Stochastic models in population biology and their deterministic analogs

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure

Nonabelian Phenomena on D-branes

A remarkable feature of D-branes is the appearance of a nonabelian gauge theory in the description of several (nearly) coincident branes. This nonabelian structure plays an important role in realizing various geometric effects with D-branes. In particular, the branes' transverse displacements are described by matrix-valued scalar fields and so noncommutative geometry naturally appears in this framework. I review the action governing this nonabelian theory, as well as various related physical phenomena such as the dielectric effect, giant gravitons and fuzzy funnels.Comment: Lecture at Leuven workshop on ``The quantum structure of spacetime and the geometrical nature of fundamental interactions'' (September 13-19, 2002); ref.'s adde

Identification of Radiopure Titanium for the LZ Dark Matter Experiment and Future Rare Event Searches

The LUX-ZEPLIN (LZ) experiment will search for dark matter particle interactions with a detector containing a total of 10 tonnes of liquid xenon within a double-vessel cryostat. The large mass and proximity of the cryostat to the active detector volume demand the use of material with extremely low intrinsic radioactivity. We report on the radioassay campaign conducted to identify suitable metals, the determination of factors limiting radiopure production, and the selection of titanium for construction of the LZ cryostat and other detector components. This titanium has been measured with activities of $^{238}$U$_{e}$~$<$1.6~mBq/kg, $^{238}$U$_{l}$~$<$0.09~mBq/kg, $^{232}$Th$_{e}$~$=0.28\pm 0.03$~mBq/kg, $^{232}$Th$_{l}$~$=0.25\pm 0.02$~mBq/kg, $^{40}$K~$<$0.54~mBq/kg, and $^{60}$Co~$<$0.02~mBq/kg (68\% CL). Such low intrinsic activities, which are some of the lowest ever reported for titanium, enable its use for future dark matter and other rare event searches. Monte Carlo simulations have been performed to assess the expected background contribution from the LZ cryostat with this radioactivity. In 1,000 days of WIMP search exposure of a 5.6-tonne fiducial mass, the cryostat will contribute only a mean background of $0.160\pm0.001$(stat)$\pm0.030$(sys) counts.Comment: 13 pages, 3 figures, accepted for publication in Astroparticle Physic

The Majorana Project

Building a \BBz experiment with the ability to probe neutrino mass in the inverted hierarchy region requires the combination of a large detector mass sensitive to \BBz, on the order of 1-tonne, and unprecedented background levels, on the order of or less than 1 count per year in the \BBz signal region. The MAJORANA Collaboration proposes a design based on using high-purity enriched Ge-76 crystals deployed in ultra-low background electroformed Cu cryostats and using modern analysis techniques that should be capable of reaching the required sensitivity while also being scalable to a 1-tonne size. To demonstrate feasibility, the collaboration plans to construct a prototype system, the MAJORANA DEMONSTRATOR, consisting of 30 kg of 86% enriched \Ge-76 detectors and 30 kg of natural or isotope-76-depleted Ge detectors. We plan to deploy and evaluate two different Ge detector technologies, one based on a p-type configuration and the other on n-type.Comment: paper submitted for the 2008 Carolina International Symposium on Neutrino Physic

Cohomology of Filippov algebras and an analogue of Whitehead's lemma

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.Comment: plain latex, no figures, 29 page

An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments

<p>Abstract</p> <p>Background</p> <p>Metabolic fluxes provide invaluable insight on the integrated response of a cell to environmental stimuli or genetic modifications. Current computational methods for estimating the metabolic fluxes from ¹³<it>C </it>isotopomer measurement data rely either on manual derivation of analytic equations constraining the fluxes or on the numerical solution of a highly nonlinear system of isotopomer balance equations. In the first approach, analytic equations have to be tediously derived for each organism, substrate or labelling pattern, while in the second approach, the global nature of an optimum solution is difficult to prove and comprehensive measurements of external fluxes to augment the ¹³<it>C </it>isotopomer data are typically needed.</p> <p>Results</p> <p>We present a novel analytic framework for estimating metabolic flux ratios in the cell from ¹³<it>C </it>isotopomer measurement data. In the presented framework, equation systems constraining the fluxes are derived automatically from the model of the metabolism of an organism. The framework is designed to be applicable with all metabolic network topologies, ¹³<it>C </it>isotopomer measurement techniques, substrates and substrate labelling patterns.</p> <p>By analyzing nuclear magnetic resonance (NMR) and mass spectrometry (MS) measurement data obtained from the experiments on glucose with the model micro-organisms <it>Bacillus subtilis </it>and <it>Saccharomyces cerevisiae </it>we show that our framework is able to automatically produce the flux ratios discovered so far by the domain experts with tedious manual analysis. Furthermore, we show by <it>in silico </it>calculability analysis that our framework can rapidly produce flux ratio equations – as well as predict when the flux ratios are unobtainable by linear means – also for substrates not related to glucose.</p> <p>Conclusion</p> <p>The core of ¹³<it>C </it>metabolic flux analysis framework introduced in this article constitutes of flow and independence analysis of metabolic fragments and techniques for manipulating isotopomer measurements with vector space techniques. These methods facilitate efficient, analytic computation of the ratios between the fluxes of pathways that converge to a common junction metabolite. The framework can been seen as a generalization and formalization of existing tradition for computing metabolic flux ratios where equations constraining flux ratios are manually derived, usually without explicitly showing the formal proofs of the validity of the equations.</p

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Participatory Workshops are Not Enough to Prevent Policy Implementation Failures: An Example of a Policy Development Process Concerning the Drug Interferon-beta for Multiple Sclerosis

A possible explanation for policy implementation failure is that the views of the policy’s target groups are insufficiently taken into account during policy development. It has been argued that involving these groups in an interactive process of policy development could improve this. We analysed a project in which several target populations participated in workshops aimed to optimise the utilisation of an expensive novel drug (interferon beta) for patients with Multiple Sclerosis. All participants seemed to agree on the appropriateness of establishing a central registry of Multiple Sclerosis patients and developing guidelines. Nevertheless, these policy measures were not implemented. Possible explanations include (1) the subject no longer had high priority when the costs appeared lower than expected, (2) the organisers had paid insufficient attention to the perceived problems of parties involved, and (3) changes within the socio-political context. The workshops in which representatives of the policy’s target populations participated did not provide enough interactivity to prevent policy implementation failure