A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Catabolic ornithine carbamoyltransferase of Pseudomonas aeruginosa. Importance of the N-terminal region for dodecameric structure and homotropic carbamoylphosphate cooperativity.

Pseudomonas aeruginosa has an anabolic (ArgF) and a catabolic (ArcB) ornithine carbamoyltransferase (OTCase). Despite extensive sequence similarities, these enzymes function unidirectionally in vivo. In the dodecameric catabolic OTCase, homotropic cooperativity for carbamoylphosphate strongly depresses the anabolic reaction; the residue Glu1O5 and the C-terminus are known to be essential for this cooperativity. When Glu1O5 and nine C-terminal amino acids of the catabolic OTCase were introduced, by in vitro genetic manipulation, into the closely related, trimeric, anabolic (ArgF) OTCase of Escherichia coli, the enzyme displayed Michaelis-Menten kinetics and no cooperativity was observed. This indicates that additional amino acid residues are required to produce homotropic cooperativity and a dodecameric assembly. To localize these residues, we constructed several hybrid enzymes by fusing, in vivo or in vitro, the E. coli argF gene to the P. aeruginosa arcB gene. A hybrid enzyme consisting of 101 N-terminal ArgF amino acids fused to 233 C-terminal ArcB residues and the reciprocal ArcB-ArgF hybrid were both trimers with little or no cooperativity. Replacing the seven N-terminal residues of the ArcB enzyme by the corresponding six residues of E. coli ArgF enzyme produced a dodecameric enzyme which showed a reduced affinity for carbamoylphosphate and an increase in homotropic cooperativity. Thus, the N-terminal amino acids of catabolic OTCase are important for interaction with carbamoylphosphate, but do not alone determine dodecameric assembly. Hybrid enzymes consisting of either 26 or 42 N-terminal ArgF amino acids and the corresponding C-terminal ArcB residues were both trimeric, yet they retained some homotropic cooperativity. Within the N-terminal ArcB region, a replacement of motif 28-33 by the corresponding ArgF segment destabilized the dodecameric structure and the enzyme existed in trimeric and dodecameric states, indicating that this region is important for dodecameric assembly. These findings were interpreted in the light of the three-dimensional structure of catabolic OTCase, which allows predictions about trimer-trimer interactions. Dodecameric assembly appears to require at least three regions: the N- and C-termini (which are close to each other in a monomer), residues 28-33 and residues 147-154. Dodecameric structure correlates with high carbamoylphosphate cooperativity and thermal stability, but some trimeric hybrid enzymes retain cooperativity, and the dodecameric Glu1O5-->Ala mutant gives hyperbolic carbamoylphosphate saturation, indicating that dodecameric structure is neither necessary nor sufficient to ensure cooperativity.

Calibration of a Structured Light-Based Stereo Catadioptric Sensor

Catadioptric sensors are combinations of mirrors and lenses made in order to obtain a wide field of view. In this paper we propose a new sensor that has omnidirectional viewing ability and it also provides depth information about the nearby surrounding. The sensor is based on a conventional camera coupled with a laser emitter and two hyperbolic mirrors. Mathematical formulation and precise specifications of the intrinsic and extrinsic parameters of the sensor are discussed. Our approach overcomes limitations of the existing omni-directional sensors and eventually leads to reduced costs of production

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Evaluation of four whole-plant inoculation methods to analyze the pathogenicity of Erwinia amylovora under quarantine conditions

Four methods were tested to assess the fire-blight disease response on grafted pear plants. The leaves of the plants were inoculated with Erwinia amylovora suspensions by pricking with clamps, cutting with scissors, local infiltration, and painting a bacterial suspension onto the leaves with a paintbrush. The effects of the inoculation methods were studied in dose-time-response experiments carried out in climate chambers under quarantine conditions. A modified Gompertz model was used to analyze the disease-time relatiobbnships and provided information on the rate of infection progression (rg) and time delay to the start of symptoms (t0). The disease-pathogen-dose relationships were analyzed according to a hyperbolic saturation model in which the median effective dose (ED50) of the pathogen and maximum disease level (ymax) were determined. Localized infiltration into the leaf mesophile resulted in the early (short t0) but slow (low rg) development of infection whereas in leaves pricked with clamps disease symptoms developed late (long t0) but rapidly (high rg). Paintbrush inoculation of the plants resulted in an incubation period of medium length, a moderate rate of infection progression, and low ymax values. In leaves inoculated with scissors, fire-blight symptoms developed early (short t0) and rapidly (high rg), and with the lowest ED50 and the highest ymax

Information-theoretical derivation of an extended thermodynamical description of radiative systems

