Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

Spin Structure of the Nucleon - Status and Recent Results

After the initial discovery of the so-called "spin crisis in the parton model" in the 1980's, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q^2 dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g_1 and g_2 of the nucleon and their moments.Comment: 69 pages, 46 figures. Report to be published in "Progress in Particle and Nuclear Physics". v2 with added references and minor edit

Ground resonance analysis using a substructure modeling approach

A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented

Using Variable Dwell Time to Accelerate Gaze-Based Web Browsing with Two-Step Selection

In order to avoid the "Midas Touch" problem, gaze-based interfaces for selection often introduce a dwell time: a fixed amount of time the user must fixate upon an object before it is selected. Past interfaces have used a uniform dwell time across all objects. Here, we propose a gaze-based browser using a two-step selection policy with variable dwell time. In the first step, a command, e.g. "back" or "select", is chosen from a menu using a dwell time that is constant across the different commands. In the second step, if the "select" command is chosen, the user selects a hyperlink using a dwell time that varies between different hyperlinks. We assign shorter dwell times to more likely hyperlinks and longer dwell times to less likely hyperlinks. In order to infer the likelihood each hyperlink will be selected, we have developed a probabilistic model of natural gaze behavior while surfing the web. We have evaluated a number of heuristic and probabilistic methods for varying the dwell times using both simulation and experiment. Our results demonstrate that varying dwell time improves the user experience in comparison with fixed dwell time, resulting in fewer errors and increased speed. While all of the methods for varying dwell time resulted in improved performance, the probabilistic models yielded much greater gains than the simple heuristics. The best performing model reduces error rate by 50% compared to 100ms uniform dwell time while maintaining a similar response time. It reduces response time by 60% compared to 300ms uniform dwell time while maintaining a similar error rate.Comment: This is an Accepted Manuscript of an article published by Taylor & Francis in the International Journal of Human-Computer Interaction on 30 March, 2018, available online: http://www.tandfonline.com/10.1080/10447318.2018.1452351 . For an eprint of the final published article, please access: https://www.tandfonline.com/eprint/T9d4cNwwRUqXPPiZYm8Z/ful

Discovering cultural differences (and similarities) in facial expressions of emotion

Understanding the cultural commonalities and specificities of facial expressions of emotion remains a central goal of Psychology. However, recent progress has been stayed by dichotomous debates (e.g., nature versus nurture) that have created silos of empirical and theoretical knowledge. Now, an emerging interdisciplinary scientific culture is broadening the focus of research to provide a more unified and refined account of facial expressions within and across cultures. Specifically, data-driven approaches allow a wider, more objective exploration of face movement patterns that provide detailed information ontologies of their cultural commonalities and specificities. Similarly, a wider exploration of the social messages perceived from face movements diversifies knowledge of their functional roles (e.g., the ‘fear’ face used as a threat display). Together, these new approaches promise to diversify, deepen, and refine knowledge of facial expressions, and deliver the next major milestones for a functional theory of human social communication that is transferable to social robotics