Related papers: Chinese Remainder Theorem Approach to Montgomery-T…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
We present algorithms which, given a genus 2 curve $C$ defined over a finite field and a quartic CM field $K$, determine whether the endomorphism ring of the Jacobian $J$ of $C$ is the full ring of integers in $K$. In particular, we present…
Residue number systems based on pairwise relatively prime moduli are a powerful tool for accelerating integer computations via the Chinese Remainder Theorem. We study a structured family of moduli of the form $2^n - 2^k + 1$, originally…
Recurrent neural network (RNN)'s architecture is a key factor influencing its performance. We propose algorithms to optimize hidden sizes under running time constraint. We convert the discrete optimization into a subset selection problem.…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
In [1], we give Dickson's conjecture on $N^n$. In this paper, we further give Dickson's conjecture on $Z^n$ and obtain an equivalent form of Green-Tao's conjecture [2]. Based on our work, it is possible to establish a general theory that…
We investigate the properties of a Block Decomposition Method (BDM), which extends the power of a Coding Theorem Method (CTM) that approximates local estimations of algorithmic complexity based upon Solomonoff-Levin's theory of algorithmic…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…
Injective resolutions of modules are key objects of homological algebra, which are used for the computation of derived functors. Semiinjective resolutions of chain complexes are more general objects, which are used for the computation of…
We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…
We address the problem of latent truth discovery, LTD for short, where the goal is to discover the underlying true values of entity attributes in the presence of noisy, conflicting or incomplete information. Despite a multitude of…