An Evaluation of Gault by a Sociologist

Symposium on Juvenile Problems: In re Gaul

An Evaluation of Gault by a Sociologist

Symposium on Juvenile Problems: In re Gaul

Distribution of infected mass in disease spreading in scale-free networks

We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and investigate in detail the distribution of $M$, We find that for dense networks this function is bimodal, while for sparse networks it is a smoothly decreasing function, with the distinction between the two being a function of $q$. We thus recover the full crossover transition from one case to the other. This has a result that on the same network a disease may die out immediately or persist for a considerable time, depending on the initial point where it was originated. Thus, we show that the disease evolution is significantly influenced by the structure of the underlying population.Comment: 7 pages, 3 figures, submitted to Physica A; Improved the discussion and shifted the emphasis on the distributions of figure 2. Because of this we had to change the title of the pape

Classification of scale-free networks

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.Comment: 6 Pages, 6 Figures, 1 tabl

Criminal Justice Policy : Issues, Doubts, and Dilemmas

Sentencing decisions entail difficult compromises among a set of more or less incompatible goals: rehabilitation, deterrence, incapacitation, just deserts, and moral education. Furthermore, moral questions can be raised about all of these objectives; there is little evidence that any of them are very effective in reducing crime; and there is little reason to expect them to be very effective, since the criminal justice system is only a small part of the social apparatus for social control. Investment of additional resources in the criminal justice system is not likely to affect crime rates significantly. However, it may (1) enhance people\u27s perception of the quality of justice and (2) help offset the demoralizing effect of the fear of crime on the routine activities of everyday life. The sense that one is doing something and the belief that it works is, like magic, an incentive to more vigorous and sustained effort.宣告刑の決定は，リハビリテーション（矯正），デターランス（抑止），インキャパシテーション（無害化），ジャスト・デザーツ（応報），道徳教育といった，あい矛盾した刑罰の諸目的の妥協の産物にならざるをえない。しかし，これら刑罰目的のすべてについて，道義的疑念が提起されうる。刑事司法制度は社会統制装置のごく一部を占めているにすぎず，これらの目的のいずれも犯罪の軽減に効果的であるとの根拠は乏しいからである。刑事司法制度に対してさらに追加的に資源を投入することによって犯罪率を著しく減少できるとは考えられない。しかし，それは①司法的正義についての人々の認識を高め，②日常生活における犯罪への恐怖という士気阻喪的影響を中和・相殺する上で役立つであろう。絶えず努力しているのだという意識，それが効果的であるとする信念は，一種の魔術といってもよいが，それこそが，次々と精力的になされるさまざまな試みの動機づけになっているのである。社会学部設立二十周年記念特

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge on the network. We determine, for all strategies, the critical fraction p_c of nodes that must be removed for disintegrating the network. We find that for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p_c. At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.Comment: Accepted in PR

Evolution of scale-free random graphs: Potts model formulation

We study the bond percolation problem in random graphs of $N$ weighted vertices, where each vertex $i$ has a prescribed weight $P_i$ and an edge can connect vertices $i$ and $j$ with rate $P_iP_j$. The problem is solved by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous interactions for all pairs of spins. We apply this approach to the static model having $P_i\propto i^{-\mu} (0<\mu<1)$ so that the resulting graph is scale-free with the degree exponent $\lambda=1+1/\mu$. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density, and their associated critical exponents are also obtained. Finite-size scaling behaviors are derived using the largest cluster size in the critical regime, which is calculated from the cluster size distribution, and checked against numerical simulation results. We find that the process of forming the giant cluster is qualitatively different between the cases of $\lambda >3$ and $2 < \lambda <3$. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite $N$ shows double peaks.Comment: 34 pages, 9 figures, elsart.cls, final version appeared in NP

Sandpile avalanche dynamics on scale-free networks

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-\eta}$ with $0\leq\eta<1$, where $k_i$ is the degree of node $i$. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents $\tau$ and $\delta$, respectively. They are given as $\tau=(\gamma-2 \eta)/(\gamma-1-\eta)$ and $\delta=(\gamma-1-\eta)/(\gamma-2)$ for $\gamma<3-\eta$, 3/2 and 2 for $\gamma>3-\eta$, respectively. The power-law distributions are modified by a logarithmic correction at $\gamma=3-\eta$.Comment: 8 pages, elsart styl

Mean-field theory for clustering coefficients in Barabasi-Albert networks

We applied a mean field approach to study clustering coefficients in Barabasi-Albert networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees. Clustering coefficient of a whole network calculated from our approach perfectly fits numerical data.Comment: 8 pages, 3 figure

Correlations in Scale-Free Networks: Tomography and Percolation

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabasi-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussig the shell structure of the networks around their arbitrary node. In spite of different correlation behavior, all three constructions exhibit similar percolation properties.Comment: 6 pages, 2 figures; added reference