Related papers: Finite Difference Calculus for Alternating Permuta…
Counting problems are fundamental across mathematics and computer science. Among the most subtle are those whose associated decision problem is solvable in polynomial time, yet whose exact counting version appears intractable. For some such…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
Complete non-ambiguous trees (CNATs) are combinatorial objects which appear in various contexts.Recently, Chen and Ohlig studied the notion of permutations associated to these objects, and proposed a series of nice conjectures.Most of them…
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…
We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…
We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground $\lambda$-term corresponds to some property…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a…
We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…
We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…