In the Garden of Branching Processes

The current paper surveys and develops numerical methods for Markovian multitype branching processes in continuous time. Particular attention is paid to the calculation of means, variances, extinction probabilities, and marginal distributions in the presence of a Poisson stream of immigrant particles. The Poisson process assumption allows for temporally complex patterns of immigration and facilitates application of marked Poisson processes and Campbell’s formulas. The methods and formulas derived are applied to four models: two population genetics models, a model for vaccination against an infectious disease in a community of households, and a model for the growth of resistant HIV virus in patients undergoing drug therap

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Hadronic decay of the gravitino in the early universe and its implications to inflation

We discuss the effects of the gravitino on the big-bang nucleosynthesis (BBN), paying particular attention to the hadronic decay mode of the gravitino. We will see that the hadronic decay of the gravitino significantly affect the BBN and, for the case where the hadronic branching ratio is sizable, very stringent upper bound on the reheating temperature after inflation is obtained.Comment: 6 pages, 2 Postscript figures, Talk given at PASCOS'04 (Boston, MA, August 16 -- 22 (2004

Search for Interstellar Water in the Translucent Molecular Cloud toward HD 154368

We report an upper limit of 9 x 10^{12} cm-2 on the column density of water in the translucent cloud along the line of sight toward HD 154368. This result is based upon a search for the C-X band of water near 1240 \AA carried out using the Goddard High Resolution Spectrograph of the Hubble Space Telescope. Our observational limit on the water abundance together with detailed chemical models of translucent clouds and previous measurements of OH along the line of sight constrain the branching ratio in the dissociative recombination of H_3O+ to form water. We find at the $3\sigma$ level that no more than 30% of dissociative recombinations of H_3O+ can lead to H_2O. The observed spectrum also yielded high-resolution observations of the Mg II doublet at 1239.9 \AA and 1240.4 \AA, allowing the velocity structure of the dominant ionization state of magnesium to be studied along the line of sight. The Mg II spectrum is consistent with GHRS observations at lower spectral resolution that were obtained previously but allow an additional velocity component to be identified.Comment: Accepted by ApJ, uses aasp

Flora robotica -- An Architectural System Combining Living Natural Plants and Distributed Robots

Key to our project flora robotica is the idea of creating a bio-hybrid system of tightly coupled natural plants and distributed robots to grow architectural artifacts and spaces. Our motivation with this ground research project is to lay a principled foundation towards the design and implementation of living architectural systems that provide functionalities beyond those of orthodox building practice, such as self-repair, material accumulation and self-organization. Plants and robots work together to create a living organism that is inhabited by human beings. User-defined design objectives help to steer the directional growth of the plants, but also the system's interactions with its inhabitants determine locations where growth is prohibited or desired (e.g., partitions, windows, occupiable space). We report our plant species selection process and aspects of living architecture. A leitmotif of our project is the rich concept of braiding: braids are produced by robots from continuous material and serve as both scaffolds and initial architectural artifacts before plants take over and grow the desired architecture. We use light and hormones as attraction stimuli and far-red light as repelling stimulus to influence the plants. Applied sensors range from simple proximity sensing to detect the presence of plants to sophisticated sensing technology, such as electrophysiology and measurements of sap flow. We conclude by discussing our anticipated final demonstrator that integrates key features of flora robotica, such as the continuous growth process of architectural artifacts and self-repair of living architecture.Comment: 16 pages, 12 figure

Critical dynamics of the k-core pruning process

We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree of the initial network is above, equal to, or below the threshold _c corresponding to the emergence of the giant k-core. We find that above the threshold the network relaxes exponentially to the k-core. The system manifests the phenomenon known as "critical slowing down", as the relaxation time diverges when tends to _c. At the threshold, the dynamics become critical characterized by a power-law relaxation (1/t^2). Below the threshold, a long-lasting transient process (a "plateau" stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when tends to _c. We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly k are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time dependent distribution function of branching. These theoretical results are supported by our simulations of the $k$-core pruning in Erdos-Renyi graphs.Comment: 12 pages, 10 figure

Implicit learning of recursive context-free grammars

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning