A new approach for using path analysis to appraise the verisimilitude of theories is described. Rather than trying to test a model's truth (correctness), this method corroborates a class of path diagrams by determining how well they predict intradata relations in comparison with other diagrams. The observed correlation matrix is partitioned into disjoint sets. One set is used to estimate the mo...

The simplest approach that we can propose for high energy interaction is based 1,2 on the BFKL Pomeron 3 and reggeon-like diagram technique for the BFKL Pomeron interactions . This technique which is a generalization of Gribov Reggeon Calculus , can be written in the elegant form of the functional integral (see Ref. 5 and the next section); and it is a challenge to solve this theory in QCD find...

This work develops some technology for accessing the loop expansion of the Kontsevich integral of a knot. The setting is an application of the LMO invariant to certain surgery presentations of knots by framed links in the solid torus. A consequence of this technology is a certain recent conjecture of Rozansky’s. Rozansky conjectured that the Kontsevich integral could be organised into a series ...

From their inception in the early 20th century, causal systems models (more commonly known as structural-equations models) were accompanied by graphi-cal representations or path diagrams that provided compact summaries of qualitative assumptions made by the models. Fig. 1 provides a graph that would correspond to any system of 5 equations encoding these assumptions:

The analysis of the nonequilibrium cr T diagrams constructed from the results oftension/cornpression thermornechanical tests with [001] Cu-based shape memory alloy/SMA/ single crystals was found to be a good way how to understand complex path dependent phenomena exhibited by SMA single crystals. Particularly, it has been shown that the yi martensite phase forming in Cu-based SMA may exist in mu...

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive , two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of ex...

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of oneand two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less triv...

Wheeling: A Diagrammatic Analogue of the Duflo Isomorphism We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application...

The path integral gives us the time evolution operator, which in principle contains all the information about the dynamics of the system. However, in order to use the path integral to do physics we need to find a way to describe initial and final particle states in path integral language. The way to do this is to couple the fields to spacetimedependent background fields (“sources”) that can cre...

We study statistics on ordered set partitions whose generating functions are related to p, q-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of Steingŕımsson(Arxiv:math.CO/0605670). Our basic idea is to encode ordered partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structu...