Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Initial state of ultrarelativistic heavy ion collision

A model for energy, pressure, and flow velocity distributions at the beginning of ultrarelativistic heavy ion collisions is presented, which can be used as an initial condition for hydrodynamic calculations. Our model takes into account baryon recoil for both target and projectile, arising from the acceleration of partons in an effective field F mu nu produced in the collision. The typical field strength (string tension) for RHIC energies is about 512 GeV/fm, which allows us to talk about string ropes. The results show that a quark-gluon plasma forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. Such initial conditions may lead to the creation of antiflow or third flow component [L. P. Csernai and D. Rhrich, Phys. Rev. Lett. B 458, 454 (1999)].

hMMP9 as predictive factor for response and progression free survival in breast cancer patients treated with bevacizumab and pegylated liposomal doxorubicin (PLD)

Background: The anti-angiogenic drug, bevacizumab (Bv), is currently used in the treatment of different malignancies including breast cancer. Many angiogenesis-associated molecules are found in the circulation of cancer patients. Until now, there are no prognostic or predictive factors identified in breast cancer patients treated with Bv. We present here the first results of the prospective monitoring of 6 angiogenesis-related molecules in the peripheral blood of breast cancer patients treated with a combination of Bv and PLD in the phase II trial, SAKK 24/06. Methods: Patients were treated with PLD (20 mg/m2) and Bv (10 mg/kg) on days 1 and 15 of each 4-week cycle for a maximum of 6 cycles, followed by Bv monotherapy maintenance (10 mg/m2 q2 weeks) until progression or severe toxicity. Plasma and serum samples were collected at baseline, after 2 months of therapy, then every 3 months and at treatment discontinuation. Enzyme-linked immunosorbent assays (Quantikine, R&D Systems and Reliatech) were used to measure the expression levels of human vascular endothelial growth factor (hVEGF), placental growth factor (hPlGF), matrix metalloproteinase 9 (hMMP9) and soluble VEGF receptors hsVEGFR-1, hsVEGFR-2 and hsVEGFR-3. The log-transformed data (to reduce the skewness) for each marker was analyzed using an analysis of variance (ANOVA) model to determine if there was a difference between the mean of the subgroups of interest (where α = 0.05). The untransformed data was also analyzed in the same manner as a "sensitivity" check. Results: 132 blood samples were collected in 41 out of 43 enrolled patients. Baseline levels of the molecules were compared to disease status according to RECIST. There was a statistically significant difference in the mean of the log-transformed levels of hMMP9 between responders [CR+PR] versus the mean in patients with PD (p-value=0.0004, log fold change=0.7536), and between patients with disease control [CR+PR+SD] and those with PD (p-value=<0.0001, log fold change=0.81559), with the log-transformed level of hMMP9 being higher for the responder group. The mean of the log-transformed levels of hsVEGFR-1 was statistically significantly different between patients with disease control [CR+PR+SD] and those with PD (p-value=0.0068, log fold change=-0.6089), where the log-transformed level of hsVEGFR-1 was lower for the responder group. The log-transformed level of hMMP9 at baseline was identified as a significant prognostic factor in terms of progression free survival (PFS): p-value=0.0417, hazard ratio (HR)=0.574 with a corresponding 95% confidence interval (0.336 - 0.979)). No strong correlation was shown either between the log-transformed levels of hsVEGF, hPlGF, hsVEGFR-2 or hsVEGFR-3 and clinical response or the occurrence of severe toxicity, or between the levels of the different molecules. Conclusions: Our results suggest that baseline plasma level of the matrix metalloproteinase, hMMP9, could predict tumor response and PFS in patients treated with a combination of Bv and PLD. These data justify further investigation in breast cancer patients treated with anti-angiogenic therapy.

Optical-model potential for electron and positron elastic scattering by atoms

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkur approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from ~100 eV up to ~5 keV. At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.

Ion assisted deposition of thin films by substrate tuned radio frequency magnetron sputtering

The substrate tuning technique was applied to a radio frequency magnetron sputtering system to obtain a variable substrate bias without an additional source. The dependence of the substrate bias on the value of the external impedance was studied for different values of chamber pressure, gas composition and rf input power. A qualitative explanation of the results is given, based on a simple model, and the role of the stray capacitance is clearly disclosed. Langmuir probe measurements show that this system allows independent control of the ion flux and the ion energy bombarding the growing film. For an argon flow rate of 2.8 sccm and a radio frequency power of 300 W (intermediate values of the range studied) the ion flux incident on the substrate was 1.3 X 1020-m-2-s-1. The maximum ion energy available in these conditions can be varied in the range 30-150 eV. As a practical application of the technique, BN thin films were deposited under different ion bombardment conditions. An ion energy threshold of about 80 eV was found, below which only the hexagonal phase was present in the films, while for higher energies both hexagonal and cubic phase were present. A cubic content of about 60% was found for an ion energy of 120 V.

Absence of epidemic threshold in scale free networks with degree correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors degree, enforced by the degree detailed balance condition.

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

Preparation, maintenance, and use of serum-free aggregating brain cell cultures.

Serum-free aggregating brain cell cultures are free-floating three-dimensional primary cell cultures able to reconstitute spontaneously a histotypic brain architecture to reproduce critical steps of brain development and to reach a high level of structural and functional maturity. This culture system offers, therefore, a unique model for neurotoxicity testing both during the development and at advanced cellular differentiation, and the high number of aggregates available combined with the excellent reproducibility of the cultures facilitates routine test procedures. This chapter presents a detailed description of the preparation, maintenance, and use of these cultures for neurotoxicity studies and a comparison of the developmental characteristics between cultures derived from the telencephalon and cultures derived from the whole brain. For culture preparation, mechanically dissociated embryonic brain tissue is used. The initial cell suspension, composed of neural stem cells, neural progenitor cells, immature postmitotic neurons, glioblasts, and microglial cells, is kept in a serum-free, chemically defined medium under continuous gyratory agitation. Spherical aggregates form spontaneously and are maintained in suspension culture for several weeks. Within the aggregates, the cells rearrange and mature, reproducing critical morphogenic events, such as migration, proliferation, differentiation, synaptogenesis, and myelination. For experimentation, replicate cultures are prepared by the randomization of aggregates from several original flasks. The high yield and reproducibility of the cultures enable multiparametric endpoint analyses, including "omics" approaches.

ROLES OF ACID-SENSING ION CHANNELS (ASICS) IN PERIPHERAL NEUROPEPTIDE SECRETION AND PAIN

Acid-sensing ion channels (ASICs) are non-voltage-gated sodium channels activated by an extracellular acidification. They are widely expressed in neurons of the central and peripheral nervous system. ASICs have a role in learning, the expression of fear, in neuronal death after cerebral ischemia, and in pain sensation. Tissue damage leads to the release of inflammatory mediators. There is a subpopulation of sensory neurons which are able to release the neuropeptides calcitonin gene-related peptide (CGRP) and substance P (SP). Neurogenic inflammation refers to the process whereby peripheral release of the neuropeptides CGRP and SP induces vasodilation and extravasation of plasma proteins, respectively. Our laboratory has previously shown that calcium-permeable homomeric ASIC1a channels are present in a majority of CGRP- or SP-expressing small diameter sensory neurons. In the first part of my thesis, we tested the hypothesis that a local acidification can produce an ASIC-mediated calcium-dependant neuropeptide secretion. We have first verified the co-expression of ASICs and CGRP/SP using immunochemistry and in-situ hybridization on dissociated rat dorsal root ganglion (DRG) neurons. We found that most CGRP/SP-positive neurons also expressed ASIC1a and ASIC3 subunits. Calcium imaging experiments with Fura-2 dye showed that an extracellular acidification can induce an increase of intracellular Ca2+ concentration, which is essential for secretion. This increase of intracellular Ca2+ concentration is, at least in some cells, ASIC-dependent, as it can be prevented by amiloride, an ASIC antagonist, and by Psalmotoxin (PcTx1), a specific ASIC1a antagonist. We identified a sub-population of neurons whose acid-induced Ca2+ entry was completely abolished by amiloride, an amiloride-resistant population which does not express ASICs, but rather another acid-sensing channel, possibly transient receptor potential vanilloïde 1 (TRPV1), and a population expressing both H+-gated channel types. Voltage-gated calcium channels (Cavs) may also mediate Ca2+ entry. Co-application of the Cavs inhibitors (ω-conotoxin MVIIC, Mibefradil and Nifedipine) reduced the Ca2+ increase in neurons expressing ASICs during an acidification to pH 6. This indicates that ASICs can depolarise the neuron and activate Cavs. Homomeric ASIC1a are Ca2+-permeable and allow a direct entry of Ca2+ into the cell; other ASICs mediate an indirect entry of Ca2+ by inducing a membrane depolarisation that activates Cavs. We showed with a secretion assay that CGRP secretion can be induced by extracellular acidification in cultured rat DRG neurons. Amiloride and PcTx1 were not able to inhibit the secretion at acidic pH, but BCTC, a TRPV1 inhibitor was able to decrease the secretion induced by an extracellular acidification in our in vitro secretion assay. In conclusion, these results show that in DRG neurons a mild extracellular acidification can induce a calcium-dependent neuropeptide secretion. Even if our data show that ASICs can mediate an increase of intracellular Ca2+ concentration, this appears not to be sufficient to trigger neuropeptide secretion. TRPV1, a calcium channel whose activation induces a sustained current - in contrary of ASICs - played in our experimental conditions a predominant role in neurosecretion. In the second part of my thesis, we focused on the role of ASICs in neuropathic pain. We used the spared nerve injury (SNI) model which consists in a nerve injury that induces symptoms of neuropathic pain such as mechanical allodynia. We have previously shown that the SNI model modifies ASIC currents in dissociated rat DRG neurons. We hypothesized that ASICs could play a role in the development of mechanical allodynia. The SNI model was performed on ASIC1a, -2, and -3 knock-out mice and wild type littermates. We measured mechanical allodynia on these mice with calibrated von Frey filaments. There were no differences between the wild-type and the ASIC1, or ASIC2 knockout mice. ASIC3 null mice were less sensitive than wild type mice at 21 day after SNI, indicating a role for ASIC3. Finally, to investigate other possible roles of ASICs in the perception of the environment, we measured the baseline heat responses. We used two different models; the tail flick model and the hot plate model. ASIC1a null mice showed increased thermal allodynia behaviour in the hot plate test at three different temperatures (49, 52, 55°C) compared to their wild type littermates. On the contrary, ASIC2 null mice showed reduced thermal allodynia behaviour in the hot plate test compared to their wild type littermates at the three same temperatures. We conclude that ASIC1a and ASIC2 in mice can play a role in temperature sensing. It is currently not understood how ASICs are involved in temperature sensing and what the reason for the opposed effects in the two knockout models is.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Prediction of resting energy expenditure from fat-free mass and fat mass.

