Quantum inference of states and processes

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are considered.Comment: 7 pages, 4 figure

1923 - A.C.C Bible Lecture Week, Abilene Christian College

This is program for the 1923 Sixth Annual Bible Lecture Week at Abilene Christian College. Uploaded by Jackson Hager

An overview of jets and outflows in stellar mass black holes

In this book chapter, we will briefly review the current empirical understanding of the relation between accretion state and and outflows in accreting stellar mass black holes. The focus will be on the empirical connections between X-ray states and relativistic (`radio') jets, although we are now also able to draw accretion disc winds into the picture in a systematic way. We will furthermore consider the latest attempts to measure/order jet power, and to compare it to other (potentially) measurable quantities, most importantly black hole spin.Comment: Accepted for publication in Space Science Reviews. Also to appear in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Second order optimality conditions and their role in PDE control

If f : Rn R is twice continuously differentiable, f’(u) = 0 and f’’(u) is positive definite, then u is a local minimizer of f. This paper surveys the extension of this well known second order suffcient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled order sufficient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled? It turns out that infinite dimensions cause new difficulties that do not occur in finite dimensions. We will be faced with the surprising fact that the space, where f’’(u) exists can be useless to ensure positive definiteness of the quadratic form v f’’(u)v2. In this context, the famous two-norm discrepancy, its consequences, and techniques for overcoming this difficulty are explained. To keep the presentation simple, the theory is developed for problems in function spaces with simple box constraints of the form a = u = ß. The theory of second order conditions in the control of partial differential equations is presented exemplarily for the nonlinear heat equation. Different types of critical cones are introduced, where the positivity of f’’(u) must be required. Their form depends on whether a so-called Tikhonov regularization term is part of the functional f or not. In this context, the paper contains also new results that lead to quadratic growth conditions in the strong sense. As a first application of second-order sufficient conditions, the stability of optimal solutions with respect to perturbations of the data of the control problem is discussed. Second, their use in analyzing the discretization of control problems by finite elements is studied. A survey on further related topics, open questions, and relevant literature concludes the paper.The first author was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2011-22711, the second author by DFG in the framework of the Collaborative Research Center SFB 910, project B6

Clusters of galaxies: setting the stage

Clusters of galaxies are self-gravitating systems of mass ~10^14-10^15 Msun. They consist of dark matter (~80 %), hot diffuse intracluster plasma (< 20 %) and a small fraction of stars, dust, and cold gas, mostly locked in galaxies. In most clusters, scaling relations between their properties testify that the cluster components are in approximate dynamical equilibrium within the cluster gravitational potential well. However, spatially inhomogeneous thermal and non-thermal emission of the intracluster medium (ICM), observed in some clusters in the X-ray and radio bands, and the kinematic and morphological segregation of galaxies are a signature of non-gravitational processes, ongoing cluster merging and interactions. In the current bottom-up scenario for the formation of cosmic structure, clusters are the most massive nodes of the filamentary large-scale structure of the cosmic web and form by anisotropic and episodic accretion of mass. In this model of the universe dominated by cold dark matter, at the present time most baryons are expected to be in a diffuse component rather than in stars and galaxies; moreover, ~50 % of this diffuse component has temperature ~0.01-1 keV and permeates the filamentary distribution of the dark matter. The temperature of this Warm-Hot Intergalactic Medium (WHIM) increases with the local density and its search in the outer regions of clusters and lower density regions has been the quest of much recent observational effort. Over the last thirty years, an impressive coherent picture of the formation and evolution of cosmic structures has emerged from the intense interplay between observations, theory and numerical experiments. Future efforts will continue to test whether this picture keeps being valid, needs corrections or suffers dramatic failures in its predictive power.Comment: 20 pages, 8 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 2; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Do Femtonewton Forces Affect Genetic Function? A Review

Protein-Mediated DNA looping is intricately related to gene expression. Therefore any mechanical constraint that disrupts loop formation can play a significant role in gene regulation. Polymer physics models predict that less than a piconewton of force may be sufficient to prevent the formation of DNA loops. Thus, it appears that tension can act as a molecular switch that controls the much larger forces associated with the processive motion of RNA polymerase. Since RNAP can exert forces over 20 pN before it stalls, a ‘substrate tension switch’ could offer a force advantage of two orders of magnitude. Evidence for such a mechanism is seen in recent in vitro micromanipulation experiments. In this article we provide new perspective on existing theory and experimental data on DNA looping in vitro and in vivo . We elaborate on the connection between tension and a variety of other intracellular mechanical constraints including sequence specific curvature and supercoiling. In the process, we emphasize that the richness and versatility of DNA mechanics opens up a whole new paradigm of gene regulation to explore.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41816/1/10867_2005_Article_9002.pd