Hyperbolic Hubbard-Stratonovich transformations and bosonisation of granular fermionic systems

The present work consists of two parts. The first part deals with hyperbolic Hubbard-Stratonovich transformations. Such transformations are used to derive non-linear sigma models that describe the low energy behaviour of disordered electron systems. For a long time the mathematical status of hyperbolic Hubbard-Stratonovich transformations of Pruisken-Schäfer type remained unclear. Only recently the two special cases of pseudounitary and pseudoorthogonal symmetry were proven . In this thesis we prove the transformation for a general (essentially semisimple) symmetry group. The proof is descriptive and shows explicitly the connection to the standard Gaussian integrals. In the second part we develop a novel method to bosonise granular fermionic systems. The method is related to the method of coherent states. In particular it is not based on the well known bosonisation of (1+1)-dimensional systems. One approach is to use the colour-flavour transformation to transform the Grassmann path integral representation of a grand canonical partition function in a way that allows to eliminate the Grassmann variables. The result is a path integral in generalised coherent states with special boundary conditions

Classical and quantum LTB model for the non-marginal case

We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the non-marginal case (defined by the fact that the shells of the dust cloud start with a non-vanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.Comment: 23 pages, no figures, typos correcte

Induction of the lac promoter in the absence of DNA loops and the stoichiometry of induction

In vivo induction of the Escherichia coli lactose operon as a function of inducer concentration generates a sigmoidal curve, indicating a non-linear response. Suggested explanations for this dependence include a 2:1 inducer–repressor stoichiometry of induction, which is the currently accepted view. It is, however, known for decades that, in vitro, operator binding as a function of inducer concentration is not sigmoidal. This discrepancy between in vivo and in vitro data has so far not been resolved. We demonstrate that the in vivo non-linearity of induction is due to cooperative repression of the wild-type lac operon through DNA loop formation. In the absence of DNA loops, in vivo induction curves are hyperbolic. In the light of this result, we re-address the question of functional molecular inducer–repressor stoichiometry in induction of the lac operon

Equivalence of domains for hyperbolic Hubbard-Stratonovich transformations

We settle a long standing issue concerning the traditional derivation of non-compact non-linear sigma models in the theory of disordered electron systems: the hyperbolic Hubbard-Stratonovich (HS) transformation of Pruisken-Schaefer type. Only recently the validity of such transformations was proved in the case of U(p,q) (non-compact unitary) and O(p,q) (non-compact orthogonal) symmetry. In this article we give a proof for general non-compact symmetry groups. Moreover we show that the Pruisken-Schaefer type transformations are related to other variants of the HS transformation by deformation of the domain of integration. In particular we clarify the origin of surprising sign factors which were recently discovered in the case of orthogonal symmetry.Comment: 30 pages, 3 figure

Phenomenology of the Term Structure of Interest Rates with Pade Approximants

The classical approach in finance attempts to model the term structure of interest rates using specified stochastic processes and the no arbitrage argument. Up to now, no universally accepted theory has been obtained for the description of experimental data. We have chosen a more phenomenological approach. It is based on results obtained some twenty years ago by physicists, results which show that Pad\'e Approximants are very suitable for approximating large classes of functions in a very precise and coherent way. In this paper, we have chosen to compare Pad\'e Approximants with very low indices with the experimental densities of interest rates variations. We have shown that the data published by the Federal Reserve System in the United States are very well reproduced with two parameters only. These parameters are rather simple functions of the lag and of the maturity and are directly related to the moments of the distributions.Comment: LaTeX, 28 pages, 13 figure

A management architecture for active networks

In this paper we present an architecture for network and applications management, which is based on the Active Networks paradigm and shows the advantages of network programmability. The stimulus to develop this architecture arises from an actual need to manage a cluster of active nodes, where it is often required to redeploy network assets and modify nodes connectivity. In our architecture, a remote front-end of the managing entity allows the operator to design new network topologies, to check the status of the nodes and to configure them. Moreover, the proposed framework allows to explore an active network, to monitor the active applications, to query each node and to install programmable traps. In order to take advantage of the Active Networks technology, we introduce active SNMP-like MIBs and agents, which are dynamic and programmable. The programmable management agents make tracing distributed applications a feasible task. We propose a general framework that can inter-operate with any active execution environment. In this framework, both the manager and the monitor front-ends communicate with an active node (the Active Network Access Point) through the XML language. A gateway service performs the translation of the queries from XML to an active packet language and injects the code in the network. We demonstrate the implementation of an active network gateway for PLAN (Packet Language for Active Networks) in a forty active nodes testbed. Finally, we discuss an application of the active management architecture to detect the causes of network failures by tracing network events in time

Formalizability and Knowledge Ascriptions in Mathematical Practice

Nous examinons les conditions de vérité pour des attributions de savoir dans le cas des connaissances mathématiques. La disposition d’une démonstration formalisable semble être un critère naturel :(*) X sait que p est vrai si et seulement si X en principe dispose d’une démonstration formalisable pour p.La formalisabilité pourtant ne joue pas un grand rôle dans la pratique mathématique effective. Nous présentons des résultats d’une recherche empirique qui indiquent que les mathématiciens n’employent pas certaines spécifications de (*) quand ils attribuent du savoir. De plus, nous montrons que le concept de savoir mathématique qui est à la base de l’emploi effectif du mot « savoir » de la pratique mathématique est tout à fait compatible avec certaines intuitions philosophiques mais apparaît comme différent des concepts philosophiques formant la base de (*).We investigate the truth conditions of knowledge ascriptions for the case of mathematical knowledge. The availability of a formalizable mathematical proof appears to be a natural criterion:(*) X knows that p is true iff X has available a formalizable proof of p.Yet, formalizability plays no major role in actual mathematical practice. We present results of an empirical study, which suggest that certain readings of (*) are not necessarily employed by mathematicians when ascribing knowledge. Further, we argue that the concept of mathematical knowledge underlying the actual use of “to know” in mathematical practice is compatible with certain philosophical intuitions, but seems to differ from philosophical knowledge conceptions underlying (*)

Accurate prediction of gene expression by integration of DNA sequence statistics with detailed modeling of transcription regulation

Gene regulation involves a hierarchy of events that extend from specific protein-DNA interactions to the combinatorial assembly of nucleoprotein complexes. The effects of DNA sequence on these processes have typically been studied based either on its quantitative connection with single-domain binding free energies or on empirical rules that combine different DNA motifs to predict gene expression trends on a genomic scale. The middle-point approach that quantitatively bridges these two extremes, however, remains largely unexplored. Here, we provide an integrated approach to accurately predict gene expression from statistical sequence information in combination with detailed biophysical modeling of transcription regulation by multidomain binding on multiple DNA sites. For the regulation of the prototypical lac operon, this approach predicts within 0.3-fold accuracy transcriptional activity over a 10,000-fold range from DNA sequence statistics for different intracellular conditions.Comment: 15 pages, 5 figure