Related papers: On circuits and serial symmetric basis-exchange in…
We prove a general result concerning cyclic orderings of the elements of a matroid. For each matroid $M$, weight function $\omega:E(M)\rightarrow\mathbb{N}$, and positive integer $D$, the following are equivalent. (1) For all $A\subseteq…
The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-level matroids generalize series-parallel graphs, which have been already…
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…
A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every…
By means of layer resolved ion irradiation the mechanisms involved in the irradiation driven modifications of the exchange bias effect in NiFe/FeMn bilayers have been investigated. It is shown that not only the locations of the defects but…
We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending…
We study the number of hamiltonian circuits, containing a fixed basis, and the number of hyperplanes, which do not contain a fixed basis in perfect matroid designs. Projective and affine finite geometries are considered as examples of such…
Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in…
One generalization of ordinary matroids is symplectic matroids. While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic matroids in terms of circuits. We give…
We characterize the class of threshold matroids by the structure of their defining bases. We also give an example of a shifted matroid which is not threshold, answering a question of Deza and Onn. We conclude by exploring consequences of…
A method is derived for calculating the pairing kernel in exchange mediated superconductors including matrix element effects. Various models for the interaction vertex are considered, including spin exchange, orbital exchange, and…
We study the evolution of random matroids represented by the sequence of random matrices over ${\mathbb F}_q$ where columns are added one after the other, and each column vector is a uniformly random vector in ${\mathbb F}_q^n$, independent…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
Some of the main experimental observations related to the occurrence of exchange bias in magnetic systems are reviewed, focusing the attention on the peculiar phenomenology associated to nanoparticles with core/shell structure as compared…
Given a simple Eulerian binary matroid $M$, what is the minimum number of disjoint circuits necessary to decompose $M$? We prove that $|M| / (\operatorname{rank}(M) + 1)$ many circuits suffice if $M = \mathbb F_2^n \setminus \{0\}$ is the…
The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field the exchange interaction is practically…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
For a simplicial complex ${\mathcal C}$ denote by $\beta({\mathcal C})$ the minimal number of edges from ${\mathcal C}$ needed to cover the ground set. If ${\mathcal C}$ is a matroid then for every partition $A_1, \ldots, A_m$ of the ground…
The phenomenology of exchange bias effects observed in structurally single-phase alloys and compounds but composed of a variety of coexisting magnetic phases such as ferromagnetic, antiferromagnetic, ferrimagnetic, spin-glass, cluster-glass…
The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street within a congested network, may in fact lead to larger costs for the players in an equilibrium. In…