On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Junction between surfaces of two topological insulators

We study the properties of a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time-reversal invariant system, we show that the line junction is characterized by an arbitrary parameter alpha which determines the scattering from the junction. If the surface velocities have the same sign, we show that there can be edge states which propagate along the line junction with a velocity and spin orientation which depend on alpha and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle phi with respect to each other. We study the scattering and differential conductance through the line junction as functions of phi and alpha. We also find that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on phi. Finally, if the surface velocities have opposite signs, we find that the electrons must transmit into the two-dimensional interface separating the two topological insulators.

Counterterms, critical gravity, and holography

We consider counterterms for odd dimensional holographic conformal field theories (CFTs). These counterterms are derived by demanding cutoff independence of the CFT partition function on S-d and S-1 x Sd-1. The same choice of counterterms leads to a cutoff independent Schwarzschild black hole entropy. When treated as independent actions, these counterterm actions resemble critical theories of gravity, i.e., higher curvature gravity theories where the additional massive spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these are theories where at least one of the central charges associated with the trace anomaly vanishes. Connections between these theories and logarithmic CFTs are discussed. For a specific choice of parameters, the theories arising from counterterms are nondynamical and resemble a Dirac-Born-Infeld generalization of gravity. For even dimensional CFTs, analogous counterterms cancel log-independent cutoff dependence.

Quantum capacitance in bilayer graphene nanoribbon

We address a physically based analytical model of quantum capacitance (C-Q) in a bilayer graphene nanoribbon (BGN) under the application of an external longitudinal static bias. We demonstrate that as the gap (Delta) about the Dirac point increases, a phenomenological population inversion of the carriers in the two sets of subbands occurs. This results in a periodic and composite oscillatory behavior in the C-Q with the channel potential, which also decreases with increase in Delta. We also study the quantum size effects on the C-Q, which signatures heavy spatial oscillations due to the occurrence of van Hove singularities in the total density-of-states function of both the sets of subbands. All the mathematical results as derived in this paper converge to the corresponding well-known solution of graphene under certain limiting conditions and this compatibility is an indirect test of our theoretical formalism. (C) 2012 Elsevier By. All rights reserved.

Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Lepton masses and flavor violation in the Randall-Sundrum model

Lepton masses and mixing angles via localization of 5-dimensional fields in the bulk are revisited in the context of Randall-Sundrum models. The Higgs is assumed to be localized on the IR brane. Three cases for neutrino masses are considered: (a) The higher-dimensional neutrino mass operator (LH.LH), (b) Dirac masses, and (c) Type I seesaw with bulk Majorana mass terms. Neutrino masses and mixing as well as charged lepton masses are fit in the first two cases using chi(2) minimization for the bulk mass parameters, while varying the O(1) Yukawa couplings between 0.1 and 4. Lepton flavor violation is studied for all the three cases. It is shown that large negative bulk mass parameters are required for the right-handed fields to fit the data in the LH.LH case. This case is characterized by a very large Kaluza-Klein (KK) spectrum and relatively weak flavor-violating constraints at leading order. The zero modes for the charged singlets are composite in this case, and their corresponding effective 4-dimensional Yukawa couplings to the KK modes could be large. For the Dirac case, good fits can be obtained for the bulk mass parameters, c(i), lying between 0 and 1. However, most of the ``best-fit regions'' are ruled out from flavor-violating constraints. In the bulk Majorana terms case, we have solved the profile equations numerically. We give example points for inverted hierarchy and normal hierarchy of neutrino masses. Lepton flavor violating rates are large for these points. We then discuss various minimal flavor violation schemes for Dirac and bulk Majorana cases. In the Dirac case with minimal-flavor-violation hypothesis, it is possible to simultaneously fit leptonic masses and mixing angles and alleviate lepton flavor violating constraints for KK modes with masses of around 3 TeV. Similar examples are also provided in the Majorana case.

Leptonic minimal flavour violation in warped extra dimensions

Lepton mass hierarchies and lepton flavour violation are revisited in the framework of Randall-Sundrum models. Models with Dirac-type as well as Majorana-type neutrinos are considered. The five-dimensional c-parameters are fit to the charged lepton and neutrino masses and mixings using chi(2) minimization. Leptonic flavour violation is shown to be large in these cases. Schemes of minimal flavour violation are considered for the cases of an effective LLHH operator and Dirac neutrinos and are shown to significantly reduce the limits from lepton flavour violation.

Spin injection into a metal from a topological insulator

We study a junction of a topological insulator with a thin two-dimensional nonmagnetic or partially polarized ferromagnetic metallic film deposited on a three-dimensional insulator. We show, by deriving generic boundary conditions applicable to electrons traversing the junction, that there is a finite spin-current injection into the film whose magnitude can be controlled by tuning a voltage V applied across the junction. For ferromagnetic films, the direction of the component of the spin current along the film magnetization can also be tuned by tuning the barrier potential V-0 at the junction. We point out the role of the chiral spin-momentum locking of the Dirac electrons behind this phenomenon and suggest experiments to test our theory.

