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This paper deals with predator–prey dynamics in individual and population perspectives. First, we build a discrete Markov model on predator–prey interactions in individual perspective. By shortening the time gap, from discrete time to continuous time, and increasing the number of individuals to infinity, a continuity equation on the predator–prey interactions is derived in a large population regime. Then, with the leading items of the continuity equation, that is the mean-field equation, following the approximate model, which entails qualitative analysis, we can obtain an asymptotically stable closed orbit or simply put, the parameter conditions where equilibrium point exists. These qualitative conclusions are the performance of individual microscopic interactions on macro-level groups, or can be treated as one component of microscopic models of various random statistical average results.This paper explored the accuracy and operability of the model constructed on individual level, which differs from traditional method, constructing population model directly via differential equations and difference equations. Therefore, by operating variables and data from individual behavior, it is probable for us to construct more accurate models for population dynamic. © 2014, Springer Science+Business Media Dordrecht (outside the USA).

Ballistic photon models of radiative transfer in discrete absorbing random media have demonstrated deviations from the Beer-Lambert-Bouguer law of exponential attenuation. A number of theoretical constructs to quantify the deviation from the Beer-Lambert-Bouguer law have appeared in the literature, several of which rely principally on a statistical measure related to the statistics of the absorber spatial positions alone. Here, we utilize a simple computational model to explore the interplay between the geometric size of the absorbing obstacles and the statistics governing the placement of the absorbers in the volume. We find that a description of the volume that depends on particle size and the spatial statistics of absorbers is not sufficient to fully characterize deviations from the Beer-Lambert-Bouguer law. Implications for future further theoretical and computational explorations of the problem are explored. © 2013 Elsevier Ltd.

Group work is widely used in tertiary institutions due to the considerable advantages of collaborative learning. Previous studies indicated that the group diversity had positive influence on the group work achievement. Therefore, how to achieve diversity within a group effectively and automatically is an interesting question. In this paper we propose a novel clustering-based grouping model. The proposed technique first employs balanced K-means algorithm to divide the students into several size-balanced clusters, such that the students within the same cluster are more similar (in some sense) to each other than to those in other clusters, then adopts one-sample-each-cluster strategy to construct the groups. We evaluated the proposed technique based on two small-scale case studies. The result observed may indicate that the clustering-based grouping model is feasible and effective. © 2014 IEEE.

Due to the complex causality of failure and the special characteristics of test cases, the faults in GUI (Graphic User Interface) applications are difficult to localize. This paper adapts feature selection algorithms to localize GUI-related faults in a given program. Features are defined as the subsequences of events executed. By employing statistical feature ranking techniques, the events can be ranked by the suspiciousness of events being responsible to exhibit faulty behavior. The features defined in a given source code implementing (event handle) the underlying event are then ranked in suspiciousness order. The evaluation of the proposed technique based on some open source Java projects verified the effectiveness of this feature selection based fault localization technique for GUI applications. © 2014 IEEE.

For a Noetherian local ring (R, m), the first two Hilbert coefficients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noetherian local rings. © American Mathematical Society.

Hoffmann and Kriegel showed that an orthogonal gallery with n vertices and an unspecified number of holes can be protected by at most n/3 vertex guards. We improve this bound to (17n − 8)/52.

A problem posed by Vasconcelos [33] on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well. © 2011 Elsevier B.V.

For a Noetherian local ring, we analyze conjectural relationships between the first Hilbert coefficient of a parameter ideal and the first partial Euler characteristic of its Koszul complex. Given their similar role as predictors of the Cohen-Macaulay property, we consider a direct comparison between them. For parameter ideals generated by d-sequences these numbers are related in an explicit formula. We then turn to study of families of parameter ideals that have the same Hilbert function. © 2012 Elsevier Inc.

In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of finite co-length. Because three of the corresponding modules are Artinian, some of these relationships are very effective, with the novel approach opening up tracks to the determination of the equations and also to processes of going from homologically defined sets of equations to higher degrees ones. While not specifically directed towards the extraction of elimination equations, it will show how some of these arise naturally. © 2012 Sociedade Brasileira de Matemática.

In this paper, we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration. Our algorithms involve a total of O(n2) atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication. © 2011 Cambridge University Press.

We show that the discrete Heisenberg group has unbounded dead-end depth with respect to every finite generating set. We also show that, in contrast, it has bounded retreat depth. © 2011 Hebrew University Magnes Press.

The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e 1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied. © 2010 London Mathematical Society.

Let R be an analytically unramified local ring with maximal ideal m and d = dimR > 0. If R is unmixed, then e1I (R) = 0 for every m-primary ideal I in R, where e1I (R) denotes the first coefficient of the normal Hilbert polynomial of R with respect to I. Thus the positivity conjecture on e1I(R) posed by Wolmer V. Vasconcelos is settled affirmatively. © 2010 American Mathematical Society.

OBJECTIVE: This study examined alcohol consumption patterns and trends at a public university in the Northeast from 2002 to 2008., PARTICIPANTS: Stratified random sampling was used to select undergraduate students enrolled in courses during spring semesters in 2002, 2004, 2006, and 2008., METHODS: Data were collected during regularly scheduled classes for 4 measures of alcohol consumption and 5 demographic categories using the Core Alcohol and Drug Survey., RESULTS: Four groups showed significant increases in both frequency and volume of alcohol consumption-students who were female, over 21 years of age or over, living off-campus, or performing well academically. There were no decreasing trends for any demographic group. These results differ from national college health surveys, which have shown alcohol use remaining steady during this period., CONCLUSIONS: Campus-specific trend data can provide unique perspectives and guide programming efforts. These trends suggest a need for new intervention strategies on this campus.

A conjecture by Albertson states that if χ(G) ≥ n then cr(G) ≥ cr(Kn), where χ(G) is the chromatic number of G and cr(G) is the crossing number of G. This conjecture is true for positive integers n ≤ 16, but it is still open for n ≥ 17. In this paper we consider the statements corresponding to this conjecture where the crossing number of G is replaced with the skewness µ(G) (the minimum number of edges whose removal makes G planar), the genus γ(G) (the minimum genus of the orientable surface on which G is embeddable), and the thickness θ(G) (the minimum number of planar subgraphs of G whose union is G.) We show that the corresponding statements are true for all positive integers n when cr(G) is replaced with µ(G) or γ(G). We also show that the corresponding statement is true for infinitely many values of n, but not for all n, when cr(G) is replaced with θ(G).