Operator hyperreflexivity of subspace lattices

We introduce and study the notion of operator hyperreflexivity of subspace lattices. This notion is a natural analogue of the operator reflexivity and is related to hyperreflexivity of subspace lattices introduced by Davidson and Harrison.

Physical model for the generation of ideal resources in multipartite quantum networking

We propose a physical model for generating multipartite entangled states of spin-s particles that have important applications in distributed quantum information processing. Our protocol is based on a process where mobile spins induce the interaction among remote scattering centers. As such, a major advantage lies in the management of stationary and well-separated spins. Among the generable states, there is a class of N-qubit singlets allowing for optimal quantum telecloning in a scalable and controllable way. We also show how to prepare Aharonov, W, and Greenberger-Horne-Zeilinger states.

Optimal control of atom transport for quantum gates in optical lattices

By means of optimal control techniques we model and optimize the manipulation of the external quantum state (center-of-mass motion) of atoms trapped in adjustable optical potentials. We consider in detail the cases of both noninteracting and interacting atoms moving between neighboring sites in a lattice of a double-well optical potentials. Such a lattice can perform interaction-mediated entanglement of atom pairs and can realize two-qubit quantum gates. The optimized control sequences for the optical potential allow transport faster and with significantly larger fidelity than is possible with processes based on adiabatic transport.

Phase diagram of spin-1 bosons on one-dimensional lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S=1 Heisenberg model with biquadratic interaction.

Non-competitive phenotypic differences can have a strong effect on ideal free distributions

1. We present a model of the ideal free distribution (IFD) where differences between phenotypes other than those involved in direct competition for resources are considered. We show that these post-acquisitional differences can have a dramatic impact on the predicted distributions of individuals.

2. Specifically, we predict that, when the relative abilities of phenotypes are independent of location, there will be a continuum of mixed evolutionarily stable strategy (ESS) distributions (where all phenotypes are present in all patches).

3, When the relative strengths of the post-acquisitional trait in the two phenotypes differ between patches, however, we predict only a single ESS at equilibrium. Further, this distribution may be fully or partially segregated (with the distribution of at least one phenotype being spatially restricted) but it will never be mixed.

4, Our results for post-acquisitional traits mirror those of Parker (1982) for direct competitive traits. This comparison illustrates that it does not matter whether individual differences are expressed before or after competition for resources, they will still exert considerable influence on the distribution of the individuals concerned.

How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks

A conceptual model is described for generating distributions of grazing animals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behaviors ranging from random diffusion, through taxis and cognitively aided navigation (i.e., using memory), to the optimization extreme of the Ideal Free Distribution. These behaviors are generated from simulation of biased diffusion that operates at multiple scales simultaneously, formalizing ideas of multiple-scale foraging behavior. It uses probabilistic bias to represent decisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bias to arise at multiple scales within the environment, each weighted relative to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows different constraints to be applied to the animal's ability (e.g., applying food-patch accessibility and information limits). Simulations show that foraging-decision randomness and spatial scale of decision bias have potentially profound effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can differentially change the spatial pattern of resource abundance in the environment to one characteristic of the foraging strategy.</

Beyond the ideal free distribution: More general models of predator distribution

The ideal free distribution model which relates the spatial distribution of mobile consumers to that of their resource is shown to be a limiting case of a more general model which we develop using simple concepts of diffusion. We show how the ideal free distribution model can be derived from a more general model and extended by incorporating simple models of social influences on predator spacing. First, a free distribution model based on patch switching rules, with a power-law interference term, which represents instantaneous biased diffusion is derived. A social bias term is then introduced to represent the effect of predator aggregation on predator fitness, separate from any effects which act through intake rate. The social bias term is expanded to express an optimum spacing for predators and example solutions of the resulting biased diffusion models are shown. The model demonstrates how an empirical interference coefficient, derived from measurements of predator and prey densities, may include factors expressing the impact of social spacing behaviour on fitness. We conclude that empirical values of log predator/log prey ratio may contain information about more than the relationship between consumer and resource densities. Unlike many previous models, the model shown here applies to conditions without continual input. (C) 1997 Academic Press Limited.</p>