Related papers: A statistical framework for analyzing shape in a t…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…
In the pattern matching approach to imaging science, the process of \emph{metamorphosis} in template matching with dynamical templates was introduced in \cite{ty05b}. In \cite{HoTrYo2009} the metamorphosis equations of \cite{ty05b} were…
We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct…
This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
We consider diffusion-controlled release of particles from $d$-dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the proportion of particles remaining within the geometry over…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…