Recursive contracts

We obtain a recursive formulation for a general class of contractingproblems involving incentive constraints. Under these constraints,the corresponding maximization (sup) problems fails to have arecursive solution. Our approach consists of studying the Lagrangian.We show that, under standard assumptions, the solution to theLagrangian is characterized by a recursive saddle point (infsup)functional equation, analogous to Bellman's equation. Our approachapplies to a large class of contractual problems. As examples, westudy the optimal policy in a model with intertemporal participationconstraints (which arise in models of default) and intertemporalcompetitive constraints (which arise in Ramsey equilibria).

A recursive presentation for Mihailova's subgroup

"Vegeu el resum a l'inici del document del fitxer adjunt."

Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Speed of convergence of recursive least squares learning with ARMA perceptions

This paper fills a gap in the existing literature on least squareslearning in linear rational expectations models by studying a setup inwhich agents learn by fitting ARMA models to a subset of the statevariables. This is a natural specification in models with privateinformation because in the presence of hidden state variables, agentshave an incentive to condition forecasts on the infinite past recordsof observables. We study a particular setting in which it sufficesfor agents to fit a first order ARMA process, which preserves thetractability of a finite dimensional parameterization, while permittingconditioning on the infinite past record. We describe how previousresults (Marcet and Sargent [1989a, 1989b] can be adapted to handlethe convergence of estimators of an ARMA process in our self--referentialenvironment. We also study ``rates'' of convergence analytically and viacomputer simulation.

On-line event detection by recursive dynamic principal component analysis and gas sensor arrays under drift conditions

Leakage detection is an important issue in many chemical sensing applications. Leakage detection hy thresholds suffers from important drawbacks when sensors have serious drifts or they are affected by cross-sensitivities. Here we present an adaptive method based in a Dynamic Principal Component Analysis that models the relationships between the sensors in the may. In normal conditions a certain variance distribution characterizes sensor signals. However, in the presence of a new source of variance the PCA decomposition changes drastically. In order to prevent the influence of sensor drifts the model is adaptive and it is calculated in a recursive manner with minimum computational effort. The behavior of this technique is studied with synthetic signals and with real signals arising by oil vapor leakages in an air compressor. Results clearly demonstrate the efficiency of the proposed method.

Dielectric formulation for Many-Particle Systems with General Interactions

An extension of the self-consistent field approach formulation by Cohen in the preceding paper is proposed in order to include the most general kind of two-body interactions, i.e., interactions depending on position, momenta, spin, isotopic spin, etc. The dielectric function is replaced by a dielectric matrix. The evaluation of the energies involves the computation of a matrix inversion and trace.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Front form and point form formulation in P.R.M. noninteractions theorems

The front form and the point form of dynamics are studied in the framework of predictive relativistic mechanics. The non-interaction theorem is proved when a Poincar-invariant Hamiltonian formulation with canonical position coordinates is required.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

The use of the SeDeM diagram expert system for the formulation of Captopril SR matrix tablets by direct compression

The SeDeM Diagram Expert System has been used to study excipients, Captopril and designed formulations for their galenic characterization and to ascertain the critical points of the formula affecting product quality to obtain suitable formulations of Captopril Direct Compression SR Matrix Tablets. The application of the Sedem Diagram Expert System enables selecting excipients with in order to optimize the formula in the preformulation and formulation studies. The methodology is based on the implementation of ICH Q8, establishing the design space of the formula with the use of experiment design, using the parameters of the SeDeM Diagram Expert System as system responses.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 30-40% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.