Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Intestinal Epithelial Serum Amyloid A Modulates Bacterial Growth In Vitro and Pro-Inflammatory Responses in Mouse Experimental Colitis

<p>Abstract</p> <p>Background</p> <p>Serum Amyloid A (SAA) is a major acute phase protein of unknown function. SAA is mostly expressed in the liver, but also in other tissues including the intestinal epithelium. SAA reportedly has anti-bacterial effects, and because inflammatory bowel diseases (IBD) result from a breakdown in homeostatic interactions between intestinal epithelia and bacteria, we hypothesized that SAA is protective during experimental colitis.</p> <p>Methods</p> <p>Intestinal SAA expression was measured in mouse and human samples. Dextran sodium sulfate (DSS) colitis was induced in SAA 1/2 double knockout (DKO) mice and in wildtype controls. Anti-bacterial effects of SAA1/2 were tested in intestinal epithelial cell lines transduced with adenoviral vectors encoding the CE/J SAA isoform or control vectors prior to exposure to live <it>Escherichia coli</it>.</p> <p>Results</p> <p>Significant levels of SAA1/SAA2 RNA and SAA protein were detected by in situ hybridization and immunohistochemistry in mouse colonic epithelium. SAA3 expression was weaker, but similarly distributed. SAA1/2 RNA was present in the ileum and colon of conventional mice and in the colon of germfree mice. Expression of SAA3 was strongly regulated by bacterial lipopolysaccharides in cultured epithelial cell lines, whereas SAA1/2 expression was constitutive and not LPS inducible. Overexpression of SAA1/2 in cultured epithelial cell lines reduced the viability of co-cultured <it>E. coli</it>. This might partially explain the observed increase in susceptibility of DKO mice to DSS colitis. SAA1/2 expression was increased in colon samples obtained from Crohn's Disease patients compared to controls.</p> <p>Conclusions</p> <p>Intestinal epithelial SAA displays bactericidal properties in vitro and could play a protective role in experimental mouse colitis. Altered expression of SAA in intestinal biopsies from Crohn's Disease patients suggests that SAA is involved in the disease process..</p

Autoimmune enteropathy with a CD8+ CD7- T-cell small bowel intraepithelial lymphocytosis: case report and literature review

<p>Abstract</p> <p>Background</p> <p>Adult onset autoimmune enteropathy (AIE) is a rare condition characterized by diarrhea refractory to dietary therapy diagnosed in patients with evidence of autoimmune conditions. Auto-antibodies to gut epithelial cells and other tissues are commonly demonstrated. Despite increasing awareness, the pathogenesis, histologic, immunologic and clinical features of AIE remain uncertain. There remains controversy regarding the diagnostic criteria, the frequency and types of auto-antibodies and associated autoimmune conditions, and the extent and types of histologic and immunologic abnormalities. CD4+ T-cells are thought to at least responsible for this condition; whether other cell types, including B- and other T-cell subsets are involved, are uncertain. We present a unique case of AIE associated with a CD8+CD7- lymphocytosis and review the literature to characterize the histologic and immunologic abnormalities, and the autoantibodies and autoimmune conditions associated with AIE.</p> <p>Case Presentation</p> <p>We present a case of immune mediated enteropathy distinguished by the CD8+CD7- intra-epithelial and lamina propria lymphocytosis. Twenty-nine cases of AIE have been reported. The majority of patients had auto-antibodies (typically anti-enterocyte), preferential small bowel involvement, and predominately CD3+ CD4+ infiltrates. Common therapies included steroids or immuno-suppressive agents and clinical response with associated with histologic improvement.</p> <p>Conclusions</p> <p>AIE is most often characterized (1) IgG subclass anti-epithelial cell antibodies, (2) preferential small bowel involvement, and (3) CD3+ alphabeta TCR+ infiltrates; there is insufficient evidence to conclude CD4+ T-cells are solely responsible in all cases of AIE.</p

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Cervical dysplasia and cancer and the use of hormonal contraceptives in Jamaican women

<p>Abstract</p> <p>Background</p> <p>This study was conducted to determine whether use of hormonal contraceptives is associated with cervical dysplasia and cancer in a population where there is widespread use of hormonal contraception and the rates of cervical cancer remain high at 27.5/100,000.</p> <p>Methods</p> <p>A case-control study was conducted among women visiting the colposcopy and gynaelogical clinics at a tertiary referral hospital. Two hundred and thirty six cases CIN I (72), II (59), III (54), cancer (51) and 102 controls, consented and were interviewed on use of contraceptives using a structured questionnaire. Logistic regression was used to determine odds ratios (ORs) and 95% confidence intervals (CIs) associated with use of hormonal contraception in cases and controls and in low and high risk cases. Recruitment was carried out from 2001–2002.</p> <p>Results</p> <p>Contraceptives used were: oral contraceptives – 35%, injections (depot medroxy progesterone acetate (Depo-provera) – 10%, Intrauterine devices – 2%, combinations of these and tubal ligation – 30%. 23% reported use of 'other' methods, barrier contraceptives or no form of contraception. Barrier contraceptive use was not significantly different between cases and controls. Current and/or past exposure to hormonal contraceptives (HC) by use of the pill or injection, alone or in combination with other methods was significantly higher in the cases. In multivariate analysis with age and number of sexual partners as co-variates, use of hormonal contraception was associated both with disease, [OR, 1.92 (CI 1.11, 3.34; p = 0.02] and severity of the disease [OR, 2.22 (CI 1.05, 4.66) p = 0.036]. When parity and alcohol consumption were added to the model, hormonal contraception was no longer significant. The significant association with high risk disease was retained when the model was controlled for age and number of sexual partners. Depo-provera use (with age and number of sexual partners as covariates) was also associated with disease [OR, 2.43 (CI 1.39, 4.57), p = 0.006] and severity of disease [OR 2.51 (1.11, 5.64) p = 0.027]. With parity and alcohol added to this model, depo-provera use retained significance. Exposure to HC > 4 years conferred more risk for disease and severity of disease.</p> <p>Conclusion</p> <p>Hormonal contraception did confer some risk of dysplasia and women using HC should therefore be encouraged to do regular Pap smear screening.</p

Koilocytes indicate a role for human papilloma virus in breast cancer

Background: High-risk human papilloma viruses (HPVs) are candidates as causal viruses in breast cancer. The scientific challenge is to determine whether HPVs are causal and not merely passengers or parasites. Studies of HPV-related koilocytes in breast cancer offer an opportunity to address this crucial issue. Koilocytes are epithelial cells characterised by perinuclear haloes surrounding condensed nuclei and are commonly present in cervical intraepithelial neoplasia. Koilocytosis is accepted as pathognomonic (characteristic of a particular disease) of HPV infection. The aim of this investigation is to determine whether putative koilocytes in normal and malignant breast tissues are because of HPV infection. Methods: Archival formalin-fixed normal and malignant breast specimens were investigated by histology, in situ PCR with confirmation of the findings by standard PCR and sequencing of the products, plus immunohistochemistry to identify HPV E6 oncoproteins. Results: human papilloma virus-associated koilocytes were present in normal breast skin and lobules and in the breast skin and cancer tissue of patients with ductal carcinoma in situ (DCIS) and invasive ductal carcinomas (IDCs). Interpretation: As koilocytes are known to be the precursors of some HPV-associated cervical cancer, it follows that HPVs may be causally associated with breast cancer.6 page(s