A radiative equation of the Cattaneo–Vernotte type is derived from information theory and the radiative transfer equation. The equation thus derived is a radiative analog of the equation that is used for the description of hyperbolic heat conduction. It is shown, without recourse to any phenomenological assumption, that radiative transfer may be included in a natural way in the framework of extendedirreversible thermodynamics

Relationship between imatinib population pharmacokinetics and alpha-1-acid glycoprotein

Objectives: Considering the large inter-individual differences in the function of the systems involved in imatinib disposition, exposure to this drug can be expected to vary widely among patients. Among those known systems is alpha-1-acid glycoprotein (AGP), a circulating protein that strongly binds imatinib. This observational study aimed to explore the influence of plasma AGP on imatinib pharmacokinetics. Methods: A population pharmacokinetic analysis was performed using NONMEM based on 278 plasma samples from 51 oncologic patients, for whom both total imatinib and AGP plasma concentrations were measured. The influence of this biological covariate on oral clearance and volume of distribution was examined. Results: A one-compartment model with first-order absorption appropriately described the data. A hyperbolic relationship between plasma AGP levels and oral clearance, as well as volume of distribution was observed. A mechanistic approach was built up, postulating that only the unbound imatinib concentration was able to undergo first-order elimination through an unbound clearance process, and integrating the dissociation constant as a parameter in the model. This approach allowed determining an average (± SEM) free clearance of 1310 (± 172) L/h and a volume of distribution of 301 (± 23) L. By comparison, the total clearance previously determined was 14 (± 1) L/h. Free clearance was affected by body weight and pathology diagnosis. Moreover, this model provided consistent estimates of the association constant between imatinib and AGP (5.5?106 L/mol) and of the average in vivo free fraction of imatinib (1.1%). The variability observed (17% for free clearance and 66% for volume of distribution) was less than the one previously reported without considering AGP impact. AGP explained indeed about one half of the variability observed in total imatinib disposition. Conclusion: Such findings clarify in part the in vivo impact of protein binding on imatinib disposition and might raise again the question whether high levels of AGP could represent a resistance factor to imatinib. This remains however questionable, as it is not expected to affect free drug concentrations. On the other hand, would imatinib be demonstrated as a drug requiring therapeutic drug monitoring, either the measurement of free concentration or the correction of the total concentration by the actual AGP plasma levels should be considered for accurate interpretation of the results.

Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The pseudo-spectral time-domain (PSTD) method is an alternative time-marching method to classicalleapfrog finite difference schemes in the simulation of wave-like propagating phenomena. It is basedon the fundamentals of the Fourier transform to compute the spatial derivatives of hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acoustics simulations. However, one of the first issues to be solved consists on modeling wallabsorption. Unfortunately, there are no references in the technical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals to overcome this problem are presented, validated and compared to analytical solutions in different scenarios.

Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The Pseudo-Spectral Time Domain (PSTD) method is an alternative time-marching method to classical leapfrog finite difference schemes inthe simulation of wave-like propagating phenomena. It is based on the fundamentals of the Fourier transform to compute the spatial derivativesof hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acousticssimulations. However, one of the first issues to be solved consists on modeling wall absorption. Unfortunately, there are no references in thetechnical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals toovercome this problem are presented, validated and compared to analytical solutions in different scenarios.

Credit card debt puzzles

Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper'framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework canactually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers.

Equities and inequality

Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper'framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework canactually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers.

Manifolds on the verge of a hyperbolicity breakdown

We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.

The evolution of social discounting in hierarchically clustered populations.

The expression of a social behaviour may affect the fitness of actors and recipients living in the present and in the future of the population. When there is a risk that a future reward will not be experienced in such a context, the value of that reward should be discounted; but by how much? Here, we evaluate social discount rates for delayed fitness rewards to group of recipients living at different positions in both space and time than the actor in a hierarchically clustered population. This is a population where individuals are grouped into families, families into villages, villages into clans, and so on, possibly ad infinitum. The group-wide fitness effects are assumed to either increase or decrease the fecundity or the survival of recipients and can be arbitrarily extended in space and time. We find that actions changing the survival of individuals living in the future are generally more strongly discounted than fecundity-changing actions for all future times and that the value of future rewards increases as individuals live longer. We also find that delayed fitness effects may not only be discounted by a constant factor per unit delay (exponential discounting), but that, as soon as there is localized dispersal in a population, discounting per unit delay is likely to fall rapidly for small delays and then slowly for longer delays (hyperbolic discounting). As dispersal tends to be localized in natural populations, our results suggest that evolution is likely to favour individuals that express present-biased behaviours and that may be time-inconsistent with respect to their group-wide effects.