Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.

Drell-Yan as a probe of small x partons at the LHC

The predictions of Drell-Yan production of low-mass lepton pairs, at high rapidity at the LHC, are known to depend sensitively on the choice of factorization and renormalization scales. We show how this sensitivity can be greatly reduced by fixing the factorization scale of the LO contribution based on the known NLO matrix element, so that observations of this process at the LHC can make direct measurements of parton distribution functions in the low x domain; x less than or similar to 10(-4).

A regional multirnodulus algorithm for blind equalization of QAM signals: Introduction and steady-state analysis

It is well known that constant-modulus-based algorithms present a large mean-square error for high-order quadrature amplitude modulation (QAM) signals, which may damage the switching to decision-directed-based algorithms. In this paper, we introduce a regional multimodulus algorithm for blind equalization of QAM signals that performs similar to the supervised normalized least-mean-squares (NLMS) algorithm, independently of the QAM order. We find a theoretical relation between the coefficient vector of the proposed algorithm and the Wiener solution and also provide theoretical models for the steady-state excess mean-square error in a nonstationary environment. The proposed algorithm in conjunction with strategies to speed up its convergence and to avoid divergence can bypass the switching mechanism between the blind mode and the decision-directed mode. (c) 2012 Elsevier B.V. All rights reserved.

Rationale, study design, and analysis plan of the Alveolar Recruitment for ARDS Trial (ART): Study protocol for a randomized controlled trial

Background: Acute respiratory distress syndrome (ARDS) is associated with high in-hospital mortality. Alveolar recruitment followed by ventilation at optimal titrated PEEP may reduce ventilator-induced lung injury and improve oxygenation in patients with ARDS, but the effects on mortality and other clinical outcomes remain unknown. This article reports the rationale, study design, and analysis plan of the Alveolar Recruitment for ARDS Trial (ART). Methods/Design: ART is a pragmatic, multicenter, randomized (concealed), controlled trial, which aims to determine if maximum stepwise alveolar recruitment associated with PEEP titration is able to increase 28-day survival in patients with ARDS compared to conventional treatment (ARDSNet strategy). We will enroll adult patients with ARDS of less than 72 h duration. The intervention group will receive an alveolar recruitment maneuver, with stepwise increases of PEEP achieving 45 cmH(2)O and peak pressure of 60 cmH2O, followed by ventilation with optimal PEEP titrated according to the static compliance of the respiratory system. In the control group, mechanical ventilation will follow a conventional protocol (ARDSNet). In both groups, we will use controlled volume mode with low tidal volumes (4 to 6 mL/kg of predicted body weight) and targeting plateau pressure <= 30 cmH2O. The primary outcome is 28-day survival, and the secondary outcomes are: length of ICU stay; length of hospital stay; pneumothorax requiring chest tube during first 7 days; barotrauma during first 7 days; mechanical ventilation-free days from days 1 to 28; ICU, in-hospital, and 6-month survival. ART is an event-guided trial planned to last until 520 events (deaths within 28 days) are observed. These events allow detection of a hazard ratio of 0.75, with 90% power and two-tailed type I error of 5%. All analysis will follow the intention-to-treat principle. Discussion: If the ART strategy with maximum recruitment and PEEP titration improves 28-day survival, this will represent a notable advance to the care of ARDS patients. Conversely, if the ART strategy is similar or inferior to the current evidence-based strategy (ARDSNet), this should also change current practice as many institutions routinely employ recruitment maneuvers and set PEEP levels according to some titration method.

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system's instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

Complexity of inferences in polytree-shaped semi-qualitative probabilistic networks

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provade a very Complexity of inferences in polytree-shaped semi-qualitative probabilistic networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the bayesian networks. This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that interferences can be performed in time linear in the number of nodes if there is a single observed node. Because our proof is construtive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynominal-time algorithm for SQPn. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Aumento della risoluzione spaziale per il sondaggio di temperatura e umidità da satellite geostazionario mediante radiometria ad onde millimetriche e submillimetriche

The purpose of this study is to develop and evaluate techniques that improve the spatial resolution of the channels already selected in the preliminary studies for Geostationary Observatory for Microwave Atmospheric Soundings (GOMAS). Reference high resolution multifrequency brightness temperatures scenarios have been derived by applying radiative transfer calculation to the spatially and microphysically detailed output of meteorological events simulated by the University of Wisconsin - Non-hydrostatic Model System (UW-NMS). Three approaches, Wiener filter, Super-Resolution and Image Fusion have been applied to some representative GOMAS frequency channels to enhance the resolution of antenna temperatures. The Wiener filter improved resolution of the largely oversampled images by a factor 1.5- 2.0 without introducing any penalty in the radiometric accuracy. Super-resolution, suitable for not largely oversampled images, improved resolution by a factor ~1.5 but introducing an increased radiometric noise by a factor 1.4-2.5. The image fusion allows finally to further increase the spatial frequency of the images obtained by the Wiener filter increasing the total resolution up to a factor 5.0 with an increased radiometric noise closely linked to the radiometric frequency and to the examined case study.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.

