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Register a new userAnalyzing the Degree Distribution of the One-mode Projection of an Alphabetic Bipartite Network (alpha-BIN)
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The paper is being withdrawn since the authors felt that the submission is a little premature after a careful reading by some of the experts in this field.
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It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations.
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network; the networks are considered to be static in the sense that no compensatory measures are allowed for recovery of the original structure. Real world networks such as the world wide web, however, are not static and experience a considerable amount of turnover, where nodes and edges are both added and deleted. Considering degree-based node removals, we examine the possibility of preserving networks from these types of disruptions. We recover the original degree distribution by allowing the network to react to the attack by introducing new nodes and attaching their edges via specially tailored schemes. We focus particularly on the case of non-uniform failures, a subject that has received little attention in the context of evolving networks. Using a combination of analytical techniques and numerical simulations, we demonstrate how to preserve the exact degree distribution of the studied networks from various forms of attack.
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities $p_k$. To illustrate the techniques and support our findings using Monte-Carlo simulations, we introduce the exemplary linking rule $p_k$ proportional to $k^{-alpha}$, with $alpha$ between -1 and plus infinity. This parameter may be used to interpolate between different regimes. For negative $alpha$, links are most likely attached to high-degree nodes. On the other hand, in case $alpha>0$, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.
Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter
We present a complementary estimation of the critical exponent $alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $alpha = 0.12(2)$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$.
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