On the basis of literature values, the relationship between fat-free mass (FFM), fat mass (FM), and resting energy expenditure [REE (kJ/24 h)] was determined for 213 adults (86 males, 127 females). The objectives were to develop a mathematical model to predict REE based on body composition and to evaluate the contribution of FFM and FM to REE. The following regression equations were derived: 1) REE = 1265 + (93.3 x FFM) (r2 = 0.727, P < 0.001); 2) REE = 1114 + (90.4 x FFM) + (13.2 x FM) (R2 = 0.743, P < 0.001); and 3) REE = (108 x FFM) + (16.9 x FM) (R2 = 0.986, P < 0.001). FM explained only a small part of the variation remaining after FFM was accounted for. The models that include both FFM and FM are useful in examination of the changes in REE that occur with a change in both the FFM and FM. To account for more of the variability in REE, FFM will have to be divided into organ mass and skeletal muscle mass in future analyses.

Combined use of the GGSFT data base and on Board Marine Collected Data to Model the Moho Beneath the Powell Basin, Antarctica

The Powell Basin is a small oceanic basin located at the NE end of the Antarctic Peninsula developed during the Early Miocene and mostly surrounded by the continental crusts of the South Orkney Microcontinent, South Scotia Ridge and Antarctic Peninsula margins. Gravity data from the SCAN 97 cruise obtained with the R/V Hespérides and data from the Global Gravity Grid and Sea Floor Topography (GGSFT) database (Sandwell and Smith, 1997) are used to determine the 3D geometry of the crustal-mantle interface (CMI) by numerical inversion methods. Water layer contribution and sedimentary effects were eliminated from the Free Air anomaly to obtain the total anomaly. Sedimentary effects were obtained from the analysis of existing and new SCAN 97 multichannel seismic profiles (MCS). The regional anomaly was obtained after spectral and filtering processes. The smooth 3D geometry of the crustal mantle interface obtained after inversion of the regional anomaly shows an increase in the thickness of the crust towards the continental margins and a NW-SE oriented axis of symmetry coinciding with the position of an older oceanic spreading axis. This interface shows a moderate uplift towards the western part and depicts two main uplifts to the northern and eastern sectors.

