Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Decreased compliance on arterial anastomoses.

The present study was undertaken to examine the cross-sectional vascular compliance at the anastomotic site. METHODS AND MATERIAL: We performed end-to-end anastomosis on the carotid artery of six pigs using continuous 6/0 polypropylene. Four carotid arteries were excised and mounted in a perfusion chamber while the remaining two were left in living animals. We used pulsed ultrasound (NIUS 02) to generate detailed longitudinal profiles of diameter and compliance in the proximity and on the anastomosis. RESULTS: On the anastomosis, the vessel diameter decreases (-1 to -2.6% of diastolic diameter) when blood pressure increases with an exponential correlation (R2 = 0.75). The arterial compliance at the anastomosis was negative: the vessel cross-section reduction for a pulse pressure of 1 up to 32 mmHg was 0.9 to 2% of diastolic vessel cross-section. CONCLUSIONS: Vessel movement generated a dynamic stenosis whose magnitude seems to depend on blood pressure level. Increasing blood pressure causes the retraction of vessel ends which causes vessel lumen reduction. These results suggest that continuous suture does not provide the continuity of mechanical properties of the artery.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Protein-protein interaction investigated by steered molecular dynamics: the TCR-pMHC complex.

We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.

Physiology and transcriptome of the polycyclic aromatic hydrocarbon-degrading Sphingomonas sp. LH128 after long-term starvation.

The survival, physiology and gene expression profile of the phenanthrene-degrading Sphingomonas sp. LH128 was examined after an extended period of complete nutrient starvation and compared with a non-starved population that had been harvested in exponential phase. After 6 months of starvation in an isotonic solution, only 5 % of the initial population formed culturable cells. Microscopic observation of GFP fluorescent cells, however, suggested that a larger fraction of cells (up to 80 %) were still alive and apparently had entered a viable but non-culturable (VBNC) state. The strain displayed several cellular and genetic adaptive strategies to survive long-term starvation. Flow cytometry, microscopic observation and fatty acid methyl ester (FAME) analysis showed a reduction in cell size, a change in cell shape and an increase in the degree of membrane fatty acid saturation. Transcriptome analysis showed decreased expression of genes involved in ribosomal protein biosynthesis, chromosomal replication, cell division and aromatic catabolism, increased expression of genes involved in regulation of gene expression and efflux systems, genetic translocations, and degradation of rRNA and fatty acids. Those phenotypic and transcriptomic changes were not observed after 4 h of starvation. Despite the starvation situation, the polycyclic aromatic hydrocarbon (PAH) catabolic activity was immediate upon exposure to phenanthrene. We conclude that a large fraction of cells maintain viability after an extended period of starvation apparently due to tuning the expression of a wide variety of cellular processes. Due to these survival attributes, bacteria of the genus Sphingomonas, like strain LH128, could be considered as suitable targets for use in remediation of nutrient-poor PAH-contaminated environments.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Transcriptional control of the hydrogen cyanide biosynthetic genes hcnABC by the anaerobic regulator ANR and the quorum-sensing regulators LasR and RhlR in Pseudomonas aeruginosa.

Virulence factors of Pseudomonas aeruginosa include hydrogen cyanide (HCN). This secondary metabolite is maximally produced at low oxygen tension and high cell densities during the transition from exponential to stationary growth phase. The hcnABC genes encoding HCN synthase were identified on a genomic fragment complementing an HCN-deficient mutant of P. aeruginosa PAO1. The hcnA promoter was found to be controlled by the FNR-like anaerobic regulator ANR and by the quorum-sensing regulators LasR and RhlR. Primer extension analysis revealed two transcription starts, T1 and T2, separated by 29 bp. Their function was confirmed by transcriptional lacZ fusions. The promoter sequence displayed an FNR/ANR box at -42.5 bp upstream of T2 and a lux box centered around -42.5 bp upstream of T1. Expression of the hcn genes was completely abolished when this lux box was deleted or inactivated by two point mutations in conserved nucleotides. The lux box was recognized by both LasR [activated by N-(oxododecanoyl)-homoserine lactone] and RhlR (activated by N-butanoyl-homoserine lactone), as shown by expression experiments performed in quorum-sensing-defective P. aeruginosa mutants and in the N-acyl-homoserine lactone-negative heterologous host P. fluorescens CHA0. A second, less conserved lux box lying 160 bp upstream of T1 seems to account for enhanced quorum-sensing-dependent expression. Without LasR and RhlR, ANR could not activate the hcn promoter. Together, these data indicate that expression of the hcn promoter from T1 can occur under quorum-sensing control alone. Enhanced expression from T2 appears to rely on a synergistic action between LasR, RhlR, and ANR.

Deregulation of the arginine deiminase (arc) operon in penicillin-tolerant mutants of Streptococcus gordonii.

