Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Stochastic motion planning and applications to traffic

This paper presents a stochastic motion planning algorithm and its application to traffic navigation. The algorithm copes with the uncertainty of road traffic conditions by stochastic modeling of travel delay on road networks. The algorithm determines paths between two points that optimize a cost function of the delay probability distribution. It can be used to find paths that maximize the probability of reaching a destination within a particular travel deadline. For such problems, standard shortest-path algorithms don’t work because the optimal substructure property doesn’t hold. We evaluate our algorithm using both simulations and real-world drives, using delay data gathered from a set of taxis equipped with GPS sensors and a wireless network. Our algorithm can be integrated into on-board navigation systems as well as route-finding Web sites, providing drivers with good paths that meet their desired goals.National Science Foundation (U.S.) (grant EFRI-0710252)National Science Foundation (U.S.) (grant IIS-0426838

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199

Chirality in Bare and Passivated Gold Nanoclusters

Chiral structures have been found as the lowest-energy isomers of bare (Au$_{28}$ and Au$_{55}) and thiol-passivated (Au$_{28}(SCH$_{3})$_{16}$and Au$_{38}(SCH_{3})_{24}) gold nanoclusters. The degree of chirality existing in the chiral clusters was calculated using the Hausdorff chirality measure. We found that the index of chirality is higher in the passivated clusters and decreases with the cluster size. These results are consistent with the observed chiroptical activity recently reported for glutahione-passivated gold nanoclusters, and provide theoretical support for the existence of chirality in these novel compounds.Comment: 5 pages, 1 figure. Submitted to PR

High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this paper, we consider a feature-wise kernelized Lasso for capturing non-linear input-output dependency. We first show that, with particular choices of kernel functions, non-redundant features with strong statistical dependence on output values can be found in terms of kernel-based independence measures. We then show that the globally optimal solution can be efficiently computed; this makes the approach scalable to high-dimensional problems. The effectiveness of the proposed method is demonstrated through feature selection experiments with thousands of features.Comment: 18 page

Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7 September 2010. Published online on 9 October 2010. The final publication is available at http://www.springerlink.co

Ginzburg-Landau model with small pinning domains

We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These pinning domains model small impurities in a homogeneous superconductor and shrink to single points in the limit $\v\to0$; here, \v is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary condition $g$ on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d >0. Our main result is that, for small \v, minimizers have $d$ distinct zeros (vortices) which are inside the pinning domains and they have a degree equal to 1. The question of finding the locations of the pinning domains with vortices is reduced to a discrete minimization problem for a finite-dimensional functional of renormalized energy. We also find the position of the vortices inside the pinning domains and show that, asymptotically, this position is determined by {\it local renormalized energy} which does not depend on the external boundary conditions.Comment: 39 page

Intensity of Resistance Exercise Determines Adipokine and Resting Energy Expenditure Responses in Overweight Elderly Individuals

OBJECTIVE - To evaluate the time course of leptin, adiponectin, and testing energy expenditure (REE) responses in overweight elderly mates after acute resistance exercise protocols of various intensity configurations. RESEARCH DESIGN AND METHODS - Forty inactive men (65-82 years) were randomly assigned to one of four groups (n = 10/group): control, low-intensity resistance exercise, moderate-intensity resistance exercise, and high-intensity resistance exercise. Exercise energy cost, REE, leptin, adiponectin, cortisol, insulin, lactate, glucose, nonesterified fatty acids (NEFAs), and glycerol were determined at baseline, immediately after exercise, and during a 72-h recovery period. RESULTS - Exercise energy cost was lower in high-intensity than in low-intensity and moderate-intensity groups (221.6 +/- 8.8 vs. 295.6 +/- 10.7 and 281.6 +/- 9.8 kcal, P < 0.001). Lactate, glucose, NEFAs, and glycerol concentrations increased (P < 0.001) after exercise and returned to baseline thereafter in all groups. REE increased (P < 0.001) in all groups at 12 h in an intensity-dependent manner (P < 0.05). REE reached baseline after 48 h in the low- and mode rate-intensity groups and after 72 h in the high-intensity group. Cortisol peaked in all active groups after exercise (P < 0.001) and remained elevated (P < 0.001) for 12 h. After adjustment for plasma volume shifts, leptin remained unaltered. Adiponectin concentration increased after 12 hand remained elevated for 24 h only in the high-intensity group (P < 0.001). CONCLUSIONS - Resistance exercise does not alter circulating leptin concentration but does increase REE and adiponectin in an intensity-dependent manner for as long as 48 and 24 h, respectively, in overweight elderly individuals. It appears that resistance exercise may represent an effective approach for weight management and metabolic control in overweight elderly individuals