Expression of MYC, IgM, As Well As Non-Germinal Centre B-Cell Like Immunophenotype and Positive Immunofish Index Predict a Worse Progression Free Survival and Overall Survival in a Series of 670 De Novo Diffuse Large B-Cell Lymphomas Included in Clinical Trials: A GELA Study of the 2003 Program

Introduction: Diffuse large B-cell lymphomas (DLBCL) represent a heterogeneous disease with variable clinical outcome. Identifying phenotypic biomarkers of tumor cells on paraffin sections that predict different clinical outcome remain an important goal that may also help to better understand the biology of this lymphoma. Differentiating non-germinal centre B-cell-like (non-GCB) from Germinal Centre B-cell-like (GCB) DLBCL according to Hans algorithm has been considered as an important immunohistochemical biomarker with prognostic value among patients treated with R-CHOP although not reproducibly found by all groups. Gene expression studies have also shown that IgM expression might be used as a surrogate for the GCB and ABC subtypes with a strong preferential expression of IgM in ABC DLBCL subtype. ImmunoFISH index based on the differential expression of MUM-1, FOXP1 by immunohistochemistry and on the BCL6 rearrangement by FISH has been previously reported (C Copie-Bergman, J Clin Oncol. 2009;27:5573-9) as prognostic in an homogeneous series of DLBCL treated with R-CHOP. In addition, oncogenic MYC protein overexpression by immunohistochemistry may represent an easy tool to identify the consequences of MYC deregulation in DLBCL. Our aim was to analyse by immunohistochemistry the prognostic relevance of MYC, IgM, GCB/nonGCB subtype and ImmunoFISH index in a large series of de novo DLBCL treated with Rituximab (R)-chemotherapy (anthracyclin based) included in the 2003 program of the Groupe d'Etude des Lymphomes de l'Adulte (GELA) trials. Methods: The 2003 program included patients with de novo CD20+ DLBCL enrolled in 6 different LNH-03 GELA trials (LNH-03-1B, -B, -3B, 39B, -6B, 7B) stratifying patients according to age and age-adjusted IPI. Tumor samples were analyzed by immunohistochemistry using CD10, BCL6, MUM1, FOXP1 (according to Barrans threshold), MYC, IgM antibodies on tissue microarrays and by FISH using BCL6 split signal DNA probes. Considering evaluable Hans score, 670 patients were included in the study with 237 (35.4%) receiving intensive R-ACVBP regimen and 433 (64.6%) R-CHOP/R-mini-CHOP. Results: 304 (45.4%) DLBCL were classified as GCB and 366 (54.6%) as non-GCB according to Hans algorithm. 337/567 cases (59.4%) were positive for the ImmunoFISH index (i.e. two out of the three markers positive: MUM1 protein positive, FOXP1 protein Variable or Strong, BCL6 rearrangement). Immunofish index was preferentially positive in the non-GCB subtype (81.3%) compared to the GCB subtype (31.2%), (p<0.001). IgM was recorded as positive in tumor cells in 351/637 (52.4%) DLBCL cases with a preferential expression in non-GCB 195 (53.3%) vs GCB subtype 100(32.9%), p<0.001). MYC was positive in 170/577 (29.5%) cases with a 40% cut-off and in 44/577 (14.2%) cases with a cut-off of 70%. There was no preferential expression of MYC among GCB or non-GCB subtype (p>0.4) for both cut-offs. Progression-free Survival (PFS) was significantly worse among patients with high IPI score (p<0.0001), IgM positive tumor (p<0.0001), MYC positive tumor with a 40% threshold (p<0.001), ImmunoFISH positive index (p<0.002), non-GCB DLBCL subtype (p<0.0001). Overall Survival (OS) was also significantly worse among patients with high IPI score (p<0.0001), IgM positive tumor (p=0.02), MYC positive tumor with a 40% threshold (p<0.01), ImmunoFISH positive index (p=0.02), non-GCB DLBCL subtype (p<0.0001). All significant parameters were included in a multivariate analysis using Cox Model and in addition to IPI, only the GCB/non-GCB subtype according to Hans algorithm predicted significantly a worse PFS among non-GCB subgroup (HR 1.9 [1.3-2.8] p=0.002) as well as a worse OS (HR 2.0 [1.3-3.2], p=0.003). This strong prognostic value of non-GCB subtyping was confirmed considering only patients treated with R- CHOP for PFS (HR 2.1 [1.4-3.3], p=0.001) and for OS (HR 2.3 [1.3-3.8], p=0.002). Conclusion: Our study on a large series of patients included in trials confirmed the relevance of immunohistochemistry as a useful tool to identify significant prognostic biomarkers for clinical use. We show here that IgM and MYC might be useful prognostic biomarkers. In addition, we confirmed in this series the prognostic value of the ImmunoFISH index. Above all, we fully validated the strong and independent prognostic value of the Hans algorithm, daily used by the pathologists to subtype DLBCL.