Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

On the closed-form approximation of short-time random strike options

In this paper we propose a general technique to develop first and second order closed-form approximation formulas for short-time options withrandom strikes. Our method is based on Malliavin calculus techniques andallows us to obtain simple closed-form approximation formulas dependingon the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches ontwo-assets and three-assets spread options as Kirk's formula or the decomposition mehod presented in Alòs, Eydeland and Laurence (2011).

Biometal muscles to restore contractile function of weak heart

Objectives: Existing VADs are single-ventricle pumps needing anticoagulation. We developed a bi-ventricular external assist device that partially reproduces the physiological muscle function of the heart. This artificial muscle could wrap the heart and improve its contractile force.Methods: The device has a carbon fiber skeleton fitting a 30-40kg patient's heart, to which a Nitinol based artificial muscle is connected. The artificial muscle wraps both ventricles. The Nitinol fibers are woven on a Kevlar mesh surrounding each ventricle. The fibers are electrically driven with a dedicated control unit developed for this purpose. We assessed hemodynamic performances of this device using a previously described dedicated bench test. Volume ejected and pressure gradient have been measured with afterload ranging from 10 to 50mmHg.Results: With an afterload of 50mmHg the system has an ejection fraction of 4% on the right side and 5% on the left side. The system is able to generate a systolic ejection of 2.2mL on the right side and 3.25mL on the left side. With an afterload of 25mmHg the results are reduced of about 20%. The activation frequency can reach 80/minute resulting in a total volume displacement of 176mL/minute on the right side and 260mL/minute on the left side.Conclusions: These preliminary studies confirmed the possibility of improving the ejection fraction of a failing heart using artificial muscle for external cardiac compression avoiding anticoagulation therapy. This device could be helpful in weaning cardio-pulmonary bypass and/or for short-term cardio-circulatory support in pediatric population with cardiac failure.

Peptide modification or blocking of CD8, resulting in weak TCR signaling, can activate CTL for Fas- but not perforin-dependent cytotoxicity or cytokine production.

This study describes a form of partial agonism for a CD8+ CTL clone, S15, in which perforin-dependent killing and IFN-gamma production were lost but Fas (APO1 or CD95)-dependent cytotoxicity preserved. Cloned S15 CTL are H-2Kd restricted and specific for a photoreactive derivative of the Plasmodium berghei circumsporozoite peptide PbCS 252-260 (SYIPSAEKI). The presence of a photoactivatable group in the epitope permitted assessment of TCR-ligand binding by TCR photoaffinity labeling. Selective activation of Fas-dependent killing was observed for a peptide-derivative variant containing a modified photoreactive group. A similar functional response was obtained after binding of the wild-type peptide derivative upon blocking of CD8 participation in TCR-ligand binding. The epitope modification or blocking of CD8 resulted in an > or = 8-fold decrease in TCR-ligand binding. In both cases, phosphorylation of zeta-chain and ZAP-70, as well as calcium mobilization were reduced close to background levels, indicating that activation of Fas-dependent cytotoxicity required weaker TCR signaling than activation of perforin-dependent killing or IFN-gamma production. Consistent with this, we observed that depletion of the protein tyrosine kinase p56(lck) by preincubation of S15 CTL with herbimycin A severely impaired perforin- but not Fas-dependent cytotoxicity. Together with the observation that S15 CTL constitutively express Fas ligand, these results indicate that TCR signaling too weak to elicit perforin-dependent cytotoxicity or cytokine production can induce Fas-dependent cytotoxicity, possibly by translocation of preformed Fas ligand to the cell surface.

Approximation of quadratic irrationals and their pierce expansions

In this article two aims are pursued: on the one hand, to present arapidly converging algorithm for the approximation of square roots; on theother hand and based on the previous algorithm, to find the Pierce expansionsof a certain class of quadratic irrationals as an alternative way to themethod presented in 1984 by J.O. Shallit; we extend the method to findalso the Pierce expansions of quadratic irrationals of the form $2 (p-1)(p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Comment to "Weak instruments robust tests in GMM and the New Keynesian Phillips curve" by Frank Kleibergen and Sophocles Mavroeidis

I discuss the identifiability of a structural New Keynesian Phillips curve when it is embedded in a small scale dynamic stochastic general equilibrium model. Identification problems emerge because not all the structural parameters are recoverable from the semi-structural ones and because the objective functions I consider are poorly behaved. The solution and the moment mappings are responsible for the problems.

Weak and strong altruism in traitgGroups: Reproductive suicide, personal fitness and expected value

A simple variant of trait group selection, employing predators as themechanism underlying group selection, supports contingent reproductivesuicide as altruism (i.e., behavior lowering personal fitness whileaugmenting that of another) without kin assortment. The contingentsuicidal type may either saturate the population or be polymorphicwith a type avoiding suicide, depending on parameters. In addition tocontingent suicide, this randomly assorting morph may also exhibitcontinuously expressed strong altruism (sensu Wilson 1979) usuallythought restricted to kin selection. The model will not, however,support a sterile worker caste as such, where sterility occurs beforelife history events associated with effective altruism; reproductivesuicide must remain fundamentally contingent (facultative sensu WestEberhard 1987; Myles 1988) under random assortment. The continuouslyexpressed strong altruism supported by the model may be reinterpretedas probability of arbitrarily committing reproductive suicide, withoutbenefit for another; such arbitrary suicide (a "load" on "adaptive"suicide) is viable only under a more restricted parameter spacerelative to the necessarily concomitant adaptive contingent suicide.

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Surface collective oscillations of metal clusters and spheres: Random-phase-approximation sum-rules approach

Using the once and thrice energy-weighted moments of the random-phase-approximation strength function, we have derived compact expressions for the average energy of surface collective oscillations of clusters and spheres of metal atoms. The L=0 volume mode has also been studied. We have carried out quantal and semiclassical calculations for Na and Ag systems in the spherical-jellium approximation. We present a rather thorough discussion of surface diffuseness and quantal size effects on the resonance energies.