Further results on geometric properties of a family of relative entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

Probing the indefinite CP nature of the Higgs boson through decay distributions in the process e(+)e(-) -> t(t)over-bar Phi

The recently discovered scalar resonance at the Large Hadron Collider is now almost confirmed to be a Higgs boson, whose CP properties are yet to be established. At the International Linear Collider with and without polarized beams, it may be possible to probe these properties at high precision. In this work, we study the possibility of probing departures from the pure CP-even case, by using the decay distributions in the process e(+)e(-) -> t (t) over bar Phi, with Phi mainly decaying into a b (b) over bar pair. We have compared the case of a minimal extension of the Standard Model case (model I) with an additional pseudoscalar degree of freedom, with a more realistic case namely the CP-violating two-Higgs doublet model (model II) that permits a more general description of the couplings. We have considered the International Linear Collider with root s = 800 GeV and integrated luminosity of 300 fb(-1). Our main findings are that even in the case of small departures from the CP-even case, the decay distributions are sensitive to the presence of a CP-odd component in model II, while it is difficult to probe these departures in model I unless the pseudoscalar component is very large. Noting that the proposed degrees of beam polarization increase the statistics, the process demonstrates the effective role of beam polarization in studies beyond the Standard Model. Further, our study shows that an indefinite CP Higgs would be a sensitive laboratory to physics beyond the Standard Model.

Dynamics of prolate spheroidal mass distributions with varying eccentricity

In this paper we calculate the potential for a prolate spheroidal distribution as in a dark matter halo with a radially varying eccentricity. This is obtained by summing up the shell-by-shell contributions of isodensity surfaces, which are taken to be concentric and with a common polar axis and with an axis ratio that varies with radius. Interestingly, the constancy of potential inside a shell is shown to be a good approximation even when the isodensity contours are dissimilar spheroids, as long as the radial variation in eccentricity is small as seen in realistic systems. We consider three cases where the isodensity contours are more prolate at large radii, or are less prolate or have a constant eccentricity. Other relevant physical quantities like the rotation velocity, the net orbital and vertical frequency due to the halo and an exponential disc of finite thickness embedded in it are obtained. We apply this to the kinematical origin of Galactic warp, and show that a prolate-shaped halo is not conducive to making long-lived warps - contrary to what has been proposed in the literature. The results for a prolate mass distribution with a variable axis ratio obtained are general, and can be applied to other astrophysical systems, such as prolate bars, for a more realistic treatment.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Generalized scaling of misorientation angle distributions at meso-scale in deformed materials

Scaling behaviour has been observed at mesoscopic level irrespective of crystal structure, type of boundary and operative micro-mechanisms like slip and twinning. The presence of scaling at the meso-scale accompanied with that at the nano-scale clearly demonstrates the intrinsic spanning for different deformation processes and a true universal nature of scaling. The origin of a 1/2 power law in deformation of crystalline materials in terms of misorientation proportional to square root of strain is attributed to importance of interfaces in deformation processes. It is proposed that materials existing in three dimensional Euclidean spaces accommodate plastic deformation by one dimensional dislocations and their interaction with two dimensional interfaces at different length scales. This gives rise to a 1/2 power law scaling in materials. This intrinsic relationship can be incorporated in crystal plasticity models that aim to span different length and time scales to predict the deformation response of crystalline materials accurately.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

New Insights into Electronic and Geometric Effects in the Enhanced Photoelectrooxidation of Ethanol Using ZnO Nanorod/Ultrathin Au Nanowire Hybrids

Oxidation of small organic molecules in a fuel cell is a viable method for energy production. However, the key issue is the development of suitable catalysts that exhibit high efficiencies and remain stable during operation. Here, we demonstrate that amine-modified ZnO nanorods on which ultrathin Au nanowires are grown act as an excellent catalyst for the oxidation of ethanol. We show that the modification of the ZnO nanorods with oleylamine not only modifies the electronic structure favorably but also serves to anchor the Au nanowires on the nanorods. The adsorption of OH- species on the Au nanowires that is essential for ethanol oxidation is facilitated at much lower potentials as compared to bare Au nanowires leading to high activity. While ZnO shows negligible electrocatalytic activity under normal conditions, there is significant enhancement in the activity under light irradiation. We demonstrate a synergistic enhancement in the photoelectrocatalytic activity of the ZnO/Au nanowire hybrid and provide mechanistic explanation for this enhancement based on both electronic as well as geometric effects. The principles developed are applicable for tuning the properties of other metal/semiconductor hybrids with potentially interesting applications beyond the fuel cell application demonstrated here.

Descending from infinity: Convergence of tailed distributions

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not eliminated. Relaxation stronger than linear suppresses long tails immediately, but may lead to strong transient peaks in the probability distribution. We also find that a delta-function initial distribution under stronger than linear decay displays not one but two different regimes of diffusive spreading.

Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

A note on D1-D5 entropy and geometric quantization

We quantize the space of 2-charge fuzzballs in IIB supergravity on K3. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of K3 fuzzballs, filling a small gap in the literature.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.