High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: O(1)\mathcal{O}(1) Sampling Cost via Incident-Field Windowing and Recentering

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily-long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time $T$ at $\mathcal{O}(1)$-bounded sampling cost, for arbitrarily large values of $T$, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization, time-domain integral equations, and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now including direct comparisons to existing CQ and TDIE solver implementations) (Part I of II

Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness

Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally when, in a number of different systems, the concentrations of key system components at equilibrium were observed to be robust to the total concentration levels of the system. Followup mathematical work focused on deterministic models of biochemical systems and demonstrated how chemical reaction network theory can be utilized to explain this robustness. Later mathematical work focused on the behavior of this same class of reaction networks, though under the assumption that the dynamics were stochastic. Under the stochastic assumption, it was proven that the system will undergo an extinction event with a probability of one so long as the system is conservative, showing starkly different long-time behavior than in the deterministic setting. Here we consider a general class of stochastic models that intersects with the class of ACR systems studied previously. We consider a specific system scaling over compact time intervals and prove that in a limit of this scaling the distribution of the abundances of the ACR species converges to a certain product-form Poisson distribution whose mean is the ACR value of the deterministic model. This result is in agreement with recent conjectures pertaining to the behavior of ACR networks endowed with stochastic kinetics, and helps to resolve the conflicting theoretical results pertaining to deterministic and stochastic models in this setting

'If I cannot access services then there is no reason for me to test': the impact of health service charges on HIV testing and treatment amongst migrants in England

Policy governing entitlement to access government health care for foreign nationals in England is a subject of debate, controversy and confusion. Of particular concern to health providers has been the impact of National Health Service charges on delaying HIV testing and anti-retroviral treatment uptake and adherence amongst certain migrant groups. Data obtained through focus groups with 70 migrants from southern Africa, suggest that confusion over health care entitlements exists amongst those seeking health care and is reported amongst health service providers. This confusion, as well as financial difficulties and fears over deportation facing some migrants, can in turn be a factor influencing their decisions to avoid formal health services, resort to alternative and often ineffective or potentially adverse forms of therapy, and delay HIV testing and treatment uptake

How Remote Response Devices Enable Student Learning: A Four-Year Analysis

The use of Personal Response Systems (PRS) / Classroom Performance Systems (CPS) has expanded considerably since introduction in the early 2000s.  Much of the exploration of the technology has focused on methodology, student participation, and student perception.  This paper examines actual testing results over nine semesters to provide some insights to the impact of the technology on student grades.&nbsp

The determination of the alkalinity of sea water

In a previous paper one of us (3) described a _ method for the determination of the alkalinity of sea water-then termed the buffer capacity of sea water. This method was very rapid, eliminated the need for a titration process, and was particularly advantageous when working under rigorous field conditions. However considerable difficulty was sometimes experienced in the preparation of color comparison standards from base-free sea water. The method was later improved by Mitchell and Rakestraw (2). The present paper deals with a modification of the original method. The glass electrode is used for the measurement of excess acid and gives a precision greater than that obtained with color standards. If suitable shelter is available the method may be performed as readily in the field as in the laboratory. Following is a description of the apparatus and the method used

Gravitational Waves: Just Plane Symmetry

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.Comment: 10 pages, TeX, uses IOP style file

Error analysis of tau-leap simulation methods

We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of the system. We argue that this is a more appropriate scaling than that found in previous error analyses in which the size of the time discretization goes to zero independent of the rest of the model. Under the present scaling, we show that midpoint tau-leaping achieves a higher order of accuracy, in both a weak and a strong sense, than Euler tau-leaping; a result that is in contrast to previous analyses. We present examples that demonstrate our findings.Comment: Published in at http://dx.doi.org/10.1214/10-AAP756 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org