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.

A Role for cis Interaction between the Inhibitory Ly49A receptor and MHC class I for natural killer cell education.

Natural killer (NK) cells show enhanced functional competence when they express inhibitory receptors specific for inherited major histocompatibility complex class I (MHC-I) molecules. Current models imply that NK cell education requires an interaction of inhibitory receptors with MHC-I expressed on other cells. However, the inhibitory Ly49A receptor can also bind MHC-I ligand on the NK cell itself (in cis). Here we describe a Ly49A variant, which can engage MHC-I expressed on other cells but not in cis. Even though this variant inhibited NK cell effector function, it failed to educate NK cells. The association with MHC-I in cis sequestered wild-type Ly49A, and this was found to relieve NK cells from a suppressive effect of unengaged Ly49A. These data explain how inhibitory MHC-I receptors can facilitate NK cell activation. They dissociate classical inhibitory from educating functions of Ly49A and suggest that cis interaction of Ly49A is necessary for NK cell education.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Ly49D engagement on T lymphocytes induces TCR-independent activation and CD8 effector functions that control tumor growth.

Recent data showing expression of activating NK receptors (NKR) by conventional T lymphocytes raise the question of their role in the triggering of TCR-independent responses that could be damaging for the host. Transgenic mice expressing the activating receptor Ly49D/DAP12 offer the opportunity to better understand the relevance of ITAM signaling in the biology of T cells. In vitro experiments showed that Ly49D engagement on T lymphocytes by a cognate MHC class I ligand expressed by Chinese hamster ovary (CHO) cells or by specific Ab triggered cellular activation of both CD4 and CD8 populations with modulation of activation markers and cytokine production. The forced expression of the ITAM signaling chain DAP12 is mandatory for Ly49D-transgenic T cell activation. In addition, Ly49D stimulation induced T lymphocyte proliferation, which was much stronger for CD8 T cells. Phenotypic analysis of anti-Ly49D-stimulated CD8 T cells and their ability to produce high levels of IFN-gamma and to kill target cells indicate that Ly49D ligation generates effector cytotoxic CD8 T cells. Ly49D engagement by itself also triggered cytotoxic activity of activated CD8 T cells. Adoptive transfer experiments confirmed that Ly49D-transgenic CD8 T cells are able to control growth of CHO tumor cells or RMA cells transfected with Hm1-C4, the Ly49D ligand normally expressed by CHO. In conclusion, Ly49D engagement on T cells leads to T cell activation and to a full range of TCR-independent effector functions of CD8 T cells.

Equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories

A geometrical treatment of the path integral for gauge theories with first-class constraints linear in the momenta is performed. The equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories is established. In the process of carrying this out we find a modified version of the original Faddeev-Popov formula which is derived under much more general conditions than the usual one. Throughout this paper we emphasize the fact that we only make use of the information contained in the action for the system, and of the natural geometrical structures derived from it.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Pedotransfer functions to estimate water retention parameters of soils in northeastern Brazil

Pedotransfer functions (PTF) were developed to estimate the parameters (α, n, θr and θs) of the van Genuchten model (1980) to describe soil water retention curves. The data came from various sources, mainly from studies conducted by universities in Northeast Brazil, by the Brazilian Agricultural Research Corporation (Embrapa) and by a corporation for the development of the São Francisco and Parnaíba river basins (Codevasf), totaling 786 retention curves, which were divided into two data sets: 85 % for the development of PTFs, and 15 % for testing and validation, considered independent data. Aside from the development of general PTFs for all soils together, specific PTFs were developed for the soil classes Ultisols, Oxisols, Entisols, and Alfisols by multiple regression techniques, using a stepwise procedure (forward and backward) to select the best predictors. Two types of PTFs were developed: the first included all predictors (soil density, proportions of sand, silt, clay, and organic matter), and the second only the proportions of sand, silt and clay. The evaluation of adequacy of the PTFs was based on the correlation coefficient (R) and Willmott index (d). To evaluate the PTF for the moisture content at specific pressure heads, we used the root mean square error (RMSE). The PTF-predicted retention curve is relatively poor, except for the residual water content. The inclusion of organic matter as a PTF predictor improved the prediction of parameter a of van Genuchten. The performance of soil-class-specific PTFs was not better than of the general PTF. Except for the water content of saturated soil estimated by particle size distribution, the tested models for water content prediction at specific pressure heads proved satisfactory. Predictions of water content at pressure heads more negative than -0.6 m, using a PTF considering particle size distribution, are only slightly lower than those obtained by PTFs including bulk density and organic matter content.

