An approach to black hole quantization is proposed wherein it is assumed that quantum coherence is preserved. A consequence of this is that the Penrose diagram describing gravitational collapse will show the same topological structure as flat Minkowski space. After giving our motivations for such a quantization procedure we formulate the background field approximation, in which particles are divided into "hard" particles and "soft" particles. The background space-time metric depends both on the in-states and on the out-states. We present some model calculations and extensive discussions. In particular, we show, in the context of a toy model, that the S-matrix describing soft particles in the hard particle background of a collapsing star is unitary, nevertheless, the spectrum of particles is shown to be approximately thermal. We also conclude that there is an important topological constraint on functional integrals.

Networks offer a powerful tool for understanding and visualizing inter-species ecological and evolutionary interactions. Previously considered examples, such as trophic networks, are just representations of experimentally observed direct interactions. However, species interactions are so rich and complex it is not feasible to directly observe more than a small fraction. In this paper, using data mining techniques, we show how potential interactions can be inferred from geographic data, rather than by direct observation. An important application area for this methodology is that of emerging diseases, where, often, little is known about inter-species interactions, such as between vectors and reservoirs. Here, we show how using geographic data, biotic interaction networks that model statistical dependencies between species distributions can be used to infer and understand inter-species interactions. Furthermore, we show how such networks can be used to build prediction models. For example, for predicting the most important reservoirs of a disease, or the degree of disease risk associated with a geographical area. We illustrate the general methodology by considering an important emerging disease - Leishmaniasis. This data mining methodology allows for the use of geographic data to construct inferential biotic interaction networks which can then be used to build prediction models with a wide range of applications in ecology, biodiversity and emerging diseases.

Abstract:We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are "environment" dependent. Relevant environmental parameters considered are: temperature, system size, boundary conditions, and external fields. The points in the space of "coupling constants" at which such systems exhibit scale invariance coincide only with the fixed points of a global renormalization group which is necessarily environment dependent. Using such a renormalization group we give formal expressions to two loops for effective critical exponents for a generic crossover induced by a relevant mass scale g. These effective exponents are seen to obey scaling laws across the entire crossover, including hyperscaling, but in terms of an effective dimensionality, d ef f = 4 − γ λ , which represents the effects of the leading irrelevant operator. We analyze the crossover of an O(N ) model on a d dimensional layered geometry with periodic, antiperiodic and Dirichlet boundary conditions. Explicit results to two loops for effective exponents are obtained using a [2,1] Padé resummed coupling, for: the "Gaussian model" (N = −2), spherical model (N = ∞), Ising Model (N = 1), polymers (N = 0), XY-model (N = 2) and Heisenberg (N = 3) models in four dimensions. We also give two loop Padé resummed results for a three dimensional Ising ferromagnet in a transverse magnetic field and corresponding one loop results for the two dimensional model. One loop results are also presented for a three dimensional layered Ising model with Dirichlet and antiperiodic boundary conditions. Asymptotically the effective exponents are in excellent agreement with known results.

An evolution equation for a population of strings evolving under the genetic operators, selection, mutation, and crossover, is derived. The corresponding equation describing the evolution of schemata is found by performing an exact coarse graining of this equation. In particular, exact expressions for schema reconstruction are derived that allow for a critical appraisal of the ''building-block hypothesis'' of genetic algorithms. A further coarse graining is made by considering the contribution of all length-l schemata to the evolution of population observables such as fitness growth. As a test function for investigating the emergence of structure in the evolution, the increase per generation of the in-schemata fitness averaged over all schemata of length l, ⌬ l , is introduced. In finding solutions to the evolution equations we concentrate more on the effects of crossover; in particular, we consider crossover in the context of Kauffman Nk models with kϭ0,2. For k ϭ0, with a random initial population, in the first step of evolution the contribution from schema reconstruction is equal to that of schema destruction leading to a scale invariant situation where the contribution to fitness of schemata of size l is independent of l. This balance is broken in the next step of evolution, leading to a situation where schemata that are either much larger or much smaller than half the string size dominate those with lϷN/2. The balance between block destruction and reconstruction is also broken in a kϾ0 landscape. It is conjectured that the effective degrees of freedom for such landscapes are landscape connective trees that break down into effectively fit smaller blocks, and not the blocks themselves. Numerical simulations confirm this ''connective tree hypothesis'' by showing that correlations drop off with connective distance and not with intrachromosomal distance.