Lassoing and corraling rooted phylogenetic trees

The construction of a dendogram on a set of individuals is a key component of a genomewide association study. However even with modern sequencing technologies the distances on the individuals required for the construction of such a structure may not always be reliable making it tempting to exclude them from an analysis. This, in turn, results in an input set for dendogram construction that consists of only partial distance information which raises the following fundamental question. For what subset of its leaf set can we reconstruct uniquely the dendogram from the distances that it induces on that subset. By formalizing a dendogram in terms of an edge-weighted, rooted phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting is equidistant and a set of partial distances on X in terms of a set L of 2-subsets of X, we investigate this problem in terms of when such a tree is lassoed, that is, uniquely determined by the elements in L. For this we consider four different formalizations of the idea of "uniquely determining" giving rise to four distinct types of lassos. We present characterizations for all of them in terms of the child-edge graphs of the interior vertices of such a tree. Our characterizations imply in particular that in case the tree in question is binary then all four types of lasso must coincide

Interaction of matter-wave gap solitons in optical lattices

We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-the-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.Comment: 12 pages, 7 figure

Spectral Properties of Coupled Bose-Einstein Condensates

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture which is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form which suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows to recover, in the classical limit, the symmetry breaking effect that characterizes the system classically.Comment: 8 pages, 3 figures; submitted to Phys. Rev. A. The present extended form replaces the first version in the letter forma

Analysis of Localization Phenomena in Weakly Interacting Disordered Lattice Gases

Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases may be used for the production and observation of disordered quantum degenerate gases. A detailed analysis of localization effects for two possible realizations of a disordered potential is presented. In a theoretical analysis clear localization effects are observed when a superlattice is used to provide a quasiperiodic disorder. The effects of localization are analyzed by investigating the superfluid fraction and the localization length within the system. The theoretical analysis in this paper paves a clear path for the future observation of Anderson-like localization in disordered quantum gases.Comment: 9 pages, 13 figure

Generic model of an atom laser

We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in steady-state. We study the transient regime of this atom laser and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semi-classical theory of the laser.Comment: 15 pages, including 5 figures, submitted to Phys. Rev. A, revised manuscript, file also available at http://www.physik.uni-ulm.de/quan/users/kne

Thermodynamic properties of thin films of superfluid 3He-A

The pairing correlations in superfluid He-3 are strongly modified by quasiparticle scattering off a surface or an interface. We present theoretical results and predictions for the order parameter, the quasiparticle excitation spectrum and the free energy for thin films of superfluid He-3. Both specular and diffuse scattering by a substrate are considered, while the free surface is assumed to be a perfectly reflecting specular boundary. The results are based on self-consistent calculations of the order parameter and quasiparticle excitation spectrum at zero pressure. We obtain new results for the phase diagram, free energy, entropy and specific heat of thin films of superfluid He-3.Comment: Replaced with an updated versio

Langevin equations for interacting fermions and Cooper-like pairing in trapped one-dimensional fermions

Momentum correlations in a one-dimensional equilibrium ensemble of trapped fermions, with a point interaction between particles of opposite spin have been studied. In the degenerate regime correlations were observed between fermions with opposite spins and momenta, similar to Cooper pairing. These correlations appear as soon as the temperature is below the Fermi energy, which is a much less stringent condition than that of the BCS transition proper. Calculations are carried out in both perturbative and non-perturbative regimes. To achieve the latter. it is shown that interacting fermionic dynamics may be solved as a stochastic linear transformation of Grassmann algebra generators, much in the way random c-number paths are introduced in the conventional quantum stochastics of bosons. Importantly, the method thus emerging is inherently free of the sign problem

The HY5-PIF regulatory module coordinates light and temperature control of photosynthetic gene transcription

The ability to interpret daily and seasonal alterations in light and temperature signals is essential for plant survival. This is particularly important during seedling establishment when the phytochrome photoreceptors activate photosynthetic pigment production for photoautotrophic growth. Phytochromes accomplish this partly through the suppression of phytochrome interacting factors (PIFs), negative regulators of chlorophyll and carotenoid biosynthesis. While the bZIP transcription factor long hypocotyl 5 (HY5), a potent PIF antagonist, promotes photosynthetic pigment accumulation in response to light. Here we demonstrate that by directly targeting a common promoter cis-element (G-box), HY5 and PIFs form a dynamic activation-suppression transcriptional module responsive to light and temperature cues. This antagonistic regulatory module provides a simple, direct mechanism through which environmental change can redirect transcriptional control of genes required for photosynthesis and photoprotection. In the regulation of photopigment biosynthesis genes, HY5 and PIFs do not operate alone, but with the circadian clock. However, sudden changes in light or temperature conditions can trigger changes in HY5 and PIFs abundance that adjust the expression of common target genes to optimise photosynthetic performance and growth

Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typo

Surface Science of DNA Adsorption onto Citrate-Capped Gold Nanoparticles

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Langmuir copyright © American Chemical Society after peer review and technical editing by publisher. To access the final edited and published work see Zhang, X., Servos, M. R., & Liu, J. (2012). Surface Science of DNA Adsorption onto Citrate-Capped Gold Nanoparticles. Langmuir, 28(8), 3896–3902. https://doi.org/10.1021/la205036pSingle-stranded DNA can be adsorbed by citrate capped gold nanoparticles (AuNPs), resulting in increased AuNP stability, which forms the basis of a number of biochemical and analytical applications, but the fundamental interaction of this adsorption reaction remains unclear. In this study, we measured DNA adsorption kinetics, capacity, and isotherms, demonstrating that the adsorption process is governed by electrostatic forces. The charge repulsion among DNA strands and between DNA and AuNPs can be reduced by adding salt, reducing pH or by using noncharged peptide nucleic acid (PNA). Langmuir adsorption isotherms are obtained, indicating the presence of both adsorption and desorption of DNA from AuNPs. While increasing salt concentration facilitates DNA adsorption, the desorption rate is also enhanced in higher salt due to DNA compaction. DNA adsorption capacity is determined by DNA oligomer length, DNA concentration, and salt. Previous studies indicated faster adsorption of short DNA oligomers by AuNPs, we find that once adsorbed, longer DNAs are much more effective in protecting AuNPs from aggregation. DNA adsorption is also facilitated by using low pH buffers and high alcohol concentrations. A model based on electrostatic repulsion on AuNPs is proposed to rationalize the DNA adsorption/desorption behavior.University of Waterloo || Canadian Foundation for Innovation || Ontario Ministry of Research & Innovation || Canadian Institutes of Health Research || Natural Sciences and Engineering Research Council |