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Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
We study existence, uniqueness and computability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences---one that analyzes principal eigenvalues of…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We develop a simple and general method to construct arbitrary Flat Band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a…
We introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not…
Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…
It is well known that (stochastic) gradient descent has an implicit bias towards flat minima. In deep neural network training, this mechanism serves to screen out minima. However, the precise effect that this has on the trained network is…
We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show…
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
For a modular lattice $L$ of finite length, we prove that the distributivity of $L$ is a sufficient condition while its 2-distributivity is a necessary condition that those sublattices of $L$ that are closed under taking relative…
Persistent excitation (PE) is a necessary and sufficient condition for uniform exponential parameter convergence in several adaptive, identification, and learning schemes. In this article, we consider, in the context of multi-input linear…
Output stabilizability of a class of infinite dimensional linear systems is studied in this paper. A criterion for the system to be output stabilizable by a linear bounded feedback $u=Fx$, $F\in L(Z,\mathbb{R}^{^{p}})$ will be given.
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…