Free Variables and the Two Matrix Model

We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be efficiently discussed and solved. This solution determines the master field for the model in the `$C$-representation.'Comment: 8 pages, harvma

In-plant logistics systems modeling with SysML

Up till now Systems Modeling Language (SysML) has mostly been used to model physical systems of interest. This paper shows how SysML can also be used to represent an abstract model. In this application a mathematical cost model is represented using the SysML plugin for the software MagicDraw. ParaMagic, a plugin in MagicDraw supplementary to SysML, links to Mathematica to solve the model. SysML is a formal language and offers a very intuitive graphical representation. It is therefore a useful medium to create a domain specific language for a field of knowledge. The comprehensiveness of the language, which makes it possible to incorporate specification, analysis, design, verification, and validation of systems, makes it a very valuable tool for collaboration on large projects

Propagation of social representations

Based on a minimal formalism of social representations as a set of associated cognems, a simple model of propagation of representations is presented. Assuming that subjects share the constitutive cognems, the model proposes that mere focused attention on the set of cognems in the field of common conscience may replicate the pattern of representation from context into subjects, or, from subject to subject, through actualization by language, where cognems are represented by verbal signs. Limits of the model are discussed, and evolutionist perspectives are presented with the support of field data

Bernstein-Zelevinsky derivatives: a Hecke algebra approach

Let $G$ be a general linear group over a $p$-adic field. It is well known that Bernstein components of the category of smooth representations of $G$ are described by Hecke algebras arising from Bushnell-Kutzko types. We describe the Bernstein components of the Gelfand-Graev representation of $G$ by explicit Hecke algebra modules. This result is used to translate the theory of Bernstein-Zelevinsky derivatives in the language of representations of Hecke algebras, where we develop a comprehensive theory.Comment: 21 pages, extending part of arXiv:1605.05130. v2: a new appendix is added for the projectivity of the Gelfand-Graev representation, and references are update

Knowledge Representation and WordNets

Knowledge itself is a representation of “real facts”. Knowledge is a logical model that presents facts from “the real world” witch can be expressed in a formal language. Representation means the construction of a model of some part of reality. Knowledge representation is contingent to both cognitive science and artificial intelligence. In cognitive science it expresses the way people store and process the information. In the AI field the goal is to store knowledge in such way that permits intelligent programs to represent information as nearly as possible to human intelligence. Knowledge Representation is referred to the formal representation of knowledge intended to be processed and stored by computers and to draw conclusions from this knowledge. Examples of applications are expert systems, machine translation systems, computer-aided maintenance systems and information retrieval systems (including database front-ends).knowledge, representation, ai models, databases, cams

GR uniqueness and deformations

In the metric formulation gravitons are described with the parity symmetric $S_+^2\otimes S_-^2$ representation of Lorentz group. General Relativity is then the unique theory of interacting gravitons with second order field equations. We show that if a chiral $S_+^3\otimes S_-$ representation is used instead, the uniqueness is lost, and there is an infinite-parametric family of theories of interacting gravitons with second order field equations. We use the language of graviton scattering amplitudes, and show how the uniqueness of GR is avoided using simple dimensional analysis. The resulting distinct from GR gravity theories are all parity asymmetric, but share the GR MHV amplitudes. They have new all same helicity graviton scattering amplitudes at every graviton order. The amplitudes with at least one graviton of opposite helicity continue to be determinable by the BCFW recursion.Comment: v2: published version, 19 pages, description of the complexified setting expande

The First-Order Theory of Sets with Cardinality Constraints is Decidable

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is undecidable. Our language allows relating the cardinalities of sets to the values of integer variables, and can distinguish finite and infinite sets. We use quantifier elimination to show the decidability and obtain an elementary upper bound on the complexity. Precise program analyses can use our decidability result to verify representation invariants of data structures that use an integer field to represent the number of stored elements.Comment: 18 page