Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?

A new, coercive formulation of the Helmholtz equation was introduced in [Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate $h$-version Galerkin discretisations of this formulation, and the iterative solution of the resulting linear systems. We find that the coercive formulation behaves similarly to the standard formulation in terms of the pollution effect (i.e. to maintain accuracy as $k\to\infty$, $h$ must decrease with $k$ at the same rate as for the standard formulation). We prove $k$-explicit bounds on the number of GMRES iterations required to solve the linear system of the new formulation when it is preconditioned with a prescribed symmetric positive-definite matrix. Even though the number of iterations grows with $k$, these are the first such rigorous bounds on the number of GMRES iterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is a symmetric positive-definite matrix.Comment: 27 pages, 7 figure

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts

The Development of a model program for the effective management of biomedical waste in the Caribbean. A Review of barriers within public hospitals in the Caribbean.

When biomedical waste is improperly managed it poses a health hazard and risk to healthcare workers, sanitation workers and the general public in contracting infectious/dangerous diseases. Biomedical waste is also generated from individuals in their homes from the use of syringes or diagnostic lancets that are not properly managed. Biomedical waste is considered special waste and has a health and environmental hazard that can result in infections and diseases such as HIV/AIDs. Discarded sharps pose a health risk to the public particularly solid waste workers who may suffer a needle stick injury if they are not properly packaged for disposal. Needle stick injuries can require very expensive testing and treatment and can increase the risk of exposure to infectious blood borne diseases such as Hepatitis and HIV from contaminated needles. Within the Caribbean region there are many factors influencing the effective management of biomedical waste. This paper will provide a review of these factors and their impacts (risks) base on the current management practices and systems for biomedical waste in three Caribbean islands. These major influencing factors include, government environment health and safety regulations for the healthcare industry, risks associated with biomedical waste management in public hospitals, public healthcare services vs private hospitals services, training of healthcare staff, public hospitals operating standards and guidelines and biomedical waste disposal

Use of computed tomography imaging during long-term follow-up of nine feline tuberculosis cases

Case series summary: Feline tuberculosis is an increasingly recognised potential zoonosis of cats. Treatment is challenging and prognosis can vary greatly between cases. Pulmonary infection requires extended courses of antibiotics, but methodologies for sensitively monitoring response to treatment are currently lacking. In this case series, we retrospectively examined the serial computed tomography (CT) findings in nine cats that had been diagnosed with tuberculosis. Changes in pathology (where applicable to tuberculosis) were correlated with the clinical presentation of each of the cats, the treatment protocol, and previous and contemporary diagnostic investigations. This study found that changes in CT findings during the medium- to long-term management of feline tuberculosis were highly variable between cats. The majority of cats had reduced pathology at re-examination during anti-tuberculous therapy, but pathology only resolved in a minority of cases. In some cases recurrence of pathology detected by CT imaging preceded clinical deterioration, allowing for rapid therapeutic intervention. Relevance and novel information: When considered in combination with clinical findings, CT studies can aid in decision making regarding tapering of antibiotic protocols, or reintroduction of therapy in cases of recurrence or reinfection. This series also highlights that, in some cases, persistent abnormalities can be detected by CT, so complete resolution of CT pathology should not always be a goal in the management of feline tuberculosis

Affiliative Behaviors in Pairbonded Red Titi Monkeys (Callicebus Discolor)

Adult titi monkeys (Callicebus spp.) form strong pairbonds and reside in socially monogamous groups. In addition, adult males are heavily involved in infant care, exhibiting a degree of direct investment unusual even among primate species with paternal care. Most of the research exploring the nature of these social bonds has focused on captive populations, and data on wild titi populations are limited. In particular, data quantifying the pairbond and exploring the costs of infant care are rare for wild titi monkeys. I analyzed data from two groups of titi monkeys (Callicebus discolor) in Yasuní National Park and Biosphere Reserve and quantified the affiliative social interactions between the adult male and the adult female in the group to determine 1) the frequency and type of affiliative behaviors exhibited by pairmates, 2) whether there is evidence for sex differences in maintenance of affiliative behaviors and proximity, and 3) whether there is evidence of social costs within a pair during the period when infant care is provided. The most frequent affiliative behaviors involved pairmates resting in close proximity to each other. In addition, males and females spent significantly less time within five meters of each other when they were providing direct infant care, consistent with the prediction that infant care may correlate with a decrease in affiliative behaviors between pairmates. Although no solid conclusions can be drawn from this preliminary study given the small sample size, this research provides data suggesting that the presence of a dependent infant may influence the quality of the relationship between pairmates