Penicillin tolerance is an incompletely understood phenomenon that allows bacteria to resist drug-induced killing. Tolerance was studied with independent Streptococcus gordonii mutants generated by cyclic exposure to 500 times the MIC of penicillin. Parent cultures lost 4 to 5 log(10) CFU/ml of viable counts/24 h. In contrast, each of four independent mutant cultures lost < or =2 log(10) CFU/ml/24 h. The mutants had unchanged penicillin-binding proteins but contained increased amounts of two proteins with respective masses of ca. 50 and 45 kDa. One mutant (Tol1) was further characterized. The two proteins showing increased levels were homologous to the arginine deiminase and ornithine carbamoyl transferase of other gram-positive bacteria and were encoded by an operon that was >80% similar to the arginine-deiminase (arc) operon of these organisms. Partial nucleotide sequencing and insertion inactivation of the S. gordonii arc locus indicated that tolerance was not a direct consequence of arc alteration. On the other hand, genetic transformation of tolerance by Tol1 DNA always conferred arc deregulation. In nontolerant recipients, arc was repressed during exponential growth and up-regulated during postexponential growth. In tolerant transformants, arc was constitutively expressed. Tol1 DNA transformed tolerance at the same rate as transformation of a point mutation (10(-2) to 10(-3)). The tolerance mutation mapped on a specific chromosomal fragment but was physically distant from arc. Importantly, arc deregulation was observed in most (6 of 10) of additional independent penicillin-tolerant mutants. Thus, although not exclusive, the association between arc deregulation and tolerance was not fortuitous. Since penicillin selection mimicked the antibiotic pressure operating in the clinical environment, arc deregulation might be an important correlate of naturally occurring tolerance and help in understanding the mechanism(s) underlying this clinically problematic phenotype.

Establishment and characterization of a new continuous cell line from Lutzomyia longipalpis (Diptera: Psychodidae) and its susceptibility to infections with arboviruses and Leishmania chagasi

Embryonic tissue explants of the sand fly Lutzomyia longipalpis (Lutz & Neiva 1912) the main vector of Leishmania chagasi (Cunha and Chagas), were used to obtain a continuous cell line (Lulo). The tissues were seeded in MM/VP12 medium and these were incubated at 28ºC. The first subculture was obtained 45 days after explanting and 96 passages have been made to date. Lulo is composed of epithelioid cells, showed a 0.04 generations/hour exponential growth rate and population doubling time at 24.7 h. The cell line isoenzymatic profiles were determined by using PGI, PGM, MPI and 6-PGDH systems, coinciding with patterns obtained from the same species and colony's pupae and adults. The species karyotype characteristics were recognized (2n = 8), in which pair 1 is subtelocentric and pairs 2, 3 and 4 are metacentric. Lulo was free from bacterial, fungal, mycoplasmic and viral infection. Susceptibility to five arbovirus was determined, the same as Lulo interaction with Leishmania promastigotes.

Repeated injections of 131I-rituximab show patient-specific stable biodistribution and tissue kinetics.

PURPOSE: It is generally assumed that the biodistribution and pharmacokinetics of radiolabelled antibodies remain similar between dosimetric and therapeutic injections in radioimmunotherapy. However, circulation half-lives of unlabelled rituximab have been reported to increase progressively after the weekly injections of standard therapy doses. The aim of this study was to evaluate the evolution of the pharmacokinetics of repeated 131I-rituximab injections during treatment with unlabelled rituximab in patients with non-Hodgkin's lymphoma (NHL). METHODS: Patients received standard weekly therapy with rituximab (375 mg/m2) for 4 weeks and a fifth injection at 7 or 8 weeks. Each patient had three additional injections of 185 MBq 131I-rituximab in either treatment weeks 1, 3 and 7 (two patients) or weeks 2, 4 and 8 (two patients). The 12 radiolabelled antibody injections were followed by three whole-body (WB) scintigraphic studies during 1 week and blood sampling on the same occasions. Additional WB scans were performed after 2 and 4 weeks post 131I-rituximab injection prior to the second and third injections, respectively. RESULTS: A single exponential radioactivity decrease for WB, liver, spleen, kidneys and heart was observed. Biodistribution and half-lives were patient specific, and without significant change after the second or third injection compared with the first one. Blood T(1/2)beta, calculated from the sequential blood samples and fitted to a bi-exponential curve, was similar to the T(1/2) of heart and liver but shorter than that of WB and kidneys. Effective radiation dose calculated from attenuation-corrected WB scans and blood using Mirdose3.1 was 0.53+0.05 mSv/MBq (range 0.48-0.59 mSv/MBq). Radiation dose was highest for spleen and kidneys, followed by heart and liver. CONCLUSION: These results show that the biodistribution and tissue kinetics of 131I-rituximab, while specific to each patient, remained constant during unlabelled antibody therapy. RIT radiation doses can therefore be reliably extrapolated from a preceding dosimetry study.

Forces de Casimir i les seves aplicacions

Report for the scientific sojourn carried out at the Darmouth College, from august 2007 until february 2008. It has been very successful, from different viewpoints: scientific, philosophical, human. We have definitely advanced, during the past six months, towards the comprehension of the behaviour of the fluctuations of the quantum vacuum in the presence of boundaries, moving and non-moving, and also in situations where the topology of space-time changes: the dynamical Casimir effect, regularization problems, particle creation statistics, according to different BC, etc. We have solved some longstanding problems and got in this subject quite remarkable results (as we will explain in more detail below). We also pursued a general approach towards a viable modified f(R) gravity in both the Jordan and the Einstein frames (which are known to be mathematically equivalent, but physically not so). A class of exponential, realistic modified gravities has been introduced by us and investigated with care. Special focus was made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models were considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way, what makes them very promising. Moreover, it is monstrated in our work that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.