Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.Comment: 10 pages, Latex , uses revtex. 2 figures not included (hard copies available on request

A Metabolomic Signature of Acute Caloric Restriction

Context: The experimental paradigm of acute caloric restriction followed by refeeding can be used to study the homeostatic mechanisms that regulate energy homeostasis, which are relevant to understanding the adaptive response to weight loss. Objective: Metabolomics, the measurement of hundreds of small molecule metabolites, their precursors, derivatives, and degradation products, has emerged as a useful tool for the study of physiology and disease and was used here to study the metabolic response to acute caloric restriction. Participants, Design and Setting: We used four ultra high performance liquid chromatography-tandem mass spectrometry methods to characterize changes in carbohydrates, lipids, amino acids and steroids in eight normal weight men at baseline, after 48 hours of caloric restriction (CR; 10% of energy requirements) and after 48 hours of ad libitum refeeding in a tightly-controlled environment. Results: We identified a distinct metabolomic signature associated with acute CR characterized by the expected switch from carbohydrate to fat utilization with increased lipolysis and beta-fatty acid oxidation. We found an increase in omega-fatty acid oxidation and levels of endocannabinoids which are known to promote food intake. These changes were reversed with refeeding. Several plasmalogen phosphatidylethanolamines (endogenous anti-oxidants) significantly decreased with CR (all p≤0.0007). Additionally, 48 acute CR was associated with an increase in the branched chain amino acids (all p≤1.4x10-7) and dehydroepiandrosterone sulfate (p=0.0006). Conclusions We identified a distinct metabolomic signature associated with acute CR. Further studies are needed to characterise the mechanisms that mediate these changes and their potential contribution to the adaptive response to dietary restriction.This work was supported by the Wellcome Trust (to I.S.F.), the NIHR Cambridge Biomedical Research Centre, the European Research Council, the Bernard Wolfe Health Neuroscience Fund (all to I.S.F.), the Swiss National Science Foundation (P3SMP3-155318, PZ00P3-167826, to T.H.C.), and the Uehara Memorial Foundation (to T.S.). This work was supported by the NIHR Rare Diseases Translational Research Collaboration and the NeuroFAST consortium, which is funded by the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 245009

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Existence and Stability of Propagating Fronts for an Autocatalytic Reaction-Diffusion System

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are the ratio D = D_B/D_A of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D > 0 and k >= 0, we prove the existence of a family of propagating fronts (or travelling waves) describing the advance of the reaction. In particular, in the quadratic case k=0, we recover the results of Billingham and Needham [BN]. Then, if D is close to 1 and k is sufficiently small, we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted Sobolev spaces. This extends to our system part of the stability results which are known for the scalar Fisher equation.Comment: 32 pages, 1 Postscript figur

The GOODSTEP project: General Object-Oriented Database for Software Engineering Processes

The goal of the GOODSTEP project is to enhance and improve the functionality of a fully object-oriented database management system to yield a platform suited for applications such as software development environments (SDEs). The baseline of the project is the O2 database management system (DBMS). The O2 DBMS already includes many of the features regulated by SDEs. The project has identified enhancements to O2 in order to make it a real software engineering DBMS. These enhancements are essentially upgrades of the existing O2 functionality, and hence require relatively easy extensions to the O2 system. They have been developed in the early stages of the project and are now exploited and validated by a number of software engineering tools built on top of the enhanced O2 DBMS. To ease tool construction, the GOODSTEP platform encompasses tool generation capabilities which allow for generation of integrated graphical and textual tools from high-level specifications. In addition, the GOODSTEP platform provides a software process toolset which enables modeling, analysis and enaction of software processes and is also built on top of the extended O2 database. The GOODSTEP platform is to be validated using two CASE studies carried out to develop an airline application and a business application

The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis

We calculate 800 coefficients of the high-temperature expansion of the magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg measure. Log-periodic corrections to the scaling laws appear as in the case of a Ising measure. The period of oscillation appears to be a universal quantity given in good approximation by the logarithm of the largest eigenvalue of the linearized RG transformation, in agreement with a possibility suggested by K. Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma$ to be 1.300 (with a systematic error of the order of 0.002) in good agreement with the results obtained with other methods such as the $\epsilon$-expansion. We briefly discuss the relationship between the oscillations and the zeros of the partition function near the critical point in the complex temperature plane.Comment: 21 pages, 10 Postcript figures, latex file, uses revte

Fibroblasts Express Immune Relevant Genes and Are Important Sentinel Cells during Tissue Damage in Rainbow Trout (Oncorhynchus mykiss)

Fibroblasts have shown to be an immune competent cell type in mammals. However, little is known about the immunological functions of this cell-type in lower vertebrates. A rainbow trout hypodermal fibroblast cell-line (RTHDF) was shown to be responsive to PAMPs and DAMPs after stimulation with LPS from E. coli, supernatant and debris from sonicated RTHDF cells. LPS was overall the strongest inducer of IL-1β, IL-8, IL-10, TLR-3 and TLR-9. IL-1β and IL-8 were already highly up regulated after 1 hour of LPS stimulation. Supernatant stimuli significantly increased the expression of IL-1β, TLR-3 and TLR-9, whereas the debris stimuli only increased expression of IL-1β. Consequently, an in vivo experiment was further set up. By mechanically damaging the muscle tissue of rainbow trout, it was shown that fibroblasts in the muscle tissue of rainbow trout contribute to electing a highly local inflammatory response following tissue injury. The damaged muscle tissue showed a strong increase in the expression of the immune genes IL-1β, IL-8 and TGF-β already 4 hours post injury at the site of injury while the expression in non-damaged muscle tissue was not influenced. A weaker, but significant response was also seen for TLR-9 and TLR-22. Rainbow trout fibroblasts were found to be highly immune competent with a significant ability to express cytokines and immune receptors. Thus fish fibroblasts are believed to contribute significantly to local inflammatory reactions in concert with the traditional immune cells

Gastroparesis and functional dyspepsia: excerpts from the AGA/ANMS meeting

Despite the relatively high prevelance of gastroparesis and functional dyspepsia, the aetiology and pathophysiology of these disorders remain incompletely understood. Similarly, the diagnostic and treatment options for these two disorders are relatively limited despite recent advances in our understanding of both disorders.This manuscript reviews the advances in the understanding of the epidemiology, pathophysiology, diagnosis, and treatment of gastroparesis and functional dyspepsia as discussed at a recent conference sponsored by the American Gastroenterological Association (AGA) and the American Neurogastroenterology and Motility Society (ANMS). Particular focus is placed on discussing unmet needs and areas for future research.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78690/1/j.1365-2982.2009.01434.x.pd

Evaluation of a Melanocortin-4 Receptor (MC4R) agonist (Setmelanotide) in MC4R deficiency

$\textbf{Objective:}$ Pro-opiomelanocortin (POMC)-derived peptides act on neurons expressing the Melanocortin 4 receptor (MC4R) to reduce body weight. Setmelanotide is a highly potent MC4R agonist that leads to weight loss in diet-induced obese animals and in obese individuals with complete POMC deficiency. While POMC deficiency is very rare, 1e5% of severely obese individuals harbor heterozygous mutations in MC4R. We sought to assess the efficacy of Setmelanotide in human MC4R deficiency. $\textbf{Methods:}$ We studied the effects of Setmelanotide on mutant MC4Rs in cells and the weight loss response to Setmelanotide administration in rodent studies and a human clinical trial. We annotated the functional status of 369 published MC4R variants. $\textbf{Results:}$ In cells, we showed that Setmelanotide is significantly more potent at MC4R than the endogenous ligand alpha-melanocyte stimulating hormone and can disproportionally rescue signaling by a subset of severely impaired MC4R mutants. Wild-type rodents appear more sensitive to Setmelanotide when compared to MC4R heterozygous deficient mice, while MC4R knockout mice fail to respond. In a 28-day Phase 1b clinical trial, Setmelanotide led to weight loss in obese MC4R variant carriers. Patients with POMC defects upstream of MC4R show significantly more weight loss with Setmelanotide than MC4R deficient patients or obese controls. $\textbf{Conclusions:}$ Setmelanotide led to weight loss in obese people with MC4R deficiency; however, further studies are justified to establish whether Setmelanotide can elicit clinically meaningful weight loss in a subset of the MC4R deficient obese population.This work was supported by the Wellcome Trust (I.S.F.), the National Institute for Health Research Cambridge Biomedical Research Centre (S.O’R., I.S.F.), the Bernard Wolfe Health Neuroscience Fund (I.S.F.), the European Research Council (I.S.F.), and the Swiss National Science Foundation (PBLAP3-145870, P3SMP3-155318, PZ00P3-167826 to T.-H.C.). Funds were also obtained from the Clinical Research Programs on Obesity (Assistance Publique-Hôpitaux de Paris, and the Direction of Clinical Research (CRC) (PHRC 02076 to K.C.), as well as the Institut Benjamin Delessert and the Fondation pour la Recherche Médicale and the National Agency of Research (program “Investissements d’Avenir” with the reference ANR-10-IAHU-05). The clinical trial was supported by Rhythm Pharmaceuticals