Related papers: Symbolic powers, set-theoretic complete intersecti…
This article reports on a program to obtain and understand coherent states for general systems. Most recently this has included supersymmetric systems. A byproduct of this work has been studies of squeezed and supersqueezed states. To…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study a coupled quintessence scenario in which the scalar field evolves…
Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…
Let I be a complete intersection in a polynomial ring over a field, the Castelnuovo-Mumford regularity of I^n is given by using an induction method. When I, J and K are three pure power complete intersections, it is proved that reg(IJK) is…
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
We introduce the class of sparse symmetric shifted monomial ideals. These ideals have linear quotients and their Betti numbers are computed. Using this, we prove that the symbolic powers of the generalized star configuration ideal are…
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
The question of exclusion region construction in new phenomenon searches has been causing considerable discussions for many years and yet no clear mathematical definition of the problem has been stated so far. In this paper we formulate the…
We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…
Jackendoff (2002) posed four challenges that linguistic combinatoriality and rules of language present to theories of brain function. The essence of these problems is the question of how to neurally instantiate the rapid construction and…
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
The starting point of this paper is a duality for sequences of natural numbers which, under mild hypotheses, interchanges subadditive and superadditive sequences and inverts their asymptotic growth constants. We are motivated to explore…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
Let $d \geq 2$ and $m\geq 1$ be integers such that $\gcd (d,m)=1.$ Let ${\mathfrak p}$ be the defining ideal of the monomial curve in ${\mathbb A}_{ \Bbbk{k}}^d$ parametrized by $(t^{n_1}, \ldots, t^{n_d})$ where $n_i = d + (i-1)m$ for all…
We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points…
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…
The consistent histories formalism is discussed using path-projected states. These are used to analyse various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown…
We discuss the role of approximate U(1)_R symmetries for the understanding of hierarchies in Nature. Such symmetries may explain a suppressed expectation value of the superpotential and provide us with a solution to the MSSM mu problem. We…
Given a monomial ideal $I$, we study two functions that quantify ways to measure the difference between symbolic powers and usual powers of $I$. In many cases we determine the asymptotic growth rate of these two functions. We also perform…