Integrable matrix equations related to pairs of compatible associative algebras

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we investigate in details the multiplications of the A-type and integrable matrix ODEs and PDEs generated by them.Comment: 12 pages, Late

Automorphisms and isomorphisms of Chevalley groups and algebras

An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.Comment: 8 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: minor changes in Introduction and Reference

Optical Conductivity of the Trellis-Lattice t-J Model: Charge Fluctuations in NaV_2O_5

Optical conductivity of the trellis lattice t-J model at quarter filling is calculated by an exact-diagonalization technique on small clusters, whereby the valence state of V ions of NaV_2O_5 is considered. We show that the experimental features at \sim 1 eV, including peak positions, presence of shoulders, and anisotropic spectral weight, can be reproduced in reasonable range of parameter values, only by assuming that the system is in the charge disproportionated ground state. Possible reconciliation with experimental data suggesting the presence of uniform ladders at T>T_c is discussed.Comment: 4 pages, 4 gif figures. Minor revisions have been made. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to [email protected]

Defect formation in superconducting rings: external fields and finite-size effects

Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields. Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practice, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free.Comment: 10 pages, 3 figures, presentation at QFS2012, to appear in JLT

Optical properties and electronic structure of Ca-doped alpha'-NaV2O5

The dielectric function of alpha'-Na(1-x)Ca(x)V2O5 (0 < x < 20%) was measured for the a and b axes in the photon energy range 0.8-4.5 eV at room temperature. By varying the Ca-concentration we control the relative abundancy of V4+ and V5+. We observe that the intensity of the main optical absorption peak at 1 eV is proportional to the number of V5+ ions. This rules out the interpretation as a V4+ d-d excitation, and it establishes that this is the on-rung bonding-antibonding transition.Comment: 6 pages, ReVTeX, 5 figures in encapsulated postscript forma

Whole-genome sequencing shows that patient-to-patient transmission rarely accounts for acquisition of Staphylococcus aureus in an intensive care unit

BACKGROUND  Strategies to prevent Staphylococcus aureus infection in hospitals focus on patient-to-patient transmission. We used whole-genome sequencing to investigate the role of colonized patients as the source of new S. aureus acquisitions, and the reliability of identifying patient-to-patient transmission using the conventional approach of spa typing and overlapping patient stay. METHODS Over 14 months, all unselected patients admitted to an adult intensive care unit (ICU) were serially screened for S. aureus. All available isolates (n = 275) were spa typed and underwent whole-genome sequencing to investigate their relatedness at high resolution. RESULTS Staphylococcus aureus was carried by 185 of 1109 patients sampled within 24 hours of ICU admission (16.7%); 59 (5.3%) patients carried methicillin-resistant S. aureus (MRSA). Forty-four S. aureus (22 MRSA) acquisitions while on ICU were detected. Isolates were available for genetic analysis from 37 acquisitions. Whole-genome sequencing indicated that 7 of these 37 (18.9%) were transmissions from other colonized patients. Conventional methods (spa typing combined with overlapping patient stay) falsely identified 3 patient-to-patient transmissions (all MRSA) and failed to detect 2 acquisitions and 4 transmissions (2 MRSA). CONCLUSIONS Only a minority of S. aureus acquisitions can be explained by patient-to-patient transmission. Whole-genome sequencing provides the resolution to disprove transmission events indicated by conventional methods and also to reveal otherwise unsuspected transmission events. Whole-genome sequencing should replace conventional methods for detection of nosocomial S. aureus transmission

On the Economic Sustainability of Cloud Sharing Systems: Are Dynamic Single Resource Sharing Markets Stable?

The recent emergence of the small cloud (SC), both in concept and in practice, has been driven mainly by issues related to service cost and complexity of commercial cloud providers (e.g., Amazon) employing massive data centers. However, the resource inelasticity problem faced by the SCs due to their relatively scarce resources might lead to a potential degradation of customer QoS and loss of revenue. A proposed solution to this problem recommends the sharing of resources between competing SCs to alleviate the resource inelasticity issues that might arise. Based on this idea, a recent effort proposed SC-Share, a performance-driven static market model for competitive small cloud environments that results in an efficient market equilibrium jointly optimizing customer QoS satisfaction and SC revenue generation. However, an important question with a non-obvious answer still remains to be answered, without which SC sharing markets may not be guaranteed to sustain in the long-run - is it still possible to achieve a stable market efficient state when the supply of SC resources is dynamic in nature? In this short paper, we take a first step to addressing the problem of efficient market design for single SC resource sharing in dynamic environments. We answer our previous question in the affirmative through the use of Arrow and Hurwicz's disequilibrium process in economics, and the gradient play technique in game theory that allows us to iteratively converge upon efficient and stable market equilibria.Peer reviewe

"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

A Model Study of the Low-Energy Charge Dynamics of NaV_2O_5

An exact-diagonalization technique on small clusters is used to calculate the dynamical density correlation functions of the dimerized t-J chain and coupled anisotropic t-J ladders (trellis lattice) at quarter filling, i.e., the systems regarded as a network of pairs (dimers or rungs) of sites coupled weakly via the hopping and exchange interactions. We thereby demonstrate that the intersite Coulomb repulsions between the pairs induce a low-energy collective mode in the charge excitations of the systems where the internal charge degrees of freedom of the pairs play an essential role. Implications to the electronic states of NaV_2O_5, i.e., fluctuations of the valence state of V ions and phase transition as a charge ordering, are discussed.Comment: 4 pages, 4 gif figures. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to [email protected]

From AKNS to derivative NLS hierarchies via deformations of associative products

Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed method to obtain 'functional representations' can be applied. We actually consider hierarchies with dependent variables in any (possibly noncommutative) associative algebra, e.g., an algebra of matrices of functions. This also covers the case of hierarchies of coupled DNLS equations.Comment: 22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of section 2 rewritten, taking account of previously overlooked references. To appear in J. Physics A: Math. Ge