Finite one dimensional impenetrable Bose systems: Occupation numbers

Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupations $\lambda_i$ of effective single particle states $\phi_i$, in the theoretical 1d impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The $\lambda_i$ and $\phi_i$ are the eigenvalues and eigenfunctions respectively of the one body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed $i$ the occupations $\lambda_i$ are asymptotically proportional to $\sqrt{N}$ in both the circular and harmonically trapped cases.Comment: 22 pages, 8 figures (.eps), uses REVTeX

Metabolite changes in blood predict the onset of tuberculosis

Immunogenetics and cellular immunology of bacterial infectious disease

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

A low-memory algorithm for finding short product representations in finite groups

We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S of length d log_2 n, where n=#G and d >= 2 is a constant, we find that its expected running time is O(sqrt(n) log n) group operations (we give a rigorous proof for d > 4), and it only needs to store O(1) group elements. We consider applications to class groups of imaginary quadratic fields, and to finding isogenies between elliptic curves over a finite field.Comment: 12 page

Continental-scale geographic change across zealandia during paleogene subduction initiation

Data from International Ocean Discovery Program (IODP) Expedition 371 reveal vertical movements of 1-3 km in northern Zealandia during early Cenozoic subduction initiation in the western Pacific Ocean. Lord Howe Rise rose from deep (~1 km) water to sea level and subsided back, with peak uplift at 50 Ma in the north and between 41 and 32 Ma in the south. The New Caledonia Trough subsided 2-3 km between 55 and 45 Ma. We suggest these elevation changes resulted from crust delamination and mantle flow that led to slab formation. We propose a "subduction resurrection" model in which (1) a subduction rupture event activated lithospheric-scale faults across a broad region during less than ~5 m.y., and (2) tectonic forces evolved over a further 4-8 m.y. as subducted slabs grew in size and drove plate-motion change. Such a subduction rupture event may have involved nucleation and lateral propagation of slip-weakening rupture along an interconnected set of preexisting weaknesses adjacent to density anomalies

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Four-gene Pan-African Blood Signature Predicts Progression to Tuberculosis.

Contacts of tuberculosis (TB) patients constitute an important target population for preventative measures as they are at high risk of infection with Mycobacterium tuberculosis and progression to disease. We investigated biosignatures with predictive ability for incident tuberculosis. In a case-control study nested within the Grand Challenges 6-74 longitudinal HIV-negative African cohort of exposed household contacts, we employed RNA sequencing, polymerase chain reaction (PCR) and the Pair Ratio algorithm in a training/test set approach. Overall, 79 progressors, who developed tuberculosis between 3 and 24 months following exposure, and 328 matched non-progressors, who remained healthy during 24 months of follow-up, were investigated. A four-transcript signature (RISK4), derived from samples in a South African and Gambian training set, predicted progression up to two years before onset of disease in blinded test set samples from South Africa, The Gambia and Ethiopia with little population-associated variability and also validated on an external cohort of South African adolescents with latent Mycobacterium tuberculosis infection. By contrast, published diagnostic or prognostic tuberculosis signatures predicted on samples from some but not all 3 countries, indicating site-specific variability. Post-hoc meta-analysis identified a single gene pair, C1QC/TRAV27, that would consistently predict TB progression in household contacts from multiple African sites but not in infected adolescents without known recent exposure events. Collectively, we developed a simple whole blood-based PCR test to predict tuberculosis in household contacts from diverse African populations, with potential for implementation in national TB contact investigation programs