Showing papers by "University of Marne-la-Vallée published in 1997"

Backward Stochastic Differential Equations in Finance

Abstract: We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).

Ti k-edge xanes studies of ti coordination and disorder in oxide compounds: comparison between theory and experiment

Abstract: Experimental Ti $K$-edge x-ray-absorption near-edge structure (XANES) spectra for a variety of Ti(IV)-bearing crystalline oxide model compounds are compared with those calculated using the ab initio multiple-scattering code FEFF7. A scattering-theoretic interpretation of various features in the experimental spectra, including pre-edge and main-edge peaks, is presented together with an interpretation of the effects of disorder. The observed pre-edge features are found to vary in both position (by $\ensuremath{\approx}2\ifmmode\pm\else\textpm\fi{}0.1\mathrm{eV}$) and normalized height (from $\ensuremath{\approx}0.04$ to $1.0\ifmmode\pm\else\textpm\fi{}0.05$) as a function of Ti coordination (4, 5, or 6 oxygen nearest neighbors), in agreement with calculations. In aperiodic oxide compounds where the Ti coordination is unknown (e.g., titanosilicate glasses and melts), pre-edge position and height can be used to derive reliable information on Ti coordination chemistry. For example, one can distinguish between fivefold coordinated Ti (i.e., ${\mathrm{TiO}}_{5}$) and a 50:50 mixture of fourfold- and sixfold-coordinated Ti (i.e., ${\mathrm{TiO}}_{4}$ vs ${\mathrm{TiO}}_{6}$). Finally, it is proposed that the intensity of the main-edge features can be used as a probe of disorder in the short- and medium-range environment of Ti. This is exemplified by Ti XANES studies of the effect of radiation damage on ${\mathrm{CaTiSiO}}_{5}$ and the melting of ${\mathrm{K}}_{2}{\mathrm{TiSi}}_{2}{\mathrm{O}}_{7}$ glass at high temperature.

Prediction error method for second-order blind identification

Abstract: Blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest. In this paper, we introduce a second-order blind identification technique based on a linear prediction approach. In contrast to eigenstructure-based methods, it will be shown that the linear prediction error method is "robust" to order overdetermination. An asymptotic performance analysis of the proposed estimation method is carried out, consistency and asymptotic normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are finally presented to demonstrate the potential and the "robustness" of the proposed method.

Noncommutative Symmetric Functions Iv: Quantum Linear Groups andHecke Algebras at {\bi q}\,{\bf =}\,{\bf 0}

Abstract: We present representation theoretical interpretations of quasi-symmetric functions and noncommutative symmetric functions in terms of quantum linear groups and Hecke algebras at q=0. We obtain in this way a noncommutative realization of quasi-symmetric functions analogous to the plactic symmetric functions of Lascoux and Schutzenberger. The generic case leads to a notion of quantum Schur function.

Noncommutative symmetric functions II : Transformations of alphabets

Abstract: Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. It is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and various deformations of the classical sequences of Lie idempotents are obtained. In particular, we obtain several q-analogues of the Eulerian idempotents and of the Garsia-Reutenauer idempotents.

Banach spaces with small spaces of operators

Abstract: For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present several applications. Amongst them are constructions of a new prime Banach space, a space isomorphic to its subspaces of codimension two but not to its hyperplanes and a space isomorphic to its cube but not to its square.

Subspace-based techniques for blind separation of convolutive mixtures with temporally correlated sources

Abstract: This contribution addresses the blind identification of multiple input multiple output linear finite impulse response systems having a number of inputs less than the number of outputs. Recent publications have proposed an efficient second-order identification method in the single input multiple output case. Based on a subspace analysis, it allows a perfect recovery of the system parameters and excitation in a noise-free environment. Some extensions to the case of multiple inputs are also available under quite specific conditions. In this paper we indicate how to extend the original subspace-based approach to the general case.

On subspace methods for blind identification of single-input multiple-output FIR systems

Abstract: Blind identification of single-input multiple-output (SIMO) FIR systems based on second-order statistics has attracted a great deal of research effort. We focus on subspace estimation procedures, which exploit the structure of the range space of certain matrix-valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations. General subspace identifiability results are obtained, based on properties of minimal polynomial bases of rational subspaces. Several subspace estimation procedures are then derived. These estimators are all based on a weighted least-square solution of an overdetermined system of linear equations. An asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting.

Direct Construction of Compact Directed Acyclic Word Graphs

Abstract: The Directed Acyclic Word Graph (DAWG) is an efficient data structure to treat and analyze repetitions in a text, especially in DNA genomic sequences. Here, we consider the Compact Directed Acyclic Word Graph of a word. We give the first direct algorithm to construct it. It runs in time linear in the length of the string on a fixed alphabet. Our implementation requires half the memory space used by DAWGs.

