Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

Discrete canonical system and non-Abelian Toda lattice: Backlund-Darboux transformation and Weyl functions

A version of the iterated B\"acklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on the transformations of the Weyl functions, insertion of the eigenvalues, and construction of the bound states are obtained. A wide class of the explicit solutions is given. An application to the semi-infinite block Jacobi matrices is treated.Comment: Second version: Section on the explicit solutions and results on the bound states and insertion of eigenvalues are added, the presentation is slightly change

Kinematical structure of the circumstellar environments of galactic B[e]-type stars

High resolution line profiles are presented for selected forbidden and permitted emission lines of a sample of galactic B[e]-type stars. The spectral resolution corresponds to 5-7 km/s with the exception of some line profiles which were observed with a resolution of 9-13 km/s. All Ha profiles are characterized by a narrow split or single emission component with a width of about 150-250 km/s (FWHM) and broad wings with a full width of ~1000-2000 km/s. The Ha profiles can be classified into three groups: double-peaked profiles representing the majority, single-peaked emission-line profiles, and normal P Cygni-type profiles. The forbidden lines exhibit in most cases double-peaked profiles. The split forbidden line profiles have peak separations of as little as 10 km/s. The ratio of violet to red emission peak intensities, V/R, is predominantly smaller or equal to 1. Theoretical profiles were calculated for the optically thin case. A latitude-dependent stellar wind with a radial expansion and a velocity decreasing from the pole to the equator was adopted. In addition an equatorial dust ring with various optical depths was assumed. This model can explain split lines and line asymmetries observed in some stars. Moreover, the V/R ratios can be understood in terms of this model. The comparison of the observed line profiles with the models thus confirms the assumption of disk-like line-formation regions as commonly adopted for B[e]-type stars.Comment: Astronomy & Astrophysics, in pres

Young children's cognitive achievement: home learning environment, language and ethnic background

For decades, research has shown differences in cognitive assessment scores between White and minority ethnic group(s) learners as well as differences across different minority ethnic groups. More recent data have indicated that the home learning environment and languages spoken can impact cognitive assessment and other corollary outcomes. This study uses the Millennium Cohort Study to jointly assess how minority ethnic group, home learning environment and home languages predict child cognitive assessment scores. Regression analyses were conducted using two assessment measures. The following is hypothesised: (1) cognitive achievement scores vary by minority ethnic group, (2) more home learning environment in early childhood leads to higher cognitive development scores and (3) English only in the home yields the highest cognitive scores while no English in the home yields the lowest. Findings reveal that there are differences in cognitive scores along ethnic group categories although there are also some unexpected findings. Home learning environment does not play as large a role as was predicted in raising the assessment scores overall for learners while speaking English in the home does, irrespective of ethnic background

On the isospectral problem of the dispersionless Camassa-Holm equation

We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa--Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several facts for the dispersionless Camassa--Holm equation. In particular, we show that initial conditions with integrable momentum asymptotically split into a sum of peakons as conjectured by McKean.Comment: 26 page

Mothers' complex talk when sharing books with their toddlers: Book genre matters

This study investigated the influence of book genre (narrative or didactic) on mothers' language use during a book sharing interaction with their 18- to 25-month-olds. Mother-child dyads were videotaped sharing both a narrative and a didactic book, adapted from two commercially available books, and matched in terms of length, quantity of text, and target content. A greater proportion of mothers' talk was complex (i.e., predictions, text-to-life comparisons) during narrative book sharing than during didactic book sharing. Mothers also used a greater variety of verb tenses and referenced more mental states during narrative book sharing. These results differ from findings from previous studies with older children where it has been concluded that didactic books offer greater opportunities for complex talk than narrative books. The results also highlight the importance of taking situational factors into account when investigating parent-child communicative interactions. © The Author(s) 2013

Cuspons, peakons and regular gap solitons between three dispersion curves

A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, a planar waveguide or a bulk-layered medium resembling a photonic-crystal fiber. Another physical system described by the same model is a set of three internal wave modes in a density-stratified fluid. A nonlinear analysis is performed for solitons which have zero velocity in the reference frame in which the group velocity of the third wave vanishes. Disregarding the self-phase modulation (SPM) term in the equation for the third wave, we find two coexisting families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons with a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two vanishes, the soliton family remains drastically different from that in the linearly uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there again coexist two different families of generic stable soliton solutions, namely, regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical Review E, in pres

Introduction

Why do parent\u2013child argumentative interactions matter? What is the reason for such an interest? This chapter provides the reasons that motivated the study of parent\u2013child argumentation with the aim to understand the function of this type of interactions. Focusing on the activity of family mealtime, in the first part, the chapter draws attention to the distinctive features of parent\u2013child conversations. A second section of the chapter is devoted to discussing whether and, eventually, when children have the competence to construct arguments and engage in argumentative discussions with the aim to convince their parents to change opinion. In the last part of the chapter, research questions and structure of the volume are presented

Equations of the Camassa-Holm Hierarchy

The squared eigenfunctions of the spectral problem associated with the Camassa-Holm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy, and their Hamiltonian structures, can be naturally expressed using the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. Using the GFT, we explicitly describe some members of the CH hierarchy, including integrable deformations for the CH equation. We also show that solutions of some $(1+2)$ - dimensional members of the CH hierarchy can be constructed using results for the inverse scattering transform for the CH equation. We give an example of the peakon solution of one such equation.Comment: 10 page