The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

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.

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).

Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as healthand EMS services, banking or distributed ticket selling services, thelocation of service centers has a strong influence on the congestion ateach of them, and consequently, on the quality of service. In this paper,several models are presented to consider service congestion. The firstmodel addresses the issue of the location of the least number of single--servercenters such that all the population is served within a standard distance,and nobody stands in line for a time longer than a given time--limit, or withmore than a predetermined number of other clients. We then formulateseveral maximal coverage models, with one or more servers per service center.A new heuristic is developed to solve the models and tested in a 30--nodesnetwork.

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes ofQALY models (i.e., linear, power and exponential models). We first estimatedTTO utilities for 43 EQ-5D chronic health states and next these states wereembedded in health profiles. The chronic TTO utilities were then used topredict the responses to TTO questions with health profiles. We find that thepower QALY model clearly outperforms linear and exponential QALY models.Optimal power coefficient is 0.65. Our results suggest that TTO-based QALYcalculations may be biased. This bias can be avoided using a power QALY model.

Assessment of speed of human locomotion using a differential satellite global positioning system.

PURPOSE: The objective was to explore whether a satellite-based navigation system, global positioning system used in differential mode (DGPS), could accurately assess the speed of running in humans. METHODS: A subject was equipped with a portable GPS receptor coupled to a receiver for differential corrections, while running outdoors on a straight asphalt road at 27 different speeds. Actual speed (reference method) was assessed by chronometry. RESULTS: The accuracy of speed prediction had a standard deviation (SD) of 0.08 km x h(-1) for walking, 0.11 km x h(-1) for running, yielding a coefficient of variation (SD/mean) of 1.38% and 0.82%, respectively. There was a highly significant linear relationship between actual and DGPS speed assessment (r2 = 0.999) with little bias in the prediction equation, because the slope of the regression line was close to unity (0.997). CONCLUSION: the DGPS technique appears to be a valid and inconspicuous tool for "on line" monitoring of the speed of displacement of individuals located on any field on earth, for prolonged periods of time and unlimited distance, but only in specific environmental conditions ("open sky"). Furthermore, the accuracy of speed assessment using the differential GPS mode was improved by a factor of 10 as compared to non-differential GPS.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Transcript profiling suggests that differential metabolic adaptation of mice to a high fat diet is associated with changes in liver to muscle lipid fluxes.

Genetically homogenous C57Bl/6 mice display differential metabolic adaptation when fed a high fat diet for 9 months. Most become obese and diabetic, but a significant fraction remains lean and diabetic or lean and non-diabetic. Here, we performed microarray analysis of "metabolic" transcripts expressed in liver and hindlimb muscles to evaluate: (i) whether expressed transcript patterns could indicate changes in metabolic pathways associated with the different phenotypes, (ii) how these changes differed from the early metabolic adaptation to short term high fat feeding, and (iii) whether gene classifiers could be established that were characteristic of each metabolic phenotype. Our data indicate that obesity/diabetes was associated with preserved hepatic lipogenic gene expression and increased plasma levels of very low density lipoprotein and, in muscle, with an increase in lipoprotein lipase gene expression. This suggests increased muscle fatty acid uptake, which may favor insulin resistance. In contrast, the lean mice showed a strong reduction in the expression of hepatic lipogenic genes, in particular of Scd-1, a gene linked to sensitivity to diet-induced obesity; the lean and non-diabetic mice presented an additional increased expression of eNos in liver. After 1 week of high fat feeding the liver gene expression pattern was distinct from that seen at 9 months in any of the three mouse groups, thus indicating progressive establishment of the different phenotypes. Strikingly, development of the obese phenotype involved re-expression of Scd-1 and other lipogenic genes. Finally, gene classifiers could be established that were characteristic of each metabolic phenotype. Together, these data suggest that epigenetic mechanisms influence gene expression patterns and metabolic fates.

Intracranial hypertension: what additional information can be derived from ICP waveform after head injury?

OBJECTIVE: Although intracranial hypertension is one of the important prognostic factors after head injury, increased intracranial pressure (ICP) may also be observed in patients with favourable outcome. We have studied whether the value of ICP monitoring can be augmented by indices describing cerebrovascular pressure-reactivity and pressure-volume compensatory reserve derived from ICP and arterial blood pressure (ABP) waveforms. METHOD: 96 patients with intracranial hypertension were studied retrospectively: 57 with fatal outcome and 39 with favourable outcome. ABP and ICP waveforms were recorded. Indices of cerebrovascular reactivity (PRx) and cerebrospinal compensatory reserve (RAP) were calculated as moving correlation coefficients between slow waves of ABP and ICP, and between slow waves of ICP pulse amplitude and mean ICP, respectively. The magnitude of 'slow waves' was derived using ICP low-pass spectral filtration. RESULTS: The most significant difference was found in the magnitude of slow waves that was persistently higher in patients with a favourable outcome (p<0.00004). In patients who died ICP was significantly higher (p<0.0001) and cerebrovascular pressure-reactivity (described by PRx) was compromised (p<0.024). In the same patients, pressure-volume compensatory reserve showed a gradual deterioration over time with a sudden drop of RAP when ICP started to rise, suggesting an overlapping disruption of the vasomotor response. CONCLUSION: Indices derived from ICP waveform analysis can be helpful for the interpretation of progressive intracranial hypertension in patients after brain trauma.

Validity of an arterial pressure waveform analysis device: does the puncture site play a role in the agreement with intermittent pulmonary artery catheter thermodilution measurements?

OBJECTIVE: The measurement of cardiac output is a key element in the assessment of cardiac function. Recently, a pulse contour analysis-based device without need for calibration became available (FloTrac/Vigileo, Edwards Lifescience, Irvine, CA). This study was conducted to determine if there is an impact of the arterial catheter site and to investigate the accuracy of this system when compared with the pulmonary artery catheter using the bolus thermodilution technique (PAC). DESIGN: Prospective study. SETTING: The operating room of 1 university hospital. PARTICIPANTS: Twenty patients undergoing cardiac surgery. INTERVENTIONS: CO was determined in parallel by the use of the Flotrac/Vigileo systems in the radial and femoral position (CO_rad and CO_fem) and by PAC as the reference method. Data triplets were recorded at defined time points. The primary endpoint was the comparison of CO_rad and CO_fem, and the secondary endpoint was the comparison with the PAC. MEASUREMENTS AND MAIN RESULTS: Seventy-eight simultaneous data recordings were obtained. The Bland-Altman analysis for CO_fem and CO_rad showed a bias of 0.46 L/min, precision was 0.85 L/min, and the percentage error was 34%. The Bland-Altman analysis for CO_rad and PAC showed a bias of -0.35 L/min, the precision was 1.88 L/min, and the percentage error was 76%. The Bland-Altman analysis for CO_fem and PAC showed a bias of 0.11 L/min, the precision was 1.8 L/min, and the percentage error was 69%. CONCLUSION: The FloTrac/Vigileo system was shown to not produce exactly the same CO data when used in radial and femoral arteries, even though the percentage error was close to the clinically acceptable range. Thus, the impact of the introduction site of the arterial catheter is not negligible. The agreement with thermodilution was low.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.