Related papers: Pre-image Variational Principle for Bundle Random …
Machine understanding of complex images is a key goal of artificial intelligence. One challenge underlying this task is that visual scenes contain multiple inter-related objects, and that global context plays an important role in…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and…
We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invariance pressure called induced invariance pressure on…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the…
In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
This study investigates the signatures of pressure extrema on global oscillations in discs. To this end, we use the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We…
Conditions for the detectability of topology variations in dynamical networks are developed in a recent article in the IEEE Transactions on Control of Network Systems [1]. Here, an example is presented which illustrates an error in the…
This article is devoted to the study of the historic set, which was introduced by Ruelle, of Birkhoff averges in some nonuniformly hyperbolic systems via Pesin theory. Particularly, we give a conditional variational principle for historic…
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…