Related papers: Computing change of level and isogenies between ab…

For a positive integer $n$ and a finite simplicial complex $K$, we describe an algorithmic procedure constructing a maximal discrete gradient field $W(K,n)$ on Abrams' discretized configuration space $\text{DConf}(K,n)$. Computer…

The order type of a point set in $R^d$ maps each $(d{+}1)$-tuple of points to its orientation (e.g., clockwise or counterclockwise in $R^2$). Two point sets $X$ and $Y$ have the same order type if there exists a mapping $f$ from $X$ to $Y$…

Let K be a subfield of the complex numbers, and let D be the Weyl algebra of K-linear differential operators on K[x_1,...,x_n]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite…

Autograd-based software packages have recently renewed interest in image registration using homography and other geometric models by gradient descent and optimization, e.g., AirLab and DRMIME. In this work, we emphasize on using complex…

The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…

This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We obtain these results by proving improved bounds on the weight distribution of Reed-Muller codes of high degrees.…

We study how the eightfold-degeneracy in the ($\theta_{13},\delta$) plane observed in $\gamma \sim 100$ $\beta$-beams can be reduced by periodically changing the ions in the storage ring. This ``ions cocktail'' allows to change the neutrino…

We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…

Classifying orthogonal arrays is a well known important class of problems that asks for finding all non-isomorphic, non-negative integer solutions to a class of systems of constraints. Solved instances are scarce. We develop two new methods…

We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…

Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…

In recent years, there has been a growing interest in data-driven evolutionary algorithms (DDEAs) employing surrogate models to approximate the objective functions with limited data. However, current DDEAs are primarily designed for…

In this paper, we study the Cassels-Tate pairing on Jacobians of genus two curves admitting a special type of isogenies called Richelot isogenies. Let $\phi: J \rightarrow \widehat{J}$ be a Richelot isogeny between two Jacobians of genus…

Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…

Gradient-based bilevel optimisation is a powerful technique with applications in hyperparameter optimisation, task adaptation, algorithm discovery, meta-learning more broadly, and beyond. It often requires differentiating through the…

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study convergence of…

Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with $d$…

By employing the (de)homogenization technique in a relatively extensive setting, this note studies in detail the relation between non-homogeneous Gr\"obner bases and homogeneous Gr\"obner bases. As a consequence, a general principle of…

We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…

Understanding how the time-complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived…