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Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
Covering numbers are a powerful tool used in the development of approximation algorithms, randomized dimension reduction methods, smoothed complexity analysis, and others. In this paper we prove upper bounds on the covering number of…
Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…
In pure integer linear programming it is often desirable to work with polyhedra that are full-dimensional, and it is well known that it is possible to reduce any polyhedron to a full-dimensional one in polynomial time. More precisely, using…
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries.…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. Also the class of Pascal finite polynomial automorphisms was introduced. Pascal finite polynomial maps constitute a generalization of…
A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this work, we make a first step towards answering the question of…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
We focus on the non-locality concerning local copying and local discrimination, especially for a set of orthogonal maximally entangled states in prime dimensional systems, as a study of non-locality of a set of states. As a result, for such…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…