Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

Anwendung mikroanalytischer Methoden zur Lösung kunst- und kulturgeschichtlicher Probleme

Zusammenfassung Mit bekannten mikroanalytischen Arbeitsmethoden — Oberflächenreaktionen, Abstrichuntersuchungen mit dem Korundstäbchen, Schutzschichtreaktionen sowie dem Abdruckverfahren — lassen sich archaeometrische Probleme einer Lösung näherbringen. Die Art der Korrosion kupferhaltiger Oberflächen wurde diskutiert.

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Application of microanalytical methods to the solution of artistic- and cultural historical problems

Summary Archeometrical problems are brought closer to a solution by means of known microanalytical procedures-surface reactions, surface scraping studies with the corundum rod, protective layer reactions as well as the imprint method. A discussion of the corrosion of copper-bearing surfaces is included.

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Vortrag anläßlich der Tagung Chemische Analysen — Kunst- und Kulturwissenschaften im Reiß-Museum in Mannheim, 19.–21. September 1974.     

Information and Entropy Flow in the Kalman–Bucy Filter

We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract universe comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman–Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauers Principle.     

A Strong Approximation Theorem for Stochastic Recursive Algorithms

The constant stepsize analog of Gelfand–Mitter type discrete-time stochastic recursive algorithms is shown to track an associated stochastic differential equation in the strong sense, i.e., with respect to an appropriate divergence measure.     

Hereditary differential systems with constant delays. II. A class of affine systems and the adjoint problem

In this paper we (i) specialize some of the results of Delfour and Mitter (J. Differential Equations, 12, 1972, 213–235) to a class of representable affine hereditary differential systems, (ii) introduce the hereditary adjoint system, and (iii) give an integral representation of solutions.     

On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus

In previous papers, Mitter (J Stat Phys 163:1235–1246, 2016; Erratum: J Stat Phys 166:453–455, 2017; On a finite range decomposition of the resolvent of a fractional power of the Laplacian, http://arxiv.org/abs/1512.02877), we proved the existence as well as regularity of a finite range decomposition for the resolvent \(G_{\alpha } (x-y,m^2) = ((-\Delta )^{\alpha \over 2} + m^{2})^{-1} (x-y) \), for \(0<\alpha <2\) and all real m, in the lattice \({{\mathbb Z}}^{d}\) for dimension \(d\ge 2\). In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus \({{\mathbb Z}}^{d}/L^{N+1}{{\mathbb Z}}^{d} \) for \(d\ge 2\) provided \(m\ne 0\) and \(0<\alpha <2\). We also prove differentiability and uniform continuity properties with respect to the resolvent parameter \(m^{2}\). Here L is any odd positive integer and \(N\ge 2\) is any positive integer.     

Integration with respect to operator-valued measures with applications to quantum estimation theory

Summary This paper is concerned with the development of an integration theory with respect to operator-valued measures which is required in the study of certain convex optimization problems. These convex optimization problems in their turn are rigorous formulations of detection theory in a quantum communication context, which generalise classical (Bayesian) detection theory. The integration theory which is developed in this paper is used in conjunction with convex analysis in Banach spaces to give necessary and sufficient conditions of optimality for this class of convex optimization problems.This research has been supported by the Air Force Office of Scientific Research under Grants AFOSR 77-3281D and AFOSR 82-0135 and the National Science Foundation under Grant NSF ENG 76-02860. A portion of this research was done while the first author was a CNR Visiting Professor at Istituto Matematico U. Dini, Università di Firenze, Italy.     

The two-dimensionalO(N) nonlinear σ-model: Renormalisation and effective actions

We establish the existence of the Wilson Renormalised trajectory of theO(N) sigma model in perturbation theory in the effective charge. This yields a proof of perturbative renormalisability, and is also relevant in the small-field analysis of the rigorous renormalisation group construction of the continuum theory.Laboratoire associé au CNRS UA 280On leave from the Tata Institute of Fundamental Research, Bombay, 400 005, IndiaResearch funded in part by NSF grant DMS 8601978     

Critical (Φ4)3,ε

The Euclidean (⁴)_3, model in R³ corresponds to a perturbation by a ⁴ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter in the range 01. For =1 one recovers the covariance of a massless scalar field in R³. For =0, ⁴ is a marginal interaction. For 0<1 the covariance continues to be Osterwalder-Schrader and pointwise positive. We consider the infinite volume critical theory with a fixed ultraviolet cutoff at the unit length scale and we prove that for >0, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. We construct the stable critical manifold near this fixed point and prove that under Renormalization Group iterations the critical theories converge to the fixed point. Partially supported by NSERC of CanadaLaboratoire Associé au CNRS. UMR 5825Partially supported by CNR, G.N.F.M. and MURST