Blind Source Separation with Compressively Sensed Linear Mixtures

This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical Compressive Sensing (CS) theory with a linear mixing model. It allows the mixtures to be sampled independently of each other. If samples are acquired in the time domain, this means that the sensors need not be synchronized. Since Blind Source Separation (BSS) from a linear mixture is only possible up to permutation and scaling, factoring out these ambiguities leads to a minimization problem on the so-called oblique manifold. We develop a geometric conjugate subgradient method that scales to large systems for solving the problem. Numerical results demonstrate the promising performance of the proposed algorithm compared to several state of the art methods.Comment: 9 pages, 2 figure

Weak universality of dynamical Φ34\Phi^4_3: non-Gaussian noise

We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrability and mixing conditions, but not necessarily Gaussian. We show that, in the weakly nonlinear regime, if the external potential is a symmetric polynomial and a certain average of it exhibits pitchfork bifurcation, then these models all rescale to $\Phi^4_3$ near their critical point.Comment: 37 pages; updated introduction and reference

The dynamical sine-Gordon model

We introduce the dynamical sine-Gordon equation in two space dimensions with parameter $\beta$, which is the natural dynamic associated to the usual quantum sine-Gordon model. It is shown that when $\beta^2 \in (0,\frac{16\pi}{3})$ the Wick renormalised equation is well-posed. In the regime $\beta^2 \in (0,4\pi)$, the Da Prato-Debussche method applies, while for $\beta^2 \in [4\pi,\frac{16\pi}{3})$, the solution theory is provided via the theory of regularity structures (Hairer 2013). We also show that this model arises naturally from a class of $2+1$-dimensional equilibrium interface fluctuation models with periodic nonlinearities. The main mathematical difficulty arises in the construction of the model for the associated regularity structure where the role of the noise is played by a non-Gaussian random distribution similar to the complex multiplicative Gaussian chaos recently analysed by Lacoin, Rhodes and Vargas (2013).Comment: 64 page

Dynamic Variational Autoencoders for Visual Process Modeling

This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector autoregressive model and Variational Autoencoders. This results in an architecture that allows Variational Autoencoders to simultaneously learn a non-linear observation as well as a linear state model from sequences of frames. We validate our approach on artificial sequences and dynamic textures

Topological superconducting states in monolayer FeSe/SrTiO3_{3}

The monolayer FeSe with a thickness of one unit cell grown on a single-crystal SrTiO$_{3}$ substrate (FeSe/STO) exhibits striking high-temperature superconductivity with transition temperature $T_{c}$ over 65K reported by recent experimental measurements. In this work, through analyzing the distinctive electronic structure, and providing systematic classification of the pairing symmetry , we find that both $s$-and $p$-wave pairing with odd parity give rise to topological superconducting states in monolayer FeSe, and the exotic properties of $s$-wave topological superconducting states have close relations with the unique non-symmorphic lattice structure which induces the orbital-momentum locking. Our results indicate that the monolayer FeSe could be in the topological nontrivial $s$-wave superconducting states if the relevant effective pairing interactions are dominant in comparison with other candidates.Comment: 11 pages, 4 figure

An Adaptive Dictionary Learning Approach for Modeling Dynamical Textures

Video representation is an important and challenging task in the computer vision community. In this paper, we assume that image frames of a moving scene can be modeled as a Linear Dynamical System. We propose a sparse coding framework, named adaptive video dictionary learning (AVDL), to model a video adaptively. The developed framework is able to capture the dynamics of a moving scene by exploring both sparse properties and the temporal correlations of consecutive video frames. The proposed method is compared with state of the art video processing methods on several benchmark data sequences, which exhibit appearance changes and heavy occlusions