Related papers: Pre-image Variational Principle for Bundle Random …
In this paper, we propose a novel variational generator framework for conditional GANs to catch semantic details for improving the generation quality and diversity. Traditional generators in conditional GANs simply concatenate the…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
This article is devoted to the investigation of the topological pressure of generic points for nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms…
Topology optimization enables the automated design of efficient structures by optimally distributing material within a defined domain. However, traditional gradient-based methods often scale poorly with increasing resolution and…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields…
We analyze and compare different dynamical systems and groupoids which can be obtained from projection point patterns. We define the cohomology of a point pattern as the cocycle cohomology of the pattern groupoid. We describe this…
In this chapter, we review a principled way of defining and measuring contextuality in systems with deterministic inputs and random outputs, recently proposed and developed in \citep{KujalaDzhafarovLarsson2015,DKL2015FooP}.
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
We prove a variational principle for the upper and lower metric mean dimension of level sets \[ \left\{x\in X: \lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1}\varphi(f^{j}(x))=\alpha\right\} \] associated to continuous potentials $\varphi:X\to…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An…
Wrinkling of an inextensible elastic lining of an inner-lined tube under imposed pressure is considered. A simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces is derived. This equation…
We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function.…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…