Related papers: A note on irreducibility for topical maps

Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a…

Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…

This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…

The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…

Let G be a linear algebraic group, P be a parabolic subgroup of G and \beta be a cycle of dimension 1 in the Chow group of the quotient G/P. Using geometric arguments and Borel's fixed point theorem, we prove that the moduli space…

We study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on…

Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map…

The Boolean Satisfiability Problem is perhaps one of the most well-known problems in theoretical computer science. On the one hand, it is proven to be NP-complete, which means that it is generally considered hard to solve. On the other…

In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach…

We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…

We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…

We prove that the matrix of capacitance in electrostatics is a positive-singular matrix with a non-degenerate null eigenvalue. We explore the physical implications of this fact, and study the physical meaning of the eigenvalue problem for…

We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers.…

We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a…

If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\Delta_g$. We establish algebraic criteria for the existence of left…

Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…

We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalue Problem (SNIEP) is the problem of characterising all…

Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…

In this paper, we prove the moduli spaces of genus zero stable log maps to a large class of wonderful compactifications are irreducible and unirational.

The theory of eigenvalues and eigenvectors is one of the fundamental and essential components in tensor analysis. Computing the dominant eigenpair of an essentially nonnegative tensor is an important topic in tensor computation because of…