Two classes of metric spaces

The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

Using WordNet relations and semantic classes in information retrieval tasks

In this paper we explore the use of semantic classes in an existing information retrieval system in order to improve its results. Thus, we use two different ontologies of semantic classes (WordNet domain and Basic Level Concepts) in order to re-rank the retrieved documents and obtain better recall and precision. Finally, we implement a new method for weighting the expanded terms taking into account the weights of the original query terms and their relations in WordNet with respect to the new ones (which have demonstrated to improve the results). The evaluation of these approaches was carried out in the CLEF Robust-WSD Task, obtaining an improvement of 1.8% in GMAP for the semantic classes approach and 10% in MAP employing the WordNet term weighting approach.

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K: spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.

Anisotropic magnetoresistance in nanocontacts

We present ab initio calculations of the evolution of anisotropic magnetoresistance (AMR) in Ni nanocontacts from the ballistic to the tunnel regime. We find an extraordinary enhancement of AMR, compared to bulk, in two scenarios. In systems without localized states, such as chemically pure break junctions, large AMR only occurs if the orbital polarization of the current is large, regardless of the anisotropy of the density of states. In systems that display localized states close to the Fermi energy, such as a single electron transistor with ferromagnetic electrodes, large AMR is related to the variation of the Fermi energy as a function of the magnetization direction.

Anisotropic magnetoresistance in single electron transport

We study the effect of magnetic anisotropy in a single electron transistor with ferromagnetic electrodes and a non-magnetic island. We identify the variation δμ of the chemical potential of the electrodes as a function of the magnetization orientation as a key quantity that permits to tune the electrical properties of the device. Different effects occur depending on the relative size of δμ and the charging energy. We provide preliminary quantitative estimates of δμ using a very simple toy model for the electrodes.

Anisotropic intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered nonperturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the microsecond range at room temperature. Interestingly, this mechanism is anisotropic on two counts. First, the relaxation rate is different for off-plane and in-plane spin quantization axis. Second, the spin relaxation rate depends on the angle formed by the crystal momentum with the carbon-carbon bond. In addition, the spin lifetime is also valley dependent. The proposed mechanism sets an upper limit for spin lifetimes in graphene and will be relevant when samples of high quality can be fabricated free of extrinsic sources of spin relaxation.

Ledger for the Classes of 1650-1663, 1649-1660

The leather-bound volume contains accounts for the Classes of 1650-1663 and Fellows. Many of the student bills were settled with payment in kind, often in the form of grain, apples, or livestock. The Steward's accounts with the College from 1656-1659 were entered on pages 295-303 and listed as "The steward is Creditor" and "The steward is Debitor." Credit entries include food, fuel, corn, and wages; debit entries list purchases and often identify the sellers.

Ledger for the Classes of 1703-1718, 1703-1731

The parchment-bound hardcover folio volume contains accounts for Fellows, Tutors, the President, and members of the Classes of 1703-1718. Payments were often made with bills of credit, money, and notes. The Steward's accounts with the College are interspersed in the volume.

Ledger for the Classes of 1723-1731, 1719-1755

The volume, bound in a modern leather binding, contains accounts for the Classes of 1723-1731. Leaves 108-118 list the Steward's account with Harvard College arranged monthly for the years 1721-1729.