相关论文: A Dual Approach to Triangle Sequences: A Multidime…

This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given…

In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recursions, enabling it to solve large-scale algebraic Riccati…

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…

The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible…

We investigate the structure of graphs of twin-width at most $1$, and obtain the following results: - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure. - There is…

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…

A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 has a triangular realisation, and establish this conjecture…

The standard dual-numbers construction works well for forward-mode automatic differentiation (AD) and is attractive due to its simplicity; recently, it also has been adapted to reverse-mode AD, but practical performance, especially on array…

Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…

On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…

The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…

Twin-width is a recently formulated graph and matrix invariant that intuitively quantifies how far a graph is from having the structural simplicity of a co-graph. Since its introduction in 2020, twin-width has received increasing attention…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

We define an algorithm which begins with an sequence of sequences, and produces a single sequence, with following property: If at least one of the original sequences has a tail that is periodic, then the output sequence has a periodic tail,…

By using a jump transformation associated to the Romik map, we define a new continued fraction algorithm called odd-odd continued fraction, whose principal convergents are rational numbers of odd denominators and odd numerators. Among…

We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…

Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…

Parallel sentence extraction is a task addressing the data sparsity problem found in multilingual natural language processing applications. We propose an end-to-end deep neural network approach to detect translational equivalence between…