Inverse problem approach to regularized regression models with application to predicting recovery after stroke

Regression modelling is a powerful statistical tool often used in biomedical and clinical research. It could be formulated as an inverse problem that measures the discrepancy between the target outcome and the data produced by representation of the modelled predictors. This approach could simultaneously perform variable selection and coefficient estimation. We focus particularly on a linear regression issue, , where is the parameter of interest and its components are the regression coefficients. The inverse problem finds an estimate for the parameter , which is mapped by the linear operator to the observed outcome data . This problem could be conveyed by finding a solution in the affine subspace . However, in the presence of collinearity, high-dimensional data and high conditioning number of the related covariance matrix, the solution may not be unique, so the introduction of prior information to reduce the subset and regularize the inverse problem is needed. Informed by Huber's robust statistics framework, we propose an optimal regularizer to the regression problem. We compare results of the proposed method and other penalized regression regularization methods: ridge, lasso, adaptive-lasso and elastic-net under different strong hypothesis such as high conditioning number of the covariance matrix and high error amplitude, on both simulated and real data from the South London Stroke Register. The proposed approach can be extended to mixed regression models. Our inverse problem framework coupled with robust statistics methodology offer new insights in statistical regression and learning. It could open a new research development for model fitting and learning.     

Synthesis of 3-deoxy-4-O-β-D-galactopyranosyl-D-erythro-hexos-2-ulose and of some of its derivatives from lactose

3-Deoxy-4-O-β-D-galactopyranosyl-D-erythro-hexos-2-ulose (1) was obtained from lactose by reaction with benzoylhydrazine in the presence of a slightly acidic solution of p-toluidine, followed by hydrazinolysis of the product, 3-deoxy-4-O-β-D-galactopyranosyl-D-erythro-hexos-2-ulose bis(benzoylhydrazone) (3), with benzaldehyde. A variety of derivatives of 1 and 3 was prepared. Lactose aroylhydrazones were also prepared. Quantitative determination of the oxidant during the periodate oxidation of 3 was studied. Periodate oxidation of monosaccharide arylhydrazones gave glyoxal mono(arylhydrazones) which afforded the corresponding, mixed bis(hydrazones).     

Transfer factor immunotherapy in Hodgkin's and non-Hodgkin's lymphoma

Summary Human dialyzable transfer factor was administered in a double-blind fashion to patients with Hodgkin's disease and non-Hodgkin's lymphoma. Two groups were examined; patients with active disease and patients in remission. Parameters of cellular and humoral immunity were studied. The effect of transfer factor on the clinical condition was not evaluated.Transfer factor tended to intensify the skin test reactions of patients in remission to several recall antigens, but had no effect on the other parameters or the other patient group.     

A quantitative study of the phytoplankton in the Blue and White Niles at Khartoum

The variation in numbers of the major planktonic algae in the surface waters of the Blue Nile and White Nile were followed for 29 months (August 1968–December 1970). In terms of biomass, the phytoplankton was dominated by diatoms and blue-green algae; other groups were of minor importance. High phytoplankton densities occurred during winter in both rivers, and during summer in the Blue Nile, with values in the latter river greater than in the former. Melosira granulata and its variety angustissima and Anabaena flos-aquae var. intermedia f. spiroides were the most important taxa in the two Niles. Melosira distans and Attheya zachariasi, which are reported for the first time in the present study, preponderated at certain times in the Blue Nile. Microcystisflos-aqua which had been a minor component of the phytoplankton in both rivers during the early 1950s, showed a profuse growth in the Blue Nile. Lyngbya limnetica, Anabaenopsis cunningtonii and A. tanganyikae, which constituted important components of the phytoplankton in the early 1950s, either disappeared or maintained themselves in reduced numbers during the present study. This change in the algal flora of the two Niles may be attributed to the construction of the Roseres dam across the Blue Nile in 1966 and to the invasion of the White Nile by Eichhornia crassipes in 1957.     

Effectiveness of low-power laser therapy in improvement of the peripheral neuropathy induced by xenobiotics in rats

BackgroundPeripheral neuropathy (PN) is the damage and dysfunction of neurons of the peripheral nervous system. The present study was conducted to estimate the effectiveness of low-power laser therapy (LPLT) in the management of PN in a rats’ model.MethodsPN was induced by giving dichloroacetate (DCA) (250 mg/kg/day) for up to 12 weeks. Four groups of rats were used: control group, PN group, PN group treated with gabapentin and PN group treated with LPLT. The study was conducted for 8 weeks. The management of PN was estimated by behavioral tests which included hot plate and Morris water maze tests. Blood biochemical analysis were carried out.ResultsUsing of hot plate test indicated thermal hypoalgesia and using Morris water maze test showed cognitive decline in PN rats. Treatment with LPLT or gabapentin improved both the pain sensations and deteriorated memory that occurred in the PN rats. Biochemical analysis showed that LPLT significantly decreased the elevated beta-endorphin level in PN rats, while gabapentin could not reduce it. Treatment PN rats with LPLT or gabapentin shifted the high levels of TNF-α, IL-1β and IL-10 cytokines back to their normal values. Serum nitric oxide and MDA significantly increased in the PN group together with significant reduction in the rGSH level, these values were significantly improved by LPLT application while this was not the case with gabapentin treatment. Furthermore, treatment with gabapentin or LPLT significantly reduced serum ALAT and ASAT activities which are otherwise increased in the PN group. S100B, PGE2, total cholesterol, triglycerides, LDL-cholesterol, HDL-cholesterol, urea and creatinine showed insignificant changes among all groups.ConclusionsOur results showed that treatment with LPLT is more efficient than gabapentin in ameliorating the peripheral neuropathy induced by xenobiotics.     

Phytoplankton associations in two pools and their relationships with associated benthic flora

Summary The theory underlying the delineation of phytoplankton association is examined, and the associations of Abbot's pond and Priddy pool are characterised according to the conclusions derived from this examination. The importance of extended investigations is stressed. Abbot's pond has a eu-planktonic flora with abundant Asterionella formosa, Pandorina morum and Chrysococcus diaphanus. The euphytoplankton of Priddy pool consists of a very few species, of which Dinobryon sertularia is most abundant, but owing to the action of wind on the pool, many species are introduced into the open water by disturbance of benthic habitats.