Potential estimates and quasilinear parabolic equations with measure data

In this paper, we study the existence and regularity of the quasilinear parabolic equations: $$u_t-\text{div}(A(x,t,\nabla u))=B(u,\nabla u)+\mu$$ in $\mathbb{R}^{N+1}$, $\mathbb{R}^N\times(0,\infty)$ and a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$. Here $N\geq 2$, the nonlinearity $A$ fulfills standard growth conditions and $B$ term is a continuous function and $\mu$ is a radon measure. Our first task is to establish the existence results with $B(u,\nabla u)=\pm|u|^{q-1}u$, for $q>1$. We next obtain global weighted-Lorentz, Lorentz-Morrey and Capacitary estimates on gradient of solutions with $B\equiv 0$, under minimal conditions on the boundary of domain and on nonlinearity $A$. Finally, due to these estimates, we solve the existence problems with $B(u,\nabla u)=|\nabla u|^q$ for $q>1$.Comment: 120

Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimation

We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymptotic and global sense. Due to a special modelling of sparse estimation problems in the context of machine learning, the assumptions we make are milder and more natural than those made in conventional analysis of augmented Lagrangian algorithms. In addition, the new interpretation enables us to generalize DAL to wide varieties of sparse estimation problems. We experimentally confirm our analysis in a large scale $\ell_1$-regularized logistic regression problem and extensively compare the efficiency of DAL algorithm to previously proposed algorithms on both synthetic and benchmark datasets.Comment: 51 pages, 9 figure

Color Ferromagnetism of Quark Matter ; a Possible Origin of Strong Magnetic Field in Magnetars

We show a possibility that strong ``magnetic field'' $\sim 10^{15}$G is produced by color ferromagnetic quark matter in neutron stars. In the quark matter a color magnetic field is generated spontaneously owing to Savvidy mechanism and a gluon condensate arises for the stabilization of the field. Since the quark matter is electrically charged in the neutron stars, the rotation of the quarks around the color magnetic field produces the strong ``magnetic field''.Comment: 7 page

Cyclic Low-Density MDS Array Codes

We construct two infinite families of low density MDS array codes which are also cyclic. One of these families includes the first such sub-family with redundancy parameter r > 2. The two constructions have different algebraic formulations, though they both have the same indirect structure. First MDS codes that are not cyclic are constructed and then by applying a certain mapping to their parity check matrices, non-equivalent cyclic codes with the same distance and density properties are obtained. Using the same proof techniques, a third infinite family of quasi-cyclic codes can be constructed

q-Chebyshev polynomials

In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi numbers.Comment: enlarged version, 34 page

Community building and virtual teamwork in an online learning environment

In the world of OTIS, an online Internet School for occupational therapists, students from four European countries were encouraged to work collaboratively through problem based learning by interacting with each other in a virtual semi-immersive environment. This paper aims to explore the issues that there was little interaction between students from different tutorial groups and virtual teamwork developed in each of the cross cultural tutorial groups. Synchronous data from European students was captured during tutorial sessions and peer booked meetings and evidence suggests that communities of interest were established. It is possible to conclude that collaborative systems can be designed, which encourage students to build trust and teamwork in a cross cultural online learning environment. </p

TRECVID: benchmarking the effectiveness of information retrieval tasks on digital video

Many research groups worldwide are now investigating techniques which can support information retrieval on archives of digital video and as groups move on to implement these techniques they inevitably try to evaluate the performance of their techniques in practical situations. The difficulty with doing this is that there is no test collection or any environment in which the effectiveness of video IR or video IR sub-tasks, can be evaluated and compared. The annual series of TREC exercises has, for over a decade, been benchmarking the effectiveness of systems in carrying out various information retrieval tasks on text and audio and has contributed to a huge improvement in many of these. Two years ago, a track was introduced which covers shot boundary detection, feature extraction and searching through archives of digital video. In this paper we present a summary of the activities in the TREC Video track in 2002 where 17 teams from across the world took part

Interference Alignment for the Multi-Antenna Compound Wiretap Channel

We study a wiretap channel model where the sender has $M$ transmit antennas and there are two groups consisting of $J_1$ and $J_2$ receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model -- group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom. Our lower bound is based on the recently proposed \emph{real interference alignment} scheme. The upper bound provides the first known example which illustrates that the \emph{pairwise upper bound} used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the degrees of freedom are developed by extending the results on the compound wiretap channel.Comment: Minor edits. Submitted to IEEE Trans. Inf. Theor

Perturbation Theory for Antisymmetric Tensor Fields in Four Dimensions

Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.Comment: 23 page

Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations

We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ensemble which is a generalization of the real, complex and quaternion Wigner matrices. As corollaries, when n is much smaller than p, we show that the largest and smallest eigenvalues of the complex Wishart matrix are asymptotically independent; we obtain the limiting distribution of the condition numbers as a sum of two i.i.d. random variables with a Tracy-Widom distribution, which is much different from the exact square case that n=p by Edelman (1988); we propose a test procedure for a spherical hypothesis test. By the same approximation tool, we obtain the asymptotic distribution of the smallest eigenvalue of the beta-Laguerre ensemble. In the second part of the paper, under the assumption that n is much smaller than p in a certain scale, we prove the large deviation principles for three basic statistics: the largest eigenvalue, the smallest eigenvalue and the empirical distribution of eigenvalues, where the last large deviation is derived by using a non-standard method