Learning multifractal structure in large networks

Generating random graphs to model networks has a rich history. In this paper, we analyze and improve upon the multifractal network generator (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. From this result it follows that we can quickly compute moments of an important set of graph properties, such as the expected number of edges, stars, and cliques. Specifically, we show how to compute these moments in time complexity independent of the size of the graph and the number of recursive levels in the generative model. We leverage this theory to a new method of moments algorithm for fitting large networks to MFNG. Empirically, this new approach effectively simulates properties of several social and information networks. In terms of matching subgraph counts, our method outperforms similar algorithms used with the Stochastic Kronecker Graph model. Furthermore, we present a fast approximation algorithm to generate graph instances following the multi- fractal structure. The approximation scheme is an improvement over previous methods, which ran in time complexity quadratic in the number of vertices. Combined, our method of moments and fast sampling scheme provide the first scalable framework for effectively modeling large networks with MFNG

Markets Segmented by Regional - Origin Labeling with Quality Control

It is the objective of this paper to provide a methodological framework for the analysis of regional marketing programs which include regional-origin labeling as well as quality assurance and control. Such programs are increasingly introduced in Europe and other parts of the world as a means against quality uncertainty in globalized markets. An equilibrium - displacement model is developed for a segmented market with differential qualities that can be utilized for a broad variety of marketing programs. It is applied to one selected European case, i.e. "Gepruefte Qualitaet - Bayern". It is shown that the price impacts on high-quality and low-quality segments depend crucially on substitutive relationships between the markets and the advertising elasticities. Welfare implications for producers in a program depend strongly on advertising elasticities, too, but also on the costs of participation including quality control and on the co-financing mechanism between government and producers.regional-origin labeling, segmented markets, generic promotion, Gepruefte Qualitaet - Bayern, economic welfare, Marketing,

Regional-Origin Labeling with Quality Control: An Economic Analysis

Marketing,

Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of $\ell$-Interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity $O(\ell \mu^2)$ where $\mu$ measures the size of the input problem.Comment: 10 pages, submitted to WCC 201

Stable Irregular Dynamics in Complex Neural Networks

For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spike times. For delayed, purely inhibitory interactions we demonstrate that the irregular dynamics is not chaotic but rather stable and convergent towards periodic orbits. Moreover, every generic periodic orbit of these dynamical systems is stable. These results highlight that chaotic and stable dynamics are equally capable of generating irregular activity.Comment: 10 pages, 2 figure