There is a clear connection between probability and logic: both appear to tell us how we should reason. But how, exactly, are the two concepts related? The need for a coherent answer to this question has become increasingly urgent in the past few years, particularly in the field of artificial intelligence. There, both logical and probabilistic techniques are routinely applied in an attempt to s...

It is shown that for each odd integer q, there is a complex WilliamsonHadamard matrix of order 2(q)+1 ·2n (q)+1 . q. In a recent paper Craigen, Holzmann and Kharaghani [1] showed that for every odd integer q) there is an integer N( q) which does not exceed twice the number of nonzero digits in the binary expansion of q, such that the existence of an Orthogonal Design (OD) of order 2N (q)-1 impl...

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical...

Abstract We study the behavior of an algorithm derived from the cavity method for the Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms ...

In 1937, Ronald Coase argued that firms will exist only in environments in which firms perform better than markets could. To create space for firms, Coase suggested that some environments might be plagued by “transaction costs” that cause markets to perform poorly. Coase’s paper was to become the cornerstone of the economic theory of the firm (i.e., the “make or buy” decision: which activities ...

G-DNA is a polymorphic family of quadruple helical nucleic acid structures containing guanine tetrad motifs [G-quartets; Williamson, J.R., Raghuraman, M.K. and Cech, T.R. (1989) Cell 59, 871-880; Williamson, J.R. (1993) Proc. Natl. Acad. Sci. USA 90, 3124-3124]. Guanine rich oligonucleotides that are self-complimentary, as found in many telomeric G-strand repeat sequences, form G-DNA in the pre...

It is well known that two prover proof systems are a convenient tool for establishing hardness of approximation results. In this paper, we show that two prover proof systems are also convenient starting points for establishing easiness of approximation results. Our approach combines the Feige-Lovv asz (STOC92) semideenite programming relaxation of one-round two-prover proof systems, together wi...

Russo and Williamson (2007) put forward the thesis that, at least in the health sciences, to establish the claim that C is a cause of E one normally needs evidence of an underlying mechanism linking C and E as well as evidence that C makes a difference to E. This epistemological thesis poses a problem for most current analyses of causality which, in virtue of analysing causality in terms of jus...

This essay is a discussion of the role of the forensic psychiatrist in malpractice cases as an expert witness establishing the standards of care for the psychiatric profession. The occasion for these comments, which hopefully will lead to constructive dialogue and response, is the much discussed malpractice case of Weizdell Williamson v. Doctor Myron Liptzin (Cal., Orange County Sup. Ct., Dkt. ...

In chapter 9 of Knowledge and its Limits, Timothy Williamson argues for the thesis that the evidence that a subject has is constituted by propositions known by the subject (a thesis that he summarizes in the equation E=K). Moreover, Williamson also argues that whatever justifies a subject in believing a proposition is part of that subject’s evidence, and thus that only propositions that a subje...