Related papers: An algorithm for Hodge ideals
In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subrings which cover tiled orders, rings related to…
We prove a formula for the Hodge numbers of square-free divisors of Calabi-Yau threefold hypersurfaces in toric varieties. Euclidean branes wrapping divisors affect the vacuum structure of Calabi-Yau compactifications of type IIB string…
This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
We consider the multiplier ideals of the ideal of a reduced union of lines through the origin in C^3. For general arrangements of lines, we calculate the multiplier ideals.
In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The…
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…
In this paper we continue the development of a new technique for computing elimination ideals by substitution which has been called $Z$-separating re-embeddings. Given an ideal $I$ in the polynomial ring $K[x_1,\dots,x_n]$ over a field $K$,…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper we explicitly compute the derivation module of quotients of polynomial rings by ideals formed by the sum or by some other gluing technique. We discuss cases of monomial ideals and binomial ideals separately.
Any hodge integrals involving psi-classes and one lambda-class is computed as a polynomial in terms of lower-dimensional ones. Algorithm and examples are presented.
We present an efficient algorithm to compute the Hasse-Witt matrix of a hyperelliptic curve C/Q modulo all primes of good reduction up to a given bound N, based on the average polynomial-time algorithm recently introduced by Harvey. An…