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In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…
Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process.…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and studying how many grains have to…
In this review, we examine the recent progress in saliency prediction and proposed several avenues for future research. In spite of tremendous efforts and huge progress, there is still room for improvement in terms finer-grained analysis of…
We review limiting models for fracture in bundles of fibers, with statistically distributed thresholds for breakdown of individual fibers. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur,…
The Abelian sandpile model serves as a canonical example of self-organized criticality. This critical behavior manifests itself through large cascading events triggered by small perturbations. Such large-scale events, known as avalanches,…
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty,…
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…
Using a simple cellular automaton with stochastic rules we show the possible emergence of thermally activated avalanches (power law distributed) in type-II superconductors. Scaling relations between the exponents characterizing these…
Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Bayesian Neural Networks (BNNs) extend traditional neural networks to provide uncertainties associated with their outputs. On the forward pass through a BNN, predictions (and their uncertainties) are made either by Monte Carlo sampling…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether…