On the multiplicity of the hyperelliptic integrals

Let $I(t)= \oint_{\delta(t)} \omega$ be an Abelian integral, where $H=y^2-x^{n+1}+P(x)$ is a hyperelliptic polynomial of Morse type, $\delta(t)$ a horizontal family of cycles in the curves $\{H=t\}$, and $\omega$ a polynomial 1-form in the variables $x$ and $y$. We provide an upper bound on the multiplicity of $I(t)$, away from the critical values of $H$. Namely: $ord\ I(t) \leq n-1+\frac{n(n-1)}{2}$if$\deg \omega <\deg H=n+1$. The reasoning goes as follows: we consider the analytic curve parameterized by the integrals along$\delta(t)$of the$n$``Petrov'' forms of$H$(polynomial 1-forms that freely generate the module of relative cohomology of$H$), and interpret the multiplicity of$I(t)$as the order of contact of$\gamma(t)$and a linear hyperplane of$\textbf C^ n$. Using the Picard-Fuchs system satisfied by$\gamma(t)$, we establish an algebraic identity involving the wronskian determinant of the integrals of the original form$\omega$along a basis of the homology of the generic fiber of$H$. The latter wronskian is analyzed through this identity, which yields the estimate on the multiplicity of$I(t)$. Still, in some cases, related to the geometry at infinity of the curves$\{H=t\} \subseteq \textbf C^2$, the wronskian occurs to be zero identically. In this alternative we show how to adapt the argument to a system of smaller rank, and get a nontrivial wronskian. For a form$\omega$of arbitrary degree, we are led to estimating the order of contact between$\gamma(t)$and a suitable algebraic hypersurface in$\textbf C^{n+1}$. We observe that$ord I(t)$grows like an affine function with respect to$\deg \omega$.Comment: 18 page

Combustion of nickel hyperaccumulator plants investigated by experimental and thermodynamic approaches

This work was undertaken to determine whether thermodynamic calculations can predict the amount and composition of ash produced by combustion of nickel hyperaccumulator (HA) plants in the context of agromining. To this end, three HA plants containing about 1 wt% of nickel were submitted to isothermal combustion at 550, 815, 900 °C and the solid residues were characterized by complementary techniques (TGA, XRD, ICP-OES, ion chromatography, SEM-EDX), while thermodynamic calculations were performed with the FactSage software using the dry biomass composition as input. We present an in-depth evaluation of inorganics behavior based on the combination and comparison of experimental data and calculations: effect of temperature on ash yield, nature of crystallized phases, ash elemental compo­sition and inorganics volatilization. Our work confirms that equilibrium calculation is a powerful method to evaluate the behavior of inorganic elements during thermal treatment of biomass, despite some lacks in the databases. For the nickel HA plants, an innovative result is that, after combustion, nickel is always in the form of NiO particles, that can mix with MgO to form (Ni,Mg)O solid solutions. These results have direct implications for under­standing the combustion process and for better design of the following leaching step aiming at Ni recovery

How to Compute Worst-Case Execution Time by Optimization Modulo Theory and a Clever Encoding of Program Semantics

International audienceIn systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs

Protein retention in the endoplasmic reticulum rescues Aβ toxicity in Drosophila

Amyloid β (Aβ) accumulation is a hallmark of Alzheimer's disease. In adult Drosophila brains, human Aβ overexpression harms climbing and lifespan. It's uncertain whether Aβ is intrinsically toxic or activates downstream neurodegeneration pathways. Our study uncovers a novel protective role against Aβ toxicity: intra-endoplasmic reticulum (ER) protein accumulation with a focus on laminin and collagen subunits. Despite high Aβ, laminin B1 (LanB1) overexpression robustly counters toxicity, suggesting a potential Aβ resistance mechanism. Other laminin subunits and collagen IV also alleviate Aβ toxicity; combining them with LanB1 augments the effect. Imaging reveals ER retention of LanB1 without altering Aβ secretion. LanB1's rescue function operates independently of the IRE1α/XBP1 ER stress response. ER-targeted GFP overexpression also mitigates Aβ toxicity, highlighting broader ER protein retention advantages. Proof-of-principle tests in murine hippocampal slices using mouse Lamb1 demonstrate ER retention in transduced cells, indicating a conserved mechanism. Though ER protein retention generally harms, it could paradoxically counter neuronal Aβ toxicity, offering a new therapeutic avenue for Alzheimer's disease

LONG TERM CLASSICAL METHODS FOR THE PRESERVATION OF XANTHAN GUM-PRODUCING - Xanthomonas arboricola pathovar pruni STRAINS

