Harmonic Wavelet Transform and Image Approximation

In 2006, Saito and Remy proposed a new transform called the Laplace Local Sine Transform (LLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a harmonic function u such that the residual component v=f−u vanishes on the boundary of Ω. Next, we do the odd extension for v, and then do the periodic extension, i.e. we obtain a periodic odd function v *. Finally, we expand v * into Fourier sine series. In this paper, we propose to expand v * into a periodic wavelet series with respect to biorthonormal periodic wavelet bases with the symmetric filter banks. We call this the Harmonic Wavelet Transform (HWT). HWT has an advantage over both the LLST and the conventional wavelet transforms. On the one hand, it removes the boundary mismatches as LLST does. On the other hand, the HWT coefficients reflect the local smoothness of f in the interior of Ω. So the HWT algorithm approximates data more efficiently than LLST, periodic wavelet transform, folded wavelet transform, and wavelets on interval. We demonstrate the superiority of HWT over the other transforms using several standard images

Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $\delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.Comment: 23 pages, Late

Scattering in flatland: Efficient representations via wave atoms

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by thresholding the small coefficients to zero. This phenomenon was perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context of local Fourier bases \cite{BCG}. Their results have since then been extended in various ways. The purpose of this paper is to bridge a theoretical gap and prove that a well-chosen fixed expansion, the nonstandard wave atom form, provides a compression of the acoustic single and double layer potentials with wave number $k$ as $O(k)$-by-$O(k)$ matrices with $O(k^{1+1/\infty})$ nonnegligible entries, with a constant that depends on the relative $\ell_2$ accuracy \eps in an acceptable way. The argument assumes smooth, separated, and not necessarily convex scatterers in two dimensions. The essential features of wave atoms that enable to write this result as a theorem is a sharp time-frequency localization that wavelet packets do not obey, and a parabolic scaling wavelength $\sim$ (essential diameter)${}^2$. Numerical experiments support the estimate and show that this wave atom representation may be of interest for applications where the same scattering problem needs to be solved for many boundary conditions, for example, the computation of radar cross sections.Comment: 39 page

Identifying Mechanisms by Which Escherichia coli O157:H7 Subverts Interferon-γ Mediated Signal Transducer and Activator of Transcription-1 Activation

Enterohemorrhagic Escherichia coli serotype O157:H7 is a food borne enteric bacterial pathogen that causes significant morbidity and mortality in both developing and industrialized nations. E. coli O157:H7 infection of host epithelial cells inhibits the interferon gamma pro-inflammatory signaling pathway, which is important for host defense against microbial pathogens, through the inhibition of Stat-1 tyrosine phosphorylation. The aim of this study was to determine which bacterial factors are involved in the inhibition of Stat-1 tyrosine phosphorylation. Human epithelial cells were challenged with either live bacteria or bacterial-derived culture supernatants, stimulated with interferon-gamma, and epithelial cell protein extracts were then analyzed by immunoblotting. The results show that Stat-1 tyrosine phosphorylation was inhibited by E. coli O157:H7 secreted proteins. Using sequential anion exchange and size exclusion chromatography, YodA was identified, but not confirmed to mediate subversion of the Stat-1 signaling pathway using isogenic mutants. We conclude that E. coli O157:H7 subverts Stat-1 tyrosine phosphorylation in response to interferon-gamma through a still as yet unidentified secreted bacterial protein

Disclosing intimate partner violence to health care clinicians - What a difference the setting makes: A qualitative study

<p>Abstract</p> <p>Background</p> <p>Despite endorsement by national organizations, the impact of screening for intimate partner violence (IPV) is understudied, particularly as it occurs in different clinical settings. We analyzed interviews of IPV survivors to understand the risks and benefits of disclosing IPV to clinicians across specialties.</p> <p>Methods</p> <p>Participants were English-speaking female IPV survivors recruited through IPV programs in Massachusetts. In-depth interviews describing medical encounters related to abuse were analyzed for common themes using Grounded Theory qualitative research methods. Encounters with health care clinicians were categorized by outcome (IPV disclosure by patient, discovery evidenced by discussion of IPV by clinician without patient disclosure, or non-disclosure), attribute (beneficial, unhelpful, harmful), and specialty (emergency department (ED), primary care (PC), obstetrics/gynecology (OB/GYN)).</p> <p>Results</p> <p>Of 27 participants aged 18–56, 5 were white, 10 Latina, and 12 black. Of 59 relevant health care encounters, 23 were in ED, 17 in OB/GYN, and 19 in PC. Seven of 9 ED disclosures were characterized as unhelpful; the majority of disclosures in PC and OB/GYN were characterized as beneficial. There were no harmful disclosures in any setting. Unhelpful disclosures resulted in emotional distress and alienation from health care. Regardless of whether disclosure occurred, beneficial encounters were characterized by familiarity with the clinician, acknowledgement of the abuse, respect and relevant referrals.</p> <p>Conclusion</p> <p>While no harms resulted from IPV disclosure, survivor satisfaction with disclosure is shaped by the setting of the encounter. Clinicians should aim to build a therapeutic relationship with IPV survivors that empowers and educates patients and does not demand disclosure.</p

Progressive dementia associated with ataxia or obesity in patients with Tropheryma whipplei encephalitis

<p>Abstract</p> <p>Background</p> <p><it>Tropheryma whipplei</it>, the agent of Whipple's disease, causes localised infections in the absence of histological digestive involvement. Our objective is to describe <it>T. whipplei </it>encephalitis.</p> <p>Methods</p> <p>We first diagnosed a patient presenting dementia and obesity whose brain biopsy and cerebrospinal fluid specimens contained <it>T. whipplei </it>DNA and who responded dramatically to antibiotic treatment. We subsequently tested cerebrospinal fluid specimens and brain biopsies sent to our laboratory using <it>T. whipplei </it>PCR assays. PAS-staining and <it>T. whipplei </it>immunohistochemistry were also performed on brain biopsies. Analysis was conducted for 824 cerebrospinal fluid specimens and 16 brain biopsies.</p> <p>Results</p> <p>We diagnosed seven patients with <it>T. whipplei </it>encephalitis who demonstrated no digestive involvement. Detailed clinical histories were available for 5 of them. Regular PCR that targeted a monocopy sequence, PAS-staining and immunohistochemistry were negative; however, several highly sensitive and specific PCR assays targeting a repeated sequence were positive. Cognitive impairments and ataxia were the most common neurologic manifestations. Weight gain was paradoxically observed for 2 patients. The patients' responses to the antibiotic treatment were dramatic and included weight loss in the obese patients.</p> <p>Conclusions</p> <p>We describe a new clinical condition in patients with dementia and obesity or ataxia linked to <it>T. whipplei </it>that may be cured with antibiotics.</p