On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases.

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.

Hyperpolarized lithium-6 as a sensor of nanomolar contrast agents.

Lithium is widely used in psychotherapy. The (6)Li isotope has a long intrinsic longitudinal relaxation time T(1) on the order of minutes, making it an ideal candidate for hyperpolarization experiments. In the present study we demonstrated that lithium-6 can be readily hyperpolarized within 30 min, while retaining a long polarization decay time on the order of a minute. We used the intrinsically long relaxation time for the detection of 500 nM contrast agent in vitro. Hyperpolarized lithium-6 was administered to the rat and its signal retained a decay time on the order of 70 sec in vivo. Localization experiments imply that the lithium signal originated from within the brain and that it was detectable up to 5 min after administration. We conclude that the detection of submicromolar contrast agents using hyperpolarized NMR nuclei such as (6)Li may provide a novel avenue for molecular imaging.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Natural classification of knots

The principal objective of the knot theory is to provide a simple way of classifying and ordering all the knot types. Here, we propose a natural classification of knots based on their intrinsic position in the knot space that is defined by the set of knots to which a given knot can be converted by individual intersegmental passages. In addition, we characterize various knots using a set of simple quantum numbers that can be determined upon inspection of minimal crossing diagram of a knot. These numbers include: crossing number; average three-dimensional writhe; number of topological domains; and the average relaxation value

Limitations of stimulated echo acquisition mode (STEAM) techniques in cardiac applications.

Stimulated echoes are widely used for imaging functional tissue parameters such as diffusion coefficient, perfusion, and flow rates. They are potentially interesting for the assessment of various cardiac functions. However, severe limitations of the stimulated echo acquisition mode occur, which are related to the special dynamic properties of the beating heart and flowing blood. To the well-known signal decay due to longitudinal relaxation and through-plane motion between the preparation and the read-out period of the stimulated echoes, additional signal loss is often observed. As the prepared magnetization is fixed with respect to the tissue, this signal loss is caused by the tissue deformation during the cardiac cycle, which leads to a modification of the modulation frequency of the magnetization. These effects are theoretically derived and corroborated by phantom and in vivo experiments.

Reshaping the remodelled left ventricle: a new concept.

OBJECTIVE: Based on the law of Laplace, transventricular tension members were designed to diminish wall stress by changing the left ventricle (LV) globular shape to a bilobular one, thus reducing the ventricular wall radius of curvature. This concept was tested in a model of congestive heart failure. METHODS: Seven calves were used for the study (74.3+/-4.2 kg). Treatment efficacy was assessed with sonomicrometric wall motion analysis coupled with intraventricular pressure measurement. Preload increase was applied stepwise with tension members in released and tightened position. RESULTS: Tightening of the tension members improved systolic function for CVP>10 mmHg (dP/dt: 828+/-122 vs. 895+/-112 mmHg/s, P=0.019, for baseline and 20% stress level reduction respectively; wall thickening: 11.6+/-1.5 vs. 13.3+/-1.7%, P<0.001) and diastolic function (LV end-diastolic pressure: 15.9+/-4.8 vs. 13.6+/-2.7 mmHg, P<0.001, for CVP>10 mmHg; peak rate of wall thinning: -12.2+/-2.2 vs. -14+/-2.3 cm(2)/s, P<0.001 and logistic time constant of isovolumic relaxation: 48.4 +/-10.9 vs. 39.8+/-9.6ms, P<0.001, for CVP>5 mmHg). CONCLUSIONS: This less aggressive LV reduction method significantly improves contractility and relaxation parameters in this model of congestive heart failure.

Diffusion-weighted spectroscopy: a novel approach to determine macromolecule resonances in short-echo time 1H-MRS.

Quantification of short-echo time proton magnetic resonance spectroscopy results in >18 metabolite concentrations (neurochemical profile). Their quantification accuracy depends on the assessment of the contribution of macromolecule (MM) resonances, previously experimentally achieved by exploiting the several fold difference in T(1). To minimize effects of heterogeneities in metabolites T(1), the aim of the study was to assess MM signal contributions by combining inversion recovery (IR) and diffusion-weighted proton spectroscopy at high-magnetic field (14.1 T) and short echo time (= 8 msec) in the rat brain. IR combined with diffusion weighting experiments (with δ/Δ = 1.5/200 msec and b-value = 11.8 msec/μm(2)) showed that the metabolite nulled spectrum (inversion time = 740 msec) was affected by residuals attributed to creatine, inositol, taurine, choline, N-acetylaspartate as well as glutamine and glutamate. While the metabolite residuals were significantly attenuated by 50%, the MM signals were almost not affected (< 8%). The combination of metabolite-nulled IR spectra with diffusion weighting allows a specific characterization of MM resonances with minimal metabolite signal contributions and is expected to lead to a more precise quantification of the neurochemical profile.

