Related papers: On Absolute and Relative Change
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
In this paper a set of canonical collective variables is defined for a classical Klein-Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a…
The largest component (``the leader'') in evolving random structures often exhibits universal statistical properties. This phenomenon is demonstrated analytically for two ubiquitous structures: random trees and random graphs. In both cases,…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients),…
Several numerical indices that control the normalization of ideals are introduced and some relationships among them are derived.
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…
This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can…
It is shown that under certain circumstances in particular for small datasets the recently proposed citation impact indicators I3(6PR) and R(6,k) behave inconsistently when additional papers or citations are taken into consideration. Three…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…
It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics…
We employ the relative category to develop relations between the Wa\.zewski pair $(N,E)$ and the Morse decomposition of the maximal invariant set in $\ol{N\sm E}$ for infinite-dimensional dynamical systems. Via these relations, we can…
The purpose of this paper is to discuss the existence of a nontrivial tradeoff relation for estimating two unitary-shift parameters in a relativistic spin-1/2 system. It is shown that any moving observer cannot estimate two parameters…
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…
The standard approximation of a natural logarithm in statistical analysis interprets a linear change of \(p\) in \(\ln(X)\) as a \((1+p)\) proportional change in \(X\), which is only accurate for small values of \(p\). I suggest…