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Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Neural networks follow a gradient-based learning scheme, adapting their mapping parameters by back-propagating the output loss. Samples unlike the ones seen during training cause a different gradient distribution. Based on this intuition,…

This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated…

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…

In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term…

Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…

We investigate the dynamics of Eulerian walkers as a model of self-organized criticality. The evolution of the system is subdivided into characteristic periods which can be seen as avalanches. The structure of avalanches is described and…

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…

Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…

The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hence, we believe that it is worthwhile to…

This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine…

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…

A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al.…

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…