Related papers: Variations on the Newcomb-Benford Law
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We solve for the statistics of the first detection of a quantum system in a particular desired state, when the system is subject to a projective measurement at independent identically distributed random time intervals. We present formulas…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from…
Missing data has the potential to affect analyses conducted in all fields of scientific study, including healthcare, economics, and the social sciences. Several approaches to unbiased inference in the presence of non-ignorable missingness…
Most observables at particle colliders involve physics at a wide variety of distance scales. Due to asymptotic freedom of the strong interaction, the physics at short distances can be calculated reliably using perturbative techniques, while…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
The statistical distribution, when determined from an incomplete set of constraints, is shown to be suitable as host for encrypted information. We design an encoding/decoding scheme to embed such a distribution with hidden information. The…
In order to detect unknown intrusions and runtime errors of computer programs, the cyber-security community has developed various detection techniques. Anomaly detection is an approach that is designed to profile the normal runtime behavior…
Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…
The generalized gamma distribution shows up in many problems related to engineering, hydrology as well as survival analysis. Earlier work has been done that estimated the deviation of the exponential and the Weibull distribution from…
Contextual bandit algorithms have transformed modern experimentation by enabling real-time adaptation for personalized treatment and efficient use of data. Yet these advantages create challenges for statistical inference due to adaptivity.…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
In this paper we will look at the distribution with which passwords are chosen. Zipf's Law is commonly observed in lists of chosen words. Using password lists from four different on-line sources, we will investigate if Zipf's law is a good…
We show that quantum probabilities can be derived from statistical mechanics of classical fields. We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks…
We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…
It has been shown that Information-Disturbance theorem can play an important role in security proof of quantum cryptography. The theorem is by itself interesting since it can be regarded as an information theoretic version of uncertainty…
There are two distinct perspectives on the quantum time-of-arrival: one can ask for the probability that a particle is found at the detector at a given time, regardless of whether it was previously detected, or for the probability that the…
We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$, improving the previously known error term for the counting function as $T\to+\infty$. We also resolve some…