Perfect simulation for interacting point processes, loss networks and Ising models

We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and perimeter-interacting point processes (with stochastic grains), invariant measures of loss networks, and the Ising contour and random cluster models. The algorithm does not involve couplings of the process with different initial conditions and it is not tied up to monotonicity requirements. Furthermore, it directly provides perfect samples of finite windows of the infinite-volume measure, subjected to time and space ``user-impatience bias''. The algorithm is based on a two-step procedure: (i) a perfect-simulation scheme for a (finite and random) relevant portion of a (space-time) marked Poisson processes (free birth-and-death process, free loss networks), and (ii) a ``cleaning'' algorithm that trims out this process according to the interaction rules of the target process. The first step involves the perfect generation of ``ancestors'' of a given object, that is of predecessors that may have an influence on the birth-rate under the target process. The second step, and hence the whole procedure, is feasible if these ``ancestors'' form a finite set with probability one. We present a sufficiency criteria for this condition, based on the absence of infinite clusters for an associated (backwards) oriented percolation model.Comment: Revised version after referee of SPA: 39 page

Spatial birth-and-death processes in random environment

We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the following holds for almost all realizations of the birth rates: (i) the process is ergodic with at worst power-law time mixing; (ii) the unique invariant measure has exponential decay of (spatial) correlations; (iii) there exists a perfect-simulation algorithm for the invariant measure. The results are obtained by first dominating the process by a backwards oriented percolation model, and then using a multiscale analysis due to Klein to establish conditions for the absence of percolation.Comment: 48 page

Loss network representation of Peierls contours

We present a probabilistic approach for the study of systems with exclusions, in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study of the Ising model at low temperatures, but most of the results are general. We realize the equilibrium measure as the invariant measure of a loss-network process whose existence is ensured by a subcriticality condition of a dominant branching process. In this regime, the approach yields, besides existence and uniqueness of the measure, properties such as exponential space convergence and mixing, and a central limit theorem. The loss network converges exponentially fast to the equilibrium measure, without metastable traps. This convergence is faster at low temperatures, where it leads to the proof of an asymptotic Poisson distribution of contours. Our results on the mixing properties of the measure are comparable to those obtained with ``duplicated-variables expansion'', used to treat systems with disorder and coupled map lattices. It works in a larger region of validity than usual cluster-expansion formalisms, and it is not tied to the analyticity of the pressure. In fact, it does not lead to any kind of expansion for the latter, and the properties of the equilibrium measure are obtained without resorting to combinatorial or complex analysis techniques.Comment: 42 pages. Revised version after the first referee repor

John Gibson, Designer: Sculpture and Reproductive Media in the Nineteenth Century

This article discusses the British sculptor John Gibson (1790-1866), whose studio in Rome was one of the most popular for those on the Grand Tour. He disseminated his interest in classicism through his many marble sculptures inspired by ancient Greek art, such as "Cupid Disguised as a Shepherd Boy," which was reproduced in lifesize marble at least nine times during his lifetime. But Gibson also utilized new technologies to spread his interest in disegno, allowing his designs to be reproduced by others as Parian porcelain statuettes, cameos, and prints. This redefinition from sculptor to designer culminated in a number of award-winning designs exhibited in his name at the Great Exhibition of 1851

Fanny Eaton: The 'Other' Pre-Raphaelite Model

This article traces the life of Fanny Eaton (1835-1924), the mixed-race Jamaican-born daughter of a former slave, who emigrated to London and became a model for painters in the Pre-Raphaelite circle during the 1860s. Her mixed-race status made her an exotic in the theatrical sense, allowing her to adopt different guises as subjects in their paintings, and offer an alternative form of the Pre-Raphaelite 'stunner.

Portraits, Landscapes, and Genre Scenes: New Discoveries in the 19th-Century Paintings Collection at Columbia University

This article discusses three nineteenth-century paintings from the Columbia University art collection, stewarded by Art Properties, Avery Architectural & Fine Arts Library: a portrait of Lord Byron by an unknown British artist after George Sanders; "The Sandpits near Valmondois (Les Sablières près Valmondois)" by the French artist Charles-François Daubigny; and "Military Scene" by the German artist Christian Sell

The Prince and Princess of Wales: Two Eighteenth-Century Portraits at Columbia University

For more than fifty years, two large royal portraits have hung high on the south wall of the main reading room of Butler Library. Donated by Edmund Astley Prentis in 1949, they were presented to Columbia as portraits by unknown artists of King George II and his wife. New research by the author shows they are in fact portraits of their son and daughter-in-law, the Prince and Princess of Wales, Frederick Louis and Augusta, the future parents of King George III. This essay discusses these portraits in more detail, including the identity of the painters and the discovery of a signature and date on one

Developement of integrated procedures for survey, analisys and monitoring of historical buildings and antique monuments

Peer Reviewe