D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Ferrohydrodynamics: testing a new magnetization equation

A new magnetization equation recently derived from irreversible thermodynamics is employed to the calculation of an increase of ferrofluid viscosity in a magnetic field. Results of the calculations are compared with those obtained on the basis of two well-known magnetization equations. One of the two was obtained phenomenologically, another one was derived microscopically from the Fokker-Planck equation. It is shown that the new magnetization equation yields a quite satisfactory description of magnetiviscosity in the entire region of magnetic field strength and the flow vorticity. This equation turns out to be valid -- like the microscopically derived equation but unlike the former phenomenological equation -- even far from equilibrium, and so it should be recommended for further applications.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.

Overscreening Diamagnetism in Cylindrical Superconductor-Normal Metal-Heterostructures

We study the linear diamagnetic response of a superconducting cylinder coated by a normal-metal layer due to the proximity effect using the clean limit quasiclassical Eilenberger equations. We compare the results for the susceptibility with those for a planar geometry. Interestingly, for $R\sim d$ the cylinder exhibits a stronger overscreening of the magnetic field, i.e., at the interface to the superconductor it can be less than (-1/2) of the applied field. Even for $R\gg d$, the diamagnetism can be increased as compared to the planar case, viz. the magnetic susceptibility $4\pi\chi$ becomes smaller than -3/4. This behaviour can be explained by an intriguing spatial oscillation of the magnetic field in the normal layer

Enhancing Approximations for Regular Reachability Analysis

This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata representing reachable sets by merging some of their states with respect to simple syntactic criteria, or a combination of such criteria. The second approximation mechanism consists in manipulating an auxiliary automaton when applying a transducer representing the transition relation to an automaton encoding the initial states. In addition, for the second mechanism we propose a new approach to refine the approximations depending on a property of interest. The proposals are evaluated on examples of mutual exclusion protocols

Constructing Entanglement Witness Via Real Skew-Symmetric Operators

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to "optical" metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.Comment: 24 pages, accepted for publication in GR

Two different quasiparticle scattering rates in vortex line liquid phase of layered d-wave superconductors

We carry out a quantum mechanical analysis of the behavior of nodal quasiparticles in the vortex line liquid phase of planar d-wave superconductors. Applying a novel path integral technique we calculate a number of experimentally relevant observables and demonstrate that in the low-field regime the quasiparticle scattering rates deduced from photoemission and thermal transport data can be markedly different from that extracted from tunneling, specific heat, superfluid stiffness or spin-lattice relaxation time.Comment: Latex, 4 pages, no figure