The Linking Probability of Deep Spider-Web Networks

We consider crossbar switching networks with base $b$ (that is, constructed from $b\times b$ crossbar switches), scale $k$ (that is, with $b^k$ inputs, $b^k$ outputs and $b^k$ links between each consecutive pair of stages) and depth $l$ (that is, with $l$ stages). We assume that the crossbars are interconnected according to the spider-web pattern, whereby two diverging paths reconverge only after at least $k$ stages. We assume that each vertex is independently idle with probability $q$, the vacancy probability. We assume that $b\ge 2$ and the vacancy probability $q$ are fixed, and that $k$ and $l = ck$ tend to infinity with ratio a fixed constant $c>1$. We consider the linking probability $Q$ (the probability that there exists at least one idle path between a given idle input and a given idle output). In a previous paper it was shown that if $c\le 2$, then the linking probability $Q$ tends to 0 if $0<q<q_c$ (where $q_c = 1/b^{(c-1)/c}$ is the critical vacancy probability), and tends to $(1-\xi)^2$ (where $\xi$ is the unique solution of the equation $(1-q (1-x))^b=x$ in the range $0<x<1$) if $q_c<q<1$. In this paper we extend this result to all rational $c>1$. This is done by using generating functions and complex-variable techniques to estimate the second moments of various random variables involved in the analysis of the networks.Comment: i+21 p

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde

A Trio Neural Model for Dynamic Entity Relatedness Ranking

Measuring entity relatedness is a fundamental task for many natural language processing and information retrieval applications. Prior work often studies entity relatedness in static settings and an unsupervised manner. However, entities in real-world are often involved in many different relationships, consequently entity-relations are very dynamic over time. In this work, we propose a neural networkbased approach for dynamic entity relatedness, leveraging the collective attention as supervision. Our model is capable of learning rich and different entity representations in a joint framework. Through extensive experiments on large-scale datasets, we demonstrate that our method achieves better results than competitive baselines.Comment: In Proceedings of CoNLL 201

Seeing Behind the Camera: Identifying the Authorship of a Photograph

We introduce the novel problem of identifying the photographer behind a photograph. To explore the feasibility of current computer vision techniques to address this problem, we created a new dataset of over 180,000 images taken by 41 well-known photographers. Using this dataset, we examined the effectiveness of a variety of features (low and high-level, including CNN features) at identifying the photographer. We also trained a new deep convolutional neural network for this task. Our results show that high-level features greatly outperform low-level features. We provide qualitative results using these learned models that give insight into our method's ability to distinguish between photographers, and allow us to draw interesting conclusions about what specific photographers shoot. We also demonstrate two applications of our method.Comment: Dataset downloadable at http://www.cs.pitt.edu/~chris/photographer To Appear in CVPR 201

BlogForever: D2.5 Weblog Spam Filtering Report and Associated Methodology

This report is written as a first attempt to define the BlogForever spam detection strategy. It comprises a survey of weblog spam technology and approaches to their detection. While the report was written to help identify possible approaches to spam detection as a component within the BlogForver software, the discussion has been extended to include observations related to the historical, social and practical value of spam, and proposals of other ways of dealing with spam within the repository without necessarily removing them. It contains a general overview of spam types, ready-made anti-spam APIs available for weblogs, possible methods that have been suggested for preventing the introduction of spam into a blog, and research related to spam focusing on those that appear in the weblog context, concluding in a proposal for a spam detection workflow that might form the basis for the spam detection component of the BlogForever software