This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix p...

Pattern matching is advantageous for understanding and reasoning about function definitions, but it tends to tightly couple the interface and implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development o...

Matchmaking is one crucial tasks in agent-based systems and describes locating and identifying the most suitable services among all available services. This paper introduces matchmaking of mathematical services, whereby the matching is based on semantics using OpenMath object descriptions of preand post-conditions. A matchmaking architecture for mathematical services is described containing fou...

Pattern matching is a useful, convenient tool for processing algebraic data types in functional programming languages. This paper discusses a method for porting pattern matching to a family of programming languages called concatenative, which does not use named variables. The system is not fixed, like a traditional pattern matching system, but rather arbitrarily extensible: any function can be ...

Prior constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2-D point sets and graphs are learned by clustering with point matching and graph matching distance measures. The point matching distance measure is approx. invariant under affine transformations translation, rotation, scale and shear and permutations. It operates between noisy images with missi...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributedmemory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal match...

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of representations of finite groups of Lie type in mind, character sheaves are perfectly well defined for reductive algebraic groups over any algebraically clo...

We propose an Haskell-like language with the goal of unifying type classes and generalized algebraic datatypes (GADTs) into a single class construct. We treat classes as first-class types and we use objects (instead of type class instances and data constructors) to define the values of those classes. We recover the ability to define functions by pattern matching by using sealed classes. The res...

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatyp...