Related papers: An analytic derivation of the variance for the Abe…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
Spontaneous neuronal activity is a ubiquitous feature of cortex. Its spatiotemporal organization reflects past input and modulates future network output. Here we study whether a particular type of spontaneous activity is generated by a…
Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
A probability distribution allows practitioners to uncover hidden structure in the data and build models to solve supervised learning problems using limited data. The focus of this report is on Variational autoencoders, a method to learn…
For any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. Yet, its full distribution often carries extremely interesting information and can be invoked to put any…
Bayesian Neural Networks (BNNs) have become one of the promising approaches for uncertainty estimation due to the solid theorical foundations. However, the performance of BNNs is affected by the ability of catching uncertainty. Instead of…
The notion of degree and related notions concerning recurrence and transience for a class of L'evy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is examined with emphasis on the role of the…
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
Fiber bundles with statistically distributed thresholds for breakdown of individual fibers are interesting models of the static and dynamics of failures in materials under stress. They can be analyzed to an extent that is not possible for…
This paper states asymptotic equivalents for the three first moments of the Eescher transform of a distribution on R with smooth density in the upper tail. As a by product if provides a tail approximation for its moment generating function,…
The aim of this paper is to describe new statistical methods for determination of the correlations among and distributions of physical parameters from a multivariate data with general and arbitrary truncations and selection biases. These…
In this paper an attempt is made to develop a new bimodal alpha skew logistic distribution under Balakrishnan (2002) mechanism. Some of its distributional as well as moments properties are studied. Some extensions of this new distribution…
Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and…