Thermodynamics of Ising model with infinite-range interactions by generalized canonical ensemble

In this work we present the idea of how generalized ensembles can be used to simplify the operational study of non-additive physical systems. As alternative of the usual methods of direct integration or mean-field theory, we show how the solution of the Ising model with infinite-range interactions is obtained by using a generalized canonical ensemble. We describe how the thermodynamical properties of this model in the presence of an external magnetic field are founded by simple parametric equations. Without impairing the usual interpretation, we obtain an identical critical behaviour as observed in traditional approaches.

Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p(2)), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p(2)) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a noninteger power of the momentum p in the numerator of the expression for D(p(2)). In this case, an infinite-volume-limit extrapolation gives D(0) = 0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

Cediranib Plus FOLFOX/CAPOX Versus Placebo Plus FOLFOX/CAPOX in Patients With Previously Untreated Metastatic Colorectal Cancer: A Randomized, Double-Blind, Phase III Study (HORIZON II)

Purpose Cediranib is a highly potent inhibitor of vascular endothelial growth factor (VEGF) signaling with activity against all three VEGF receptors. HORIZON II [Cediranib (AZD2171, RECENTIN) in Addition to Chemotherapy Versus Placebo Plus Chemotherapy in Patients With Untreated Metastatic Colorectal Cancer] assessed infusional fluorouracil, leucovorin, and oxaliplatin/capecitabine and oxaliplatin (FOLFOX/CAPOX) with or without cediranib in patients with previously untreated metastatic colorectal cancer (mCRC). Patients and Methods Eligible patients were initially randomly assigned 1:1:1 to receive cediranib (20 or 30 mg per day) or placebo plus FOLFOX/CAPOX. In an early analysis of this and two other cediranib studies (HORIZON I [Cediranib Plus FOLFOX6 Versus Bevacizumab Plus FOLFOX6 in Patients With Previously Treated Metastatic Colorectal Cancer] and HORIZON III [Cediranib Plus FOLFOX6 Versus Bevacizumab Plus FOLFOX6 in Patients With Untreated Metastatic Colorectal Cancer]), the 20-mg dose met the predefined criteria for continuation. Subsequent patients were randomly assigned 2: 1 to the cediranib 20 mg or placebo arms. Progression-free survival (PFS) and overall survival (OS) were coprimary end points. Results In all, 860 patients received cediranib 20 mg (n = 502) or placebo (n = 358). The addition of cediranib to FOLFOX/CAPOX resulted in PFS prolongation (hazard ratio [HR], 0.84; 95% CI, 0.73 to 0.98; P = .0121; median PFS, 8.6 months for cediranib v 8.3 months for placebo) but had no impact on OS (HR, 0.94; 95% CI, 0.79 to 1.12; P = .5707; median OS, 19.7 months for cediranib v 18.9 months for placebo). There were no significant differences in the secondary end points of objective response rate, duration of response, or liver resection rate. Median chemotherapy dose-intensity was decreased by approximately 10% in patients treated with cediranib. Adverse events (AEs) associated with cediranib were manageable. Conclusion Addition of cediranib 20 mg to FOLFOX/CAPOX resulted in a modest PFS prolongation, but no significant difference in OS. The cediranib AE profile was consistent with those from previous studies. Because of the lack of improvement in OS, cediranib plus an oxaliplatin-based regimen cannot be recommended as a treatment for patients with mCRC. J Clin Oncol 30:3596-3603. (C) 2012 by American Society of Clinical Oncology

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Semilinear functional difference equations with infinite delay

We obtain boundedness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications to Volterra difference equations with infinite delay are shown. (C) 2011 Elsevier Ltd. All rights reserved.

Effects of Perspective on the Amplification of Object Sizes that Intercept the Horizon Line

We investigated the effects of texture gradient and the position of test stimulus in relation to the horizon on the perception of relative sizes. By using the staircase method, 50 participants adjusted the size of a bar presented above, below or on the horizon as it could be perceived in the same size of a bar presented in the lower visual field. Stimuli were presented during 100ms on five background conditions. Perspective gradient contributed more to the overestimation of relative sizes than compression gradient. The sizes of the objects which intercepted the horizon line were overestimated. Visual system was very effective in extracting information from perspective depth cues, making it even during very brief exposure.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

An infinite level atom coupled to a heat bath

Wir untersuchen die Mathematik endlicher, an ein Wärmebad gekoppelter Teilchensysteme. Das Standard-Modell der Quantenelektrodynamik für Temperatur Null liefert einen Hamilton-Operator H, der die Energie von Teilchen beschreibt, welche mit Photonen wechselwirken. Im Heisenbergbild ist die Zeitevolution des physikalischen Systems durch die Wirkung einer Ein-Parameter-Gruppe auf eine Menge von Observablen A gegeben: Diese steht im Zusammenhang mit der Lösung der Schrödinger-Gleichung für H. Um Zustände von A, welche das physikalische System in der Nähe des thermischen Gleichgewichts zur Temperatur T darstellen, zu beschreiben, folgen wir dem Ansatz von Jaksic und Pillet, eine Darstellung von A zu konstruieren. Die Vektoren in dieser Darstellung definieren die Zustände, die Zeitentwicklung wird mit Hilfe des Standard Liouville-Operators L beschrieben. In dieser Doktorarbeit werden folgende Resultate bewiesen bzw. hergeleitet: - die Konstuktion einer Darstellung - die Selbstadjungiertheit des Standard Liouville-Operators - die Existenz eines Gleichgewichtszustandes in dieser Darstellung - der Limes des physikalischen Systems für große Zeiten.