Status of supersymmetric type-I seesaw in SO(10) inspired models

We report on the status of supersymmetric seesaw models in the light of recent experimental results on mu -> e + gamma, theta(13) and the light Higgs mass at the LHC. SO(10)-like relations are assumed for neutrino Dirac Yukawa couplings and two cases of mixing, one large, PMNS-like, and another small, CKM-like, are considered. It is shown that for the large mixing case, only a small range of parameter space with moderate tan beta is still allowed. This remaining region can be ruled out by an order of magnitude improvement in the current limit on BR(mu -> e + gamma). We also explore a model with non-universal Higgs mass boundary conditions at the high scale. It is shown that the renormalization group induced flavor violating slepton mass terms are highly sensitive to the Higgs boundary conditions. Depending on the choice of the parameters, they can either lead to strong enhancements or cancellations within the flavor violating terms. Such cancellations might relax the severe constraints imposed by lepton flavor violation compared to mSUGRA. Nevertheless for a large region of parameter space the predicted rates lie within the reach of future experiments once the light Higgs mass constraint is imposed. We also update the potential of the ongoing and future experimental searches for lepton flavor violation in constraining the supersymmetric parameter space.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

A multichannel sampling method for 2-D finite-rate-of-innovation signals

We address the problem of sampling and reconstruction of two-dimensional (2-D) finite-rate-of-innovation (FRI) signals. We propose a three-channel sampling method for efficiently solving the problem. We consider the sampling of a stream of 2-D Dirac impulses and a sum of 2-D unit-step functions. We propose a 2-D causal exponential function as the sampling kernel. By causality in 2-D, we mean that the function has its support restricted to the first quadrant. The advantage of using a multichannel sampling method with causal exponential sampling kernel is that standard annihilating filter or root-finding algorithms are not required. Further, the proposed method has inexpensive hardware implementation and is numerically stable as the number of Dirac impulses increases.

Warped alternatives to Froggatt-Nielsen models

We consider the Randall-Sundrum (RS) setup to be a theory of flavor, as an alternative to Froggatt-Nielsen models instead of as a solution to the hierarchy problem. The RS framework is modified by taking the low-energy brane to be at the grand unified theory (GUT) scale. This also alleviates constraints from flavor physics. Fermion masses and mixing angles are fit at the GUT scale. The ranges of the bulk mass parameters are determined using a chi(2) fit taking into consideration the variation in O(1) parameters. In the hadronic sector, the heavy top quark requires large bulk mass parameters localizing the right-handed top quark close to the IR brane. Two cases of neutrino masses are considered: (a) Planck scale lepton number violation and (b) Dirac neutrino masses. Contrary to the case of weak scale RS models, both these cases give reasonable fits to the data, with the Planck scale lepton number violation fitting slightly better compared to the Dirac case. In the supersymmetric version, the fits are not significantly different except for the variation in tan beta. If the Higgs superfields and the supersymmetry breaking spurion are localized on the same brane, then the structure of the sfermion masses are determined by the profiles of the zero modes of the hypermultiplets in the bulk. Trilinear terms have the same structure as the Yukawa matrices. The resultant squark spectrum is around similar to 2-3 TeV required by the light Higgs mass to be around 125 GeV and to satisfy the flavor violating constraints.

Transport across a junction of topological insulators and a superconductor

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. The junction can have three time-reversal invariant barriers on three sides. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac- and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors, such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a nonzero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.

Light transmission through and its complete stoppage in an ultra slow wave optical medium

Light wave transmission - its compression, amplification, and the optical energy storage in an ultra slow wave medium (USWM) is studied analytically. Our phenomenological treatment is based entirely on the continuity equation for the optical energy flux, and the well-known distribution-product property of Dirac delta-function. The results so obtained provide a clear understanding of some recent experiments on light transmission and its complete stoppage in an USWM.

Mechanical and electronic properties of pristine and Ni-doped Si, Ge, and Sn sheets

Silicene, a graphene analogue of silicon, has been generating immense interest due to its potential for applications in miniaturized devices. Unlike planar graphene, silicene prefers a buckled structure. Here we explore the possibility of stabilizing the planar form of silicene by Ni doping using first principles density functional theory based calculations. It is found that planar as well as buckled structure is stable for Ni-doped silicene, but the buckled sheet has slightly lower total energy. The planar silicene sheet has unstable phonon modes. A comparative study of the mechanical properties reveals that the in-plane stiffness of both the pristine and the doped planar silicene is higher compared to that of the buckled silicene. This suggests that planar silicene is mechanically more robust. Electronic structure calculations of the planar and buckled Ni-doped silicene show that the energy bands at the Dirac point transform from linear behavior to parabolic dispersion. Furthermore, we extend our study to Ge and Sn sheets that are also stable and the trends of comparable mechanical stability of the planar and buckled phases remain the same.