Invariant measures for Burgers equation with stochastic forcing

In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts all other solutions with the same forcing. This is done by studying the so-called one-sided minimizers. We also give a detailed description of the structure and regularity properties for the stationary solutions. In particular, we prove, under some non-degeneracy conditions on the forcing, that almost surely there is a unique main shock and a unique global minimizer for the stationary solutions. Furthermore the global minimizer is a hyperbolic trajectory of the underlying system of characteristics.Comment: 84 pages, published version, abstract added in migratio

Breaking the silence of the 500-year-old smiling garden of everlasting flowers: The En Tibi book herbarium

We reveal the enigmatic origin of one of the earliest surviving botanical collections. The 16th-century Italian En Tibi herbarium is a large, luxurious book with c. 500 dried plants, made in the Renaissance scholarly circles that developed botany as a distinct discipline. Its Latin inscription, translated as “Here for you a smiling garden of everlasting flowers”, suggests that this herbarium was a gift for a patron of the emerging botanical science. We follow an integrative approach that includes a botanical similarity estimation of the En Tibi with contemporary herbaria (Aldrovandi, Cesalpino, “Cibo”, Merini, Estense) and analysis of the book’s watermark, paper, binding, handwriting, Latin inscription and the morphology and DNA of hairs mounted under specimens. Rejecting the previous origin hypothesis (Ferrara, 1542–1544), we show that the En Tibi was made in Bologna around 1558. We attribute the En Tibi herbarium to Francesco Petrollini, a neglected 16th-century botanist, to whom also belongs, as clarified herein, the controversial “Erbario Cibo” kept in Rome. The En Tibi was probably a work on commission for Petrollini, who provided the plant material for the book. Other people were apparently involved in the compilation and offering of this precious gift to a yet unknown person, possibly the Habsburg Emperor Ferdinand I. The En Tibi herbarium is a Renaissance masterpiece of art and science, representing the quest for truth in herbal medicine and botany. Our multidisciplinary approach can serve as a guideline for deciphering other anonymous herbaria, kept safely “hidden” in treasure rooms of universities, libraries and museums

PP/PP-HI/silica nanocomposites for HVDC cable insulation: Are silica clusters beneficial for space charge accumulation?

New potential High Voltage Direct Current (HVDC) cable insulation materials based on nanocomposites are developed in this study. The nanocomposites are produced by blending of polypropylene (PP), propylene-ethylene copolymer (PP–HI) and a modified fumed silica (A-silica) in a concentration of 1 and 2 wt %. The A-silica is successfully modified with (3-aminopropyl)triethoxysilane (APTES) via a solvent-free method, as proven by infrared spectroscopy, thermogravimetry and transmission electron microscope mapping. A-silica in the polymer matrix acts as a nucleating agent resulting in an increase of the crystallization temperature of the polymers and a smaller crystal size. Moreover, the silica addition modified the crystals morphology of the unfilled PP/PP-HI blend. The composite containing A-silica with 2 wt% contains bigger-size silica clusters than the composite filled with 1 wt%. The composite with the higher A-silica concentration shows lower space charge accumulation and a lower charge current value. Besides, much deeper traps and lower trap density are observed in the composite with 2 wt% A-silica addition compared to the one with a lower concentration. Surprisingly, the presence of silica clusters with dimensions of more than 200 nm exhibit a positive effect on reducing the space charge accumulation. However, the real cause of this improvement might be due to change of the electron distribution stemming from the amine-amine hydrogen bond formation, or the change of the chain mobility due to the presence of occluded polymer macromolecules constrained inside the high structure silica clusters. Both phenomena may lead to a higher energetic barrier of charge de-trapping, thus increasing the depth of the charge traps

Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected], [email protected], [email protected]

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Inverse Correlation between Promoter Strength and Excision Activity in Class 1 Integrons

Class 1 integrons are widespread genetic elements that allow bacteria to capture and express gene cassettes that are usually promoterless. These integrons play a major role in the dissemination of antibiotic resistance among Gram-negative bacteria. They typically consist of a gene (intI) encoding an integrase (that catalyzes the gene cassette movement by site-specific recombination), a recombination site (attI1), and a promoter (Pc) responsible for the expression of inserted gene cassettes. The Pc promoter can occasionally be combined with a second promoter designated P2, and several Pc variants with different strengths have been described, although their relative distribution is not known. The Pc promoter in class 1 integrons is located within the intI1 coding sequence. The Pc polymorphism affects the amino acid sequence of IntI1 and the effect of this feature on the integrase recombination activity has not previously been investigated. We therefore conducted an extensive in silico study of class 1 integron sequences in order to assess the distribution of Pc variants. We also measured these promoters' strength by means of transcriptional reporter gene fusion experiments and estimated the excision and integration activities of the different IntI1 variants. We found that there are currently 13 Pc variants, leading to 10 IntI1 variants, that have a highly uneven distribution. There are five main Pc-P2 combinations, corresponding to five promoter strengths, and three main integrases displaying similar integration activity but very different excision efficiency. Promoter strength correlates with integrase excision activity: the weaker the promoter, the stronger the integrase. The tight relationship between the aptitude of class 1 integrons to recombine cassettes and express gene cassettes may be a key to understanding the short-term evolution of integrons. Dissemination of integron-driven drug resistance is therefore more complex than previously thought

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

The influence of the accessory genome on bacterial pathogen evolution

Bacterial pathogens exhibit significant variation in their genomic content of virulence factors. This reflects the abundance of strategies pathogens evolved to infect host organisms by suppressing host immunity. Molecular arms-races have been a strong driving force for the evolution of pathogenicity, with pathogens often encoding overlapping or redundant functions, such as type III protein secretion effectors and hosts encoding ever more sophisticated immune systems. The pathogens’ frequent exposure to other microbes, either in their host or in the environment, provides opportunities for the acquisition or interchange of mobile genetic elements. These DNA elements accessorise the core genome and can play major roles in shaping genome structure and altering the complement of virulence factors. Here, we review the different mobile genetic elements focusing on the more recent discoveries and highlighting their role in shaping bacterial pathogen evolution

A mathematical model of the metabolic and perfusion effects on cortical spreading depression

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarization, CSD also involves significant changes in perfusion and metabolism -- aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium--ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD -- vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization -- found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.Comment: 17 pages including 9 figures, accepted by PLoS On

Amino Acid Metabolic Origin as an Evolutionary Influence on Protein Sequence in Yeast

The metabolic cycle of Saccharomyces cerevisiae consists of alternating oxidative (respiration) and reductive (glycolysis) energy-yielding reactions. The intracellular concentrations of amino acid precursors generated by these reactions oscillate accordingly, attaining maximal concentration during the middle of their respective yeast metabolic cycle phases. Typically, the amino acids themselves are most abundant at the end of their precursor’s phase. We show that this metabolic cycling has likely biased the amino acid composition of proteins across the S. cerevisiae genome. In particular, we observed that the metabolic source of amino acids is the single most important source of variation in the amino acid compositions of functionally related proteins and that this signal appears only in (facultative) organisms using both oxidative and reductive metabolism. Periodically expressed proteins are enriched for amino acids generated in the preceding phase of the metabolic cycle. Proteins expressed during the oxidative phase contain more glycolysis-derived amino acids, whereas proteins expressed during the reductive phase contain more respiration-derived amino acids. Rare amino acids (e.g., tryptophan) are greatly overrepresented or underrepresented, relative to the proteomic average, in periodically expressed proteins, whereas common amino acids vary by a few percent. Genome-wide, we infer that 20,000 to 60,000 residues have been modified by this previously unappreciated pressure. This trend is strongest in ancient proteins, suggesting that oscillating endogenous amino acid availability exerted genome-wide selective pressure on protein sequences across evolutionary time