Urocortins improve dystrophic skeletal muscle structure and function through both PKA- and Epac-dependent pathways.

In Duchenne muscular dystrophy, the absence of dystrophin causes progressive muscle wasting and premature death. Excessive calcium influx is thought to initiate the pathogenic cascade, resulting in muscle cell death. Urocortins (Ucns) have protected muscle in several experimental paradigms. Herein, we demonstrate that daily s.c. injections of either Ucn 1 or Ucn 2 to 3-week-old dystrophic mdx(5Cv) mice for 2 weeks increased skeletal muscle mass and normalized plasma creatine kinase activity. Histological examination showed that Ucns remarkably reduced necrosis in the diaphragm and slow- and fast-twitch muscles. Ucns improved muscle resistance to mechanical stress provoked by repetitive tetanizations. Ucn 2 treatment resulted in faster kinetics of contraction and relaxation and a rightward shift of the force-frequency curve, suggesting improved calcium homeostasis. Ucn 2 decreased calcium influx into freshly isolated dystrophic muscles. Pharmacological manipulation demonstrated that the mechanism involved the corticotropin-releasing factor type 2 receptor, cAMP elevation, and activation of both protein kinase A and the cAMP-binding protein Epac. Moreover, both STIM1, the calcium sensor that initiates the assembly of store-operated channels, and the calcium-independent phospholipase A(2) that activates these channels were reduced in dystrophic muscle by Ucn 2. Altogether, our results demonstrate the high potency of Ucns for improving dystrophic muscle structure and function, suggesting that these peptides may be considered for treatment of Duchenne muscular dystrophy.

Feasibility of in vivo 15N MRS detection of hyperpolarized 15N labeled choline in rats.

The increase of total choline in tumors has become an important biomarker in cancer diagnosis. Choline and choline metabolites can be measured in vivo and in vitro using multinuclear MRS. Recent in vivo(13)C MRS studies using labeled substrates enhanced via dynamic nuclear polarization demonstrated the tremendous potential of hyperpolarization for real-time metabolic studies. The present study demonstrates the feasibility of detecting hyperpolarized (15)N labeled choline in vivo in a rat head at 9.4 T. We furthermore report the in vitro (172 +/- 16 s) and in vivo (126 +/- 15 s) longitudinal relaxation times. We conclude that with appropriate infusion protocols it is feasible to detect hyperpolarized (15)N labeled choline in live animals.

Regional specificity of MRI contrast parameter changes in normal ageing revealed by voxel-based quantification (VBQ).

Normal ageing is associated with characteristic changes in brain microstructure. Although in vivo neuroimaging captures spatial and temporal patterns of age-related changes of anatomy at the macroscopic scale, our knowledge of the underlying (patho)physiological processes at cellular and molecular levels is still limited. The aim of this study is to explore brain tissue properties in normal ageing using quantitative magnetic resonance imaging (MRI) alongside conventional morphological assessment. Using a whole-brain approach in a cohort of 26 adults, aged 18-85years, we performed voxel-based morphometric (VBM) analysis and voxel-based quantification (VBQ) of diffusion tensor, magnetization transfer (MT), R1, and R2* relaxation parameters. We found age-related reductions in cortical and subcortical grey matter volume paralleled by changes in fractional anisotropy (FA), mean diffusivity (MD), MT and R2*. The latter were regionally specific depending on their differential sensitivity to microscopic tissue properties. VBQ of white matter revealed distinct anatomical patterns of age-related change in microstructure. Widespread and profound reduction in MT contrasted with local FA decreases paralleled by MD increases. R1 reductions and R2* increases were observed to a smaller extent in overlapping occipito-parietal white matter regions. We interpret our findings, based on current biophysical models, as a fingerprint of age-dependent brain atrophy and underlying microstructural changes in myelin, iron deposits and water. The VBQ approach we present allows for systematic unbiased exploration of the interaction between imaging parameters and extends current methods for detection of neurodegenerative processes in the brain. The demonstrated parameter-specific distribution patterns offer insights into age-related brain structure changes in vivo and provide essential baseline data for studying disease against a background of healthy ageing.

Evaluation of arterial compliance-pressure curves. Effect of antihypertensive drugs.

A new high-precision ultrasonic device was developed to determine noninvasively arterial compliance as a function of blood pressure. Because of the nonlinear elastic properties of arterial walls, measurements of compliance can be appropriately compared only if obtained over a range of pressures. This apparatus was used to evaluate in a double-blind, parallel fashion the effect of three different antihypertensive drugs and of a placebo on radial artery compliance. Thirty-two normotensive volunteers were randomly allocated to an 8-day, once-a-day oral treatment with either a placebo, 100 mg atenolol, 20 mg nitrendipine, or 20 mg lisinopril. Blood pressure, heart rate, radial artery diameter, and arterial compliance were measured immediately before as well as 6 hours after dosing on the first and last days of the study. On the eighth day of administration, within 6 hours after dosing, lisinopril induced an acute increase in radial artery diameter, from 2.99 +/- 0.06 to 3.28 +/- 0.09 mm (mean +/- SEM, p less than 0.01). The compliance-pressure curve was shifted upward on day 1 (p less than 0.01) as well as on day 8 (p less than 0.05). None of the other drugs induced any significant modification of these parameters. Arterial compliance has a strong nonlinear dependency on intra-arterial pressure and therefore has to be defined as a function of pressure. Antihypertensive drugs acting by different mechanisms may have different effects on the mechanical properties of large arteries.

Patterns of positive selection in seven ant genomes.

The evolution of ants is marked by remarkable adaptations that allowed the development of very complex social systems. To identify how ant-specific adaptations are associated with patterns of molecular evolution, we searched for signs of positive selection on amino-acid changes in proteins. We identified 24 functional categories of genes which were enriched for positively selected genes in the ant lineage. We also reanalyzed genome-wide data sets in bees and flies with the same methodology to check whether positive selection was specific to ants or also present in other insects. Notably, genes implicated in immunity were enriched for positively selected genes in the three lineages, ruling out the hypothesis that the evolution of hygienic behaviors in social insects caused a major relaxation of selective pressure on immune genes. Our scan also indicated that genes implicated in neurogenesis and olfaction started to undergo increased positive selection before the evolution of sociality in Hymenoptera. Finally, the comparison between these three lineages allowed us to pinpoint molecular evolution patterns that were specific to the ant lineage. In particular, there was ant-specific recurrent positive selection on genes with mitochondrial functions, suggesting that mitochondrial activity was improved during the evolution of this lineage. This might have been an important step toward the evolution of extreme lifespan that is a hallmark of ants.

Thalamic connectivity in patients with essential tremor treated with MR imaging-guided focused ultrasound: in vivo fiber tracking by using diffusion-tensor MR imaging.

PURPOSE: To use diffusion-tensor (DT) magnetic resonance (MR) imaging in patients with essential tremor who were treated with transcranial MR imaging-guided focused ultrasound lesion inducement to identify the structural connectivity of the ventralis intermedius nucleus of the thalamus and determine how DT imaging changes correlated with tremor changes after lesion inducement. MATERIALS AND METHODS: With institutional review board approval, and with prospective informed consent, 15 patients with medication-refractory essential tremor were enrolled in a HIPAA-compliant pilot study and were treated with transcranial MR imaging-guided focused ultrasound surgery targeting the ventralis intermedius nucleus of the thalamus contralateral to their dominant hand. Fourteen patients were ultimately included. DT MR imaging studies at 3.0 T were performed preoperatively and 24 hours, 1 week, 1 month, and 3 months after the procedure. Fractional anisotropy (FA) maps were calculated from the DT imaging data sets for all time points in all patients. Voxels where FA consistently decreased over time were identified, and FA change in these voxels was correlated with clinical changes in tremor over the same period by using Pearson correlation. RESULTS: Ipsilateral brain structures that showed prespecified negative correlation values of FA over time of -0.5 or less included the pre- and postcentral subcortical white matter in the hand knob area; the region of the corticospinal tract in the centrum semiovale, in the posterior limb of the internal capsule, and in the cerebral peduncle; the thalamus; the region of the red nucleus; the location of the central tegmental tract; and the region of the inferior olive. The contralateral middle cerebellar peduncle and bilateral portions of the superior vermis also showed persistent decrease in FA over time. There was strong correlation between decrease in FA and clinical improvement in hand tremor 3 months after lesion inducement (P < .001). CONCLUSION: DT MR imaging after MR imaging-guided focused ultrasound thalamotomy depicts changes in specific brain structures. The magnitude of the DT imaging changes after thalamic lesion inducement correlates with the degree of clinical improvement in essential tremor.