Related papers: Alpha variation problem and q-factor definition
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…
I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews' $q$-Dyson conjecture.
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is…
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
The Additive Transform of an arithmetic function represents a novel approach to examining the interplay between multiplicative arithmetic function and additive functions. This transform concept introduces a method to systematically generate…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against…
We further analyse,at next-to-leading log(s) level,the form of k-factorization and the definition of impact factors previously proposed by one of us,and we generalize them to the case of hard colourless probes. We then calculate the finite…
An algebraic framework for the investigation of linear dynamic output feedback is introduced. Pivotal in the present theory is the problem of causal factorization, i.e. the problem of factoring two systems over each other through a causal…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
An analytical formula for the contributions of the trend leftovers in DFA method is presented, based upon which the crossovers in DFA are investigated in detail. This general formula can explain the calculated results with DFA method for…