相关论文: Alpha variation problem and q-factor definition

Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each…

{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…

Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about…

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors…

Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…

The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…

We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation…

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator…

The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…

Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The…

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…

We derive explicit expressions for the generating series of the fundamental solutions of the $A_r$ quantum $Q$-system of Ref. [P. Di Francesco and R. Kedem, arXiv:1006.4774 [math-ph]], expressed in terms of any admissible initial data.…

Effects of performing R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. It was noted that estimating a model comprising R- and Q-factors has to face loading indeterminacy…