Pedotransfer functions to predict water retention for soils of the humid tropics: a review

Over the past three decades, pedotransfer functions (PTFs) have been widely used by soil scientists to estimate soils properties in temperate regions in response to the lack of soil data for these regions. Several authors indicated that little effort has been dedicated to the prediction of soil properties in the humid tropics, where the need for soil property information is of even greater priority. The aim of this paper is to provide an up-to-date repository of past and recently published articles as well as papers from proceedings of events dealing with water-retention PTFs for soils of the humid tropics. Of the 35 publications found in the literature on PTFs for prediction of water retention of soils of the humid tropics, 91 % of the PTFs are based on an empirical approach, and only 9 % are based on a semi-physical approach. Of the empirical PTFs, 97 % are continuous, and 3 % (one) is a class PTF; of the empirical PTFs, 97 % are based on multiple linear and polynomial regression of n th order techniques, and 3 % (one) is based on the k-Nearest Neighbor approach; 84 % of the continuous PTFs are point-based, and 16 % are parameter-based; 97 % of the continuous PTFs are equation-based PTFs, and 3 % (one) is based on pattern recognition. Additionally, it was found that 26 % of the tropical water-retention PTFs were developed for soils in Brazil, 26 % for soils in India, 11 % for soils in other countries in America, and 11 % for soils in other countries in Africa.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Functional analysis of monocyte MHC class II compartments.

Circulating monocytes, as dendritic cell and macrophage precursors, exhibit several functions usually associated with antigen-presenting cells, such as phagocytosis and presence of endosomal/lysosomal degradative compartments particularly enriched in Lamp-1, MHC class II molecules, and other proteins related to antigen processing and MHC class II loading [MHC class II compartments (MIICs)]. Ultrastructural analysis of these organelles indicates that, differently from the multivesicular bodies present in dendritic cells, in monocytes the MIICs are characterized by a single perimetral membrane surrounding an electron-dense core. Analysis of their content reveals enrichment in myeloperoxidase, an enzyme classically associated with azurophilic granules in granulocytes and mast cell secretory lysosomes. Elevation in intracellular free calcium levels in monocytes induced secretion of beta-hexosaminidase, cathepsins, and myeloperoxidase in the extracellular milieu; surface up-regulation of MHC class II molecules; and appearance of lysosomal resident proteins. The Ca(2+)-regulated surface transport mechanism of MHC class II molecules observed in monocytes is different from the tubulovesicular organization of the multivesicular bodies previously reported in dendritic cells and macrophages. Hence, in monocytes, MHC class II-enriched organelles combine degradative functions typical of lysosomes and regulated secretion typical of secretory lysosomes. More important, Ca(2+)-mediated up-regulation of surface MHC class II molecules is accompanied by extracellular release of lysosomal resident enzymes.

Role of major histocompatibility complex class II expression by non-hematopoietic cells in autoimmune and inflammatory disorders: facts and fiction.

