相关论文: Optimal Ate Pairing on Elliptic Curves with Embedd…
Recently, several authors have suggested the use of first order methods, such as fast dual ascent and the alternating direction method of multipliers, for embedded model predictive control. The main reason is that they can be implemented…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for relevant systems.…
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on…
In this paper we show a method for computing the set of twists of a non-singular projective curve defined over an arbitrary (perfect) field $k$. The method is based on a correspondence between twists and solutions to a Galois embedding…
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic…
We consider the \emph{$k$-edge connected spanning subgraph} (kECSS) problem, where we are given an undirected graph $G = (V, E)$ with nonnegative edge costs $\{c_e\}_{e\in E}$, and we seek a minimum-cost \emph{$k$-edge connected} subgraph…
The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…
Constellation shaping is an energy-efficient strategy involving the transmission of lower-energy signals more frequently than higher-energy signals. Previous work has shown that shaping is particularly effective when used with coded…
We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$…
We describe a systematic investigation into the existence of congruences between the mod $p$ torsion modules of elliptic curves defined over $\mathbb{Q}$, including methods to determine the symplectic type of such congruences. We classify…
We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the…
The best method for computing the adjoint matrix of an order $n$ matrix in an arbitrary commutative ring requires $O(n^{\beta+1/3}\log n \log \log n)$ operations, provided the complexity of the algorithm for multiplying two matrices is…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
We present a fast algorithm that takes as input an elliptic curve defined over $\mathbb Q$ and an integer $d$ and returns all the number fields $K$ of degree $d'$ dividing $d$ such that $E(K)_{tors}$ contains $E(F)_{tors}$ as a proper…
Suppose $p$ is a prime of the form $u^2+64$ for some integer $u$, which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves $E_0$ and $E_1$ of prime conductor $p$, and both have Mordell--Weil group $\Z/2\Z$. There is a…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…