The maintenance of viable and stable Xanthomonas cells is crucial for the xanthan reliable research and industrial production. The method, storage and recovery conditions should preserve both viability and phenotypical and genotypical features. Here, the effectiveness classical methods on the long-term preservation of different Xanthomonas arboricola pv pruni strains was to determine. Strains were preserved by monthly sub-culturing in solid medium and lyophilization. After 12 years the viability of the strains, was assessed, as well as their productive capacity and the viscosity of the xanthan gum produced by these strains kept by lyophilization and sub-culturing. Among the lyophilized strains, only those stored at -18°C were viable after 12 years. The productive capacity of the strains were poorly affected by lyophilization, the passage of the cultures into a solid nutrition medium being sufficient for them to return to their normal metabolism. The viscosity of the synthesized xanthan gum was method-dependent and higher for the lyophilized strains. The work and its findings are new and original because a work on this topic has never been published before. The results obtained allow the breaking of paradigms regarding the preservation of Xanthomonas.A manutenção de células de Xanthomonas viáveis e estáveis é crucial para se obter uma pesquisa confiável e para a produção de xantana industrial. O método, o armazenamento e as condições de recuperação devem preservar tanto a viabilidade quanto as características fenotípicas e genotípicas. O objetivo do estudo foi determinar a eficácia dos métodos clássicos na preservação a longo prazo de diferentes cepas de Xanthomonas arboricola patovar pruni. As cepas foram preservadas por subcultivo mensal em meio sólido e liofilização. Após 12 anos, avaliou-se a viabilidade das linhagens, bem como a capacidade produtiva e a viscosidade da goma xantana produzida por essas linhagens mantidas por liofilização e subcultivo. Entre as cepas liofilizadas, somente foram viáveis, após 12 anos, as armazenadas a -18 °C. A capacidade produtiva das cepas foi pouco afetada pela liofilização, sendo suficiente a passagem das culturas para um meio de cultivo sólido para que elas voltassem ao seu metabolismo normal. A viscosidade da goma xantana sintetizada foi dependente do método e maior para as cepas liofilizadas. O estudo e suas descobertas são novos e originais porque um trabalho sobre este tópico nunca foi publicado antes. Os resultados obtidos permitem quebrar paradigmas quanto à preservação de Xanthomonas

Stepwise Development of MAIT Cells in Mouse and Human

Mucosal-associated invariant T (MAIT) cells display two evolutionarily conserved features: an invariant T cell receptor (TCR)α (iTCRα) chain and restriction by the nonpolymorphic class Ib major histocompatibility complex (MHC) molecule, MHC-related molecule 1 (MR1). MR1 expression on thymus epithelial cells is not necessary for MAIT cell development but their accumulation in the gut requires MR1 expressing B cells and commensal flora. MAIT cell development is poorly known, as these cells have not been found in the thymus so far. Herein, complementary human and mouse experiments using an anti-humanVα7.2 antibody and MAIT cell-specific iTCRα and TCRβ transgenic mice in different genetic backgrounds show that MAIT cell development is a stepwise process, with an intra-thymic selection followed by peripheral expansion. Mouse MAIT cells are selected in an MR1-dependent manner both in fetal thymic organ culture and in double iTCRα and TCRβ transgenic RAG knockout mice. In the latter mice, MAIT cells do not expand in the periphery unless B cells are added back by adoptive transfer, showing that B cells are not required for the initial thymic selection step but for the peripheral accumulation. In humans, contrary to natural killer T (NKT) cells, MAIT cells display a naïve phenotype in the thymus as well as in cord blood where they are in low numbers. After birth, MAIT cells acquire a memory phenotype and expand dramatically, up to 1%–4% of blood T cells. Finally, in contrast with NKT cells, human MAIT cell development is independent of the molecular adaptor SAP. Interestingly, mouse MAIT cells display a naïve phenotype and do not express the ZBTB16 transcription factor, which, in contrast, is expressed by NKT cells and the memory human MAIT cells found in the periphery after birth. In conclusion, MAIT cells are selected by MR1 in the thymus on a non-B non-T hematopoietic cell, and acquire a memory phenotype and expand in the periphery in a process dependent both upon B cells and the bacterial flora. Thus, their development follows a unique pattern at the crossroad of NKT and γδ T cells

Protein retention in the endoplasmic reticulum rescues Aβ toxicity in Drosophila

Amyloid β (Aβ) accumulation is a hallmark of Alzheimer’s disease. In adult Drosophila brains, human Aβ overexpression harms climbing and lifespan. It’s uncertain whether Aβ is intrinsically toxic or activates downstream neurodegeneration pathways. Our study uncovers a novel protective role against Aβ toxicity: intra-endoplasmic reticulum (ER) protein accumulation with a focus on laminin and collagen subunits. Despite high Aβ, laminin B1 (LanB1) overexpression robustly counters toxicity, suggesting a potential Aβ resistance mechanism. Other laminin subunits and collagen IV also alleviate Aβ toxicity; combining them with LanB1 augments the effect. Imaging reveals ER retention of LanB1 without altering Aβ secretion. LanB1’s rescue function operates independently of the IRE1α/XBP1 ER stress response. ER-targeted GFP overexpression also mitigates Aβ toxicity, highlighting broader ER protein retention advantages. Proof-of-principle tests in murine hippocampal slices using mouse Lamb1 demonstrate ER retention in transduced cells, indicating a conserved mechanism. Though ER protein retention generally harms, it could paradoxically counter neuronal Aβ toxicity, offering a new therapeutic avenue for Alzheimer’s disease