Approximation algorithms for dynamic resource allocation

We consider a problem of allocating limited quantities of M types of resources among N independent activities that evolve over T epochs. In each epoch, we assign to each activity a task which consumes resources, generates utility, and determines the subsequent state of the activity. We study the complexity of, and approximation algorithms for, maximizing average utility.     

Effects of sputter deposition parameters and post-deposition annealing on the electrical characteristics of LaAlO3 dielectric films on Si

The influence of processing parameters on the electrical characteristics of RuO₂/LaAlO₃/Si metal-oxide-semiconductor structures was investigated. In particular, the sputtering regime during deposition of LaAlO₃ on Si and the atmosphere used in the post-deposition annealing step were addressed by determining capacitance-voltage and gate current-voltage characteristics. These results were correlated with compositional information obtained by Rutherford backscattering spectrometry and nuclear reaction analysis. A post-deposition annealing step in oxygen at 600 °C resulted in better electrical characteristics of the final structure as compared to the same treatment performed in nitrogen. This result is explained by oxygen ability to heal oxygen vacancies in the LaAlO₃ film, especially at the dielectric/semiconductor interface region. A thermalized sputtering regime during deposition of LaAlO₃ on Si leads to capacitors with electrical characteristics superior to those deposited in ballistic regime. PACS 77.84.Dy; 81.15.Cd; 81.40.Gh; 73.40.Qv; 82.80.Yc     

Structural and electronic properties of graphite layers grown on SiC(0 0 0 1)

Photoelectron spectroscopy, low-energy electron diffraction, and scanning probe microscopy were used to investigate the electronic and structural properties of graphite layers grown by solid state graphitization of SiC(0 0 0 1) surfaces. The process leads to well-ordered graphite layers which are rotated against the substrate lattice by 30°. On on-axis 6H-SiC(0 0 0 1) substrates we observe graphitic layers with up to several 100 nm wide terraces. ARUPS spectra of the graphite layers grown on on-axis 6H-SiC(0 0 0 1) surfaces are indicative of a well-developed band structure. For the graphite/n-type 6H-SiC(0 0 0 1) layer system we observe a Schottky barrier height of ?_B,n = 0.3 ± 0.1 eV. ARUPS spectra of graphite layers grown on 8° off-axis oriented 4H-SiC(0 0 0 1) show unique replicas which are explained by a carpet-like growth mode combined with a step bunching of the substrate.     

Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Electrical conduction and dielectric properties of vanadium phosphate glasses doped with lithium

AC conductivity and dielectric studies on vanadium phosphate glasses doped with lithium have been carried out in the frequency range 0.2-100 kHz and temperature range 290-493 K. The frequency dependence of the conductivity at higher frequencies in glasses obeys a power relationship, σ_ac=Aω^s. The obtained values of the power s lie in the range 0.5≤s≤1 for both undoped and doped with low lithium content which confirms the electron hopping between V⁴⁺ and V⁵⁺ ions. For doped glasses with high lithium content, the values of s≤0.5 which confirm the domination of ionic conductivity. The study of frequency dependence of both dielectric constant and dielectric loss showed a decrease with increasing frequency while they increase with increasing temperature. The results have been explained on the basis of frequency assistance of electron hopping besides the ionic polarization of the glasses. The bulk conductivity increases with increasing temperature whereas decreases with increasing lithium content which means a reduction of the V⁵⁺.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.