We discuss both the UV and IR origin of the one-loop triangle gauge anomalies for noncommutative nonabelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups. We find that gauge anomalies only come from planar triangle diagrams, the non-planar triangle contributions giving rise to no breaking of the Ward identies. Generally speaking, theories with funda...

We study modular, automatic code generation from hierarchical block diagrams with synchronous semantics. Such diagrams are the fundamental model behind widespread tools such as Simulink and SCADE. Modularity means code is generated for a given composite block independently from context, that is, without knowing in which diagrams this block is going to be used. This can be achieved by abstractin...

Virtually all scientific documents contain informational diagrams. To build knowledge bases representing this literature, the diagrams must be semantically analyzed. In our system, diagrams are represented as collections of geometric objects. The fundamental organizing principle for these objects is the Generalized Equivalence Relation (GER). Examples include Near, Parallel, and Aligned. These ...

Timing diagrams are useful for capturing temporal specifications in which all mentioned events are required to occur. We first show that translating timing diagrams with both partial orders on events and don’t-care regions to LTL potentially yields exponentially larger formulas containing several non-localized terms corresponding to the same event. This raises a more fundamental question: which...

Refinement is fundamental to software development. An earlier work proposed a refinement relation between sequence diagrams based on their required behaviors. In this paper, we first generalize the refinement relation by taking into account system variable assignment and event hiding, renaming and substitution. We then give an algorithm as a system of inference rules that does not just verify r...

In view of the result of Kontsevich, [5] now often called “the fundamental theorem of Vassiliev theory”, identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the “4T-relation” (and in the unframed case, originally considered in [7], [5], and [1], the “1T-” or “isolated chord relati...

This paper is about spider diagrams, an extension of Euler diagrams that includes syntax to make assertions about set cardinalities. Like many diagrammatic logics, spider diagrams are a monadic and first-order, so they are inexpressive. The limitation to first-order precludes the formalisation of many fundamental concepts such as the cardinality of a set being even. To this end, second-order sp...

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework...