Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Subfactors of index less than 5, part 3: quadruple points

One major obstacle in extending the classification of small index subfactors beyond 3+\sqrt{3} is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the "weeds" Q and Q' from Part 1 (arXiv:1007.1730)). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed Q' immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds Q and Q'. Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections.Comment: 21 page

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for Rational Mechanics and Analysis.} The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-017-1131-

Character D-modules via Drinfeld center of Harish-Chandra bimodules

The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining functor (Radon transform) by a result of Beilinson and Ginzburg (Represent. Theory 3, 1–31, 1999). Exactness property of the long intertwining functor on a cell subquotient of the Harish-Chandra bimodules category shows that the truncated convolution category of Lusztig (Adv. Math. 129, 85–98, 1997) can be realized as a subquotient of the category of Harish-Chandra bimodules. Together with the description of the truncated convolution category (Bezrukavnikov et al. in Isr. J. Math. 170, 207–234, 2009) this allows us to derive (under a mild technical assumption) a classification of irreducible character sheaves over ℂ obtained by Lusztig by a different method. We also give a simple description for the top cohomology of convolution of character sheaves over ℂ in a given cell modulo smaller cells and relate the so-called Harish-Chandra functor to Verdier specialization in the De Concini–Procesi compactification.United States. Defense Advanced Research Projects Agency (grant HR0011-04-1-0031)National Science Foundation (U.S.) (grant DMS-0625234)National Science Foundation (U.S.) (grant DMS-0854764)AG Laboratory HSE (RF government grant, ag. 11.G34.31.0023)Russian Foundation for Basic Research (grant 09-01-00242)Ministry of Education and Science of the Russian Federation (grant No. 2010-1.3.1-111-017-029)Science Foundation of the NRU-HSE (award 11-09-0033)National Science Foundation (U.S.) (grant DMS-0602263

Hepatocellular adenoma: what is new in 2008

Patients (85%) with hepatocellular adenoma (HCA) are women taking oral contraceptives. They can be divided into four subgroups according to their genotype/phenotype features. (1) Hepatocyte nuclear factor 1α (HNF1α) biallelic somatic mutations are observed in 35% of the HCA cases. It occurs in almost all cases in women. HNF1α-mutated HCA are most of the time, highly steatotic, with a lack of expression of liver fatty acid binding protein (LFABP) in immunohistochemistry analyses. Adenomatosis is frequently detected in this context. An HNF1α germline mutation is observed in less than 5% of HCA cases and can be associated with MODY 3 diabetes. (2) An activating β-catenin mutation was found in 10% of HCA. These β-catenin activated HCAs are observed in men and women, and specific risk factors, such as male hormone administration or glycogenosis, are associated with their development. Immunohistochemistry studies show that these HCAs overexpress β-catenin (nuclear and cytoplasmic) and glutamine synthetase. This group of tumours has a higher risk of malignant transformation into hepatocellular carcinoma. (3) Inflammatory HCAs are observed in 40% of the cases, and they are most frequent in women but are also found in men. Lesions are characterised by inflammatory infiltrates, dystrophic arteries, sinusoidal dilatation and ductular reaction. They express serum amyloid A and C-reactive protein. In this group, GGT is frequently elevated, with a biological inflammatory syndrome present. Also, there are more overweight patients in this group. An additional 10% of inflammatory HCAs express β-catenin, and are also at risk of malignant transformation. (4) Currently, less than 10% of HCAs are unclassified. It is hoped that in the near future it will be possible with clinical, biological and imaging data to predict in which of the 2 major groups (HNF1α-mutated HCA and inflammatory HCA) the patient belongs and to propose better guidelines in terms of surveillance and treatment

In Vivo Systematic Analysis of Candida albicans Zn2-Cys6 Transcription Factors Mutants for Mice Organ Colonization