Sections of convex bodies through their centroid

Abstract: We give the best estimate in the comparison of the volume of the section of a convex body in \( {\Bbb R}^n \) through its centroid by a k-dimensional affine subspace Ek with the volume of the section by any affine subspace parallel to Ek.

Symbolic dynamics and finite automata

Abstract: Symbolic dynamics is a field which was born with the work in topology of Marston Morse at the beginning of the 1920s [44]. It is, according to Morse, an “algebra and geometry of recurrence”. The idea is the following. Divide a surface into regions named by certain symbols. We then study the sequences of symbols obtained by scanning the successive regions while following a trajectory starting from a given point. A further paper by Morse and Hedlund [45] gave the basic results of this theory. Later, the theory was developed by many authors as a branch of ergodic theory (see for example the collected works in [59] or [12]). One of the main directions of research has been the problem of the isomorphism of shifts of finite type (see below the definition of these terms). This problem is not yet completely solved although the latest results of Kim and Roush [35] indicate a counterexample to a long-standing conjecture formulated by F. Williams [61].

Periodic nonlinear bubble motion in aqueous foam under oscillating shear strain

Abstract: The elastic response of aqueous foam to oscillating shear strain is probed by diffusing-wave spectroscopy. At low strains, the local bubble displacements are shown to be compatible with linear elastic behavior. At higher strains, a crossover to nonlinear but still fully periodic displacements is observed. To explain these results, we present a phenomenological model based on unstable bubble configurations.

Pattern Matching and Text Compression Algorithms.

Abstract: Pattern matching is the problem of locating a specific pattern inside raw data. The pattern is usually a collection of strings described in some formal language. Applications require two kinds of solution depending upon which string, the pattern, or the text, is given first. Solutions based on the use of automata or combinatorial properties of strings are commonly implemented to preprocess the pattern. The notion of indices realized by trees or automata is used in the second kind of solutions. The aim of data compression is to provide representation of data in a reduced form in order to save both storage place and transmission time. There is no loss of information, the compression processes are reversible. Pattern-matching and text-compression algorithms are two important subjects in the wider domain of text processing. They apply to the manipulation of texts (word editors), to the storage of textual data (text compression), and to data retrieval systems (full text search). They are basic components used in implementations of practical softwares existing under most operating systems. Moreover, they emphasize programming methods that serve as paradigms in other fields of computer science (system or software design). Finally, they also play an important role in theoretical computer science by providing challenging problems. Although data are recorded in various ways, text remains the main way to exchange information. This is particularly evident in literature or linguistics where data are composed of huge corpora and dictionaries, but applies as well to computer science where a large amount of data is stored in linear files. And it is also the case, for instance, in molecular biology because biological molecules can often be approximated as sequences of nucleotides or amino acids. Furthermore, the quantity of available data in these fields tend to double every 18 months. This is the reason that algorithms must be efficient even if the speed and storage capacity of computers increase continuously.

Coordination of Ti (super 4+) in silicate glasses; a high-resolution XANES spectroscopy study at the Ti K edge

Abstract: Abstract The coordination environment of Ti in eight Ti-bearing glasses of the Na2Si4O9-Na2Ti4O9 join (NTS) and in six ATY2 glasses (A2O·TiO2·2YO2, with A = Na, K, or Rb and Y = Si or Ge) was determined using high-resolution, X-ray absorption near-edge structure (XANES) spectroscopy at the Ti K edge in ambient conditions. Fivefold-coordinated Ti ([5]Ti) is the dominant Ti species (≥50 ± 10% of the total Ti) in all the glasses studied. Sixfold-coordinated Ti was detected mostly in sodic glasses (NTS, NTS2, NTG2), and it increases with TiO2 content (as high as 40 ± 10% of the total of Ti in the most TiO2-rich NTS glasses) and in the order Si < Ge. Fourfold-coordinated Ti was detected only in nonsodic ATY2 glasses, and its content increases in the order Na < K < Rb and Ge < Si. Fivefold-coordinated Ti4+ is probably present as square pyramidal, titanyl-bearing moieties, or (|5]Ti=O)O4. A synthesis of Ti4+ coordination for oxide glasses derived using direct methods (X-ray absorption and neutron scattering) can be used, for instance, to help in the interpretation of Raman scattering spectra collected for Ti-bearing glasses and to estimate NBO/T ratios better for titanosilicate glasses and melts.

