Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger`s column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger`s column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Transport-Regional Equity Issue Revisited

Almeida E. S. de, Haddad E. A. and Hewings G. J. D. Transport-regional equity issue revisited, Regional Studies. The objective of this paper is to analyse the relationship between transport and regional equity in Minas Gerais, Brazil. Furthermore, the existence of a trade-off between economic performance and regional equity is investigated as well. To do so, the paper develops a spatial computable general equilibrium model based on Brocker and Schneider`s approach of 2002 to implement comparative static analysis, explicitly incorporating iceberg transportation costs. Four activities are modelled, namely production, final demand, transportation and exports. Two production factors are assumed: labour and other factors. The model has 12 domestic regions and three external regions. Four counterfactual experiments are developed based on decreases in transportation costs due to a `distance shortening`. The main findings indicate that if the transport infrastructure improvement is focused only among poor regions, the promotion of regional equity is insignificant. If the transport infrastructure improvement links are concentrated among rich regions, there is an increase in regional income inequalities. However, if the improvements are targeted to the roads linking poor regions and rich ones, there is greater promotion of regional equity. The same result will occur when improvements are made to all road links of the state. [image omitted] Almeida E. S. de, Haddad E. A. et Hewings G. J. D. La question du rapport entre le transport et l`equilibre regional vue sous un jour nouveau, Regional Studies. Cet article cherche a analyser le rapport entre le transport et l`equilibre regional en Minas Gerais au Bresil. En outre, on examine la presence d`un echange entre la performance economoique et l`equilibre regional. Pour le faire, on construit un modele geographique de l`equilibre general a utiliser sur ordinateur fonde sur l`approche de Brockner et Schneider en 2002 afin de mettre en oeuvre une analyse statique comparative qui comprend explicitement les frais de transport iceberg. On modelise quatre activites, a savoir, la production, la demande finale, le transport et l`exportation. On fait deux suppositions quant aux facteurs de production: la main-d`oevre et d`autres facteurs. Le modele embrasse douze regions internes et trois regions externes. On fait quatre experiences paradoxales fondees sur la baisse des frais de transport due a une `reduction des distances`. Les principaux resultats indiquent que si l`amelioration de l`equipement de transport ne porte que sur les regions defavorisees, la promotion de l`equilibre regional s`avere negligeable. Si l`amelioration de l`equipement de transport focalise les regions riches, il s`avere un creusement des ecarts des revenus regionaux. Cependant, si les ameliorations ciblent les routes qui relient les regions defavorisees aux regions riches, il s`avere une plus grande promotion de l`equilibre regional. Il en va de meme pour la situation ou on a apporte des amenagements a toutes les liaisons routieres de l`etat. Modele geographique de l`equilibre general a utiliser sur ordinateur Equilibre regional Peformance economique Frais de transport Almeida E. S. de, Haddad E. A. und Hewings G. J. D. Die Wiederaufnahme der Frage von Verkehrswesen im Verhaltnis zu regionaler Fairness, Regional Studies. Dieser Aufsatz beabsichtigt, die Beziehung zwischen Verkehrswesen und regionaler Fairness in Minas Gerais (Brasilien) zu analysieren und zugleich auch das Vorkommen von Einbussen entweder bei wirtschaftlicher Leistung der regionaler Fairness zu untersuchen. Zu diesem Zwecke wird ein auf dem Ansatz von Brocker und Schneider (2002) aufbauendes raumliches komputables allgemeines Gleichgewichtsmodell entwickelt, um vergleichende statistische Analysen durchzufuhren, wobei verborgene `Eisberg`-Transportkosten ausdrucklich berucksichtigt werden. Es werden vier Unternehmenstatigk eiten aufgefuhrt: Herstellung, Nachfrage, Transportwesen und Exporte, und zwei Produktionsfaktoren vorausgesetzt: Arbeitskrafte und andere Faktoren. Das Modell umfasst zwolf Inlandsregionen und drei externe Regionen. Es werden vier gegensatzliche Experimente entwickelt, die auf einer Abnahme der Transportkosten infolge einer `Verkurzung der Entfernungen` beruhen. Die Hauptbefunde weisen darauf hin, dass die Forderung regionaler Fairness unbedeutend bleibt, wenn die Verbesserungen der Transportinfrastruktur sich nur auf minderbemittelte Regionen konzentrieren; werden die Verbesserungen der Verbindungen der Transportinfrastruktur in wohlhabenden Regionen durchgefuhrt, so nehmen regionale Einkommensunterschiede zu. Wenn die Verbesserungen jedoch auf Strassen abzielen, die wohlhabende Regionen mit weniger bemittelten verbinden, wird regionale Fairness starker gefordert. Das gleiche Ergebnis wird sich einstellen, wenn Verbesserungen an allen Strassenverbindungen des Staates vorgenommen werden. Raumliches, komputables, allgemeines Gleichgewichtsmodell Regionale Fairness Wirtschaftsleistung Transportkosten Almeida E. S. de, Haddad E. A. y Hewings G. J. D. Revisando el tema de la igualdad del transporte en las regiones, Regional Studies. El objetivo de este documento es analizar la relacion entre el transporte y la igualdad regional en Minas Gerais, Brasil. Asimismo investigamos la existencia de una compensacion entre el rendimiento economico y la igualdad regional. Para ello desarrollamos un modelo de equilibrio general computable y espacial basado en el enfoque de Brocker y Schneider en 2002 para hacer un analisis estatico y comparativo, explicitamente incorporando los costes ocultos de transporte. Se modelan cuatro actividades: la produccion, la demanda final, el transporte y las exportaciones. Suponemos que existen dos factores de produccion: mano de obra y otros factores. En este modelo, existen doce regiones internas y tres regiones externas. Desarrollamos cuatro experimentos contrafactuales basados en la disminucion de los costes de transporte debido a una `acortamiento de las distancias`. Los principales resultados indican que si la mejora de la infraestructura del transporte se centra solo entre las regiones mas pobres, el fomento de la igualdad regional es insignificante. Si los enlaces de la mejora de la infraestructura del transporte se concentran en las regiones ricas, aumentan las desigualdades de ingresos regionales. Sin embargo, si se mejoran los enlaces de carreteras entre las regiones pobres y ricas, se fomenta mejor la igualdad regional. El mismo resultado ocurre cuando se mejoran los enlaces de todas las carreteras del estado. Modelo de equilibrio general computable y espacial Igualdad regional Rendimiento economico Costes de transporte.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Resampling Strategies for Deforming MLS Surfaces

Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Front tracking with moving-least-squares surfaces

The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is]to surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications. (C) 2008 Elsevier Inc. All rights reserved.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

A Hopping Mechanism for Cargo Transport by Molecular Motors on Crowded Microtubules

Most models designed to study the bidirectional movement of cargos as they are driven by molecular motors rely on the idea that motors of different polarities can be coordinated by external agents if arranged into a motor-cargo complex to perform the necessary work Gross, Hither and yon: a review of bidirectional microtubule-based transport (Gross in Phys. Biol. 1:R1-R11, 2004). Although these models have provided us with important insights into these phenomena, there are still many unanswered questions regarding the mechanisms through which the movement of the complex takes place on crowded microtubules. For example (i) how does cargo-binding affect motor motility? and in connection with that-(ii) how does the presence of other motors (and also other cargos) on the microtubule affect the motility of the motor-cargo complex? We discuss these questions from a different perspective. The movement of a cargo is conceived here as a hopping process resulting from the transference of cargo between neighboring motors. In the light of this, we examine the conditions under which cargo might display bidirectional movement even if directed by motors of a single polarity. The global properties of the model in the long-time regime are obtained by mapping the dynamics of the collection of interacting motors and cargos into an asymmetric simple exclusion process (ASEP) which can be resolved using the matrix ansatz introduced by Derrida (Derrida and Evans in Nonequilibrium Statistical Mechanics in One Dimension, pp. 277-304, 1997; Derrida et al. in J. Phys. A 26: 1493-1517, 1993).

Inference From Aging Information

For many learning tasks the duration of the data collection can be greater than the time scale for changes of the underlying data distribution. The question we ask is how to include the information that data are aging. Ad hoc methods to achieve this include the use of validity windows that prevent the learning machine from making inferences based on old data. This introduces the problem of how to define the size of validity windows. In this brief, a new adaptive Bayesian inspired algorithm is presented for learning drifting concepts. It uses the analogy of validity windows in an adaptive Bayesian way to incorporate changes in the data distribution over time. We apply a theoretical approach based on information geometry to the classification problem and measure its performance in simulations. The uncertainty about the appropriate size of the memory windows is dealt with in a Bayesian manner by integrating over the distribution of the adaptive window size. Thus, the posterior distribution of the weights may develop algebraic tails. The learning algorithm results from tracking the mean and variance of the posterior distribution of the weights. It was found that the algebraic tails of this posterior distribution give the learning algorithm the ability to cope with an evolving environment by permitting the escape from local traps.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.