Related papers: Upper bounds for the entropy in the cusp for one-p…

The classical Helmholtz problem is applied for modelling and numerical investigation of inviscid cusp-ended separated flow around circular cylinder. Two coordinate systems are used: polar for initial calculations and parabolic as…

In this letter, we establish a general fact about the convergence of images of families of closed analytic surfaces in the special linear group $\operatorname{SL}_2(\mathbb{C})$ under the quotient by its maximal compact subgroup…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…

We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in…

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy…

In the first part of this thesis, we present a general technique for establishing local and uniform continuity bounds for Schur concave functions. Our technique uses a particular relationship between majorization and the trace distance…

We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets A \subset Z and show quantitative bounds on the size of A if there are no non-trivial solutions. We use the circle method…

The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…

We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…

Let $\lambda$ be a probability measure on $\mathbb T^{n-1}$ where $n=2$ or 3. Suppose $\lambda$ is invariant, ergodic and has positive entropy with respect to the linear transformation defined by a hyperbolic matrix. We get a measure $\mu $…

In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the…

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a…

In this article we give an upper bound for the number of cusps on a cuspidal curve on a Hirzebruch surface. We adapt the results that have been found for a similar question asked for cuspidal curves on the projective plane, and restate the…

Let $G$ be a group that is relatively hyperbolic with respect to a collection of subgroups $\{H_{\lambda}\}_{\lambda\in \Lambda}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ with respect to this collection. We…

We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under general assumptions using De Giorgi's minimizing movement scheme.…

A fast method is presented for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two-dimensional flows via the braiding of a large number of particle…

Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large…

We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to…

In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic…

In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…