Related papers: Pressures for Asymptotically Sub-additive Potentia…

Compliant mechanisms actuated by pneumatic loads are receiving increasing attention due to their direct applicability as soft robots that perform tasks using their flexible bodies. Using multiple materials to build them can further improve…

Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed…

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…

In this paper we deal with an invariant ergodic hyperbolic measure $\mu$ for a diffeomorphism $f,$ assuming that $f$ it is either $C^{1+\alpha}$ or $f$ is $C^1$ and the Oseledec splitting of $\mu$ is dominated. We show that this system…

Estimating the structure of physical flow networks such as power grids is critical to secure delivery of energy. This paper discusses statistical structure estimation in power grids in the "under-excited" regime, where a subset of internal…

We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of the negative entropy, and the biconjugate recovery of the…

A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…

A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By Hahn-Banach theorem, a positive strong submeasure is…

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…

This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…

There are a variety of results in the literature proving forms of computability for topological entropy and pressure on subshifts. In this work, we prove two quite general results, showing that topological pressure is always computable from…

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…

The mechanical force from light -- radiation pressure -- provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a…

Let $\phi:X\to \mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:X\to X$ over a finite alphabet. Introducing a parameter $\beta>0$ (interpreted as the inverse temperature) we study the regularity of the…

In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a compact metric space has a maximizing measure.…

Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…

This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability.…

In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on…