An undirected graph G = (V, E) is a probe split graph if its vertex set can be partitioned into two sets, N (nonprobes) and P (probes) where N is independent and there exists E′ ⊆ N ×N such that G′ = (V, E ∪ E′) is a split graph. Recently Chang et al. gave an O(V (V +E)) time recognition algorithm for probe split graphs. In this article we give O(V 2 +V E) time recognition algorithms and charac...

A method for recognition of Persian handwritten digits based on characterization loci and mixture of experts is proposed. This method utilizes the characterization loci, as the main feature. In the classification stage of our proposed method the mixture of experts are applied. This recognition method is applied to Farsi hand-written digits in the HODA database. The experimental results support ...

Recently Postnikov gave a combinatorial description of the cells in a totallynonnegative Grassmannian. These cells correspond to a special class of matroids called positroids. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a combinatorial description of positroids that is easily computable. The main proof is purely combinatorial,...

Superconductivity and magnetism are typically antithetical forms of order. After all, in conventional superconductors, magnetic impurities are destructive to superconductivity as they break Cooper pairs [1]. But the discovery in 1979 of so-called heavy fermion superconductivity, found near an antiferromagnetic phase, led to a shift in thinking on this subject [2]. Since then, some of the most i...

Aurivillius layered oxides with general formula (Bi 2 O )(A m−1 B m 3m+1 ) stand out among room-temperature magnetoelectric multiferroics for their large magnetization. However, despite extensive research, there is an obvious lack of understanding magnetism. The chemical design strategy obtaining multiferroism involves the incorporation M 3+ magnetic cations at B-site well-known ferroelectric c...

We construct the general free energy governing long-wavelength magnetism in two dimensional oxide heterostructures, which applies irrespective of the microscopic mechanism for magnetism. This leads, in the relevant regime of weak but non-negligible spin-orbit coupling, to a rich phase diagram containing in-plane ferromagnetic, spiral, cone, and Skyrmion lattice phases, as well as a nematic stat...

We show that the norm graph constructed in [13] with n vertices about 1 2n 2−1/t edges, which contains no copy of Kt,(t−1)!+1, does not contain a copy of Kt+1,(t−1)!−1.

In this paper we investigate the closure ~-* under substitution-composition of a family of graphs ~,, defined by a set Lr of forbidden configurations. We first prove that ~-* can be defined by a set L~* of forbidden subgraphs. Next, using a counterexample we show that ~* is not necessarily a finite set, even when .~ is finite. We then give a sufficient condition for ~* to be finite and a simple...