Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Strong Phases in the Decays B to pi pi

Two sources of strong phases in the decays $B$ to $\pi\pi$ are identified: (1) "quasi-elastic scattering" corresponding to intermediate states like $\pi\pi$ and $\rho\rho$, (2) ``$c\bar{c}$'' corresponding to intermediate states like $D\bar{D}$ and $D^{*}\bar{D}^{*}$. Possibilities of using data to identify these two sources are discussed and illustrated. Present data suggests both sources may be significant.Comment: 6 pages, 1 figure

Global behavior of cosmological dynamics with interacting Veneziano ghost

In this paper, we shall study the dynamical behavior of the universe accelerated by the so called Veneziano ghost dark energy component locally and globally by using the linearization and nullcline method developed in this paper. The energy density is generalized to be proportional to the Hawking temperature defined on the trapping horizon instead of Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the fate of the universe and present the bifurcation phenomenon of the dynamical system of the universe. It seems that the universe could be dominated by dark energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE

Comparison of SUSY spectrum calculations and impact on the relic density constraints from WMAP

We compare results of four public supersymmetric (SUSY) spectrum codes, Isajet, Softsusy, Spheno and Suspect to estimate the present-day uncertainty in the calculation of the relic density of dark matter in mSUGRA models. We find that even for mass differences of about 1% the spread in the obtained relic densities can be 10%. In difficult regions of the parameter space, such as large tan(beta) or large m_0, discrepancies in the relic density are much larger. We also find important differences in the stau co-annihilation region. We show the impact of these uncertainties on the bounds from WMAP for several scenarios, concentrating on the regions of parameter space most relevant for collider phenomenology. We also discuss the case of non-zero A_0 and the stop co-annihilation region. Moreover, we present a web application for the online comparison of the spectrum codes.Comment: 26 pages, 6 figures, 10 tables; version to appear in PR

Gravitino and Axino SuperWIMPs

Gravitinos and axinos produced in the late decays of other supersymmetric particles are well-motivated dark matter (DM) candidates, whose experimental evidences are very distinctive and different from other standard candidates, as thermal produced neutralinos in similar supersymmetric models. In particular, charged sleptons could appear stable because of the length of its lifetime. The direct production of such particles at both the Large Hadron Collider (LHC) and a future International Linear Collider (ILC) can give not only a clear signature of supersymmetry but also the first non-gravitational evidence of dark matter.Comment: 4 pages, LaTeX, 1 figure, Updated references. To appear in Proceedings of SUSY06, the 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions, UC Irvine, California, 12-17 June 200

Achieving precise mechanical control in intrinsically noisy systems

How can precise control be realized in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way of achieving precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons-trains of Dirac-delta functions-in biological systems to achieve precise control performance

Laboratory experiments on cohesive soil bed fluidization by water waves

Part I. Relationships between the rate of bed fluidization and the rate of wave energy dissipation, by Jingzhi Feng and Ashish J. Mehta and Part II. In-situ rheometry for determining the dynamic response of bed, by David J.A. Williams and P. Rhodri Williams. A series of preliminary laboratory flume experiments were carried out to examine the time-dependent behavior of a cohesive soil bed subjected to progressive, monochromatic waves. The bed was an aqueous, 50/50 (by weight) mixture of a kaolinite and an attapulgite placed in a plexiglass trench. The nominal bed thickness was 16 cm with density ranging from 1170 to 1380 kg/m 3, and water above was 16 to 20 cm deep. Waves of design height ranging from 2 to 8 cm and a nominal frequency of 1 Hz were run for durations up to 2970 min. Part I of this report describes experiments meant to examine the rate at which the bed became fluidized, and its relation to the rate of wave energy dissipation. Part II gives results on in-situ rheometry used to track the associated changes in bed rigidity. Temporal and spatial changes of the effective stress were measured during the course of wave action, and from these changes the bed fluidization rate was calculated. A wave-mud interaction model developed in a companion study was employed to calculate the rate of wave energy dissipation. The dependence of the rate of fluidization on the rate of energy dissipation was then explored. Fluidization, which seemingly proceeded down from the bed surface, occurred as a result of the loss of structural integrity of the soil matrix through a buildup of the excess pore pressure and the associated loss of effective stress. The rate of fluidization was typically greater at the beginning of wave action and apparently approached zero with time. This trend coincided with the approach of the rate of energy dissipation to a constant value. In general it was also observed that, for a given wave frequency, the larger the wave height the faster the rate of fluidization and thicker the fluid mud layer formed. On the other hand, increasing the time of bed consolidation prior to wave action decreased the fluidization rate due to greater bed rigidity. Upon cessation of wave action structural recovery followed. Dynamic rigidity was measured by specially designed, in situ shearometers placed in the bed at appropriate elevations to determine the time-dependence of the storage and loss moduli, G' and G", of the viscoelastic clay mixture under 1 Hz waves. As the inter-particle bonds of the space-filling, bed material matrix weakened, the shear propagation velocity decreased measurably. Consequently, G' decreased and G" increased as a transition from dynamically more elastic to more viscous response occurred. These preliminary experiments have demonstrated the validity of the particular rheometric technique used, and the critical need for synchronous, in-situ measurements of pore pressures and moduli characterizing bed rheology in studies on mud fluidization. This study was supported by WES contract DACW39-90-K-0010. (This document contains 151 pages.

A Singular Value Thresholding Algorithm for Matrix Completion

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Off-the-shelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries. This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative, produces a sequence of matrices {X^k,Y^k}, and at each step mainly performs a soft-thresholding operation on the singular values of the matrix Y^k. There are two remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X^k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal storage space and keep the computational cost of each iteration low. On the theoretical side, we provide a convergence analysis showing that the sequence of iterates converges. On the practical side, we provide numerical examples in which 1,000 × 1,000 matrices are recovered in less than a minute on a modest desktop computer. We also demonstrate that our approach is amenable to very large scale problems by recovering matrices of rank about 10 with nearly a billion unknowns from just about 0.4% of their sampled entries. Our methods are connected with the recent literature on linearized Bregman iterations for ℓ_1 minimization, and we develop a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms

One-loop Factorization for Inclusive Hadron Production in pApA Collisions in the Saturation Formalism

We demonstrate the QCD factorization for inclusive hadron production in $pA$ collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron, as well as the rapidity divergence with small-$x$ dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.Comment: 8 pages, 1 figur