It is well established that interactions between CD4(+) T cells and major histocompatibility complex class II (MHCII) positive antigen-presenting cells (APCs) of hematopoietic origin play key roles in both the maintenance of tolerance and the initiation and development of autoimmune and inflammatory disorders. In sharp contrast, despite nearly three decades of intensive research, the functional relevance of MHCII expression by non-hematopoietic tissue-resident cells has remained obscure. The widespread assumption that MHCII expression by non-hematopoietic APCs has an impact on autoimmune and inflammatory diseases has in most instances neither been confirmed nor excluded by indisputable in vivo data. Here we review and put into perspective conflicting in vitro and in vivo results on the putative impact of MHCII expression by non-hematopoietic APCs-in both target organs and secondary lymphoid tissues-on the initiation and development of representative autoimmune and inflammatory disorders. Emphasis will be placed on the lacunar status of our knowledge in this field. We also discuss new mouse models-developed on the basis of our understanding of the molecular mechanisms that regulate MHCII expression-that constitute valuable tools for filling the severe gaps in our knowledge on the functions of non-hematopoietic APCs in inflammatory conditions.

bHLH class transcription factors take centre stage in phytochrome signalling.

The phytochrome family of photoreceptors (there are five phytochromes in Arabidopsis, named phyA to phyE) maximally absorbs red and far-red light and plays important functions throughout the life cycle of plants. Several recent studies have shown that multiple related bHLH (basic helix-loop-helix) class transcription factors play key roles in phytochrome signal transduction. Somewhat surprisingly these transcription factors primarily act as negative regulators of phytochrome signalling. Moreover, in some cases, the phytochromes inhibit those negative regulators.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

NLRC5 exclusively transactivates MHC class I and related genes through a distinctive SXY module.

MHC class II (MHCII) genes are transactivated by the NOD-like receptor (NLR) family member CIITA, which is recruited to SXY enhancers of MHCII promoters via a DNA-binding "enhanceosome" complex. NLRC5, another NLR protein, was recently found to control transcription of MHC class I (MHCI) genes. However, detailed understanding of NLRC5's target gene specificity and mechanism of action remained lacking. We performed ChIP-sequencing experiments to gain comprehensive information on NLRC5-regulated genes. In addition to classical MHCI genes, we exclusively identified novel targets encoding non-classical MHCI molecules having important functions in immunity and tolerance. ChIP-sequencing performed with Rfx5(-/-) cells, which lack the pivotal enhanceosome factor RFX5, demonstrated its strict requirement for NLRC5 recruitment. Accordingly, Rfx5-knockout mice phenocopy Nlrc5 deficiency with respect to defective MHCI expression. Analysis of B cell lines lacking RFX5, RFXAP, or RFXANK further corroborated the importance of the enhanceosome for MHCI expression. Although recruited by common DNA-binding factors, CIITA and NLRC5 exhibit non-redundant functions, shown here using double-deficient Nlrc5(-/-)CIIta(-/-) mice. These paradoxical findings were resolved by using a "de novo" motif-discovery approach showing that the SXY consensus sequence occupied by NLRC5 in vivo diverges significantly from that occupied by CIITA. These sequence differences were sufficient to determine preferential occupation and transactivation by NLRC5 or CIITA, respectively, and the S box was found to be the essential feature conferring NLRC5 specificity. These results broaden our knowledge on the transcriptional activities of NLRC5 and CIITA, revealing their dependence on shared enhanceosome factors but their recruitment to distinct enhancer motifs in vivo. Furthermore, we demonstrated selectivity of NLRC5 for genes encoding MHCI or related proteins, rendering it an attractive target for therapeutic intervention. NLRC5 and CIITA thus emerge as paradigms for a novel class of transcriptional regulators dedicated for transactivating extremely few, phylogenetically related genes.

On the transcriptional role of NLRC5 and the function of NLRC5-driven MHC class I expression in the immune system

