The scaling limit of the critical one-dimensional random Schrodinger operator

We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}. Here {\omega}_k are independent random variables with mean 0 and variance 1. We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem. In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the beta-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.Comment: 36 pages, 2 figure

A PAC-style model for learning from labeled and unlabeled data

There has recently been substantial interest in practice in using unlabeled data together with labeled data in machine learning, and a number of di erent approaches have been developed. However, the assumptions these methods are based on are often quite distinct and not captured by standard theoretical models. In this paper we describe a PAC-style model that captures many of these assumptions, and analyze sample-complexity issues in this setting: that is, how much ofeachtype of data one should expect to need in order to learn well, and what are the basic quantities that these numbers depend on. Our model can be viewed as an extension of the standard PAC model, where in addition to a concept class C, one also proposes a type of compatibility that one believes the target concept should have with the underlying distribution. In this view, unlabeled data can be helpful because it allows one to estimate compatibility over the space of hypotheses, and reduce the size of the search space to those that are, in a sense, a-priori reasonable with respect to the distribution. We discuss a number of technical issues that arise in this context, and provide sample-complexity bounds both for uniform convergence and speci c-cover based algorithms. We also consider algorithmic issues, and give an algorithm for a natural problem of learning a linear separator from example-pairs, motivated by co-training.

Probing surfaces with thermal He atoms: scattering and microscopy with a soft touch

Helium atom scattering (HAS) is a well established technique, particularly suited for the investigation of insulating and/or fragile materials and light adsorbates including hydrogen. In contrast to other beam techniques based on Xrays or electrons, low energy (typically less than 100 meV) He atoms are scattered by the tail of the electron density distribution which spill out from a surface, therefore HAS is strictly a nonpenetrating technique without any sample damage. HAS has been used to investigate structural properties of crystalline surfaces, including precise determination of atomic step heights, for monitoring thin film growth, to study surface transitions such as surface melting and roughening and for determining the presence and properties of adsorbates. Energy resolved HAS can provide information about surface vibrations (phonons) in the meV range and surface diffusion. This chapter provides a brief introduction to HAS with an outlook on a new, promising surface science technique: Neutral Helium Microscopy

Marrow versus peripheral blood for geno-identical allogeneic stem cell transplantation in acute myelocytic leukemia: Influence of dose and stem cell source shows better outcome with rich marrow

Several studies have compared bone marrow (BM) and peripheral blood (PB) as stem cell sources in patients receiving allografts, but the cell doses infused have not been considered, especially for BM. Using the ALWP/EBMT registry, we retrospectively studied 881 adult patients with acute myelocytic leukemia (AML), who received a non-T-depleted allogeneic BM (n = 515) or mobilized PB (n = 366) standard transplant, in first remission (CR1), from an HLA-identical sibling, over a 5-year period from January 1994. The BM cell dose ranged from 0.17 to 29 × 108/kg with a median of 2.7 × 108/kg. The PB cell dose ranged from 0.02 to 77 × 10 8/kg with a median of 9.3 × 108/kg. The median dose for patients receiving BM (2.7 × 108/kg) gave the greatest discrimination. In multivariate analyses, high-dose BM compared to PB was associated with lower transplant-related mortality (RR = 0.61; 95% CI, 0.39-0.98; P = .04), better leukemia-free survival (RR = 0.65; 95% CI, 0.46-0.91; P = .013), and better overall survival (RR = 0.64; 95% CI, 0.44-0. 92; P = .016). The present study in patients with AML receiving allografts in first remission indicates a better outcome with BM as compared to PB, when the dose of BM infused is rich. © 2003 by The American Society of Hematology

Marrow versus peripheral blood for geno-identical allogeneic stem cell transplantation in acute myelocytic leukemia: Influence of dose and stem cell source shows better outcome with rich marrow

PubMed ID: 12829583Several studies have compared bone marrow (BM) and peripheral blood (PB) as stem cell sources in patients receiving allografts, but the cell doses infused have not been considered, especially for BM. Using the ALWP/EBMT registry, we retrospectively studied 881 adult patients with acute myelocytic leukemia (AML), who received a non-T-depleted allogeneic BM (n = 515) or mobilized PB (n = 366) standard transplant, in first remission (CR1), from an HLA-identical sibling, over a 5-year period from January 1994. The BM cell dose ranged from 0.17 to 29 × 10 8 /kg with a median of 2.7 × 10 8 /kg. The PB cell dose ranged from 0.02 to 77 × 10 8 /kg with a median of 9.3 × 10 8 /kg. The median dose for patients receiving BM (2.7 × 10 8 /kg) gave the greatest discrimination. In multivariate analyses, high-dose BM compared to PB was associated with lower transplant-related mortality (RR = 0.61; 95% CI, 0.39-0.98; P = .04), better leukemia-free survival (RR = 0.65; 95% CI, 0.46-0.91; P = .013), and better overall survival (RR = 0.64; 95% CI, 0.44-0. 92; P = .016). The present study in patients with AML receiving allografts in first remission indicates a better outcome with BM as compared to PB, when the dose of BM infused is rich. © 2003 by The American Society of Hematology