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Let P be an orthogonal polygon with n vertices, and let V⁎ and E⁎ be specified sets of vertices and edges of P. We prove that P has a guard set of cardinality at most ⌊(n+3|V⁎|+2|E⁎|)/4⌋ that includes each vertex in V⁎ and at least one point of each edge in E⁎. Our bound is sharp and reduces to the orthogonal art gallery theorem of Kahn, Klawe and Kleitman when V⁎ and E⁎ are empty. © 2016 Elsevier B.V.

Software components, which are vulnerable to being exploited, need to be identified and patched. Employing any prevention techniques designed for the purpose of detecting vulnerable software components in early stages can reduce the expenses associated with the software testing process significantly and thus help building a more reliable and robust software system. Although previous studies have demonstrated the effectiveness of adapting prediction techniques in vulnerability detection, the feasibility of those techniques is limited mainly because of insufficient training data sets. This paper proposes a prediction technique targeting at early identification of potentially vulnerable software components. In the proposed scheme, the potentially vulnerable components are viewed as mislabeled data that may contain true but not yet observed vulnerabilities. The proposed hybrid technique combines the supports vector machine algorithm and ensemble learning strategy to better identify potential vulnerable components. The proposed vulnerability detection scheme is evaluated using some Java Android applications. The results demonstrated that the proposed hybrid technique could identify potentially vulnerable classes with high precision and relatively acceptable accuracy and recall.

The set of the first Hilbert coefficients of parameter ideals relative to a module—its Chern coefficients—over a local Noetherian ring codes for considerable information about its structure–noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers. © 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals I⊂. R=. K[. x, y, z] we give the precise value of depth. R[. It] and decide whether the corresponding rational maps are birational. In the case of dimension d≥. 3, when K=R, we give structure theorems for all ideals of codimension d minimally generated by (d+12)-1 quadrics. For arbitrary fields K, we prove a polarized version. © 2014 Elsevier Inc.

In order to reduce students' test anxiety, collaborative testing was suggested as an evaluation strategy. However, few studies have focused on testing group construction, especially when an important factor, i.e., group diversity is taken into consideration. In this paper we conducted a case study to assess the association between group diversity and test anxiety in collaborative testing. The results observed may indicate that: 1) around 20% of students suffered from test anxiety to some extent in either an individual test or a collaborative test; 2) collaborative testing could alleviate test anxiety, whereas the effect is not statistically significant; 3) there exists a moderate positive correlation between group diversity and test anxiety in collaborative testing. The results of the study may suggest limiting group diversity in collaborative testing in order to alleviate test anxiety. © 2015 IEEE.

Due to the considerable advantages of collaborative learning, group work is widely used in tertiary institutions. Previous studies demonstrated that group diversity had positive influence on group work achievement. Therefore, an interesting question that arises is how to achieve maximum group diversity effectively and automatically, especially when the features to be considered are numerous and the number of students is large. In this paper we apply a multi-start algorithm composed by a greedy constructive and strategic oscillation improvement to group students. We evaluated the technique based on a small-scale case study. The results observed indicate that the multi-start algorithm-based grouping model is feasible. It improved the overall and average students diversity within group significantly, and it also enhanced students' collaborative learning outcomes compared to random grouping model. However, we did not find any evidence on monotonic positive relationship between diversity and students' learning outcomes. © 2015 IEEE.

Vulnerabilities need to be detected and removed from software. Although previous studies demonstrated the usefulness of employing prediction techniques in deciding about vulnerabilities of software components, the accuracy and improvement of effectiveness of these prediction techniques is still a grand challenging research question. This paper proposes a hybrid technique based on combining N-gram analysis and feature selection algorithms for predicting vulnerable software components where features are defined as continuous sequences of token in source code files, i.e., Java class file. Machine learning-based feature selection algorithms are then employed to reduce the feature and search space. We evaluated the proposed technique based on some Java Android applications, and the results demonstrated that the proposed technique could predict vulnerable classes, i.e., software components, with high precision, accuracy and recall. © 2015 IEEE.

We consider variations of the original art gallery problem where the domain is a polyomino, a polycube, or a polyhypercube. An m-polyomino is the connected union of m unit squares called pixels, an m-polycube is the connected union of m unit cubes called voxels, and an m-polyhypercube is the connected union of m unit hypercubes in a d dimensional Euclidean space. In this paper we generalize and unify the known results about guarding polyominoes and polycubes and obtain simpler proofs. We also obtain new art gallery theorems for guarding polyhypercubes. © 2015 Elsevier B.V.

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.

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.