Related papers: Factorization with genus 2 curves
This work developed novel complex matrix factorization methods for face recognition; the methods were complex matrix factorization (CMF), sparse complex matrix factorization (SpaCMF), and graph complex matrix factorization (GraCMF). After…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
Quantum circuit mapping is a critical process in quantum computing that involves adapting logical quantum circuits to adhere to hardware constraints, thereby generating physically executable quantum circuits. Current quantum circuit mapping…
In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
In this paper we address the problem of building a class of robust factorization algorithms that solve for the shape and motion parameters with both affine (weak perspective) and perspective camera models. We introduce a Gaussian/uniform…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementation as the conductor of…
So-called "classification trimmed likelihood curves" have been proposed as a useful heuristic tool to determine the number of clusters and trimming proportion in trimming-based robust clustering methods. However, these curves needs a…
The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time cannot be proven rigorously, but heuristic arguments show that it should…
Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
We report preliminary results on using the MEMCPU\texttrademark{} Platform to compute the prime factorization of large biprimes. The first approach, the direct model, directly returns the factors of a given biprime. The second approach, the…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
Bayesian model-based clustering is a widely applied procedure for discovering groups of related observations in a dataset. These approaches use Bayesian mixture models, estimated with MCMC, which provide posterior samples of the model…
A Howe curve is a curve of genus $4$ obtained as the fiber product of two genus-$1$ double covers of $\mathbf{P}^1$. In this paper, we present a simple algorithm for testing isomorphism of Howe curves, and we propose two main algorithms for…
Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using Probabilistic Quantum Memory (PQM) and its extension, Parameteric PQM (P-PQM) by calculating the Hamming distance between an input pattern and a…
Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…