Noisy Oncology: applications of bounded noise transitions in modelling tumor growth

I tumori macroscopici e microscopici, dopo la loro prima fase di crescita, sono composti da un numero medio elevato di cellule. Così, in assenza di perturbazioni esterne, la loro crescita e i punti di equilibrio possono essere descritti da equazioni differenziali. Tuttavia, il tumore interagisce fortemente col macroambiente che lo circonda e di conseguenza una descrizione del tutto deterministica risulta a volte inappropriata. In questo caso si può considerare l'interazione con fluttuazioni statistiche, causate da disturbi esterni, utilizzando le equazioni differenziali stocastiche (SDE). Questo è vero in modo particolare quando si cerca di modellizzare tumori altamente immunogenici che interagiscono con il sistema immunitario, in quanto la complessità di questa interazione risulta in fenomeni di multistabilità. Così, il rumore può provocare disturbi e indurre transizioni di stato (Noise-Induced-Transitions). E' importante notare che una NIT può avere implicazioni profonde sulla vita di un paziente, dal momento che una transizione da uno stato di equilibrio piccolo, nelle dimensioni del tumore, ad uno stato di equilibrio macroscopico, nella maggior parte dei casi significa il passaggio dalla vita alla morte. Generalmente l'approccio standard è quello di modellizzare le fluttuazioni stocastiche dei parametri per mezzo di rumore gaussiano bianco o colorato. In alcuni casi però questa procedura è altamente inadeguata, a causa della illimitatezza intrinseca dei rumori gaussiani che può portare a gravi incongruenze biologiche: pertanto devono essere utilizzati dei rumori "limitati", che, tuttavia, sono molto meno studiati di quelli gaussiani. Inoltre, l'insorgenza di NIT dipende dal tipo di rumore scelto, che rivela un nuovo livello di complessità in biologia. Lo scopo di questa tesi è quello di studiare le applicazioni di due tipi diversi di "rumori limitati" nelle transizioni indotte in due casi: interazione tra tumore e sistema immunitario e chemioterapia dei tumori. Nel primo caso, abbiamo anche introdotto un nuovo modello matematico di terapia, che estende, in modo nuovo, il noto modello di Norton-Simon.

Verzweigung periodischer Lösungen bei rein nichtlinearen Differentialgleichungssystemen in der Ebene

Zusammenfassung:In dieser Arbeit werden die Abzweigung stationärer Punkte und periodischer Lösungen von isolierten stationären Punkten rein nichtlinearer Differentialgleichungen in der reellenEbene betrachtet.Das erste Kapitel enthält einige technische Hilfsmittel, während im zweiten ausführlich das Verhalten von Differentialgleichungen in der Ebene mit zwei homogenen Polynomen gleichen Grades als rechter Seite diskutiert wird.Im dritten Kapitel beginnt der Hauptteil der Arbeit. Hier wird eine Verallgemeinerung des Hopf'schen Verzweigungssatzes bewiesen, der den klassischen Satz als Spezialfall enthält.Im vierten Kapitel untersuchen wir die Abzweigung stationärer Punkte und im letzten Kapitel die Abzweigung periodischer Lösungen unter Störungen, deren Ordnung echt kleiner ist, als die erste nichtverschwindende Näherung der ungestörten Gleichung.Alle Voraussetzungen in dieser Arbeit sind leicht nachzurechnen und es werden zahlreiche Beispiele ausführlich diskutiert.

