相关论文: A q-product tutorial for a q-series MAPLE package
As part of our study of the $q$-tetrahedron algebra $\boxtimes_q$ we introduce the notion of a $q$-inverting pair. Roughly speaking, this is a pair of invertible semisimple linear transformations on a finite-dimensional vector space, each…
Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on…
We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena.
The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are the generating k-tuples of the group (for a fixed…
In the present paper, we establish three special $q$-Abel transformation formulae of $q$-series via the use of Abel's lemma on summation by parts. As direct applications, we set up the corresponding $q$-contiguous relations for three kinds…
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional…
By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal…
Forecasting, to estimate future events, is crucial for business and decision-making. This paper proposes QxEAI, a methodology that produces a probabilistic forecast that utilizes a quantum-like evolutionary algorithm based on training a…
We describe one interpretation of the q-Catalan numbers in frameworks of random matrix theory and weighted partitions of the set of integers.
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
We show that certain terminating $_{6}\phi_5$ series can be factorized into a product of two $_{3}\phi_{2}$ series. As applications we prove a summation formula for a product of two $q$-Delannoy numbers along with some congruences for sums…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
We relate factorizable quantum channels on $M_n$, for $n \ge 2$, via their Choi matrix, to certain correlation matrices, which, in turn, are shown to be parametrized by traces on the unital free product $M_n * M_n$. Factorizable maps that…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be…
The goal of this paper is to introduce a new constructive geometric proof of the affine version of Chevalley's Theorem. This proof is algorithmic and a verbatim implementation resulted in an efficient code for computing the constructible…
The use of machine learning (ML) techniques has allowed rapid advancements in many scientific and engineering fields. One of these problems is that of surface soil taxonomy, a research area previously hindered by the reliance on…