arXiv subjects
Publications and source records attributed to Mikhail Volkov.
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely reachable automata in terms of certain directed graphs.
We theoretically investigate the role of intra-band transitions in laser-induced carrier-generation for different photon energy regimes: (i) strongly off-resonant, (ii) multi-photon resonant, and (iii) resonant conditions. Based on the analysis for the strongly off-resonant and multi-photon resonant cases, we find that intra-band transitions strongly enhance photo-carrier generation in both multi-photon absorption and tunneling excitation regimes, and thus, they are indispensable for describing the nonlinear photo-carrier generation processes. Furthermore, we find that intra-band transitions enhance photo-carrier generation even in the resonant condition, opening additional multi-photon excitation channels once the laser irradiation becomes sufficiently strong. The above findings suggest a potential for efficient control of photo-carrier generation via multi-color laser pulses through optimization of the contributions from intra-band transitions.
Hybridization of semiconducting and magnetic materials into a single heterostructure is believed to be potentially applicable to the design of novel functional spintronic devices. In the present work we report epitaxial stabilization of four magnetically ordered iron oxide phases (Fe3O4, γ-Fe2O3, α-Fe2O3 and most exotic metastable ε-Fe2O3) in the form of nanometer sized single crystalline films on GaN(0001) surface. The epitaxial growth of as many as four distinctly different iron oxide phases is demonstrated within the same single-target Laser MBE technological process on a GaN semiconductor substrate widely used for electronic device fabrication. The discussed iron oxides belong to a family of simple formula magnetic materials exhibiting a rich variety of outstanding physical properties including peculiar Verwey and Morin phase transitions in Fe3O4 and α-Fe2O3 and multiferroic behavior in metastable magnetically hard ε-Fe2O3 ferrite. The physical reasons standing behind the nucleation of a particular phase in an epitaxial growth process deserve interest from the fundamental point of view. The practical side of the presented study is to exploit the tunable polymorphism of iron oxides for creation of ferroic-on-semiconductor heterostructures usable in novel spintronic devices. By application of a wide range of experimental techniques the surface morphology, crystalline structure, electronic and magnetic properties of the single phase iron oxide epitaxial films on GaN have been studied. A comprehensive comparison has been made to the properties of the same ferrite materials in the bulk and nanostructured form reported by other research groups.
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the low rank approximation (reduced SVD) of such matrices. Our solution uses coresets, which is a subset of $O(k/\eps^2)$ scaled rows from the $n\times d$ input matrix, that approximates the sub of squared distances from its rows to every $k$-dimensional subspace in $\REAL^d$, up to a factor of $1\pm\eps$. An open theoretical problem has been whether we can compute such a coreset that is independent of the input matrix and also a weighted subset of its rows. %An open practical problem has been whether we can compute a non-trivial approximation to the reduced SVD of very large databases such as the Wikipedia document-term matrix in a reasonable time. We answer this question affirmatively. % and demonstrate an algorithm that efficiently computes a low rank approximation of the entire English Wikipedia. Our main technical result is a novel technique for deterministic coreset construction that is based on a reduction to the problem of $\ell_2$ approximation for item frequencies.
A new sufficient condition under which a semigroup admits no finite identity basis has been recently suggested in a joint paper by Karl Auinger, Yuzhu Chen, Xun Hu, Yanfeng Luo, and the author (see http://arxiv.org/abs/1405.0783). Here we apply this condition to show the absence of a finite identity basis for the semigroup $\mathrm{UT}_3(\mathbb{R})$ of all upper triangular real $3\times 3$-matrices with 0s and/or 1s on the main diagonal. The result holds also for the case when $\mathrm{UT}_3(\mathbb{R})$ is considered as an involution semigroup under the reflection with respect to the secondary diagonal.
We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid $\mathcal{K}_n$ are nonfinitely based for each $n\ge 3$. This result holds also for the case when $\mathcal{K}_n$ is considered as an involution semigroup under either of its natural involutions.
Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem. We also formulate a few open questions.
We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.
We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving: triangularizability of finite semigroups; which semigroups have (split) basic semigroup algebras, two-sided semidirect product decompositions of finite monoids; unambiguous products of rational languages; products of rational languages with counter; and Černý's conjecture for an important class of automata.
It is shown that the SU(2) semilocal model -- the Abelian Higgs model with two complex scalars -- admits a new class of stationary, straight string solutions carrying a persistent current and having finite energy per unit length. In the plane orthogonal to their direction they correspond to a nontrivial deformation of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by the current flowing through them. The new solutions bifurcate with the ANO vortices in the limit of vanishing current. They can be either static or stationary. In the stationary case the relative phase of the two scalars rotates at a constant velocity, giving rise to an electric field and angular momentum, while the energy remains finite. The current has a strong localizing effect on the magnetic field, thus evading the known spreading instability of the ANO-semilocal vortex solutions. The new static vortex solutions have lower energy than the ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings).