Formalização do conjunto dos números racionais e alguns jogos com frações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Myth of the Rational Market: Nudging Each Other Away from Fool’s Gold

A flurry of media commentary and several new books are focused on the recent financial crisis and near economic collapse. A Newsweek article by Zakaria (2009), “Greed is Good (To a Point),” suggests reconsidering the role of greed in capitalism. This is also the theme in Fools Gold (Tett, 2009), a story about the way derivatives markets have evolved: showing greed at its worst. In many ways this is the core source of the current set of problems. In some sense, these perspectives are integrated in The Myth of the Rational Market by Fox (2009), who traces the thinking on the efficient market hypothesis, now understood for what it is: a myth. Both books are based in large part on interviews with major players in the crisis. There are also books drawing mainly on science, but still quite accessible to general readers, as represented in Nudge by Thaler and Sunstein (2008). Both have done extensive research on human foibles in economic choice. There is also Animal Spirits (Akerlof and Schiller, 2009), a book about what Keynesian economics is really about, a look at human forces at work. Akerlof is a Nobel prize winner in economics, who before this has pointed to the problems with presuming rationality in real markets. Schiller is one of the few economists who predicted these events.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re 5 x 10(5) will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k - omega SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature. [DOI: 10.1115/1.4007571]

Lower numbers of natural killer T cells in HIV-1 and Mycobacterium leprae co-infected patients

Natural killer T (NKT) cells are a heterogeneous population of lymphocytes that recognize antigens presented by CD1d and have attracted attention because of their potential role linking innate and adaptive immune responses. Peripheral NKT cells display a memory-activated phenotype and can rapidly secrete large amounts of pro-inflammatory cytokines upon antigenic activation. In this study, we evaluated NKT cells in the context of patients co-infected with HIV-1 and Mycobacterium leprae. The volunteers were enrolled into four groups: 22 healthy controls, 23 HIV-1-infected patients, 20 patients with leprosy and 17 patients with leprosy and HIV-1-infection. Flow cytometry and ELISPOT assays were performed on peripheral blood mononuclear cells. We demonstrated that patients co-infected with HIV-1 and M.leprae have significantly lower NKT cell frequencies [median 0.022%, interquartile range (IQR): 0.0070.051] in the peripheral blood when compared with healthy subjects (median 0.077%, IQR: 0.0320.405, P < 0.01) or HIV-1 mono-infected patients (median 0.072%, IQR: 0.0300.160, P < 0.05). Also, more NKT cells from co-infected patients secreted interferon-? after stimulation with DimerX, when compared with leprosy mono-infected patients (P = 0.05). These results suggest that NKT cells are decreased in frequency in HIV-1 and M.leprae co-infected patients compared with HIV-1 mono-infected patients alone, but are at a more activated state. Innate immunity in human subjects is strongly influenced by their spectrum of chronic infections, and in HIV-1-infected subjects, a concurrent mycobacterial infection probably hyper-activates and lowers circulating NKT cell numbers.

Intrinsic ordering, combinatorial numbers and reliability engineering

[EN]A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables)...

Aspetti innovativi per la valutazione e la misura della porosità nei materiali dell'edilizia antica e moderna. La geometria frattale della porosità

New concepts on porosity appraisal in ancient and modern construction materials. The role of Fractal Geometry on porosity characterization and transport phenomena. This work studied the potential of Fractal Geometry to the characterization of porous materials. Besides the descriptive aspects of the pore size distribution, the fractal dimensions have led to the development of rational relations for the prediction of permeability coefficients to fluid and heat transfer. The research considered natural materials used in historical buildings (rock and earth) as well as currently employed materials as hydraulic cement and technologically advanced materials such as silicon carbide or YSZ ceramics. The experimental results of porosity derived from the techniques of mercury intrusion and from the image analysis. Data elaboration was carried out according to established procedures of Fractal Geometry. It was found that certain classes of materials are clearly fractal and respond to simple patterns such as Sierpinski and Menger models. In several cases, however, the fractal character is not recognised because the microstructure of the material is based on different phases at different dimensional scales, and in consequence the “fractal dimensions” calculated from porosimetric data do not come within the standard range (less than 3). Using different type and numbers of fractal units is possible, however, to obtain “virtual” microstructures that have the fraction of voids and pore size distribution equivalent with the experimental ones for almost any material. Thus it was possible to take the expressions for the permeability and the thermal conduction which does not require empirical “constants”, these expressions have also provided values that are generally in agreement with the experimental available data. More problematic has been the fractal discussion of the geometry of the rupture of the material subjected to mechanical stress both external and internal applied. The results achieved on these issues are qualitative and prone to future studies. Keywords: Materials, Microstructure, Porosity, Fractal Geometry, Permeability, Thermal conduction, Mechanical strength.

Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Rational design of selective anion receptors

The new family of the anion receptors based on oligoureas with varied flexibility was developed and studied. The preparation of the urea chains containing two different units in various sequences was elaborated. The complete sets of four cyclic trimers and six tetramers based on the two units were prepared. Their conformational and complexation properties were studied with NMR spectroscopy and X-ray structure determinations, their behaviour towards various anions was evaluated and compared. The synthesis and the same studies were performed also with four different cyclic hexamers. During these studies the remarkable templation by two halide anions was observed.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

High numbers of DC-SIGN+ dendritic cells in lesional skin of cutaneous T-cell lymphoma

The role of dendritic cells (DCs) in disease progression of primary cutaneous T-cell lymphoma (CTCL) is not well understood. With their unique ability to induce primary immune responses as well as immunotolerance, DCs play a critical role in mediation of anti-tumor immune responses. Tumor-infiltrating DCs have been determined to represent important prognostic factors in a variety of human tumors.