Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

We consider stochastic processes, S^t \equiv (S_x^t : x \in Z^d), with each S_x^t taking values in some fixed finite set, in which spin flips (i.e., changes of S_x^t) do not raise the energy. We extend earlier results of Nanda-Newman-Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.Comment: 11 page

A New Theory of Consciousness: The Missing Link - Organization

What is consciousness and what is the missing link between the sensory input and the cortical centre in the brain for consciousness? In the literature there are more than a million pages written about consciousness. The perspectives range from the field of metaphysics to those of quantum mechanics. However, no one today has produced a theory which is universally accepted. Consciousness is “something” which the majority of humans know that they posses, they use it when they want to understand their environment. However, no individual human knows whether other humans also posses consciousness. unless some tests such as she is looking at me, he is talking etc., are performed. We are caught in an intellectual sort of recursive carousel – we need consciousness to understand consciousness. To understand consciousness we have to understand the mechanism of its function, which is to effectively organize sensory inputs from our environment. Consciousness is the outcome of the process of organizing these sensory inputs. This implies that organization is an act which precedes consciousness. Since every activity in nature is to organize/disorganize, what is the element which compels this action? I am proposing that just like energy is the physical element that causes action, there is another physical element I have called it NASCIUM which has the capacity to cause organization. This is the missing link. Understanding the nature of organization, i.e. nascium, will enhance our capability to understand consciousness

Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in ${\bf Z}^2$, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, polls its 4 neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times $t< \infty$, but the cluster of a fixed site diverges (in diameter) as $t \to \infty$; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.Comment: 16 pages, 1 figur

myExperiment: An ontology for e-Research

myExperiment describes itself as a "Social Virtual Research Environment" that provides the ability to share Research Objects (ROs) over a social infrastructure to facilitate actioning of research. The myExperiment Ontology is a logical representation of the data model used by this environment, allowing its data to be published in a standard RDF format, whilst providing a generic extensible framework that can be reused by similar projects. ROs are data structures designed to semantically enhance research publications by capturing and preserving the research method so that it can be reproduced in the future. This paper provides some motivation for an RO specification and briefly considers how existing domain-specifific ontologies might be integrated. It concludes by discussing the future direction of the myExperiment Ontology and how it will best support these ROs

Self-organized Criticality on Small World Networks

We study the BTW-height model of self-organized criticality on a square lattice with some long range connections giving to the lattice the character of small world network. We find that as function of the fraction $p$ of long ranged bonds the power law of the avalanche size and lifetime distribution changes following a crossover scaling law with crossover exponents 2/3 and 1 for size and lifetime respectively.Comment: 7 figure

Growth and structure of Slovenia's scientific collaboration network

We study the evolution of Slovenia's scientific collaboration network from 1960 till present with a yearly resolution. For each year the network was constructed from publication records of Slovene scientists, whereby two were connected if, up to the given year inclusive, they have coauthored at least one paper together. Starting with no more than 30 scientists with an average of 1.5 collaborators in the year 1960, the network to date consists of 7380 individuals that, on average, have 10.7 collaborators. We show that, in spite of the broad myriad of research fields covered, the networks form "small worlds" and that indeed the average path between any pair of scientists scales logarithmically with size after the largest component becomes large enough. Moreover, we show that the network growth is governed by near-liner preferential attachment, giving rise to a log-normal distribution of collaborators per author, and that the average starting year is roughly inversely proportional to the number of collaborators eventually acquired. Understandably, not all that became active early have till now gathered many collaborators. We also give results for the clustering coefficient and the diameter of the network over time, and compare our conclusions with those reported previously.Comment: 10 pages, 3 figures; accepted for publication in Journal of Informetrics [related work available at http://arxiv.org/abs/1003.1018 and http://www.matjazperc.com/sicris/stats.html

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.Comment: 7 pages, 3 figures, 2 table

Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the Tagged Particle at time $t$ depends on the initial configuration, by the number of empty sites in the interval $[0,(p-q)\alpha t]$ divided by $\alpha$ in the hyperbolic and in a longer time scale, namely $N^{4/3}$.Comment: 28 pages, no figure

Scientific Social Objects: The Social Objects and Multidimensional Network of the myExperiment Website

Scientific research is increasingly conducted digitally and online, and consequently we are seeing the emergence of new digital objects shared as part of the conduct and discourse of science. These Scientific Social Objects are more than lumps of domain-specific data: they may comprise multiple components which can also be shared separately and independently, and some contain descriptions of scientific processes from which new objects will be generated. Using the myExperiment social website as a case study we explore Scientific Social Objects and discuss their evolution