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In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the…
Intrinsic image decomposition is the process of separating the reflectance and shading layers of an image, which is a challenging and underdetermined problem. In this paper, we propose to systematically address this problem using a deep…
Decomposing a graph into a hierarchical structure via $k$-core analysis is a standard operation in any modern graph-mining toolkit. $k$-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere…
The segmentation of ultra-high resolution images poses challenges such as loss of spatial information or computational inefficiency. In this work, a novel approach that combines encoder-decoder architectures with domain decomposition…
This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…
A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the…
We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
This paper proposes a framework for automatic formal controller synthesis for general hybrid systems with a subset of safety and reachability specifications. The framework uses genetic programming to automatically co-synthesize controllers…
In this work we introduce a biologically inspired long-range skip connection for the UNet architecture that relies on the perceptual illusion of hybrid images, being images that simultaneously encode two images. The fusion of early encoder…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
A simplicial complex is a generalization of a graph: a collection of n-ary relationships (instead of binary as the edges of a graph), named simplices. In this paper, we develop a new tool to study the structure of simplicial complexes: we…
This paper presents an extension of a recently proposed hierarchical control framework applied to a cryogenic system. While in the previous work, each sub-system in the decomposition needed to show at least one component of the control…
Decoupling is a powerful modeling paradigm for representing multivariate functions as compositions of linear transformations and univariate nonlinear functions. A single-layer decoupling can be viewed as a fully connected neural network…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…