On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

The Irish Infancy Narratives and their Relationship with Latin Sources

(Résumé de l'ouvrage) In 1927 M. R. James published Latin Infancy Gospels, identified by him in two related but not identical manuscripts (one the British Library Arundel 404; the other from Hereford), together with a parallel text from the Irish manuscript known as the Leabhar Breac. Later researches brought to light more manuscripts of this Latin work, and also of the Irish text. James recognized that his apocryphal Latin Infancy text was compiled from a combination of the Protevangelium of James and a hitherto unknown text which he named "The Source". Recent research has identified a full Latin translation of the Protevangelium of James. A hitherto unrecognized Irish Infancy Narrative has also been identified in the Dublin manuscript known as the Liber Flavus Fergusiorum. A deep study of this related tradition was called for. This has been carried out over the past ten years by an Irish team in conjunction with Professor Daniel Kaestli and AELAC. The fruits of this labour are published in these two volumes. Volume 13 has a general introduction with a historical sketch of New Testament apocrypha in Ireland and a history of research on the subject. This is followed by a comparison of the Infancy Narratives in the Leabhar Breac and the Liber Flavus Fergusiorum. There are special introductions to these Infancy texts, followed by critical editions of the Irish texts, accompanied by English translations and rich annotation. Next there is similar treatment of the Irish versified Narrative (from ca. 700) of the Childhood Deeds of Jesus (commonly known as the Infancy Narrative (or Gospel) of Thomas. There is then (in volume 14, but with continuous pagination) the edition and translation of an Irish thirteenth-century poem with elements from Infancy Narratives, and both Latin and Irish texts on the wonders at Christ's birth, accompanied by translations and notes. The edition of the Irish material is followed by a critical edition of the full Arundel and Hereford forms of the Infancy Narrative (here referred to as the "J Compilation"), together with a detailed study of all the questions relating to this work. The volume concludes with a critical edition (by Rita Beyers) of the Latin text of the Protevangelium of James, accompanied by a detailed study of the work.. The work contains a detailed study of the Latin translations of the Protevangelium of James and the transmission of this work in the West. The "J Compilation" (a combination of the Protevangelium and texts of Pseudo-Matthew) can be traced back in manuscript transmission to ca. 800,and must have originated some time earlier. Behind it stands an earlier "I ("I" for Irish) Compilation" without influence from Pseudo-Matthew, the form found in the Irish witnesses. It is argued that M. R. James's "Source" may be of Judaeo-Christian origin and may really be the Gospel of the Nazoreans. Among the indexes there is a list of all the Irish words found in the texts. This edition of the Irish and related Latin texts is a major contribution to the study of the apocryphal Infancy Narratives. It should also be of particular interest to Celtic scholars, to students of Irish ecclesiastical learning, and in general to all medievalists.

Latin Infancy Gospels: The J Compilation. Introduction and Edition

(Résumé de l'ouvrage) In 1927 M. R. James published Latin Infancy Gospels, identified by him in two related but not identical manuscripts (one the British Library Arundel 404; the other from Hereford), together with a parallel text from the Irish manuscript known as the Leabhar Breac. Later researches brought to light more manuscripts of this Latin work, and also of the Irish text. James recognized that his apocryphal Latin Infancy text was compiled from a combination of the Protevangelium of James and a hitherto unknown text which he named "The Source". Recent research has identified a full Latin translation of the Protevangelium of James. A hitherto unrecognized Irish Infancy Narrative has also been identified in the Dublin manuscript known as the Liber Flavus Fergusiorum. A deep study of this related tradition was called for. This has been carried out over the past ten years by an Irish team in conjunction with Professor Daniel Kaestli and AELAC. The fruits of this labour are published in these two volumes. Volume 13 has a general introduction with a historical sketch of New Testament apocrypha in Ireland and a history of research on the subject. This is followed by a comparison of the Infancy Narratives in the Leabhar Breac and the Liber Flavus Fergusiorum. There are special introductions to these Infancy texts, followed by critical editions of the Irish texts, accompanied by English translations and rich annotation. Next there is similar treatment of the Irish versified Narrative (from ca. 700) of the Childhood Deeds of Jesus (commonly known as the Infancy Narrative (or Gospel) of Thomas. There is then (in volume 14, but with continuous pagination) the edition and translation of an Irish thirteenth-century poem with elements from Infancy Narratives, and both Latin and Irish texts on the wonders at Christ's birth, accompanied by translations and notes. The edition of the Irish material is followed by a critical edition of the full Arundel and Hereford forms of the Infancy Narrative (here referred to as the "J Compilation"), together with a detailed study of all the questions relating to this work. The volume concludes with a critical edition (by Rita Beyers) of the Latin text of the Protevangelium of James, accompanied by a detailed study of the work.. The work contains a detailed study of the Latin translations of the Protevangelium of James and the transmission of this work in the West. The "J Compilation" (a combination of the Protevangelium and texts of Pseudo-Matthew) can be traced back in manuscript transmission to ca. 800,and must have originated some time earlier. Behind it stands an earlier "I ("I" for Irish) Compilation" without influence from Pseudo-Matthew, the form found in the Irish witnesses. It is argued that M. R. James's "Source" may be of Judaeo-Christian origin and may really be the Gospel of the Nazoreans. Among the indexes there is a list of all the Irish words found in the texts. This edition of the Irish and related Latin texts is a major contribution to the study of the apocryphal Infancy Narratives. It should also be of particular interest to Celtic scholars, to students of Irish ecclesiastical learning, and in general to all medievalists.

