Connectivity Threshold for random subgraphs of the Hamming graph

We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d.\ Bernoulli bond percolation on $H(d,n)$ with parameter $p$. We identify the window of the transition: when $np- \log n \to - \infty$ the probability that the graph is connected goes to $0$, while when $np- \log n \to + \infty$ it converges to $1$. We also investigate the connectivity probability inside the critical window, namely when $np- \log n \to t \in \mathbb{R}$. We find that the threshold does not depend on $d$, unlike the phase transition of the giant connected component the Hamming graph (see [Bor et al, 2005]). Within the critical window, the connectivity probability does depend on d. We determine how.Comment: 10 pages, no figure

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of finite-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.Comment: 20 pages, 10 figures, uses epsfig.sty. Partially presented at StatPhys XX in a talk by one of the authors (FRT). Added 1 reference in the new versio

Am I Done? Predicting Action Progress in Videos

In this paper we deal with the problem of predicting action progress in videos. We argue that this is an extremely important task since it can be valuable for a wide range of interaction applications. To this end we introduce a novel approach, named ProgressNet, capable of predicting when an action takes place in a video, where it is located within the frames, and how far it has progressed during its execution. To provide a general definition of action progress, we ground our work in the linguistics literature, borrowing terms and concepts to understand which actions can be the subject of progress estimation. As a result, we define a categorization of actions and their phases. Motivated by the recent success obtained from the interaction of Convolutional and Recurrent Neural Networks, our model is based on a combination of the Faster R-CNN framework, to make frame-wise predictions, and LSTM networks, to estimate action progress through time. After introducing two evaluation protocols for the task at hand, we demonstrate the capability of our model to effectively predict action progress on the UCF-101 and J-HMDB datasets