Effective constructions in plethysms and Weintraub's conjecture

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power

Log-concavity and lower bounds for arithmetic circuits

One question that we investigate in this paper is, how can we build log-concave polynomials using sparse polynomials as building blocks? More precisely, let $f = \sum\_{i = 0}^d a\_i X^i \in \mathbb{R}^+[X]$ be a polynomial satisfying the log-concavity condition a\_i^2 \textgreater{} \tau a\_{i-1}a\_{i+1} for every $i \in \{1,\ldots,d-1\},$ where \tau \textgreater{} 0. Whenever $f$ can be written under the form $f = \sum\_{i = 1}^k \prod\_{j = 1}^m f\_{i,j}$ where the polynomials $f\_{i,j}$ have at most $t$ monomials, it is clear that $d \leq k t^m$. Assuming that the $f\_{i,j}$ have only non-negative coefficients, we improve this degree bound to $d = \mathcal O(k m^{2/3} t^{2m/3} {\rm log^{2/3}}(kt))$ if \tau \textgreater{} 1, and to $d \leq kmt$ if $\tau = d^{2d}$. This investigation has a complexity-theoretic motivation: we show that a suitable strengthening of the above results would imply a separation of the algebraic complexity classes VP and VNP. As they currently stand, these results are strong enough to provide a new example of a family of polynomials in VNP which cannot be computed by monotone arithmetic circuits of polynomial size

Negative Energies in the Dirac equation

It is easy to check that both algebraic equation Det (hat p - m) =0 and Det (hat p + m) =0 for u- and v- 4-spinors have solutions with p_0= pm E_p = pm sqrt bf p^2 +m^2. The same is true for higher-spin equations. Meanwhile, every book considers the equality p_0=E_p for both u- and v- spinors of the (1/2,0)+(0,1/2)) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both s=1/2 and higher spin particles.Comment: 8 pages, no figures. Accepted in Zeitschrift fur Naturforschun

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor improvements. 44 pages, 14 figure

Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

Hepatitis E Virus Seroprevalence among Blood Donors in Southwest Switzerland

Aim: The aim of this study was to determine the seroprevalence of Hepatitis E virus (HEV) among blood donors in southwest Switzerland.Background: HEV is recognized as a food-borne disease in industrialized countries, transmitted mainly through pork meat. Cases of transmission through blood transfusion have also been reported. Recent studies have revealed seroprevalence rates of 13.5%, 16.6% and 20.6% among blood donors in England, France and Denmark, respectively.Methods: We analyzed 550 consecutive blood donor samples collected in the region of Lausanne, canton of Vaud, Switzerland, for the presence of anti-HEV IgG, using the MP Diagnostics HEV ELISA kit. For each donor, we documented age, sex and alanine aminotransferase (ALT) value.Results: The study panel was composed of 332 men (60.4%) and 218 women (39.6%). Overall, anti-HEV IgG was found in 27 of 550 samples (4.9%). The seroprevalence was 5.4% (18/332) in men and 4.1% (9/218) in women. The presence of anti-HEV IgG was not correlated with age, gender or ALT values. However, we observed a peak in seroprevalence of 5.3% in individuals aged 51 to 70 years old.Conclusions: Compared with other European countries, HEV seroprevalence among blood donors in southwest Switzerland is low. The low seroprevalence may be explained by the sensitivity of commercial tests used and/or the strict regulation of animal and meat imports. Data regarding HEV prevalence in Swiss livestock are lacking and merit exploration

High specificity of line-immunoassay based algorithms for recent HIV-1 infection independent of viral subtype and stage of disease

ABSTRACT: BACKGROUND: Serologic testing algorithms for recent HIV seroconversion (STARHS) provide important information for HIV surveillance. We have shown that a patient's antibody reaction in a confirmatory line immunoassay (INNO-LIATM HIV I/II Score, Innogenetics) provides information on the duration of infection. Here, we sought to further investigate the diagnostic specificity of various Inno-Lia algorithms and to identify factors affecting it. METHODS: Plasma samples of 714 selected patients of the Swiss HIV Cohort Study infected for longer than 12 months and representing all viral clades and stages of chronic HIV-1 infection were tested blindly by Inno-Lia and classified as either incident (up to 12 m) or older infection by 24 different algorithms. Of the total, 524 patients received HAART, 308 had HIV-1 RNA below 50 copies/mL, and 620 were infected by a HIV-1 non-B clade. Using logistic regression analysis we evaluated factors that might affect the specificity of these algorithms. RESULTS: HIV-1 RNA <50 copies/mL was associated with significantly lower reactivity to all five HIV-1 antigens of the Inno-Lia and impaired specificity of most algorithms. Among 412 patients either untreated or with HIV-1 RNA ≥50 copies/mL despite HAART, the median specificity of the algorithms was 96.5% (range 92.0-100%). The only factor that significantly promoted false-incident results in this group was age, with false-incident results increasing by a few percent per additional year. HIV-1 clade, HIV-1 RNA, CD4 percentage, sex, disease stage, and testing modalities exhibited no significance. Results were similar among 190 untreated patients. CONCLUSIONS: The specificity of most Inno-Lia algorithms was high and not affected by HIV-1 variability, advanced disease and other factors promoting false-recent results in other STARHS. Specificity should be good in any group of untreated HIV-1 patients

Effect of Cavtratin, a Caveolin-1 Scaffolding Domain Peptide, on Oligodendroglial Signaling Cascades

Caveolin and caveolin containing rafts are involved in the signaling of growth factors in various cell types. Previous reports of our lab indicated a co-localization of caveolin and the high affinity nerve growth factor (NGF) receptor tyrosine kinase A (TrkA). Mutual effects have been observed among which a caveolin-1 knock-down resulted in an impairment of the NGF signaling cascade rather than in an increase of activity as expected from other growth factor reports. On the other hand, an over-expression of caveolin-1 impaired the NGF stimulated activity of p42/44 mitogen activated protein kinases (MAPK). In this study, we used a caveolin-1 scaffolding domain (CSD) peptide (cavtratin) of which an inhibitory effect on growth factor receptors was reported. Our data showed that cavtratin suppresses the NGF-induced phosphorylation of TrkA as well as the activation of MAPK in porcine oligodendrocytes significantly