Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Detailed studies of the binding mechanism of the Sinorhizobium meliloti transcriptional activator ExpG to DNA

Baumgarth B, Bartels FW, Anselmetti D, Becker A, Ros R. Detailed studies of the binding mechanism of the Sinorhizobium meliloti transcriptional activator ExpG to DNA. Microbiology. 2005;151(1):259-268.The exopolysaccharide galactoglucan promotes the establishment of symbiosis between the nitrogen-fixing Gram-negative soil bacterium Sinorhizobium meliloti 2011 and its host plant alfalfa. The transcriptional regulator ExpG activates expression of galactoglucan biosynthesis genes by direct binding to the expA1, expG/expD1 and expE1 promoter regions. ExpG is a member of the MarR family of regulatory proteins. Analysis of target sequences of an ExpG(His)6 fusion protein in the exp promoter regions resulted in the identification of a binding site composed of a conserved palindromic region and two associated sequence motifs. Association and dissociation kinetics of the specific binding of ExpG(His)6 to this binding site were characterized by standard biochemical methods and by single-molecule spectroscopy based on the atomic force microscope (AFM). Dynamic force spectroscopy indicated a distinct difference in the kinetics between the wild-type binding sequence and two mutated binding sites, leading to a closer understanding of the ExpG-DNA interaction

Specific binding of the regulatory protein ExpG to promoter regions of the galactoglucan biosynthesis gene cluster of Sinorhizobium meliloti: a combined molecular biology and force spectroscopy investigation

Bartels FW, Baumgarth B, Anselmetti D, Ros R, Becker A. Specific binding of the regulatory protein ExpG to promoter regions of the galactoglucan biosynthesis gene cluster of Sinorhizobium meliloti: a combined molecular biology and force spectroscopy investigation. Journal of structural biology. 2003;143(2):145-152.Specific protein-DNA interaction is fundamental for all aspects of gene transcription. We focus on a regulatory DNA-binding protein in the Gram-negative soil bacterium Sinorhizobium meliloti 2011, which is capable of fixing molecular nitrogen in a symbiotic interaction with alfalfa plants. The ExpG protein plays a central role in regulation of the biosynthesis of the exopolysaccharide galactoglucan, which promotes the establishment of symbiosis. ExpG is a transcriptional activator of exp gene expression. We investigated the molecular mechanism of binding of ExpG to three associated target sequences in the exp gene cluster with standard biochemical methods and single molecule force spectroscopy based on the atomic force microscope (AFM). Binding of ExpG to expA1, expG-expD1, and expE1 promoter fragments in a sequence specific manner was demonstrated, and a 28 bp conserved region was found. AFM force spectroscopy experiments confirmed the specific binding of ExpG to the promoter regions, with unbinding forces ranging from 50 to 165pN in a logarithmic dependence from the loading rates of 70-79000 pN/s. Two different regimes of loading rate-dependent behaviour were identified. Thermal off-rates in the range of k off = (1.2 ± 1.0) × 10 -3 s -1 were derived from the lower loading rate regime for all promoter regions. In the upper loading rate regime, however, these fragments exhibited distinct differences which are attributed to the molecular binding mechanism

Proof of the double bubble conjecture

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.Morgan has partial support from a National Science Foundation grant. Ritoré and Ros have partial support from DGICYT research group n. PB97-0785

Scenic: A Language for Scenario Specification and Scene Generation

We propose a new probabilistic programming language for the design and analysis of perception systems, especially those based on machine learning. Specifically, we consider the problems of training a perception system to handle rare events, testing its performance under different conditions, and debugging failures. We show how a probabilistic programming language can help address these problems by specifying distributions encoding interesting types of inputs and sampling these to generate specialized training and test sets. More generally, such languages can be used for cyber-physical systems and robotics to write environment models, an essential prerequisite to any formal analysis. In this paper, we focus on systems like autonomous cars and robots, whose environment is a "scene", a configuration of physical objects and agents. We design a domain-specific language, Scenic, for describing "scenarios" that are distributions over scenes. As a probabilistic programming language, Scenic allows assigning distributions to features of the scene, as well as declaratively imposing hard and soft constraints over the scene. We develop specialized techniques for sampling from the resulting distribution, taking advantage of the structure provided by Scenic's domain-specific syntax. Finally, we apply Scenic in a case study on a convolutional neural network designed to detect cars in road images, improving its performance beyond that achieved by state-of-the-art synthetic data generation methods.Comment: 41 pages, 36 figures. Full version of a PLDI 2019 paper (extending UC Berkeley EECS Department Tech Report No. UCB/EECS-2018-8

It's a hard knock life for some: Heterogeneity in infection life history of salmonids influences parasite disease outcomes.

