Hodge polynomials of some moduli spaces of Coherent Systems

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which $(n,d,k)=(3,d,1)$ and $d$ is even, obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of coherent systems on algebraic curves and their Hodge--Poincar\'e polynomials". The paper has been substantially shorten. Theorem 8.20 has been revised and corrected. Final version accepted for publication in International Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0407523 by other author

Curve counting via stable pairs in the derived category

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page

Comparison of systemic, compartmental and CFD modelling approaches: Application to the simulation of a biological reactor of wastewater treatment

Nowadays there exist two main approaches to simulate the hydrodynamics of chemical reactors: the systemic method, based on the description of a given reactor as a limited number of elementary reactors, and the more theoretical CFD approach, based on the resolution of the Navier-Stokes equations in a large number of computing cells. This work describes another recent modelling approach based on the description of the reactor as a network of both structural and functional compartments. The complete methodology to build such a model, using CFD simulations, tracer experiments, mass transfer and chemical processes, is described. The simulation results with such a model are then compared to those obtained with the systemic and CFD models in the case of a biological gas-liquid reactor for wastewater treatment, involving oxygen transfer and complex biological kinetics. This work shows that the compartmental model gives results very similar to those of a full CFD simulation but with lower calculation time (10 times in most cases) with the advantage of remaining almost as simple to manipulate as the systemic approach

Characterization of nanomedicines’ surface coverage using molecular probes and capillary electrophoresis

International audienceA faithful characterization of nanomedicine (NM) is needed for a better understanding of their in vivo outcomes. Size and surface charge are studied with well-established methods. However, other relevant parameters for the understanding of NM behavior in vivo remain largely inaccessible. For instance, the reactive surface of nanomedicines, which are often grafted with macromolecules to decrease their recognition by the immune system, is excluded from a systematic characterization. Yet, it is known that a subtle modification of NMs' surface characteristics (grafting density, molecular architecture and conformation of macromolecules) is at the root of major changes in the presence of biological components. In this work, a method that investigates the steric hindrance properties of the NMs’ surface coverage based on its capacity to exclude or allow adsorption of well-defined proteins was developed based on capillary electrophoresis. A series of proteins with different molecular weights (MW) were used as molecular probes to screen their adsorption behavior on nanoparticles bearing different molecular architectures at their surface. This novel strategy evaluating to some degree a functionality of NMs can bring additional information about their shell property and might allow for a better perception of their behavior in the presence of biological components. The developed method could discriminate nanoparticles with a high surface coverage excluding high MW proteins from nanoparticles with a low surface coverage that allowed high MW proteins to adsorb on their surface. The method has the potential for further standardization and automation for a routine use. It can be applied in quality control of NMs and to investigate interactions between proteins and NM in different situations

Selection of oligonucleotides for whole-genome microarrays with semi-automatic update

Summary: Oligonucleotide microarray probes are designed to match specific transcripts present in databases that are regularly updated. As a consequence probes should be checked every new database release. We thus developed an informatics tool allowing the semi-automatic update of probe collections of long oligonucleotides and applied it to the mouse RefSeq database

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

Accounting for meteorological biases in simulated plumes using smarter metrics

In the next few years, numerous satellites with high-resolution instruments dedicated to the imaging of atmospheric gaseous compounds will be launched, to finely monitor emissions of greenhouse gases and pollutants. Processing the resulting images of plumes from cities and industrial plants to infer the emissions of these sources can be challenging. In particular traditional atmospheric inversion techniques, relying on objective comparisons to simulations with atmospheric chemistry transport models, may poorly fit the observed plume due to modelling errors rather than due to uncertainties in the emissions. The present article discusses how these images can be adequately compared to simulated concentrations to limit the weight of modelling errors due to the meteorology used to analyse the images. For such comparisons, the usual pixel-wise ℒ2 norm may not be suitable, since it does not linearly penalise a displacement between two identical plumes. By definition, such a metric considers a displacement as an accumulation of significant local amplitude discrepancies. This is the so-called double penalty issue. To avoid this issue, we propose three solutions: (i) compensate for position error, due to a displacement, before the local comparison; (ii) use non-local metrics of density distribution comparison; and (iii) use a combination of the first two solutions. All the metrics are evaluated using first a catalogue of analytical plumes and then more realistic plumes simulated with a mesoscale Eulerian atmospheric transport model, with an emphasis on the sensitivity of the metrics to position error and the concentration values within the plumes. As expected, the metrics with the upstream correction are found to be less sensitive to position error in both analytical and realistic conditions. Furthermore, in realistic cases, we evaluate the weight of changes in the norm and the direction of the four-dimensional wind fields in our metric values. This comparison highlights the link between differences in the synoptic-scale winds direction and position error. Hence the contribution of the latter to our new metrics is reduced, thus limiting misinterpretation. Furthermore, the new metrics also avoid the double penalty issue.</p

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

Comparative analysis of the fecal microbiota from different species of domesticated and wild suids

This study was supported by the Ministry of Economy and Competitiveness (MINECO) from the Spanish Government (grant number AGL2016-78160-C2-1-R). The authors are also grateful to the Centres de Recerca de Catalunya (CERCA) Programme and Global Alliance for Research on African swine fever (GARA). The authors thank Frederic Paboeuf and Audrey Fougeroux for providing SPF and domestic pig samples.Most of the microorganisms living in a symbiotic relationship in different animal body sites (microbiota) reside in the gastrointestinal tract (GIT). Several studies have shown that the microbiota is involved in host susceptibilities to pathogens. The fecal microbiota of domestic and wild suids was analyzed. Bacterial communities were determined from feces obtained from domestic pigs (Sus scrofa) raised under different conditions: specific-pathogen-free (SPF) pigs and domestic pigs from the same bred, and indigenous domestic pigs from a backyard farm in Kenya. Secondly, the fecal microbiota composition of the African swine fever (ASF) resistant warthogs (Phacochoerus africanus) from Africa and a European zoo was determined. African swine fever (ASF) is a devastating disease for domestic pigs. African animals showed the highest microbial diversity while the SPF pigs the lowest. Analysis of the core microbiota from warthogs (resistant to ASF) and pigs (susceptible to ASF) showed 45 shared OTUs, while 6 OTUs were exclusively present in resistant animals. These six OTUs were members of the Moraxellaceae family, Pseudomonadales order and Paludibacter, Anaeroplasma, Petrimonas, and Moraxella genera. Further characterization of these microbial communities should be performed to determine the potential involvement in ASF resistance