

The safety assessment of the Pacoima arch dam is investigated in this paper. A Load – Resistance (L-R) method was used to ensure that the dam is safe or if it is at risk of failure. The “probabilistic design system” ANSYS finite element software was used to calculate the probability of failure. The Monte Carlo (MC) method with 50,000 iterations utilized for simulation and the Latin Hypercube method were used for Sampling. Input random variables with normal distribution and coefficient of variation of 15% due to uncertainties were considered and the six random variables used are the concrete modulus of elasticity, Poisson’s ratio of concrete, concrete mass, up-stream normal water level of the reservoir, and the allowable tensile and compressive strength of the concrete. Linear elastic behavior was assumed for the constitutive law of concrete material and if the stress exceeds the allowable stress of the concrete this is considered as a failure limit state. The maximum and minimum principal stresses were considered as the output parameter. Dam body safety was investigated only under self-weight and upstream hydrostatic pressure at the normal water level. The probability of failure of the dam body system was determined as β system =3.98, the safety index as pf system =3.42×10−15 and the dam is at risk of failure. The first and third principal stresses in the dam body were also S1max=2.03MPa and S3min=4.6MPa, respectively for the worst case of MC simulation.