Heterogeneity in immunity occurs across numerous disease systems with individuals from the same population having diverse disease outcomes. Proliferative kidney disease (PKD) caused by Tetracapsuloides bryosalmonae, is a persistent parasitic disease negatively impacting both wild and farmed salmonids. Little is known of how PKD is spread or maintained within wild susceptible populations. We investigated an aspect of fish disease that has been largely overlooked, that is, the role of the host phenotypic heterogeneity in disease outcome. We examined how host susceptibility to T. bryosalmonae infection, and the disease PKD, varied across different infection life-history stages and how it differs between naïve, re-infected and persistently infected hosts. We investigated the response to parasite exposure in host phenotypes with (a) different ages and (b) heterogeneous infection life histories. Among (a) the age phenotypes were young-of-the-year (YOY) fish and juvenile 1+ fish (fish older than one) and, for (b) juvenile 1+ infection survivors were either re-exposed or not re- exposed to the parasite and response phenotypes were assigned post-hoc dependant on infection status. In fish not re-exposed this included fish that cleared infection (CI) or had a persistent infection (PI). In fish re-exposed these included fish that were re-infected (RI), or re-exposed and uninfected (RCI). We assessed both parasite-centric (infection prevalence, parasite burden, malacospore transmission) and host-centric parameters (growth rates, disease severity, infection tolerance and the immune response). In (a), YOY fish, parasite success and disease severity were greater and differences in the immune response occurred, demonstrating an ontogenetic decline of susceptibility in older fish. In (b), in PI and RI fish, parasite success and disease severity were comparable. However, expression of several adaptive immunity markers was greater in RI fish, indicating concomitant immunity, as re-exposure did not intensify infection. We demonstrate the relevance of heterogeneity in infection life history on disease outcome and describe several distinctive features of immune ontogeny and protective immunity in this model not previously reported. The relevance of such themes on a population level requires greater research in many aquatic disease systems to generate clearer framework for understanding the spread and maintenance of aquatic pathogens

Expression of proadrenomedullin derived peptides in the mammalian pituitary: co-localization of follicle stimulating hormone and proadrenomedullin N-20 terminal peptide-like peptide in the same secretory granules of the gonadotropes

Expression of proadrenomedullin-derived peptides in the rat, cow and human pituitary was studied by a variety of techniques. Immunocytochemical detection showed a widespread expression of adrenomedullin peptide in the adenohypophysis and the neural lobe, with low expression in the intermediate pituitary. Proadrenomedullin N-20 terminal peptide (PAMP)-immunoreactivity was also present in the anterior pituitary but showed a more marked heterogeneous distribution, with cells going from very strong to negative immunostaining. Lower levels of PAMP were found in the neural lobe. Interestingly, the distribution of adrenomedullin and PAMP immunoreactivity in the anterior pituitary did not completely overlap. In the present study, we concentrated our efforts to determine which cell type of the adenohypophysis expresses PAMP. Paraffin and semithin serial sections immunostained for PAMP and the classical pituitary hormones revealed that a subpopulation of the gonadotropes expresses high levels of PAMP-immunoreactive material. Ultrastructural analysis clearly showed PAMP-immunoreactivity in the follicle stimulating hormone (FSH)-containing large secretory granules of the gonadotropes, suggesting simultaneous secretion of PAMP and FSH by this cell type. Three mouse adenohypophysis-derived cell lines (AtT20, GH3, and alphaT3-1 derived from corticotropes, lacto/somatotropes and gonadotropes, respectively) were also analysed and showed expression of both proadrenomedullin-derived peptides and their mRNA. Functional studies in these three cell lines showed that neither adrenomedullin nor PAMP was able to stimulate cAMP production in our experimental conditions. Taken together, our results support that proadrenomedullin derived peptides are expressed in the pituitary in cell-specific and not overlapping patterns, that could be explained by differences in postranslational processing. Our data showing costorage of PAMP and FSH in the same secretory granules open a way by which PAMP could be involved in the control of reproductive physiology in a coordinated manner with FSH