Spectral Theory for Networks with Attractive and Repulsive Interactions

There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;, the behavior of groups, or cliques, in social networks; the study of optimal convergence for consensus algorithm; and many other examples. Frequently the problems involve computing the index of a matrix, i.e. the number of positive and negative eigenvalues, and the dimension of the kernel. In this paper we consider one of the most common examples, where the matrix takes the form of a signed graph Laplacian. We show that the there are topological constraints on the index of the Laplacian matrix related to the dimension of a certain homology group. In certain situations, when the homology group is trivial, the index of the operator is rigid and is determined only by the topology of the network and is independent of the strengths of the interactions. In general these constraints give upper and lower bounds on the number of positive and negative eigenvalues, with the dimension of the homology group counting the number of eigenvalue crossings. The homology group also gives a natural decomposition of the dynamics into "fixed" degrees of freedom, whose index does not depend on the edge-weights, and an orthogonal set of "free" degrees of freedom, whose index changes as the edge weights change. We also present some numerical studies of this problem for large random matrices.Comment: 27 pages; 9 Figure

The Energy Problem: Choices for an Uncertain Future

Analyzes discussions from National Issues Forums to assess how the public defines the energy problem, what it sees as the causes and solutions, where confusion and tensions over the energy problem lie, and why there is no consensus on how to resolve it

COMPRESSION-BASED ANALYSIS OF METAMORPHIC MALWARE

Recent work has presented a technique based on structural entropy measurement as an effective way to detect metamorphic malware. The technique uses two steps, file segmentation and sequence comparison, to calculate file similarity. In another previous work, it was observed that similar malware have similar measures of Kolmogorov complexity. A proposed method of estimating Kolmogorov complexity was to calculate the compression ratio of a given malware which could then be used to cluster the malicious software. Malware detection has also been attempted through the use of adaptive data compression and showed promising results. In this paper, we attempt to combine these concepts and propose using compression ratios as an alternative measure of entropy with the purpose of segmenting files according to their structural characteristics. We then compare the segment-based sequences of two given files to determine file similarity. The idea is that even after malware is transformed using a metamorphic engine, the resulting variants still share identifiable structural similarities with the original. Using this proposed technique to identify metamorphic malware, we compare our results with previous work

The Effects of Cultural Dispositions on Behavior in Social Dilemmas: Examining the Impact of Expectations on Cooperation and Competition

Many groups require cooperation in order to efficiently complete tasks in a manner that benefits all group members. The antecedents of cooperative and competitive behavior have been well studied using a particular class of problems called social dilemmas. Cultural variables, such as collectivism, are often thought to influence cooperative behavior in groups, but experimental evidence has seen mixed results. The current study attempts to add to our understanding of the effects of cultural variables on cooperative and competitive behavior in groups by advancing two major ideas: (1) that the Input-Process-Output (I-PO) framework-a theoretical framework of group functioning which proposes that group members' individual characteristics, dispositions, etc. influence the processes of groups when interacting which, in turn, impact the outcomes the group produces-can be used as a conceptualization for understanding the impact of cultural variables on potential group outcomes, provided that a distinction is made between potentially meaningful but taskunrelated distal inputs such as collectivism and task-related proximal inputs, and (2) that group process can be indexed using variance components calculated from the Social Relations Model (SRM}-a statistical tool used to analyze dyadic data. Using two social dilemmas as experimental media, participants were placed in groups of four and asked to report what they expected each of their group members to do during the social dilemmas and how much they trusted each of their fellow group members. Results demonstrate that collectivism increases the tendency to expect similar behavior from fellow group members and to trust fellow group members at similar levels when given little diagnostic information. In turn, more competitive behavior is demonstrated in groups that have members who all expect similar behavior from each group member, but show variability regarding what the behavior will be. The study demonstrates (1) a significant relationship between collectivism and expectations of other group members' behavior, (2) expectations will synthesize into meaningful variance components as calculated using SRM, (3) SRM variance components serve as useful indicators of group process and, (4) SRM variance components can be used to predict cooperative and competitive behavior in social dilemma situations. This research demonstrates the value of using SRM variances as indices of process and underscores the theoretical utility of the I-P-O framework as an explanatory tool of group behavior

A methodology for sorting haploid and diploid corn seed using terahertz time domain spectroscopy and machine learning

Terahertz technology has been rapidly expanding both in its use and in attention given to it. A possible application is in corn breeding, specifically when the doubled haploid method is used. Haploid kernels are induced in corn plants in order to decrease the time to reach homozygous genetic corn lines. These haploid kernels must be separated from the surrounding diploid kernels; presently this is done by extensive manual labor using visual markers. This work represents a proof of concept that haploid classification can be automated using terahertz time domain spectroscopy (THz-TDS) paired with a machine learning algorithm, like a probabilistic neural network (PNN). In this work, a THz-TDS system was used to collect time domain waveforms from a sample of mixed haploid and diploid corn kernels. Variabilities in beam focus and kernel geometry were reduced by taking multiple scans at different heights and at many scan positions. A watershed image segmentation technique was used to reduce the data quantity and organize them by kernel. The waveform data were then transformed to the frequency domain and further classified by PNN with a training set random subsampling technique. Leave-one-out and K-folds cross-validation procedures were used to train the model. The preliminary results show promise yielding an average classification rate of 75 percent correct by 5-fold cross-validation. THz ability to penetrate material leads to immense potential for similar applications in nondestructive evaluation, biomed, and agriculture

The reproductive morphology and physiological age-grading of female Cyrtobagous salviniae, the salvinia weevil

Over 1000 dissections were performed on field, greenhouse and lab specimens in order to describe the reproductive system of Cyrtobagous salviniae, a biocontrol agent of Salvinia molesta (giant salvinia). The reproductive morphology of C. salviniae was described, the classes of reproductive development were characterized, and oviposition assessed. The reproductive system of C. salviniae consists of two ovaries, each of which is comprised of two membraneous ovarioles. These are each divided into a distal germarium and a proximal vitellarium that is connected to a lateral oviduct. The lateral oviducts unite to form a common oviduct through which eggs must pass for oviposition to take place. A schlerotized spermatheca and accessory glands are also present. There are 5 classes of reproductive development, 2 nonparous (no oviposition) and three parous. These are differentiated primarily by the number and maturity of follicles in the vitellarium, the presence of eggs in the oviducts, and the presence or absence of follicular relics. The number of eggs oviposited was quantified by holding one hundred C. salviniae weevils individually on sprigs of salvinia at 29.5 ° C, with 12:12 daylength, and counting the number of ovipositions per weevil each week. During the course of the five month study, over 12,000 eggs were enumerated. At the end of the study, all of the weevils were dissected, basic statistics calculated, and the data analyzed by ANOVA, Tukey-Kramer, and Chi-square procedures (p=.0001). The mean number of eggs oviposited for each of the parous classes (i.e., P1, P2, and P3) were 22.6, 84.3, and 208.3, respectively. ANOVA indicated that mean egg numbers for each class were significantly different (F=176.51, P\u3c.0001), and Tukey-Kramer analysis (P\u3c.0001) showed that each of the three classes were significantly different from each other (P\u3c.0001). Values obtained from the oviposition study were related to the reproductive classes to create a physiological age-grading system, which can be used as a reference to gain a deeper understanding of the population dynamics of this important biocontrol agent