Early appraisal of the fixation probability in directed networks

In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen in a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant's fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value, and counting that event as having led to a total spread of the mutation. For large populations, and regardless of the network's topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about 100 mutants leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10000 nodes

Biodiversity of Camp Joseph T. Robinson Military Installation in North Little Rock, Arkansas 1994-1995

In 1994 the University of Arkansas - Little Rock (UALR), in cooperation with the Nature Conservancy and the Arkansas Natural Heritage Commission, began a faunal assessment of Camp Joseph T. Robinson MilitaryInstallation in North LittleRock, Arkansas. The purpose ofthe study was (1) to determine the distribution and the abundance ofnative ? fauna on the installation, (2) to survey the installation for rare and endangered species, and (3) to determine the impact ofhuman activities on sensitive habitats and on the fauna. During the fall (1994-1996), winter (1995-1996) and spring « (1995-1996) seasons, mammals were located by either live-trapping, mist-netting, scent stations, pitfall trapping, active hunting orspotlighting. Arc/INFO® and ArcView® 2.0 were used to visualize and analyze the data. ERDAS Imagine\u27\u27 was « used for satellite imagery interpretation. We recorded 315 individuals representing 29 of the 54 possible mammalian species within central Arkansas. Two additional species were documented from UALR museum records. When habitats * were categorized into either Hardwood or Mixed Hardwood/Pine, we found more species occurring in Mixed Hardwood/Pine areas than in Hardwood areas. When the two habitat-associations were compared (techniques by ? Hutcheson; 1970 and Zar; 1996) there was no significant difference (

Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to gene regulation networks, fixed minor errors and replaced fig. 4. Main body of paper (model and calculations) remains unchanged. Submitted for publicatio

Linear solar module - Refinement, measurement, and evaluation of optics Final report

Optical section using xenon or mercury-xenon arc lamp source for solar simulato

Statistical mechanics of ecosystem assembly

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the endstate of the process), which is therefore resistant to invasions. This also shows that the endstate is independent on the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.Comment: Accepted for publication in Physical Review Letter

Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory

Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular and widely applicable, very few examples of this heuristic are rigorously shown to converge to optimality, and even fewer to do so efficiently. In this paper we present a general framework which is amenable to rigorous analysis, and expose its applicability. Its main feature is that the local optimization domains are each a group of invertible matrices, together naturally acting on tensors, and the optimization problem is minimizing the norm of an input tensor under this joint action. The solution of this optimization problem captures a basic problem in Invariant Theory, called the null-cone problem. This algebraic framework turns out to encompass natural computational problems in combinatorial optimization, algebra, analysis, quantum information theory, and geometric complexity theory. It includes and extends to high dimensions the recent advances on (2-dimensional) operator scaling. Our main result is a fully polynomial time approximation scheme for this general problem, which may be viewed as a multi-dimensional scaling algorithm. This directly leads to progress on some of the problems in the areas above, and a unified view of others. We explain how faster convergence of an algorithm for the same problem will allow resolving central open problems. Our main techniques come from Invariant Theory, and include its rich non-commutative duality theory, and new bounds on the bitsizes of coefficients of invariant polynomials. They enrich the algorithmic toolbox of this very computational field of mathematics, and are directly related to some challenges in geometric complexity theory (GCT)

Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments

Economical (k,m)-threshold controlled quantum teleportation

We study a (k,m)-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over GF(p) with prime p > m-1 needs to distribute a d-dimensional qudit with d >= p to each controller for this purpose. We propose a scheme using m qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.Comment: 11 pages, 2 figures, v2: minor revision, discussions improved, an equation corrected in procedure (A) of section 4.3, v3: major revision, protocols extended, citations added, v4: minor grammatical revision, v5: minor revision, discussions extende

A Combinatorial Interpretation of the Free Fermion Condition of the Six-Vertex Model

The free fermion condition of the six-vertex model provides a 5 parameter sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing explicit solutions. Such conditions arose originally in early field-theoretic S-matrix approaches. Here we provide a combinatorial explanation for the condition in terms of a generalised Gessel-Viennot involution. By doing so we extend the use of the Gessel-Viennot theorem, originally devised for non-intersecting walks only, to a special weighted type of \emph{intersecting} walk, and hence express the partition function of $N$ such walks starting and finishing at fixed endpoints in terms of the single walk partition functions