The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Behavioural and neural correlates of emotion recognition as a function of psychopathic personality traits

Psychopathy is associated with well-known characteristics such as a lack of empathy and impulsive behaviour, but it has also been associated with impaired recognition of emotional facial expressions. The use of event-related potentials (ERPs) to examine this phenomenon could shed light on the specific time course and neural activation associated with emotion recognition processes as they relate to psychopathic traits. In the current study we examined the PI , N170, and vertex positive potential (VPP) ERP components and behavioural performance with respect to scores on the Self-Report Psychopathy (SRP-III) questionnaire. Thirty undergraduates completed two tasks, the first of which required the recognition and categorization of affective face stimuli under varying presentation conditions. Happy, angry or fearful faces were presented under with attention directed to the mouth, nose or eye region and varied stimulus exposure duration (30, 75, or 150 ms). We found that behavioural performance to be unrelated to psychopathic personality traits in all conditions, but there was a trend for the Nl70 to peak later in response to fearful and happy facial expressions for individuals high in psychopathic traits. However, the amplitude of the VPP was significantly negatively associated with psychopathic traits, but only in response to stimuli presented under a nose-level fixation. Finally, psychopathic traits were found to be associated with longer N170 latencies in response to stimuli presented under the 30 ms exposure duration. In the second task, participants were required to inhibit processing of irrelevant affective and scrambled face distractors while categorizing unrelated word stimuli as living or nonliving. Psychopathic traits were hypothesized to be positively associated with behavioural performance, as it was proposed that individuals high in psychopathic traits would be less likely to automatically attend to task-irrelevant affective distractors, facilitating word categorization. Thus, decreased interference would be reflected in smaller N170 components, indicating less neural activity associated with processing of distractor faces. We found that overall performance decreased in the presence of angry and fearful distractor faces as psychopathic traits increased. In addition, the amplitude of the N170 decreased and the latency increased in response to affective distractor faces for individuals with higher levels of psychopathic traits. Although we failed to find the predicted behavioural deficit in emotion recognition in Task 1 and facilitation effect in Task 2, the findings of increased N170 and VPP latencies in response to emotional faces are consistent wi th the proposition that abnormal emotion recognition processes may in fact be inherent to psychopathy as a continuous personality trait.

Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.

Dynamics in large scale networks

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the massively multiplayer online game (MMOG) Planetside 2. We are particularly interested in removal patterns in these networks. Our main finding is that in both of these networks the nodes which are most commonly removed are minor near isolated nodes. We also investigate the process of merging of two large networks using data captured during the merger of servers of Planetside 2. We found that the original network structures do not really merge but rather they get gradually replaced by newcomers not associated with the original structures. In the final part of the thesis we investigate the concept of motifs in the Barabási-Albert random graph. We establish some bounds on the number of motifs in this graph.