Related papers: Comparative results on eigenvalues,pseudospectra a…
We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
Symmetries are key properties of physical models and of experimental designs, but any proposed symmetry may or may not be realized in nature. In this paper, we introduce a practical and general method to test such suspected symmetries in…
This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger…
In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…
Recently, time scales calculus is developed to unify continuous and discrete analysis. By extending the definition of time scales properly, this paper introduces the concept of a signal set as well as its stability properties in terms of…
Eigenvalue-based detectors are considered as an important method of spectrum sensing since they do not require the information about the primary user (PU) signal. In this paper we propose a method to improve the performance of the…
In this paper we make a detailed numerical comparison between three algorithms for the computation of the full Lyapunov spectrum as well as the associated eigen-vectors of general dynamical systems. They are : (a) the standard method, (b) a…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…