Sigma pole position and errors of a once and twice subtracted dispersive analysis of pi-pi scattering data

We show how the new precise data on kaon decays together with forward dispersion relations, sum rules and once- and twice-subtracted Roy's equations allow for a precise determination of the sigma meson pole position. We present a comparison and a study of the different sources of uncertainties when using either once- or twice-subtracted Roy's equations to analyze the data. Finally we present a preliminary determination of the sigma pole from the constrained dispersive data analysis.Comment: 4 pages, 6 figures. Contribution to the proceedings of the QCD08 14th International QCD Conference. 7-12th July 2008 Montpellier (France); one reference removed, changed errors in Eqs (4), (5) and (7

Fast and slow light in zig-zag microring resonator chains

We analyze fast and slow light transmission in a zig-zag microring resonator chain. This novel device permits the operation in both regimes. In the superluminal case, a new ubiquitous light transmission effect is found whereby the input optical pulse is reproduced in an almost simultaneous manner at the various system outputs. When the input carrier is tuned to a different frequency, the system permits to slow down the propagating optical signal. Between these two extreme cases, the relative delay can be tuned within a broad range

Regge trajectory of the f_0(500) resonance from a dispersive connection to its pole

We report here our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the {\rho}(770) and the f_0(500) resonances. Whereas for the former we obtain a linear Regge trajectory, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. This provides a strong indication of the non-ordinary nature of the sigma meson.Comment: 4 pages, 2 figures, to appear in the proceedings of the "Seventh International Symposium on Chiral Symmetry in Hadrons and Nuclei

New dispersion relations in the description of ππ\pi\pi scattering amplitudes

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $\pi\pi$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $\pi\pi$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $\pi\pi$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.Comment: 8 pages, 2 figures, to appear in the Proceedings of the Meson 2008 conference, June 6-10, 2008, Cracow, Polan

Some Remarks on the Pade Unitarization of Low-Energy Amplitudes

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect results for the mass and width of the sigma. Alternative sequences of Pades are studied and we find that the diagonal sequences (i.e., [N/N]) have much better convergence properties.Comment: 12 pages, 4 fig

Development of the Neuron Assessment for Measuring Biology Students’ Use of Experimental Design Concepts and Representations

Researchers, instructors, and funding bodies in biology education are unanimous about the importance of developing students’ competence in experimental design. Despite this, only limited measures are available for assessing such competence development, especially in the areas of molecular and cellular biology. Also, existing assessments do not measure how well students use standard symbolism to visualize biological experiments. We propose an assessment-design process that 1) provides background knowledge and questions for developers of new “experimentation assessments,” 2) elicits practices of representing experiments with conventional symbol systems, 3) determines how well the assessment reveals expert knowledge, and 4) determines how well the instrument exposes student knowledge and difficulties. To illustrate this process, we developed the Neuron Assessment and coded responses from a scientist and four undergraduate students using the Rubric for Experimental Design and the Concept-Reasoning Mode of representation (CRM) model. Some students demonstrated sound knowledge of concepts and representations. Other students demonstrated difficulty with depicting treatment and control group data or variability in experimental outcomes. Our process, which incorporates an authentic research situation that discriminates levels of visualization and experimentation abilities, shows potential for informing assessment design in other disciplines

Steady State Detection of Chemical Reaction Networks Using a Simplified Analytical Method

Chemical reaction networks (CRNs) are susceptible to mathematical modelling. The dynamic behavior of CRNs can be investigated by solving the polynomial equations derived from its structure. However, simple CRN give rise to non-linear polynomials that are difficult to resolve. Here we propose a procedure to locate the steady states of CRNs from a formula derived through algebraic geometry methods. We have applied this procedure to define the steady states of a classic CRN that exhibits instability, and to a model of programmed cell death

Security improvement of two dynamic ID-based authentication schemes by Sood-Sarje-Singh

In 2010, Sood-Sarje-Singh proposed two dynamic ID-based remote user authentication schemes. The first scheme is a security improvement of Liao et al.’s scheme and the second scheme is a security improvement of Wang et al.’s scheme. In both cases, the authors claimed that their schemes can resist many attacks. However, we find that both schemes have security flaws. In addition, their schemes require a verification table and time-synchronization, making the schemes unfeasible and unsecured for electronic services. In order to remedy the security flaws of Sood et al.’s schemes, we propose a robust scheme which resists the well-known attacks and achieves all the desirable security goals.Peer ReviewedPostprint (published version