Numerous computational methods exist to assess the mode and strength of natural selection in protein-coding sequences, yet how distinct methods relate to one another remains largely unknown. Here, we elucidate the relationship between two widely used phylogenetic modeling frameworks: dN/dS models and mutation-selection (MutSel) models. We derive a mathematical relationship between dN/dS and sca...

The portfolio selection problem (PSP) uses mathematical approaches to model stock exchange investments. Its aim is to find an optimal set of assets to invest on, as well as the optimal investments for each asset. In this paper, a portfolio selection problem (FPSP) with fuzzy objective function coefficient (FPSP) a multiple objective problem including uncertainties is investigated. The FPSP is c...

We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional covariates and p increases moderately. However, it is the case that only a small part of the covariates are re...

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for Re(si) sufficiently large, that has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. A heuristic definition of such series was given in [BB...

A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (Hn, In) are exhibited. For n = 1 we recover Clebsch sytem. All these systems are also integrable at the quantum level.

Abstract. In a recent paper [1] we have constructed the spin and tensor representations of SO(4) from which the invariant weight can be derived for the Barrett-Crane model in quantum gravity. By analogy with the SO(4) group, we present the complexified Clebsch-Gordan coefficients in order to construct the Biedenharn-Dolginov function for the SO(3,1) group and the spherical function as the Loren...

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules Lh(g) of the quantized enveloping algebras Uh(g). On them the quantum Lie bracket is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie alge...

The 1|1-supertransvectants are the osp(1|2)-invariant bilinear operations on weighted densities on the supercircle S, the projective version of R. These operations are analogues of the famous Gordan transvectants (or Rankin-Cohen brackets). We prove that supertransvectants coincide with the iterated Poisson and ghost Poisson brackets on R and apply this result to construct star-products.

Feature selection is a critical step in the data preprocessing phase field of pattern recognition and machine learning. The core feature to analyze quantify relevance, irrelevance, redundancy between features class labels. While existing methods give multiple explanations for these relationships, they ignore multi-value bias class-independent dependent features. Therefore, method (Maximal indep...

The problem of GNSS multipath mitigation is pursued through developing two stochastic-gradient-based adaptive tracking algorithms. Using these techniques, instead of direct estimation of the multipath channel coefficients, the resulting distortion on the correlation function of the received GNSS signal is compensated by passing the correlation function samples through a filter whose coefficient...