Andrea Spence McKane in a Senior Voice Recital

This is the program for the senior voice recital of soprano Andrea Spence McKane. Pianist Terri Pierce Lucas assisted the performance. The recital took place on March 1, 1993, in the Mabee Fine Arts Center Recital Hall

Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds explicit in all parameters. In particular, the (weighted) $H^1$ norm of the solution is bounded by the $L^2$ norm of the source term, independently of the wavenumber. These bounds then imply the existence of a resonance-free strip beneath the real axis. The main novelty is that the only comparable results currently in the literature are for smooth, convex obstacles with strictly positive curvature, while here we assume only Lipschitz regularity and star-shapedness with respect to a point. Furthermore, our bounds are obtained using identities first introduced by Morawetz (essentially integration by parts), whereas the existing bounds use the much-more sophisticated technology of microlocal analysis and propagation of singularities. We also recap existing results that show that if the assumption on the wavenumbers is lifted, then no bound with polynomial dependence on the wavenumber is possible.Comment: 26 pages, 2 figure

Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem

We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral operators grow rapidly through an increasing sequence of frequencies, even though this is not the case for the solution operator of the transmission problem; we call this phenomenon that of spurious quasi-resonances. We give a rigorous explanation of why and when spurious quasi-resonances occur, and propose modified boundary integral equations that are not affected by them

Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media

We consider the time-harmonic Maxwell equations posed in $\mathbb{R}^3$. We prove a priori bounds on the solution for $L^\infty$ coefficients $\epsilon$ and $\mu$ satisfying certain monotonicity properties, with these bounds valid for arbitrarily-large frequency, and explicit in the frequency and properties of $\epsilon$ and $\mu$. The class of coefficients covered includes (i) certain $\epsilon$ and $\mu$ for which well-posedness of the time-harmonic Maxwell equations had not previously been proved, and (ii) scattering by a penetrable $C^0$ star-shaped obstacle where $\epsilon$ and $\mu$ are smaller inside the obstacle than outside. In this latter setting, the bounds are uniform across all such obstacles, and the first sharp frequency-explicit bounds for this problem at high-frequency

Prokofiev was (almost) right: a cross-cultural investigation of auditory-conceptual associations in Peter and the Wolf

Over recent decades, studies investigating cross-modal correspondences have documented the existence of a wide range of consistent cross-modal associations between simple auditory and visual stimuli or dimensions (e.g., pitch-lightness). Far fewer studies have investigated the association between complex and realistic auditory stimuli and visually presented concepts (e.g., musical excerpts-animals). Surprisingly, however, there is little evidence concerning the extent to which these associations are shared across cultures. To address this gap in the literature, two experiments using a set of stimuli based on Prokofiev’s symphonic fairy tale Peter and the Wolf are reported. In Experiment 1, 293 participants from several countries and with very different language backgrounds rated the association between the musical excerpts, images and words representing the story’s characters (namely, bird, duck, wolf, cat, and grandfather). The results revealed that participants tended to consistently associate the wolf and the bird with the corresponding musical excerpt, while the stimuli of other characters were not consistently matched across participants. Remarkably, neither the participants’ cultural background, nor their musical expertise affected the ratings. In Experiment 2, 104 participants were invited to rate each stimulus on eight emotional features. The results revealed that the emotional profiles associated with the music and with the concept of the wolf and the bird were perceived as more consistent between observers than the emotional profiles associated with the music and the concept of the duck, the cat, and the grandpa. Taken together, these findings therefore suggest that certain auditory-conceptual associations are perceived consistently across cultures and may be mediated by emotional associations