Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

Detection of Vibrio cholerae and Acanthamoeba species from same natural water samples collected from different cholera endemic areas in Sudan

<p>Abstract</p> <p>Background</p> <p><it>Vibrio cholerae </it>O1 and <it>V. cholerae </it>O139 infect humans, causing the diarrheal and waterborne disease cholera, which is a worldwide health problem. <it>V. cholerae </it>and the free-living amoebae <it>Acanthamoeba </it>species are present in aquatic environments, including drinking water and it has shown that <it>Acanthamoebae </it>support bacterial growth and survival. Recently it has shown that <it>Acanthamoeba </it>species enhanced growth and survival of <it>V. cholerae </it>O1 and O139. Water samples from different cholera endemic areas in Sudan were collected with the aim to detect both <it>V. cholerae </it>and <it>Acanthamoeba </it>species from same natural water samples by polymerase chain reaction (PCR).</p> <p>Findings</p> <p>For the first time both <it>V. cholerae </it>and <it>Acanthamoeba </it>species were detected in same natural water samples collected from different cholera endemic areas in Sudan. 89% of detected <it>V. cholerae </it>was found with <it>Acanthamoeba </it>in same water samples.</p> <p>Conclusions</p> <p>The current findings disclose <it>Acanthamoedae </it>as a biological factor enhancing survival of <it>V. cholerae </it>in nature.</p

Hepatotoxicity and effectiveness of a Nevirapine-based antiretroviral therapy in HIV-infected patients with or without viral hepatitis B or C infection in Cameroon

Background: Coinfection with hepatitis B virus (HBV) or hepatitis C virus (HCV) in HIV-infected patients receiving a commonly used nevirapine-based antiretroviral therapy is a major concern for African clinicians owing to its high prevalence, the infrequent testing and treatment of viral hepatitis, and the impact of liver disease on the tolerability and effectiveness of anti-HIV treatment. We compared the hepatotoxicity and the immunological, virological and clinical effectiveness of a nevirapine-based antiretroviral therapy between patients infected with HIV only and patients coinfected with hepatitis B or C virus in Cameroon. Methods: A retrospective cohort study was conducted among HIV-1-infected patients. Plasma HBV DNA and HCV RNA were tested in positive or indeterminate samples for HBsAg or HCV antibodies, respectively. All patients received nevirapine and lamivudine plus stavudine or zidovudine. Results: Of 169 HIV-1-infected patients with a median baseline CD4 count of 135 cells/mm(3) (interquartile range [IQR] 67 218), 21% were coinfected with HBV or HCV. In coinfected patients, the median viral load was 2.47 x 107 IU/mL for HBV (IQR 3680-1.59 x 10(8)) and 928 000 IU/mL for HCV (IQR 178 400-2.06 x 10(6)). Multivariate analyses showed that the risk of hepatotoxicity was 2-fold higher in coinfected patients (p < 0.01). The response to antiretroviral therapy was however comparable between monoinfected and coinfected patients in terms of CD4 cell count increase (p = 0.8), HIV-1 viral load below 400 copies/mL (p = 0.9), death (p = 0.3) and death or new AIDS-defining event (p = 0.1). Nevirapine was replaced by a protease inhibitor in 4 patients owing to hepatotoxicity. Conclusion: This study suggests that the nevirapine-based antiretroviral therapy could be used safely as first-line treatment in patients with low CD4 cell count in Africa despite frequent coinfections with HBV or HCV and infrequent testing of these infections. Although testing for HBV and HCV should be systematically performed before initiating antiretroviral therapy, transaminases elevations at baseline or during treatment should be a decisive argument for testing when hepatitis status is unknown