Le "Protévangile de Jacques" en latin. Etat de la question et perspectives nouvelles

Dans la première partie, on décrit et classifie les témoins qui contribuent à la connaissance du Protévangile de Jacques (PJ) en latin : 23 mss latins, les évangiles irlandais de l'enfance du Liber Flavus Fergusiorum (LFF) et du Leabhar Breac (LB). On clarifie dans une seconde partie plusieurs questions touchant à la diversité des formes textuelles du PJ en Occident, démontrant l'existence d'au moins deux traductions latines indépendantes. (I) L'une, plutôt littérale, est conservée en partie dans Montpellier 55 (M2) et Paris, n.a.l. 718 (S). (II) L'autre, caractérisée par des amplifications, est représentée par 4 témoins : Sainte-Geneviève 2787 (G; texte presque complet); l'homélie Inquirendum est (ch. 1-8, mss KPRBDO); l'Evangile latin de l'enfance combinant une partie du PJ, le Pseudo-Matthieu et une source inconnue, de coloration docète (compilation J, 8 témoins); le récit du LFF (ch. 1-16). Une troisième traduction indépendante est peut-être attestée (mss TUE). On montre ainsi l'existence de deux étapes successives d'amplification de la traduction II (IIa et IIb), illustrant le besoin d'expliciter la narration concise du PJ original. Cette traduction amplifiée a servi de modèle à l'auteur du remaniement latin du Pseudo-Matthieu. On éclaire enfin les antécédents, les caractéristiques et l'évolution de J, qui a vu le jour avant 800. La présente étude trouvera son prolongement dans l'édition critique des diverses formes du Protévangile latin

Least squares regression with errors in both variables: case studies

Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant.

Nicolaus Trevet Anglicus, Expositio in Boethium de consolatione philosophiae (1-166v). - Pseudo-Boethius, De disciplina scolarium (167-184v).

Ce ms. a appartenu à l'église paroissiale de Chaumont-en-Bassigny (Haute-Marne), comme en témoigne la mention du XVe s. "Ce livre cy appartient a l'eglise de Chaumont" (f. 184). En-dessous de cette mention figure la signature "H. Vigniery" (XVIe s.). En 1655, Claude Joly, chantre de Notre-Dame de Paris, l'a acheté à cette église (cf. l'inscription au contreplat sup., datée d'octobre 1658). Il a ensuite appartenu à la bibliothèque du chapitre de Notre-Dame de Paris, dont il porte l'ex-libris "A la bibliotheque de l'Eglise de Paris", précédé de la cote L5 (XVIIe s., contreplat sup.). Notre-Dame.

On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization

The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.

Sparse modeling using orthogonal forward regression with PRESS statistic and regularization

The paper introduces an efficient construction algorithm for obtaining sparse linear-in-the-weights regression models based on an approach of directly optimizing model generalization capability. This is achieved by utilizing the delete-1 cross validation concept and the associated leave-one-out test error also known as the predicted residual sums of squares (PRESS) statistic, without resorting to any other validation data set for model evaluation in the model construction process. Computational efficiency is ensured using an orthogonal forward regression, but the algorithm incrementally minimizes the PRESS statistic instead of the usual sum of the squared training errors. A local regularization method can naturally be incorporated into the model selection procedure to further enforce model sparsity. The proposed algorithm is fully automatic, and the user is not required to specify any criterion to terminate the model construction procedure. Comparisons with some of the existing state-of-art modeling methods are given, and several examples are included to demonstrate the ability of the proposed algorithm to effectively construct sparse models that generalize well.

M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Nonlinear equalization of Hammerstein OFDM systems

A practical orthogonal frequency-division multiplexing (OFDM) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. In this contribution, we advocate a novel nonlinear equalization scheme for OFDM Hammerstein systems. We model the nonlinear HPA, which represents the static nonlinearity of the OFDM Hammerstein channel, by a B-spline neural network, and we develop a highly effective alternating least squares algorithm for estimating the parameters of the OFDM Hammerstein channel, including channel impulse response coefficients and the parameters of the B-spline model. Moreover, we also use another B-spline neural network to model the inversion of the HPA’s nonlinearity, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalization of the OFDM Hammerstein channel can then be accomplished by the usual one-tap linear equalization as well as the inverse B-spline neural network model obtained. The effectiveness of our nonlinear equalization scheme for OFDM Hammerstein channels is demonstrated by simulation results.

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.