相关论文: New geometric results in eigenstructure assignment

A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…

The bulk-edge correspondence is one of the most important ingredients in the theory of topological phases of matter. While the bulk-edge correspondence is applicable for Hermitian junction systems where two subsystems with independent…

In this paper, we develop a new technique which we call representation theory of the real hyperrectangle, which describes how to compute the eigenvectors and eigenvalues of certain matrices arising from hyperrectangles. We show that these…

We argue that the spectral theory of non-reversible Markov chains may often be more effectively cast within the framework of the naturally associated weighted-$L_\infty$ space $L_\infty^V$, instead of the usual Hilbert space $L_2=L_2(\pi)$,…

There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead…

Generative models rely on the key idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation is important because it suggests that the latent space manifold is simpler to…

This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…

This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are…

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…

We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the…

We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings…

A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…

We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…

The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs…

Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse…

I propose, as geometric structure in an internal space, a helical field that is responsible for intrinsic properties of point particles, particularly, electron. For the novel theoretical development, plasma astrophysical analogy is made…

This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…