The incidence of fungal infections in immuno-compromised patients increased considerably over the last 30 years. New treatments are therefore needed against pathogenic fungi. With Candida albicans as a model, study of host-fungal pathogen interactions might reveal new sources of therapies. Transcription factors (TF) are of interest since they integrate signals from the host environment and participate in an adapted microbial response. TFs of the Zn2-Cys6 class are specific to fungi and are important regulators of fungal metabolism. This work analyzed the importance of the C. albicans Zn2-Cys6 TF for mice kidney colonization. For this purpose, 77 Zn2-Cys6 TF mutants were screened in a systemic mice model of infection by pools of 10 mutants. We developed a simple barcoding strategy to specifically detect each mutant DNA from mice kidney by quantitative PCR. Among the 77 TF mutant strains tested, eight showed a decreased colonization including mutants for orf19.3405, orf19.255, orf19.5133, RGT1, UGA3, orf19.6182, SEF1 and orf19.2646, and four an increased colonization including mutants for orf19.4166, ZFU2, orf19.1685 and UPC2 as compared to the isogenic wild type strain. Our approach was validated by comparable results obtained with the same animal model using a single mutant and the revertant for an ORF (orf19.2646) with still unknown functions. In an attempt to identify putative involvement of such TFs in already known C. albicans virulence mechanisms, we determined their in vitro susceptibility to pH, heat and oxidative stresses, as well as ability to produce hyphae and invade agar. A poor correlation was found between in vitro and in vivo assays, thus suggesting that TFs needed for mice kidney colonization may involve still unknown mechanisms. This large-scale analysis of mice organ colonization by C. albicans can now be extended to other mutant libraries since our in vivo screening strategy can be adapted to any preexisting mutants

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

The FEBEX benchmark test: case definition and comparison of modelling approaches

The FEBEX (Full-scale Engineered Barriers Experiment in Crystalline Host Rock) ‘‘in situ’’ test was installed at the Grimsel Test Site underground laboratory (Switzerland) and is a near-to-real scale simulation of the Spanish reference concept of deep geological storage in crystalline host rock. A modelling exercise, aimed at predicting field behaviour, was divided in three parts. In Part A, predictions for both the total water inflow to the tunnel as well as the water pressure changes induced by the boring of the tunnel were required. In Part B, predictions for local field variables, such as temperature, relative humidity, stresses and displacements at selected points in the bentonite barrier, and global variables, such as the total input power to the heaters were required. In Part C, predictions for temperature, stresses, water pressures and displacements in selected points of the host rock were required. Ten Modelling Teams from Europe, North America and Japan were involved in the analysis of the test. Differences among approaches may be found in the constitutive models used, in the simplifications made to the balance equations and in the geometric symmetries considered. Several aspects are addressed in the paper: the basic THM physical phenomena which dominate the test response are discussed, a comparison of different modelling results with actual measurements is presented and a discussion is given to explain the performance of the various predictions.Peer Reviewe

Asthma Pregnancy Alters Postnatal Development of Chromaffin Cells in the Rat Adrenal Medulla

Background: Adrenal neuroendocrine plays an important role in asthma. The activity of the sympathoadrenal system could be altered by early life events. The effects of maternal asthma during pregnancy on the adrenal medulla of offspring remain unknown. Methodology/Principal Findings: This study aims to explore the influence of maternal asthma during pregnancy on the development and function of adrenal medulla in offspring from postnatal day 3 (P3) to postnatal day 60 (P60). Asthmatic pregnant rats (AP), nerve growth factor (NGF)-treated pregnant rats (NP) and NGF antibody-treated pregnant rats (ANP) were sensitized and challenged with ovalbumin (OVA); NP and ANP were treated with NGF and NGF antibody respectively. Offspring rats from the maternal group were divided into four groups: offspring from control pregnant rats (OCP), offspring from AP (OAP), offspring from NP (ONP), and offspring from ANP (OANP). The expressions of phenylethanolamine N-methyltransferase (PNMT) protein in adrenal medulla were analyzed. The concentrations of epinephrine (EPI), corticosterone and NGF in serum were measured. Adrenal medulla chromaffin cells (AMCC) were prone to differentiate into sympathetic nerve cells in OAP and ONP. Both EPI and PNMT were decreased in OAP from P3 to P14, and then reached normal level gradually from P30 to P60, which were lower from birth to adulthood in ONP. Corticosterone concentration increased significantly in OAP and ONP. Conclusion/Significance: Asthma pregnancy may promote AMCC to differentiate into sympathetic neurons in offspring rats and inhibit the synthesis of EPI, resulting in dysfunction of bronchial relaxation