Die Rolle von Hopfkategorien und Operaden in störungstheoretischen Quantenfeldtheorien

Die Vorhersagen störungstheoretischer Quantenfeldtheorienzeigen eine gute Übereinstimmung mit experimentellgemessenen Werten. Bei diesen störungstheoretischenBerechnungen treten allerdings Ultraviolettdivergenzen auf,die keine physikalische Interpretation der Ergebnisseermöglichen. Durch Renormierung dieser Theorien erhält manjedoch berechnbare Ergebnisse mit hoher experimentellerVorhersagekraft. Der Renormierungsvorgang kann durch eineHopfalgebra, die sogenannte 'Hopfalgebra der Wurzelbäume',beschrieben werden.Die vorliegende Arbeit leistet einen Beitrag für weitereUntersuchungen dieser Hopfalgebrenstruktur und Bestimmungneuer mathematischer Methoden zur Beschreibung desRenormierungsvorgangs. Dazu wird die algebraische Strukturvon Renormierung aus der Sicht der Kategorientheorie und derTheorie von Operaden untersucht.Aus Sicht der Kategorientheorie lassen sich die den Renormierungsprozess beschreibenden mathematischen Größen ineiner Kategorie zusammenfassen. Eine additive Strukturermöglicht dabei die Berücksichtigung beliebigerRenormierungsschemata. Auf dieser Kategorie kann einassoziativitätsverletzendes Produkt definiert werden, wobeidie Verletzung durch einen sogenannten 'Assoziator'kontrolliert werden kann. Die Struktur wird auf die einerHopfkategorie erweitert, so daß eine kategorientheoretischeUntersuchung des Renormierungsprozesses ermöglicht wird.Diese Hopfkategorie wird aus Sicht von Renormierunginterpretiert, wobei Beispielrechnungen die definierteStruktur verdeutlichen.Aus algebraischer Sicht kann aufgrund der graphischenDarstellung des Operadenproduktes eine Bijektivität zwischenWurzelbäumen und Operaden gezeigt werden. Auf diesenOperaden kann wiederum eine Hopfalgebrenstruktur definiertwerden. Beispiele verdeutlichen diese Bijektivität.

Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik

In den letzten fünf Jahren hat sich mit dem Begriff desspektralen Tripels eine Möglichkeit zur Beschreibungdes an Spinoren gekoppelten Gravitationsfeldes auf(euklidischen) nichtkommutativen Räumen etabliert. Die Dynamik dieses Gravitationsfeldes ist dabei durch diesogenannte spektrale Wirkung, dieSpur einer geeigneten Funktion des Dirac-Operators,bestimmt. Erstaunlicherweise kann man die vollständige Lagrange-Dichtedes (an das Gravitationsfeld gekoppelten) Standardmodellsder Elementarteilchenphysik, also insbesondere auch denmassegebenden Higgs-Sektor, als spektrale Wirkungeines entsprechenden spektralen Tripels ableiten. Diesesspektrale Tripel ist als Produkt des spektralenTripels der (kommutativen) Raumzeit mit einem speziellendiskreten spektralen Tripel gegeben. In der Arbeitwerden solche diskreten spektralen Tripel, die bis vorKurzem neben dem nichtkommutativen Torus die einzigen,bekannten nichtkommutativen Beispiele waren, klassifiziert. Damit kannnun auch untersucht werden, inwiefern sich dasStandardmodell durch diese Eigenschaft gegenüber anderenYang-Mills-Higgs-Theorien auszeichnet. Es zeigt sichallerdings, dasses - trotz mancher Einschränkung - eine sehr große Zahl vonModellen gibt, die mit Hilfe von spektralen Tripelnabgeleitet werden können. Es wäre aber auch denkbar, dass sich das spektrale Tripeldes Standardmodells durch zusätzliche Strukturen,zum Beispiel durch eine darauf ``isometrisch'' wirkendeHopf-Algebra, auszeichnet. In der Arbeit werden, um dieseFrage untersuchen zu können, sogenannte H-symmetrischespektrale Tripel, welche solche Hopf-Isometrien aufweisen,definiert.Dabei ergibt sich auch eine Möglichkeit, neue(H-symmetrische) spektrale Tripel mit Hilfe ihrerzusätzlichen Symmetrienzu konstruieren. Dieser Algorithmus wird an den Beispielender kommutativen Sphäre, deren Spin-Geometrie hier zumersten Mal vollständig in der globalen, algebraischen Sprache der NichtkommutativenGeometrie beschrieben wird, sowie dem nichtkommutativenTorus illustriert.Als Anwendung werden einige neue Beipiele konstruiert. Eswird gezeigt, dass sich für Yang-Mills Higgs-Theorien, diemit Hilfe von H-symmetrischen spektralen Tripeln abgeleitetwerden, aus den zusätzlichen Isometrien Einschränkungen andiefermionischen Massenmatrizen ergeben. Im letzten Abschnitt der Arbeit wird kurz auf dieQuantisierung der spektralen Wirkung für diskrete spektraleTripel eingegangen.Außerdem wird mit dem Begriff des spektralen Quadrupels einKonzept für die nichtkommutative Verallgemeinerungvon lorentzschen Spin-Mannigfaltigkeiten vorgestellt.