Efficient Yield Curve Estimation and Forecasting in Brazil

Term Structure of the Interest Rate, Yield Curve, State-Space Model, Kalman Filter.

On topological spin excitations on a rigid torus

We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, $R\to\infty$, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R=0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus ($R>r$) such excitations present no core where energy could blow up. At the limit $R\to\infty$ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus ($R=r$) a singular core takes place, while for $R<r$ (spindle torus) two such singularities appear. If $R$ is further diminished until vanish we recover vortex configuration on a sphere.Comment: 11 pages, 9 figure

On multigraded generalizations of Kirillov-Reshetikhin modules

We study the category of Z^l-graded modules with finite-dimensional graded pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre subcategories with finitely many isomorphism classes of simple objects. We construct projective resolutions for the simple modules in these categories and compute the Ext groups between simple modules. We show that the projective covers of the simple modules in these Serre subcategories can be regarded as multigraded generalizations of Kirillov-Reshetikhin modules and give a recursive formula for computing their graded characters

Topological insulator particles as optically induced oscillators: towards dynamical force measurements and optical rheology

We report the first experimental study upon the optical trapping and manipulation of topological insulator (TI) particles. By virtue of the unique TI properties, which have a conducting surface and an insulating bulk, the particles present a peculiar behaviour in the presence of a single laser beam optical tweezers: they oscillate in a plane perpendicular to the direction of the laser propagation, as a result of the competition between radiation pressure and gradient forces. In other words, TI particles behave as optically induced oscillators, allowing dynamical measurements with unprecedented simplicity and purely optical control. Actually, optical rheology of soft matter interfaces and biological membranes, as well as dynamical force measurements in macromolecules and biopolymers, may be quoted as feasible possibilities for the near future.Comment: 6 pages, 5 figures. Correspondence and requests for Supplementary Material should be addressed to [email protected]

Ground-state configurations in ferromagnetic nanotori

Magnetization ground states are studied in toroidal nanomagnets. The energetics associated to the ferromagnetic, vortex and onion-like configurations are explicitly computed. The analysis reveals that the vortex appears to be the most prominent of such states, minimizing total energy in every torus with internal radius $r\gtrsim10\,{\rm nm}$ (for Permalloy). For $r\lesssim10\,{\rm nm}$ the vortex remains the most favorable pattern whenever $R/\ell_{ex}\gtrsim1.5$ ($R$ is the torus external radius and $\ell_{ex}$ is the exchange length), being substituted by the ferromagnetic state whenever $R/\ell_{ex}\lesssim1.5$.Comment: 16 pages, 9 figures, 3 apendices, Revtex forma

On the multiplicity of the hyperelliptic integrals

Let $I(t)= \oint_{\delta(t)} \omega$ be an Abelian integral, where $H=y^2-x^{n+1}+P(x)$ is a hyperelliptic polynomial of Morse type, $\delta(t)$ a horizontal family of cycles in the curves $\{H=t\}$, and $\omega$ a polynomial 1-form in the variables $x$ and $y$. We provide an upper bound on the multiplicity of $I(t)$, away from the critical values of $H$. Namely: $ord\ I(t) \leq n-1+\frac{n(n-1)}{2}$if$\deg \omega <\deg H=n+1$. The reasoning goes as follows: we consider the analytic curve parameterized by the integrals along$\delta(t)$of the$n$``Petrov'' forms of$H$(polynomial 1-forms that freely generate the module of relative cohomology of$H$), and interpret the multiplicity of$I(t)$as the order of contact of$\gamma(t)$and a linear hyperplane of$\textbf C^ n$. Using the Picard-Fuchs system satisfied by$\gamma(t)$, we establish an algebraic identity involving the wronskian determinant of the integrals of the original form$\omega$along a basis of the homology of the generic fiber of$H$. The latter wronskian is analyzed through this identity, which yields the estimate on the multiplicity of$I(t)$. Still, in some cases, related to the geometry at infinity of the curves$\{H=t\} \subseteq \textbf C^2$, the wronskian occurs to be zero identically. In this alternative we show how to adapt the argument to a system of smaller rank, and get a nontrivial wronskian. For a form$\omega$of arbitrary degree, we are led to estimating the order of contact between$\gamma(t)$and a suitable algebraic hypersurface in$\textbf C^{n+1}$. We observe that$ord I(t)$grows like an affine function with respect to$\deg \omega$.Comment: 18 page

Onset of chaotic advection in open flows

Non peer reviewedPublisher PD

Magnetic monopole and string excitations in a two-dimensional spin ice

We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.Comment: 8 pages. Accepted by Journal of Applied Physics (2009

Random fluctuation leads to forbidden escape of particles

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.Comment: 6 pages, 6 figures - Up to date with corrections suggested by referee

Fasting Glucose Metabolism in Pregnancy

The HAPO study found a continuous association between hyperglycemia at 24-32 weeks of gestation, below the diagnostic levels of gestational diabetes mellitus (GDM), and adverse pregnancy outcomes, suggesting the need to reconsider the diagnostic criteria for GDM. Recently, a consensus for diagnosis of diabetes in pregnancy was published, based on the results of the HAPO study. Diagnosing for diabetes is considered already in the first trimester with fasting plasma glucose (FPG), but oral glucose tolerance test is recommended to be performed only at 24-28 weeks of gestation. Identifying all pregnant women at risk for GDM in the first trimester would allow an individualization of obstetric care and establishment of a dietetic and exercise plan since earlier stages of pregnancy with potential benefits for both mother and fetus. The glycemic metabolism varies throughout pregnancy, as insulin resistance increases during pregnancy. However the cut-off values for blood glucose tests in screening and diagnosing GDM are independent of gestational age. The objectives of this study are to verify if the pregnant women with and without GDM diagnosed in the second/third trimester are already different from each other in the first trimester regarding FPG levels and to study the evolution of the FPG throughout pregnancy