Related papers: Higher-Order Autocorrelations on Finite Abelian Gr…
Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…
In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. We give a necessary and sufficient condition for the integrality of Cayley graphs over…
We consider the problem of classifying gradings by groups on a finite-dimensional algebra $A$ (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such…
Applications of machine learning often involve making predictions based on both model outputs and the opinions of human experts. In this context, we investigate the problem of querying experts for class label predictions, using as few human…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Understanding the causal relationships that underlie a system is a fundamental prerequisite to accurate decision-making. In this work, we explore how expert knowledge can be used to improve the data-driven identification of causal graphs,…
Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in G$, there…
Top quarks are a prime system for hunting for new physics. Nonetheless, two decades on from their discovery few of their couplings have been measured to high precision. We present an overview of current determinations and the expected…
Bayesian field-level inference of galaxy clustering guarantees optimal extraction of all cosmological information, provided that the data are correctly described by the forward model employed. The latter is unfortunately never strictly the…
Given a finite group $G$, the \emph{Prime Order Element (POE) Graph} $\Gamma(G)$ consists of the group elements as the vertices, and two vertices $x$ and $y$ are adjacent if and only if $o(xy)$ is prime. This paper presents a thorough…
Causal discovery procedures aim to deduce causal relationships among variables in a multivariate dataset. While various methods have been proposed for estimating a single causal model or a single equivalence class of models, less attention…
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations…
We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from…
The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…