Adsorption of Thorium on Amorphous Silica: An EXAFS Study

Abstract: Wet samples of Th(IV) sorbed on colloidal amorphous silica particles (Aerosil OX 200) have been studied with extended X-ray absorption fine structure spectroscopy (EXAFS) at the Th LIII edge (16.3 keV). The samples were collected with sample surface coverages ranging from 3.8 to 230%. No fundamental changes in the structural environment of Th in terms of the types and distances of nearest neighbors with increasing surface loading were detected, but the results indicate an increasing degree of structural disorder with increasing surface coverage. The O shell around Th shows a distorted configuration with two O atoms at 2.33 A distance and four to six O atoms at 2.55 A. Only one Si shell is observed, with two Si atoms at a distance of 3.8-3.9 A. These results have been interpreted with a double corner-sharing surface complex of Th on silica, where the Th atom shares one O atom with each of two coordinated SiO4 tetrahedra, accounting for the first O coordination shell detected as well as the Th-Si distances. The longer Th-O distances result from coordinated water molecules from solution. No Th-Th interactions could be detected in the EXAFS spectra. Copyright 1997 Academic Press. Copyright 1997Academic Press

On Compact Directed Acyclic Word Graphs

Abstract: The Directed Acyclic Word Graph (DAWG) is a space-efficient data structure to treat and analyze repetitions in a text, especially in DNA genomic sequences. Here, we consider the Compact Directed Acyclic Word Graph of a word. We give the first direct algorithm to construct it. It runs in time linear in the length of the string on a fixed alphabet. Our implementation requires half the memory space used by DAWGs.

Fivefold-coordinated Ti (super 4+) in metamict zirconolite and titanite; a new occurrence shown by Ti K-edge XANES spectroscopy

Abstract: Abstract The coordination environments of Ti in two fully metamict zirconolite samples and two partially metamict titanite samples were determined using high-resolution. X-ray absorption near-edge structure (XANES) spectroscopy at the Ti K edge. Fivefold-coordinated Ti is the dominant Ti species in the zirconolite samples (~-80 ± 10% of the total Ti atoms). This unusual Ti coordination is also possible in the titanite samples. No significant evidence for [4]Ti was found in any of the samples studied. Comparison with other amorphous materials, such as other metamict minerals (aes- chynite and pyrochlore) and titanosilicate glasses and melts, suggests that fivefold coordination is rather common for Ti4+ in aperiodic structures. However, the metamict state is characterized by the presence of unusual trigonal bipyramids around |5|Ti4+.

Inégalités de Brascamp-Lieb et convexité

Abstract: Resume Cette Note donne une demonstration elementaire d’une inegalite de Brascamp-Lieb et d’une nouvelle inegalite duale qui a de nombreuses applications en convexite : minoration du volume de projections, du volume ratio exterieur et estimation MM* dans le cas non symetrique

On the volume of macromolecules

Abstract: The surface accessible to the solvent and the volume contained within this surface are key notions both for the general description of proteins and other macromolecules, and for studying their interactions with the solvent and protein stability under a change of various parameters. There are many geometrical recipes for assigning a surface area and a volume to a protein. These recipes are not equivalent, and involve parameters whose definition is not always unique. We discuss the relative merits of the molecular and Voronoi definitions of protein volume, and their relation to experimentally measurable quantities like “intrinsic compressibility.” The molecular volume of a protein has the contradictory feature of not reflecting the packing of solvent molecules around it, being at the same time a function of the probe radius. The Voronoi volume does take into account modifications occurring in the solvent due to the presence of the protein and to possible external perturbations. Using the Voronoi volume results in a much better approximation of the experimental intrinsic compressibility. We suggest an explanation for the incorrect behavior of the molecular volume as a function of pressure, and propose using a pressure-dependent probe radius as a remedy in such cases when the molecular volume computation might be preferable. © 1997 John Wiley & Sons, Inc. Biopoly 41: 785–797, 1997

q-Deformed Fock spaces and modular representations of spin symmetric groups

Abstract: We use the Fock-space representation of the quantum affine algebra of type to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture relating this basis to decomposition matrices of spin symmetric groups in characteristic 2n+1.

On White Noises Driven by Hidden Markov Chains

Abstract: We consider a time series model where the variance of the underlying process depends on the state of a non-observed Markov chain. Maximum likelihood estimates are shown to be consistent. Estimators with asymptotic Gaussian distribution are proposed. Prediction and identification are also mentioned. This is illustrated by means of real and simulated data sets

Operators on Subspaces of Hereditarily Indecomposable Banach Spaces

Abstract: We show that if X is a complex hereditarily indecomposable space, then every operator from a subspace Y of X to X is of the form λ I + S , where I is the inclusion map and S is strictly singular.

Chains and Superchains for ω-Rational Sets, Automata and Semigroups

Abstract: We introduce several equivalent notions that generalize ones introduced by Klaus Wagner for finite Muller automata under the name of chains and superchains. We define such objects in relation to ω-rational sets, Muller automata or also ω-semigroups. We prove their equivalence and derive some basic properties of these objects. In a subsequent paper, we show how these concepts allow us to derive a new presentation of the hierarchy due to K. Wagner and W. Wadge.