By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP).The first hierarchical method we present is base ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
Loop closure detection helps simultaneous localization and mapping systems reduce map and state uncertainty via recognizing previously visited places along the path of a mobile robot. However, visual loop closure detection is susceptible to scenes with dyn ...
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...
We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in al ...
We study a fixed point property for linear actions of discrete groups on weakly complete convex proper cones in locally convex topological vector spaces. We search to understand the class of discrete groups which enjoys this property and we try to generali ...
In this paper, we present the first general solution to the automatic reconfiguration problem of timed discrete-event systems. We extend the recursive forcible backtracking approach which had been already solved the automatic reconfiguration problem of unt ...
In the present paper, we revisit gravitational theories which are invariant under TDiffs-transverse (volume-preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invar ...
This note is motivated by a recently published paper (Biswas and Mukherjee in Commun Math Phys 322(2):373-384, 2013). We prove a no-go result for the existence of suitable solutions of the Strominger system in a compact complex parallelizable manifold . Fo ...
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the backgrou ...
We present an intercomparison of three subgrid-scale (SGS) models for large-eddy simulation (LES) of katabatic flows. The SGS closures we study include the Smagorinsky formulation, a scale-invariant dynamic model, and a scale-dependent dynamic model. Downs ...
Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-inva ...
We address the question whether a scale invariant theory can contain interacting minimal fields of canonical dimensionality. It is known that the answer to this question is negative provided the scale symmetry is respected by the ground state. We present a ...
Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...
Gaussian measures μβ,ν are associated to some stochastic 2D models of turbulence.They are Gibbs measures constructed by means of an invariant quantity of the system depending on some parameter β (related to the 2D nature of the fluid) and the viscosity ν.W ...
Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...
The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an impor ...
A new method for measuring shape rectangularity is introduced. The new shape measure is invariant with respect to similarity transformations, ranges over the interval (0,1] and picks the value 1 if and only if the measured shape is a rectangle. The measure ...
