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A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
Embedding data into vector spaces is a very popular strategy of pattern recognition methods. When distances between embeddings are quantized, performance metrics become ambiguous. In this paper, we present an analysis of the ambiguity…
This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement…
We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…
We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
We present the SI and other unit systems, including cgs-em and cgs-es, in a framework whereby a system of fully independent and dimensionally orthogonal base units is modified by conventions designed to simplify the equations that are used…
This paper introduces new structures called conic frameworks and their rigidity. They are composed by agents and a set of directed constraints between pairs of agents. When the structure cannot be flexed while preserving the constraints, it…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…
This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical…
We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…