13,689 research outputs found
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 : 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 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 , which is the natural dynamic associated to the usual quantum
sine-Gordon model. It is shown that when the
Wick renormalised equation is well-posed. In the regime ,
the Da Prato-Debussche method applies, while for , 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 -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
Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
We study the Glauber dynamics of a two dimensional Blume-Capel model (or
dilute Ising model) with Kac potential parametrized by - the
"inverse temperature" and the "chemical potential". We prove that the locally
averaged spin field rescales to the solution of the dynamical equation
near a curve in the plane and to the solution of the dynamical
equation near one point on this curve. Our proof relies on a discrete
implementation of Da Prato-Debussche method as in a result by Mourrat-Weber but
an additional coupling argument is needed to show convergence of the linearized
dynamics.Comment: 42 pages, 1 figur
Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem
Upon its inception the theory of regularity structures allowed for the
treatment for many semilinear perturbations of the stochastic heat equation
driven by space-time white noise. When the driving noise is non-Gaussian the
machinery of theory can still be used but must be combined with an infinite
number of stochastic estimates in order to compensate for the loss of
hypercontractivity. In this paper we obtain a more streamlined and automatic
set of criteria implying these estimates which facilitates the treatment of
some other problems including non-Gaussian noise such as some general phase
coexistence models - as an example we prove here a generalization of the
Wong-Zakai Theorem found by Hairer and Pardoux.Comment: 37 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
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