Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

Designing potentials by sculpturing wires

Magnetic trapping potentials for atoms on atom chips are determined by the current flow in the chip wires. By modifying the shape of the conductor we can realize specialized current flow patterns and therefore micro-design the trapping potentials. We have demonstrated this by nano-machining an atom chip using the focused ion beam technique. We built a trap, a barrier and using a BEC as a probe we showed that by polishing the conductor edge the potential roughness on the selected wire can be reduced. Furthermore we give different other designs and discuss the creation of a 1D magnetic lattice on an atom chip.Comment: 6 pages, 8 figure

A modified expression of the major hydrolase activator in Hypocrea jecorina (Trichoderma reesei) changes enzymatic catalysis of biopolymer degradation

AbstractHypocrea jecorina (anamorph Trichoderma reesei) is a saprophytic fungus that produces hydrolases, which are applied in different types of industries and used for the production of biofuel. A recombinant Hypocrea strain, which constantly expresses the main transcription activator of hydrolases (Xylanase regulator 1), was found to grow faster on xylan and its monomeric backbone molecule d-xylose. This strain also showed improved ability of clearing xylan medium on plates. Furthermore, this strain has a changed transcription profile concerning genes encoding for hydrolases and enzymes associated with degradation of (hemi)celluloses. We demonstrated that enzymes of this strain from a xylan cultivation favoured break down of hemicelluloses to the monomer d-xylose compared to the parental strain, while the enzymes of the latter one formed more xylobiose. Applying supernatants from cultivation on carboxymethylcellulose in enzymatic conversion of hemicelluloses, the enzymes of the recombinant strain were clearly producing more of both, d-xylose and xylobiose, compared to the parental strain. Altogether, these results point to a changed hydrolase expression profile, an enhanced capability to form the xylan-monomer d-xylose and the assumption that there is a disordered induction pattern if the Xylanase regulator 1 is de-regulated in Hypocrea

Long-Range Order in Electronic Transport through Disordered Metal Films

Ultracold atom magnetic field microscopy enables the probing of current flow patterns in planar structures with unprecedented sensitivity. In polycrystalline metal (gold) films we observe long-range correlations forming organized patterns oriented at +/- 45 deg relative to the mean current flow, even at room temperature and at length scales orders of magnitude larger than the diffusion length or the grain size. The preference to form patterns at these angles is a direct consequence of universal scattering properties at defects. The observed amplitude of the current direction fluctuations scales inversely to that expected from the relative thickness variations, the grain size and the defect concentration, all determined independently by standard methods. This indicates that ultracold atom magnetometry enables new insight into the interplay between disorder and transport

Disorder Potentials near Lithographically Fabricated Atom Chips

We show that previously observed large disorder potentials in magnetic microtraps for neutral atoms are reduced by about two orders of magnitude when using atom chips with lithographically fabricated high quality gold layers. Using one dimensional Bose-Einstein condensates, we probe the remaining magnetic field variations at surface distances down to a few microns. Measurements on a 100 um wide wire imply that residual variations of the current flow result from local properties of the wire.Comment: submitted on September 24th, 200

Cluster density functional theory for lattice models based on the theory of Mobius functions

Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed a partial order, so that the coefficients of the cluster expansion are connected to its Mobius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice model with any kind of short-range interaction (repulsive or attractive, hard or soft, one- or multi-component...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d'<d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty (included

Future directions for the management of pain in osteoarthritis.

Osteoarthritis (OA) is the predominant form of arthritis worldwide, resulting in a high degree of functional impairment and reduced quality of life owing to chronic pain. To date, there are no treatments that are known to modify disease progression of OA in the long term. Current treatments are largely based on the modulation of pain, including NSAIDs, opiates and, more recently, centrally acting pharmacotherapies to avert pain. This review will focus on the rationale for new avenues in pain modulation, including inhibition with anti-NGF antibodies and centrally acting analgesics. The authors also consider the potential for structure modification in cartilage/bone using growth factors and stem cell therapies. The possible mismatch between structural change and pain perception will also be discussed, introducing recent techniques that may assist in improved patient phenotyping of pain subsets in OA. Such developments could help further stratify subgroups and treatments for people with OA in future

How to share a quantum secret

We investigate the concept of quantum secret sharing. In a ((k,n)) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k-1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum "no-cloning theorem", which requires that n < 2k, and, in all such cases, we give an efficient construction of a ((k,n)) threshold scheme. We also explore similarities and differences between quantum secret sharing schemes and quantum error-correcting codes. One remarkable difference is that, while most existing quantum codes encode pure states as pure states, quantum secret sharing schemes must use mixed states in some cases. For example, if k <= n < 2k-1 then any ((k,n)) threshold scheme must distribute information that is globally in a mixed state.Comment: 5 pages, REVTeX, submitted to PR

Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.Comment: 13 pages, 13 figures, few typos correcte