相关论文: Hidden Structure in the Solutions Set of the N Que…

Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the…

Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…

In this paper we present a new method of coding/decoding algorithms using Fibonacci $Q$-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different…

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…

Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…

It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie-Hamilton system related to the book algebra $\mathfrak{b}_2$ can always be solved by quadratures, providing an explicit solution of…

Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…

We consider the problem of placing $n$ nonattacking queens on a symmetric $n \times n$ Toeplitz matrix. As in the $N$-queens Problem on a chessboard, two queens may attack each other if they share a row or a column in the matrix. However,…

We consider the space M of NxN matrices as a reduced quantum plane and discuss its geometry under the action and coaction of finite dimensional quantum groups (a quotient of U_q(SL(2)), q being an N-th root of unity, and its dual). We also…

Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…

There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…

Within the Matrix Product Formalism we have already introduced a multi- species exclusion process in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an…

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive…

We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…

It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…

An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable…

Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…

The quaternion equation X^n=A is solved for any integer number n > 1. A is a given quaternion with komplex numbers as its elements. We use the isomorphism between quaternions and (4,4)-matrices to solve this equation.

Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we…