New Results in Light-Front Phenomenology

The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and to define a kinematical definition of angular momentum. The AdS/CFT correspondence of large $N_C$ supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent analyses which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Comment: Presented at LightCone 2004, Amsterdam, The Netherlands, 16-20 August 200

The maximum of Brownian motion minus a parabola

We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.Comment: 7 pages, 4 figures, to appear in the Electronic Journal of Probabilit

Safe Schedulability of Bounded-Rate Multi-Mode Systems

Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. The schedulability problem for BMMS is defined as an infinite-round game between two players---the scheduler and the environment---where in each round the scheduler proposes a time and a mode while the environment chooses an allowable rate for that mode, and the state of the system changes linearly in the direction of the rate vector. The goal of the scheduler is to keep the state of the system within a pre-specified safe set using a non-Zeno schedule, while the goal of the environment is the opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS where a winning strategy of the scheduler corresponds to a robust energy-optimal policy. We present an algorithm to decide whether the scheduler has a winning strategy from an arbitrary starting state, and give an algorithm to compute such a winning strategy, if it exists. We show that the schedulability problem for BMMS is co-NP complete in general, but for two variables it is in PTIME. We also study the discrete schedulability problem where the environment has only finitely many choices of rate vectors in each mode and the scheduler can make decisions only at multiples of a given clock period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201

On a Problem of Harary and Schwenk on Graphs with Distinct Eigenvalues

Harary and Schwenk posed the problem forty years ago: Which graphs have distinct adjacency eigenvalues? In this paper, we obtain a necessary and sufficient condition for an Hermitian matrix with simple spectral radius and distinct eigenvalues. As its application, we give an algebraic characterization to the Harary-Schwenk's problem. As an extension of their problem, we also obtain a necessary and sufficient condition for a positive semidefinite matrix with simple least eigenvalue and distinct eigenvalues, which can provide an algebraic characterization to their problem with respect to the (normalized) Laplacian matrix.Comment: 11 page

An Algorithm for Unconstrained Quadratically Penalized Convex Optimization

A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized estimation in machine learning and statistics. In addition to values of $F$, QQMM requires the (sub)gradient of $V$. Two features of QQMM help keep low the number of evaluations of the objective function it needs. First, QQMM provides good control over stopping the iterative search. This feature makes QQMM well adapted to statistical problems because in such problems the objective function is based on random data and therefore stopping early is sensible. Secondly, QQMM uses a complex method for determining trial minimizers of $F$. After a description of the problem and algorithm a simulation study comparing QQMM to the popular BFGS optimization algorithm is described. The simulation study and other experiments suggest that QQMM is generally substantially faster than BFGS in the problem domain for which it was designed. A QQMM-BFGS hybrid is also generally substantially faster than BFGS but does better than QQMM when QQMM is very slow.Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Codes and Designs Related to Lifted MRD Codes

Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly different representation of this design makes it similar to a $q-$analog of a transversal design. The structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain a lifted MRD code. Codes which attain these bounds are constructed. These codes are the largest known codes for the given parameters. These transversal designs can be also used to derive a new family of linear codes in the Hamming space. Bounds on the minimum distance and the dimension of such codes are given.Comment: Submitted to IEEE Transactions on Information Theory. The material in this paper was presented in part in the 2011 IEEE International Symposium on Information Theory, Saint Petersburg, Russia, August 201

On the pinning strategy of complex networks

In pinning control of complex networks, a tacit believing is that the system dynamics will be better controlled by pinning the large-degree nodes than the small-degree ones. Here, by changing the number of pinned nodes, we find that, when a significant fraction of the network nodes are pinned, pinning the small-degree nodes could generally have a higher performance than pinning the large-degree nodes. We demonstrate this interesting phenomenon on a variety of complex networks, and analyze the underlying mechanisms by the model of star networks. By changing the network properties, we also find that, comparing to densely connected homogeneous networks, the advantage of the small-degree pinning strategy is more distinct in sparsely connected heterogenous networks

Commuting birth-and-death processes

We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the $m$-dimensional lattice and for which the $m$ matrices that record the transition probabilities in each of the lattice directions commute pairwise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute $n$ step transition probabilities. The set of commuting birth-and-death processes decomposes as a union of toric varieties, with the main component being the closure of all processes whose nearest neighbor transition probabilities are positive. We exhibit an explicit monomial parametrization for this main component, and we explore the boundary components using primary decomposition.Comment: Published in at http://dx.doi.org/10.1214/09-AAP615 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Clinical and urodynamic findings in women affected by mixed urinary incontinence

The definition of mixed urinary incontinence (MUI) of the International Continence Society exclusively assesses patient-reported symptoms without consideration of physical and urodynamic results, what is inadequate to reliably predict the pathophysiology of the underlying pathology. We investigated and compared clinical and urodynamic findings in women with MUI and assessed predictive variables for the different MUI clinical presentations