Discrete-Time Path Distributions on Hilbert Space

We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials

Three-dimensional Quantum Slit Diffraction and Diffraction in Time

We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We derive corrections to the standard formula for the diffraction pattern, and we point out situations in which this might be observable. In particular, we discuss the diffraction in space and time in the presence of gravity

Do Malaria Vector control Measures Impact Disease-Related Behaviour and Knowledge? Evidence from a Large-scale Larviciding Intervention in Tanzania.

Recent efforts of accelerated malaria control towards the long-term goal of elimination had significant impacts in reducing malaria transmission. While these efforts need to be sustained over time, a scenario of low transmission could bring about changes in individual disease risk perception, hindering adherence to protective measures, and affecting disease-related knowledge. The goal of this study was to investigate the potential impact of a successful malaria vector control intervention on bed net usage and malaria-related knowledge. Dar es Salaam's Urban Malaria Control Program was launched in 2004 with the aim of developing a sustainable larviciding intervention. Larviciding was scaled-up using a stepped-wedge design. Cross-sectional and longitudinal data were collected using a randomized cluster sampling design (2004--2008). Prevalence ratios (PR) for the effect of the larviciding intervention on bed net usage (N = 64,537) and household heads' knowledge of malaria symptoms and transmission (N = 11,254) were obtained from random effects regression models.\ud The probability that individuals targeted by larviciding had used a bed net was reduced by 5% as compared to those in non-intervention areas (PR = 0.95; 95% credible intervals (CrI): 0.94-0.97) and the magnitude of this effect increased with time. Larviciding also led to a decline in household heads' knowledge of malaria symptoms (PR = 0.88; 95% CrI: 0.83-0.92) but no evidence of effect on knowledge of malaria transmission was found. Successful control interventions could bring about further challenges to sustaining gains in reducing malaria transmission if not accompanied by strategies to avoid changes in individual knowledge and behaviour. This study points to two major research gaps. First, there is an urgent need to gather more evidence on the extent to which countries that have achieved significant decline in malaria transmission are also observing changes in individual behaviour and knowledge. Second, multidisciplinary assessments that combine quantitative and qualitative data, utilizing theories of health behaviour and theories of knowledge, are needed to optimize efforts of national malaria control programmes, and ultimately contribute to sustained reduction in malaria transmission

(2+1)(2+1)-dd Glueball Spectrum within a Constituent Picture

The quantum numbers and mass hierarchy of the glueballs observed in $(2+1)$-dimensional lattice QCD with gauge group SU($N_c$) are shown to be in agreement with a constituent picture. The agreement is maintained when going from glueballs to gluelumps, and when the gauge group SO($2N_c$) is taken instead of SU($N_c$)

String deformations induced by retardation effects

The rotating string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a new framework to include the retardation effects in the rotating string model, but the string was still kept straight. We now go a step further and show that the retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.Comment: 3 figure

Recognizing well-parenthesized expressions in the streaming model

Motivated by a concrete problem and with the goal of understanding the sense in which the complexity of streaming algorithms is related to the complexity of formal languages, we investigate the problem Dyck(s) of checking matching parentheses, with $s$ different types of parenthesis. We present a one-pass randomized streaming algorithm for Dyck(2) with space \Order(\sqrt{n}\log n), time per letter \polylog (n), and one-sided error. We prove that this one-pass algorithm is optimal, up to a \polylog n factor, even when two-sided error is allowed. For the lower bound, we prove a direct sum result on hard instances by following the "information cost" approach, but with a few twists. Indeed, we play a subtle game between public and private coins. This mixture between public and private coins results from a balancing act between the direct sum result and a combinatorial lower bound for the base case. Surprisingly, the space requirement shrinks drastically if we have access to the input stream in reverse. We present a two-pass randomized streaming algorithm for Dyck(2) with space \Order((\log n)^2), time \polylog (n) and one-sided error, where the second pass is in the reverse direction. Both algorithms can be extended to Dyck(s) since this problem is reducible to Dyck(2) for a suitable notion of reduction in the streaming model.Comment: 20 pages, 5 figure

Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of the usual maximum likelihood estimator, Bayesian inference based on composite likelihoods has yet to be explored. In this paper we investigate the use of the Metropolis--Hastings algorithm to compute a pseudo-posterior distribution based on the composite likelihood. Two methodologies for adjusting the algorithm are presented and their performance on approximating the true posterior distribution is investigated using simulated data sets and real data on spatial extremes of rainfall