Compositional hierarchical monitoring automaton construction for LTL

In this paper we give a compositional (or inductive) construction of monitoring automata for LTL formulas. Our construction is similar in spirit to the compositional construction of Kesten and Pnueli [5]. We introduce the notion of hierarchical Büchi automata and phrase our constructions in the framework of these automata. We give detailed constructions for all the principal LTL operators including past operators, along with proofs of correctness of the constructions.

Structure constants of beta deformed super Yang-Mills

We study the structure constants of the N = 1 beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS(5) x S-5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Performance analysis of boron nitride embedded armchair graphene nanoribbon metal-oxide-semiconductor field effect transistor with Stone Wales defects

We study the performance of a hybrid Graphene-Boron Nitride armchair nanoribbon (a-GNR-BN) n-MOSFET at its ballistic transport limit. We consider three geometric configurations 3p, 3p + 1, and 3p + 2 of a-GNR-BN with BN atoms embedded on either side (2, 4, and 6 BN) on the GNR. Material properties like band gap, effective mass, and density of states of these H-passivated structures are evaluated using the Density Functional Theory. Using these material parameters, self-consistent Poisson-Schrodinger simulations are carried out under the Non Equilibrium Green's Function formalism to calculate the ballistic n-MOSFET device characteristics. For a hybrid nanoribbon of width similar to 5 nm, the simulated ON current is found to be in the range of 265 mu A-280 mu A with an ON/OFF ratio 7.1 x 10(6)-7.4 x 10(6) for a V-DD = 0.68 V corresponding to 10 nm technology node. We further study the impact of randomly distributed Stone Wales (SW) defects in these hybrid structures and only 2.5% degradation of ON current is observed for SW defect density of 3.18%. (C) 2014 AIP Publishing LLC.

Boosting Higgs CP properties via VH production at the Large Hadron Collider

We consider ZH and WH production at the Large Hadron Collider, where the Higgs decays to a b (b) over bar pair. We use jet substructure techniques to reconstruct the Higgs boson and construct angular observables involving leptonic decay products of the vector bosons. These efficiently discriminate between the tensor structure of the HVV vertex expected in the Standard Model and that arising from possible new physics, as quantified by higher dimensional operators. This can then be used to examine the CP nature of the Higgs as well as CP mixing effects in the HZZ and HWW vertices separately. (C) 2014 Elsevier B.V.

Quantum simulation using fidelity-profile optimization

Experimental quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution unitary U = exp(-iHt) in terms of native unitary operators of the experimental system. Here, using a genetic algorithm, we numerically evaluate the most generic UOD (valid over a continuous range of Hamiltonian parameters) of the unitary operator U, termed fidelity-profile optimization. The optimization is obtained by systematically evaluating the functional dependence of experimental unitary operators (such as single-qubit rotations and time-evolution unitaries of the system interactions) to the Hamiltonian (H) parameters. Using this technique, we have solved the experimental unitary decomposition of a controlled-phase gate (for any phase value), the evolution unitary of the Heisenberg XY interaction, and simulation of the Dzyaloshinskii-Moriya (DM) interaction in the presence of the Heisenberg XY interaction. Using these decompositions, we studied the entanglement dynamics of a Bell state in the DM interaction and experimentally verified the entanglement preservation procedure of Hou et al. Ann. Phys. (N.Y.) 327, 292 (2012)] in a nuclear magnetic resonance quantum information processor.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury-Arveson module on the -dimensional unit ball is defined. For , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.

A FUNCTIONAL MODEL FOR PURE Gamma-CONTRACTIONS

A pair of commuting operators (S,P) defined on a Hilbert space H for which the closed symmetrized bidisc Gamma = {(z(1) + z(2), z(1)z(2)) : vertical bar z(1)vertical bar <= 1, vertical bar z(2)vertical bar <= 1} subset of C-2 is a spectral set is called a Gamma-contraction in the literature. A Gamma-contraction (S, P) is said to be pure if P is a pure contraction, i.e., P*(n) -> 0 strongly as n -> infinity Here we construct a functional model and produce a set of unitary invariants for a pure Gamma-contraction. The key ingredient in these constructions is an operator, which is the unique solution of the operator equation S - S*P = DpXDp, where X is an element of B(D-p), and is called the fundamental operator of the Gamma-contraction (S, P). We also discuss some important properties of the fundamental operator.

Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

Spectrum of the three-dimensional fuzzy well

We develop the formalism of quantum mechanics on three-dimensional fuzzy space and solve the Schrodinger equation for the free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well are calculated.

STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.

On Hermite pseudo-multipliers

In this article we deal with a variation of a theorem of Mauceri concerning the L-P boundedness of operators M which are known to be bounded on L-2. We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted L-P estimates. As an application we prove L-P boundedness of Hermite pseudo-multipliers. (C) 2014 Elsevier Inc. All rights reserved.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.