Three results are shown which demonstrate how Vassiliev invariants behave like polynomials. 0. Introduction. The purpose of this note is to show how the phrase \Vassiliev invariants are like polynomials" can be a useful working paradigm. This has been illustrated in other talks at this conference: Deguchi used Vassiliev invariants because they are computable in polynomial time (see below) and B...

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general formula for the superpotential and justify it comparing the supersymmetry condit...

Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the ‘cubic’ point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In particular, we get a natural explanation why they behave like polynomials. AM...

There is growing interest in modeling nonlinear behavior in the speech signal, particularly for applications such as speech recognition. Conventional tools for analyzing speech data use information from the power spectral density of the time series, and hence are restricted to the first two moments of the data. These moments do not provide a sufficient representation of a signal with strong non...

We consider a Leray-type regularization of the compressible Euler equations for an isothermal gas. The regularized system depends on a small parameter α > 0. Using Riemann invariants, we prove the existence of smooth solutions for the regularized system for every α > 0. The regularization mechanism is a nonlinear bending of characteristics that prevents their finite-time crossing. We prove that...

The “Object Constraint Language” (OCL) offers a formal notation for constraining model elements in UML diagrams. OCL consists of a navigational expression language which, for instance, can be used to state invariants and preand post-conditions in class diagrams. We discuss some problems in ensuring non-local, navigating OCL class invariants, as for bidirectional associations, in programming lan...

This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynami...

Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of estimating confidence intervals, however, such confidence intervals do not reflect variability in the underlying dynamics. We propose a surrogate based method to ...

As algebraic topologists, we study geometric objects via their algebraic invariants. Ideally, we want the invariants that we study to have some degree of computational universality with regards to our spaces–that is, we like to be able to compute our invariants on lots of different spaces with the same sorts of techniques. Perhaps the best example of such invariants are complex oriented cohomol...

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, biomedicine, where estimations based on graph invariants have made available for effectively communicating with the different challenging tasks. Irregularity are mostly characterization nonregul...