Related papers: Power Law in a Bounded Range: Estimating the Lower…
We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the…
Advanced science and technology provide a wealth of big data from different sources for extreme value analysis. Classical extreme value theory was extended to obtain an accelerated max-stable distribution family for modelling competing…
This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating,…
We address how to exploit power control data, gathered from a monitored environment, for performing power control in an unexplored environment. We adopt offline deep reinforcement learning, whereby the agent learns the policy to produce the…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
Spectra in astroparticle physics are commonly approximated by simple power laws. The steeply falling nature of these power laws, however, makes the detection of additional components rather challenging. This holds true especially, if the…
Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely…
Optimal power flow (OPF) is one of the fundamental tasks for power system operations. While machine learning (ML) approaches such as deep neural networks (DNNs) have been widely studied to enhance OPF solution speed and performance, their…
We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a and variance va. These two control parameters determine if the…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given $n$ points $\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution where $X_i \in…
Research often necessitates of samples, yet obtaining large enough samples is not always possible. When it is, the researcher may use one of two methods for deciding upon the required sample size: rules-of-thumb, quick yet uncertain, and…
The total measurable level of a pathogen is due to many sources, which produce a variety of pulses, overlapping in time, that rise suddenly and then decay. What is measured is the level of the total contribution of the sources at a given…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
We calculate reduced moments $\overline \xi_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…