Re‐emitted positron spectroscopy of cobalt and nickel silicide films

The techniques of re‐emitted positron spectroscopy (RPS) have been employed in the first systematic investigation of the positronic properties of the various stoichiometric phases (M2Si, MSi, and MSi2) of Co and Ni silicide films grown in situ on Si substrates. The positron work function is found to be negative for all of the different phases; thus implanted positrons may be re‐emitted. The energy of the re‐emitted positrons is found to have a surprisingly large variation for the different phases. This feature should provide the image contrast necessary to observe each phase on a microscopic scale using the positron re‐emission microscope (PRM). The positron deformation potential, E+d≡V(∂Σ/∂V), was determined for CoSi2 films; it can be used to estimate the size of the positron diffusion constant, which is found to be comparable to that of other metals. Thus the short positron diffusion length (of order 150 Å) determined from depth‐profiling measurements of CoSi2 films must be a result of positron trapping in either the film or at the interface with the Si substrate. RPS results considered as a function of film thickness support the conclusion that defects in the film (misfit dislocations and/or vacancies) represent the major source of positron trapping.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87603/2/264_1.pd

Positron tunneling microscopy

A new technique for analyzing thin film growth processes, called positron tunneling microscopy (PTM), is proposed as an extension of the recently developed positron reemission microscope. The unique feature of a PTM is that image contrast is provided by the exponential reemission probability for positrons tunneling through thin-film overlayers that present an energy barrier to reemission. Results of positron tunneling experiments show that PTM should have monolayer thickness resolution to processes that locally affect either the tunneling barrier's width, such as islanding and subsurface roughness, or the barrier's energy, such as lattice strain in pseudomorphic growth and compositional mixing in interdiffusion alloying. In the case of these latter effects where there may be no topological contrasts at all, experimental results are discussed in greater detail. Comparisons of PTM with existing electron microscopies are presented where appropriate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28554/1/0000356.pd

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions

A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure

An overview of the Michigan Positron Microscope Program

An overview of the Michigan Positron Microscope Program is presented with particular emphasis on the second generation microscope that is presently near completion. The design and intended applications of this microscope will be summarized.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87602/2/391_1.pd

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

First Passage Properties of the Erdos-Renyi Random Graph

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma

Regularized Linear Inversion with Randomized Singular Value Decomposition

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value decomposition, Tikhonov regularization, and general Tikhonov regularization with a smoothness penalty. One distinct feature of the proposed approach is that it explicitly preserves the structure of the regularized solution in the sense that it always lies in the range of a certain adjoint operator. We provide error estimates between the approximation and the exact solution under canonical source condition, and interpret the approach in the lens of convex duality. Extensive numerical experiments are provided to illustrate the efficiency and accuracy of the approach.Comment: 20 pages, 4 figure

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

Minimal vertex covers on finite-connectivity random graphs - a hard-sphere lattice-gas picture

The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapping to a lattice gas of hard spheres of (chemical) radius one, and they are found to be in excellent agreement with numerical simulations. We give a detailed description of the replica-symmetric phase, including the size and the entropy of the minimal vertex covers, and the structure of the unfrozen component which is found to percolate at connectivity $c\simeq 1.43$. The replica-symmetric solution breaks down at $c=e\simeq 2.72$. We give a simple one-step replica symmetry broken solution, and discuss the problems in interpretation and generalization of this solution.Comment: 32 pages, 9 eps figures, to app. in PRE (01 May 2001

Achievement and Aspiration

In contrast to previous work, our study considers both meaning and mediation factors in the achievement-aspiration relationship. In a sample of graduate students ("academic-career aspirants"), we examine sex differences in the achievement- aspiration relationship as they vary with type of academic achievement and professional aspirations, and as it is mediated by individuals' perceptions of their professional roles and their faculty's support. We find: (1) Women's achievement-aspiration conversion is different from, but not necessarily lower than, men's. Rather, the strength and direction of the relationship vary with aspiration type (traditional versus alternative) and, to some extent, with specific types of academic achievement (e.g., paper publication and GPA). (2) The mediators of the achievement-aspiration relationship also vary by sex and aspiration type. Notably, women's aspirations for traditional career rewards are largely a function of their perceptions of the structural availability of job opportunity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68567/2/10.1177_073088848100800403.pd