Horizon entropy from scratch

Scopo di questo lavoro di tesi è lo studio di alcune proprietà delle teorie generali della gravità in relazione alla meccanica e la termodinamica dei buchi neri. In particolare, la trattazione che seguirà ha lo scopo di fornire un percorso autoconsistente che conduca alla nozione di entropia di un orizzonte descritta in termini delle carica di Noether associata all'invarianza del funzionale d'azione, che descrive la teoria gravitazionale in considerazione, per trasformazioni di coordinate generali. Si presterà particolare attenzione ad alcune proprietà geometriche della Lagrangiana, proprietà che sono indipendenti dalla particolare forma della teoria che si sta prendendo in considerazione; trattasi cioè non di proprietà dinamiche, legate cioè alla forma delle equazioni del moto del campo gravitazionale, ma piuttosto caratteristiche proprie di qualunque varietà rappresentante uno spaziotempo curvo. Queste caratteristiche fanno sì che ogni teoria generale della gravità possieda alcune grandezze definite localmente sullo spaziotempo, in particolare una corrente di Noether e la carica ad essa associata. La forma esplicita della corrente e della carica dipende invece dalla Lagrangiana che si sceglie di adottare per descrivere il campo gravitazionale. Il lavoro di tesi sarà orientato prima a descrivere come questa corrente di Noether emerge in qualunque teoria della gravità invariante per trasformazioni generali e come essa viene esplicitata nel caso di Lagrangiane particolari, per poi identificare la carica ad essa associata come una grandezza connessa all' entropia di un orizzonte in qualunque teoria generale della gravità.

Le Havre. Forme e caratteri dello spazio urbano nel progetto di Auguste Perret

Oggetto del presente studio è il progetto di ricostruzione del centro urbano di Le Havre ad opera di Auguste Perret. Suo obiettivo è il riconoscimento di quell’idea di città posta a fondamento del progetto, per il quale ci si propone di indagare il senso e le grammatiche costitutive della sua forma. Quella di Le Havre costituisce una dimostrazione di come una forma urbana ancora compatta ed evocativa della città storica possa definirsi a partire dalle relazioni stabilite con gli elementi della geografia fisica. Nei suoi luoghi collettivi e monumentali, che rimandano chiaramente a una cultura dell’abitare che affonda le proprie radici nella più generale esperienza della costruzione della città francese, la città riconosce un valore formale e sceglie di rappresentare il proprio mondo civico dinanzi a quei grandi elementi della geografia fisica che costituiscono l’identità del luogo nel quale questa si colloca. Sembra infatti possibile affermare che gli spazi pubblici della città atlantica riconoscano e traducano nella forma della Place de l’Hôtel de Ville le ripide pendici della falesia del Bec-de-Caux, in quella della Porte Océane l’orizzonte lontano dell’Oceano, e nel Front-de-mer Sud l’altra riva dell’estuario della Senna. Questa relazione fondativa sembra essere conseguita anche attraverso la definizione di un’appropriata grammatica dello spazio urbano, la cui significatività è nel fondarsi sull’assunzione, allo stesso tempo, del valore dello spazio circoscritto e del valore dello spazio aperto. La riflessione sullo spazio urbano investe anche la costruzione dell’isolato, sottoposto a una necessaria rifondazione di forma e significato, allo scopo di rendere intellegibile le relazioni tra gli spazi finiti della città e quelli infiniti della natura. La definizione dell’identità dello spazio urbano, sembra fondarsi, in ultima analisi, sulle possibilità espressive delle forme della costruzione che, connotate come forme dell’architettura, definiscono il carattere dei tipi edilizi e dello spazio da questi costruito.

Evoluzione tecnologica in ambito End User Computing: un caso d'uso basato su Horizon Workspace Portal

L'obbiettivo del progetto di cui tratta questa tesi è costituire un ambiente intuitivo e facilmente utilizzabile dall'utente finale che permetta di accedere sia alle applicazioni aziendali sia ai desktop virtuali da qualsiasi dispositivo effettui l'accesso. Grazie alle recenti tecnologie di End User Computing messe a disposizione da VMware è possibile virtualizzare qualsiasi applicazione Windows e renderla disponibile tramite Internet a qualsiasi utente la richieda, indifferentemente dal sistema operativo o dal luogo in cui si trova. Il progetto descritto nella tesi spiega come implementare tale ambiente tramite il prodotto Horizon Workspace Portal integrato nella suite Horizon 6.