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.

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, andthe firm decides the best subset to offer at any given moment to maximize expected revenue. The resultingdynamic program for the firm is intractable and approximated by a deterministic linear programcalled the CDLP which has an exponential number of columns. However, under the choice-set paradigmwhen the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has beenproposed but finding an entering column has been shown to be NP-hard. In this paper, starting with aconcave program formulation based on segment-level consideration sets called SDCP, we add a class ofconstraints called product constraints, that project onto subsets of intersections. In addition we proposea natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methodson the benchmark data sets in the literature. Both the product constraints and the ?SDCP method arevery simple and easy to implement and are applicable to the case of overlapping segment considerationsets. In our computational testing on the benchmark data sets in the literature, SDCP with productconstraints achieves the CDLP value at a fraction of the CPU time taken by column generation and webelieve is a very promising approach for quickly approximating CDLP when segment consideration setsoverlap and the consideration sets themselves are relatively small.

Enhanced radar precipitation estimates using a combined clutter and beam blockage correction technique

Weather radar observations are currently the most reliable method for remote sensing of precipitation. However, a number of factors affect the quality of radar observations and may limit seriously automated quantitative applications of radar precipitation estimates such as those required in Numerical Weather Prediction (NWP) data assimilation or in hydrological models. In this paper, a technique to correct two different problems typically present in radar data is presented and evaluated. The aspects dealt with are non-precipitating echoes - caused either by permanent ground clutter or by anomalous propagation of the radar beam (anaprop echoes) - and also topographical beam blockage. The correction technique is based in the computation of realistic beam propagation trajectories based upon recent radiosonde observations instead of assuming standard radio propagation conditions. The correction consists of three different steps: 1) calculation of a Dynamic Elevation Map which provides the minimum clutter-free antenna elevation for each pixel within the radar coverage; 2) correction for residual anaprop, checking the vertical reflectivity gradients within the radar volume; and 3) topographical beam blockage estimation and correction using a geometric optics approach. The technique is evaluated with four case studies in the region of the Po Valley (N Italy) using a C-band Doppler radar and a network of raingauges providing hourly precipitation measurements. The case studies cover different seasons, different radio propagation conditions and also stratiform and convective precipitation type events. After applying the proposed correction, a comparison of the radar precipitation estimates with raingauges indicates a general reduction in both the root mean squared error and the fractional error variance indicating the efficiency and robustness of the procedure. Moreover, the technique presented is not computationally expensive so it seems well suited to be implemented in an operational environment.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Activation of Srk1 by the Mitogen-activated Protein Kinase Sty1/Spc1 Precedes Its Dissociation from the Kinase and Signals Its Degradation

Control of cell cycle progression by stress-activated protein kinases (SAPKs) is essential for cell adaptation to extracellular stimuli. The Schizosaccharomyces pombe SAPK Sty1/Spc1 orchestrates general changes in gene expression in response to diverse forms of cytotoxic stress. Here we show that Sty1/Spc1 is bound to its target, the Srk1 kinase, when the signaling pathway is inactive. In response to stress, Sty1/Spc1 phosphorylates Srk1 at threonine 463 of the regulatory domain, inducing both activation of Srk1 kinase, which negatively regulates cell cycle progression by inhibiting Cdc25, and dissociation of Srk1 from the SAPK, which leads to Srk1 degradation by the proteasome.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Thermal activation and ATP dependence of the cytoskeleton remodeling dynamics

The cytoskeleton (CSK) is a nonequilibrium polymer network that uses hydrolyzable sources of free energy such as adenosine triphosphate (ATP) to remodel its internal structure. As in inert nonequilibrium soft materials, CSK remodeling has been associated with structural rearrangements driven by energy-activated processes. We carry out particle tracking and traction microscopy measurements of alveolar epithelial cells at various temperatures and ATP concentrations. We provide the first experimental evidence that the remodeling dynamics of the CSK is driven by structural rearrangements over free-energy barriers induced by thermally activated forces mediated by ATP. The measured activation energy of these forces is ~40kBTr (kB being the Boltzmann constant and Tr being the room temperature). Our experiments provide clues to understand the analogy between the dynamics of the living CSK and that of inert nonequilibrium soft materials.

Analysis of the near-intrinsic and extrinsic photocapacitance due to the EL2 level in boron implanted GaAs

A detailed analysis of the photocapacitance signal at the near‐band and extrinsic energetic ranges in Schottky barriers obtained on horizontal Bridgman GaAs wafers, which were implanted with boron at different doses and annealed at several temperatures, has been carried out by using the optical isothermal transient spectroscopy, OITS. The optical cross sections have been determined as well as the quenching efficiency of the EL2 level which has been found to be independent of the annealing temperature. Moreover, the quenching relaxation presents two significant features: (i) a strong increase of the quenching efficiency from 1.35 eV on and (ii) a diminution of the quenching transient amplitude in relation with that shown by the fundamental EL2 level. In order to explain this behavior, different cases are discussed assuming the presence of several energy levels, the existence of an optical recuperation, or the association of the EL2 trap with two levels located, respectively, at Ev+0.45 eV and Ec−0.75 eV. The theoretical simulation, taking into account these two last cases, is in agreement with the experimental photocapacitance data at low temperature, as well as at room temperature where the EL2 filling phototransient shows an anomalous behavior. Moreover, unlike the previous data reported for the EL2 electron optical cross section, the values found using our experimental technique are in agreement with the behavior deduced from the theoretical calculation. The utilization of the OITS method has also allowed the determination of another level, whose faster optical contribution is often added to that of the EL2 level when the DLOS or standard photocapacitance is used.

Atomic diffusion induced by stress relaxation in InGaAs/GaAs epitaxial layers

The origin of the microscopic inhomogeneities in InxGa12xAs layers grown on GaAs by molecular beam epitaxy is analyzed through the optical absorption spectra near the band gap. It is seen that, for relaxed thick layers of about 2.8 mm, composition inhomogeneities are responsible for the band edge smoothing into the whole compositional range (0.05,x,0.8). On the other hand, in thin enough layers strain inhomogeneities are dominant. This evolution in line with layer thickness is due to the atomic diffusion at the surface during growth, induced by the strain inhomogeneities that arise from stress relaxation. In consequence, the strain variations present in the layer are converted into composition variations during growth. This process is energetically favorable as it diminishes elastic energy. An additional support to this hypothesis is given by a clear proportionality between the magnitude of the composition variations and the mean strain.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Relaxation times in a bistable system with parametric, white noise: Theory and experiment

We consider the effects of external, multiplicative white noise on the relaxation time of a general representation of a bistable system from the points of view provided by two, quite different, theoretical approaches: the classical Stratonovich decoupling of correlations and the new method due to Jung and Risken. Experimental results, obtained from a bistable electronic circuit, are compared to the theoretical predictions. We show that the phenomenon of critical slowing down appears as a function of the noise parameters, thereby providing a correct characterization of a noise-induced transition.