Limit theorem for a time-dependent coined quantum walk on the line

We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, limit theorems for two special cases are presented

Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions

We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.Comment: 4 pages, 2 figure

Use of whole-genus genome sequence data to develop a multilocus sequence typing tool that accurately identifies Yersinia isolates to the species and subspecies levels

The genus Yersinia is a large and diverse bacterial genus consisting of human-pathogenic species, a fish-pathogenic species, and a large number of environmental species. Recently, the phylogenetic and population structure of the entire genus was elucidated through the genome sequence data of 241 strains encompassing every known species in the genus. Here we report the mining of this enormous data set to create a multilocus sequence typing-based scheme that can identify Yersinia strains to the species level to a level of resolution equal to that for whole-genome sequencing. Our assay is designed to be able to accurately subtype the important human-pathogenic species Yersinia enterocolitica to whole-genome resolution levels. We also report the validation of the scheme on 386 strains from reference laboratory collections across Europe. We propose that the scheme is an important molecular typing system to allow accurate and reproducible identification of Yersinia isolates to the species level, a process often inconsistent in nonspecialist laboratories. Additionally, our assay is the most phylogenetically informative typing scheme available for Y. enterocolitica

Parameter Estimation and Quantitative Parametric Linkage Analysis with GENEHUNTER-QMOD

Objective: We present a parametric method for linkage analysis of quantitative phenotypes. The method provides a test for linkage as well as an estimate of different phenotype parameters. We have implemented our new method in the program GENEHUNTER-QMOD and evaluated its properties by performing simulations. Methods: The phenotype is modeled as a normally distributed variable, with a separate distribution for each genotype. Parameter estimates are obtained by maximizing the LOD score over the normal distribution parameters with a gradient-based optimization called PGRAD method. Results: The PGRAD method has lower power to detect linkage than the variance components analysis (VCA) in case of a normal distribution and small pedigrees. However, it outperforms the VCA and Haseman-Elston regression for extended pedigrees, nonrandomly ascertained data and non-normally distributed phenotypes. Here, the higher power even goes along with conservativeness, while the VCA has an inflated type I error. Parameter estimation tends to underestimate residual variances but performs better for expectation values of the phenotype distributions. Conclusion: With GENEHUNTER-QMOD, a powerful new tool is provided to explicitly model quantitative phenotypes in the context of linkage analysis. It is freely available at http://www.helmholtz-muenchen.de/genepi/downloads. Copyright (C) 2012 S. Karger AG, Base

Semimicroscopical description of the simplest photonuclear reactions accompanied by excitation of the giant dipole resonance in medium-heavy mass nuclei

A semimicroscopical approach is applied to describe photoabsorption and partial photonucleon reactions accompanied by the excitation of the giant dipole resonance (GDR). The approach is based on the continuum-RPA (CRPA) with a phenomenological description for the spreading effect. The phenomenological isoscalar part of the nuclear mean field, momentum-independent Landau-Migdal particle-hole interaction, and separable momentum-dependent forces are used as input quantities for the CRPA calculations. The experimental photoabsorption and partial $(n,\gamma)$-reaction cross sections in the vicinity of the GDR are satisfactorily described for $^{89}$Y, $^{140}$Ce and $^{208}$Pb target nuclei. The total direct-neutron-decay branching ratio for the GDR in $^{48}$Ca and $^{208}$Pb is also evaluated.Comment: 19 pages, 5 eps figure

The trans-activation domain of the sporulation response regulator Spo0A revealed by X-ray crystallography

Sporulation in Bacillus involves the induction of scores of genes in a temporally and spatially co-ordinated programme of cell development. Its initiation is under the control of an expanded two-component signal transduction system termed a phosphorelay. The master control element in the decision to sporulate is the response regulator, Spo0A, which comprises a receiver or phosphoacceptor domain and an effector or transcription activation domain. The receiver domain of Spo0A shares sequence similarity with numerous response regulators, and its structure has been determined in phosphorylated and unphosphorylated forms. However, the effector domain (C-Spo0A) has no detectable sequence similarity to any other protein, and this lack of structural information is an obstacle to understanding how DNA binding and transcription activation are controlled by phosphorylation in Spo0A. Here, we report the crystal structure of C-Spo0A from Bacillus stearothermophilus revealing a single alpha -helical domain comprising six alpha -helices in an unprecedented fold. The structure contains a helix-turn-helix as part of a three alpha -helical bundle reminiscent of the catabolite gene activator protein (CAP), suggesting a mechanism for DNA binding. The residues implicated in forming the sigma (A)-activating region clearly cluster in a flexible segment of the polypeptide on the opposite side of the structure from that predicted to interact with DNA. The structural results are discussed in the context of the rich array of existing mutational data

Pulsed Feedback Defers Cellular Differentiation

Environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well-characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable “polyphasic” positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a “timer” that operates over timescales much longer than a cell cycle

Discrete-time quantum walks on one-dimensional lattices

In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the return probability, which shows scaling behavior $P(0,t)\sim t^{-1}$ and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The average mixing time $M_{\epsilon}$ closes to the limiting probability in linear $N$ (size of the lattice) for large values of thresholds $\epsilon$. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.Comment: 17 pages research not

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian oracles; v3: published version, with improved analysis of phase estimatio

Analysis of Five Field Event Performances at the Drake Relays by Age and Gender, 1978-2008

Advisor: David S. SenchinaWe analyzed gender and age differences in Drake Relays performance distances for 2 jumping (long jump and triplejump) and 3 throwing (discus, javelin, shotput) field events for 31 years (1978-2008). The top 10 performances were taken each year for 4 groups: high school (HS) boys, HS girls, college/university (C/U) men, C/U women. Our data set included 4403 performances total, because not all ages/genders competed in all events or for the same number of years. Generally, females significantly improved their jumping or throwing distances whereas males showed no improvements or significantly declined in performance. HS girls showed statistically significant improvements in all 3 of their events (discus, shotput, long jump), and C/U women showed improvements in 4 of their 5 events (discus, javelin, shotput, triplejump) and demonstrated no change in long jump performance. In comparison, HS boys showed no changes in 2 of their 3 events (discus and shotput) and significantly shorter distance in long jump, and C/U men demonstrated significantly shorter throwing or jumping distances in 4 of their 5 events (javelin, shotput, long jump, triplejump) and no change in discus. Despite the improvements in female performance distances, males threw or jumped further than females in all events for all years except for discus, where C/U women were out-throwing HS boys by 2008. As the Drake Relays includes athletes from across the country, these differences likely reflect national trends and are possibly explained by forces such as increased pressure for youth sport specialization, declining popularity of track-and-field, and Title IX.Drake University, College of Arts and Sciences, Department of Biology, Biochemistry, Cell and Molecular Biology ; College of Pharmacy and Health Science