Random growth models with polygonal shapes

We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for asymptotic shapes arising from finite initial seeds. Such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases. In many cases, exact stability is observed. That is, for small perturbations, the shapes of the deterministic and random processes agree exactly. We give a complete characterization of such cases, and show that they are prevalent among threshold growth CA with box neighborhood. We also design a nontrivial family of CA in which the shape is exactly computable for all values of its probability parameter.Comment: Published at http://dx.doi.org/10.1214/009117905000000512 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Aesthetic Philosophy of John Cage and the Visual Arts of the Twentieth Century

This thesis presents a biographical analysis of the role of American composer, writer, and artist John Cage (1912-1992) in the evolution of visual arts in the twentieth century. The origins of Cage\u27s aesthetic stance are discussed, particularly his melding of Marcel Duchamp\u27s Dada orientation with philosophical positions derived from the study of Zen Buddhism. The influence of His views on painters, sculptors, and performance artists of the postwar period is documented, along with the aesthetic foundations of his own work in the visual arts

Damage spreading and coupling in Markov chains

In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional spin glasses and hard spheres we point out that the obstacle to the application of perfect-sampling schemes is posed by damage spreading rather than by the survey problem of the entire configuration space. We find dynamical damage-spreading transitions deeply inside the paramagnetic and liquid phases, and show that critical values of the transition temperatures and densities depend on the coupling scheme. We discuss our findings in the light of a classic proof that for arbitrary Monte Carlo algorithms damage spreading can be avoided through non-Markovian coupling schemes.Comment: 6 pages, 8 figure

War sirens: how the sheet music industry sold World War I

Title from PDF of title page, viewed on August 26, 2011Thesis advisor: Sarah TyrrellVitaIncludes bibliographical references (p. 126-135)Thesis (M.M.)--Conservatory of Music and Dance. University of Missouri--Kansas City, 2011During World War I the U.S. Committee on Public Information (CPI) sponsored a national culture of war in posters, speeches, and films. Against this war-soaked cultural backdrop, the sheet music industry echoed the pervasive messages of the CPI, often using images of women to appeal to the American people. Connections between sheet music and CPI poster themes reflect the cultural dominance of war messages, and themes from various CPI-sponsored materials recur as motifs in the era's sheet music. The sheet music covers, lyrics, and musical cues reinforced prototypical roles for women during the war (from angelic nurses to flirtatious tomboy recruits) as established in the poster art, revealing a gendered cultural code. By purchasing sheet music and carrying it into their homes, American citizens literally bought into the war propaganda, heeding the siren call of the female imagery in CPI advertising to invest materially and emotionally in the war effort. Analysis of cover art, titles, lyrics, and musical examples highlights the use of archetypal images of women from poster and advertising traditions, suggesting that the sheet music industry was an unofficial partner of the CPI.Introduction -- Motherhood and war -- Sister Susie sews at home -- The girls they left behind -- Angels and madonnas -- Red Cross girlies and Salvation lassies -- The American girl vs. the French fling -- Columbia, the Amazon warrior --Joan of Arc -- Conclusio

Transmission of packets on a hierarchical network: Statistics and explosive percolation

We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell - Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2-D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V- lattice, the critical case of the 2-D lattice. We discuss the implications of our analysis.Comment: 24 pages, 41 figure

Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion

Growth and Decay in Life-Like Cellular Automata

We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding box placed around them? And do there exist patterns that die out completely? If both of these conditions are true, then a cellular automaton rule is likely to support spaceships, small patterns that move and that form the building blocks of many of the more complex patterns that are known for Life. If one or both of these conditions is not true, then there may still be phenomena of interest supported by the given cellular automaton rule, but we will have to look harder for them. Although our classification is very crude, we argue that it is more objective than Wolfram's (due to the greater ease of determining a rigorous answer to these questions), more predictive (as we can classify large groups of rules without observing them individually), and more accurate in focusing attention on rules likely to support patterns with complex behavior. We support these assertions by surveying a number of known cellular automaton rules.Comment: 30 pages, 23 figure

Maximum Likelihood Estimator for Hidden Markov Models in continuous time

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions of the chain.Comment: Warning: due to a flaw in the publishing process, some of the references in the published version of the article are confuse

Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table