Related papers: Further Comments on "Residue-to-Binary Converters …
The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which…
We present a new algorithm to compute the classical modular polynomial Phi_n in the rings Z[X,Y] and (Z/mZ)[X,Y], for a prime n and any positive integer m. Our approach uses the graph of n-isogenies to efficiently compute Phi_n mod p for…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
In 1982-83, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in $\Bbb P^n$ relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subseqently simplified by…
We welcome Allagui et al.'s discussions about our recent paper that has proposed revisions to the existing theory of capacitors. It gives us an opportunity to emphasize on the physical underpinnings of the mathematical expressions that are…
In this paper, we introduce and analyze a new iterative algorithm for solving a class of variational inclusions involving H-monotone operators. The strong convergence of this algorithm is proved and estimate of its convergence rate is…
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in…
A self-consistent calculation scheme for correlated electron systems is created based on the density-functional theory (DFT). Our scheme is a multi-reference DFT (MR-DFT) calculation in which the electron charge density is reproduced by an…
Contribution of Indian Mathematics since Vedic Period has been recognised by the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text related to the description and analysis of meters in poetic work, describes algorithms…
We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree-cluster protects the information from transmission loss and enables long-range quantum communication through…
The Rutherford scattering experiment, conceived by Ernest Rutherford and carried out by Hans Geiger and Ernest Marsden, provided the first direct evidence of a compact atomic nucleus, fundamentally altering the understanding of atomic…
In recent years, algorithm research in the area of recommender systems has shifted from matrix factorization techniques and their latent factor models to neural approaches. However, given the proven power of latent factor models, some newer…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…
We propose a novel algorithm for computing the Walsh-Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. We prove that the algorithm, which we call the Cascading Haar Wavelet (CHW) algorithm, shares precisely the…
Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
A 2024 paper of Sun, Ding and Wang introduced a second class of constacyclic codes over finite fields, denoted $C(q,m,r,\ell)$, with length $(q^m-1)/r$, where $r\mid(q-1)$ and the defining monomials have total $q$-ary degree congruent to…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…