the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxent-normal ” approximation. We describe the relationship between four different methods that can be used

solutions to this problem. Corporate finance has relied on clustered standard errors, while asset pricing has used the Fama-MacBeth procedure to estimate standard errors. This paper examines the different methods used in the literature and explains when the different methods yield the same (and correct

In my Les–Houches lectures of 1982 I described the inverse scattering method of solving the integrable field–theoretical models in 1+1 dimensional space–time. Both classical case, stemming from the famous paper by Gardner, Green, Kruskal and Miura of 1967 on KdV equation, and its quantum

For many years the structure of 1+1 dimensional systems (one space + one time dimension) has been of great interest for mathematical physics. The Bethe Ansatz is a unifying method connecting a wide range of different problems in these areas. It has been applied to magnetic chains in solid state

, and adaptation. Here, we develop a new ‘‘relaxed-clock’’ phylogenetic method to estimate absolute rates of synonymous and nonsynonymous substitution through time. We identify an unexpected association between the synonymous substitution rate of HIV and disease progression parameters. Since immune activation

(Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102 Capability Maturity Model SM for Software, Version 1.1 Mark C. Paulk, Bill Curtis, Mary Beth Chrissis, Charles V. Weber In November 1986, the Software Engineering Institute (SEI), with assistance from the Mitre Corporation, began developing a process

mediators or contradicting recommendations, it is necessary to have a means of estimating its trustworthiness. In this paper we present a method for the valuation of trustworthiness which can be used to accept or reject an entity as being suitable for sensitive tasks. It constitutes an extension of the work

set of non-linear equations, so-called the Bethe equation. On the other hand, the BP algorithm is a popular heuristic method for estimating marginal distribution in a graphical model. Although they are inspired and developed from different directions, Yedidia, Freeman and Weiss (2004) established a

better performance and, for attractive models, yields a fully polynomial-time approximation scheme (FPTAS) without any degree restriction. Further, our methods apply to general (nonattractive) models, though with no polynomial time guarantee in this case, demonstrating that approximating log of the Bethe

The paper is a review of recent works devoted to analysis of classical integrable structures in quantum integrable models solved by one or another version of the Bethe ansatz. Similarities between elements of the quantum and classical theories of integrable systems are discussed. Some key notions