Major histocompatibility complex (MHC) molecules are of crucial importance for the immune system to recognize and defend the body against external attacks. Foreign antigens are presented by specialized cells, called antigen presenting cells, to T lymphocytes in the context of MHC molecules, thereby inducing T cell activation. In addition, MHC molecules are essential for Natural Killer (NK) cell biology, playing a role in NK cell education and activation. Recently, the NOD-like receptor (NLR) family member NLRC5 (NLR caspase recruitment domain containing protein 5) was found to act as transcriptional regulator of MHC class I, in particular in T and NK cells. Its role in MHC class I expression is however minor in dendritic cells (DCs). This raised the question of whether inflammatory conditions, which augment the levels of NLRC5 in DCs, could increase its contribution to MHC class I expression. Our work shows that MHC class I transcript and intracellular levels depend on NLRC5, while its role in MHC class I surface expression is instead negligible. We describe however a general salvage mechanism that enables cells with low intracellular MHC class I levels to nevertheless maintain relatively high MHC class I on the cell surface. In addition, we lack a thorough understanding of NLRC5 target gene specificity and mechanism of action. Our work delineates the unique consensus sequence in MHC class I promoters required for NLRC5 recruitment and pinpoints conserved features conferring its specificity. Furthermore, through genome-wide analyses, we confirm that NLRC5 regulates classical MHC class I genes and identify novel target genes all encoding non-classical MHC class I molecules exerting an array of functions in immunity and tolerance. We finally asked why a dedicated factor co-regulates MHC class I expression specifically in T and NK lymphocytes. We show that deregulated NLRC5 expression affects the education of NK cells and alters the crosstalk between T and NK cells, leading to NK cell-mediated killing of T lymphocytes. Altogether this thesis work brings insights into molecular and physiological aspects of NLRC5 function, which might help understand certain aspects of immune responses and disorders. -- Les molécules du complexe majeur d'histocompatibilité (CMH) sont essentielles au système immunitaire pour l'initiation de la réponse immunitaire. En effet, l'activation des lymphocytes T nécessite la reconnaissance d'un antigène étranger présenté par les cellules présentatrices d'antigènes sur une molécule du CMH. Les molécules du CMH ont également un rôle fondamental pour la fonction des cellules Natural Killer (NK) puisqu'elles sont nécessaires à leur processus d'éducation et d'activation. Récemment, NLRC5 (NLR caspase recruitment domain containing protein 5), un membre de la famille des récepteurs de type NOD (NLRs), a été décrit comme un facteur de transactivation de l'expression des gènes du CMH de classe I. A l'état basai, cette fonction transcriptionnelle est essentielle dans les lymphocytes T et NK, alors que ce rôle reste mineur pour l'expression des molécules du CMH de classe I dans les cellules dendritiques (DCs). Dans des conditions inflammatoires, l'expression de NLRC5 augmente dans les DCs. Notre travail démontre que, dans ces conditions, les transcrits et les niveaux intracellulaires des molécules du CMH de classe I augmentent aussi d'une façon dépendante de NLRC5. A contrario, le rôle de NLRC5 sur les niveaux de molécules de surface reste minoritaire. Cette observation nous a conduits à l'identification d'un mécanisme général de compensation qui permet aux cellules de maintenir des niveaux relativement élevés de molécules de CMH de class I à leur surface malgré de faibles niveaux intracellulaires. De plus, il semblait nécessaire de s'orienter vers une approche plus globale afin de déterminer l'étendue de la fonction transcriptionnelle de NLRC5. Par une approche du génome entier, nous avons pu décrire une séquence consensus conservée présente dans les promoteurs des gènes du CMH de classe I, sur laquelle NLRC5 est spécifiquement recruté. Nous avons pu également identifier de nouveaux gènes cibles codant pour des molécules de CMH de classe I non classiques impliqués dans l'immunité et la tolérance. Finalement, nous nous sommes demandé quel est l'intérêt d'avoir un facteur transcriptionnel, en l'occurrence NLRC5, qui orchestre l'expression du CMH de classe I dans les lymphocytes T et NK. Nous montrons que la dérégulation de l'expression de NLRC5 affecte l'éducation des cellules NK et conduit à la mort cellulaire des lymphocytes T médiée par les cellules NK. Dans l'ensemble ce travail de thèse contribue à la caractérisation du rôle de NLRC5, tant au niveau moléculaire que physiologique, ce qui présente un intérêt dans le cadre de la compréhension de certains aspects physiopathologique de la réponse immunitaire.