Equilibrium Statistical Mechanics of Fermion Lattice Systems

We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the equivalence of the KMS condition and the variational principle with a minimal assumption for the dynamics and without any explicit assumption on the potential. It holds also for spin lattice systems as well, yielding a vast improvement over known results. All formulations are in terms of a C*-dynamical systems for the Fermion (CAR) algebra with all or a part of the following assumptions: (I) The interaction is even with respect to the Fermion number. (Automatically satisfied when (IV) below is assumed.) (II) All strictly local elements of the algebra have the first time derivative. (III) The time derivatives in (II) determine the dynamics. (IV) The interaction is lattice translation invariant. A major technical tool is the conditional expectation from the total algebra onto the local subalgebra for any finite subset of the lattice, which induces a system of commuting squares. This technique overcomes the lack of tensor product structures for Fermion systems and even simplifies many known arguments for spin lattice systems.Comment: 103 pages, no figure. The Section 13 has become simpler and a problem in 14.1 is settled thanks to a referee. The format has been revised according to the suggestion of this and the other referee

A tight analysis of Kierstead-Trotter algorithm for online unit interval coloring

Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their algorithm is an optimal online algorithm for the online interval coloring problem. In this paper, for online unit interval coloring, we show that the number of colors used by the Kierstead-Trotter algorithm is at most $3 \omega(G) - 3$, where $\omega(G)$ is the size of the maximum clique in a given graph $G$, and it is the best possible.Comment: 4 page

Maximally entangled fermions

Fermions play an essential role in many areas of quantum physics and it is desirable to understand the nature of entanglement within systems that consists of fermions. Whereas the issue of separability for bipartite fermions has extensively been studied in the present literature, this paper is concerned with maximally entangled fermions. A complete characterization of maximally entangled quasifree (gaussian) fermion states is given in terms of the covariance matrix. This result can be seen as a step towards distillation protocols for maximally entangled fermions.Comment: 13 pages, 1 figure, RevTex, minor errors are corrected, section "Conclusions" is adde

Bayesian Value-of-Information Analysis: An Application to a Policy Model of Alzheimer's Disease

A framework is presented which distinguishes the conceptually separate decisions of which treatment strategy is optimal from the question of whether more information is required to inform this choice in the future. The authors argue that the choice of treatment strategy should be based on expected utility and the only valid reason to characterise the uncertainty surrounding outcomes of interest is to establish the value of acquiring additional information. A Bayesian decision theoretic approach is demonstrated though a probabilistic analysis of a published policy model of Alzheimer’s disease. The expected value of perfect information is estimated for the decision to adopt a new pharmaceutical for the population of US Alzheimer’s disease patients. This provides an upper bound on the value of additional research. The value of information is also estimated for each of the model inputs. This analysis can focus future research by identifying those parameters where more precise estimates would be most valuable, and indicating whether an experimental design would be required. We also discuss how this type of analysis can also be used to design experimental research efficiently (identifying optimal sample size and optimal sample allocation) based on the marginal cost and marginal benefit of sample information. Value-of-information analysis can provide a measure of the expected payoff from proposed research, which can be used to set priorities in research and development. It can also inform an efficient regulatory framework for new health care technologies: an analysis of the value of information would define when a claim for a new technology should be deemed “substantiated” and when evidence should be considered “competent and reliable” when it is not cost-effective to gather anymore information.stochastic CEA; Bayesian decision theory; value of information.

Monotonicity of quantum relative entropy revisited

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong sub-additivity of the von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantity.The relation to quantum Markovian states is briefly indicated.Comment: 13 pages, LATEX fil