Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the
Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.
Rheumatoid arthritis clinical trials are strategically designed to collect the disease activity score of each patient over multiple clinical visits, meanwhile a patient may drop out before their intended completion due to various reasons. The dropout
terminates the longitudinal data collection on the patients activity score. In the presence of informative dropout, that is, the dropout depends on latent variables from the longitudinal process, simply applying a model to analyze the longitudinal outcomes may lead to biased results because the assumption of random dropout is violated. In this paper we develop a data driven Bayesian joint model for modeling DAS28 scores and competing risk informative drop out. The motivating example is a clinical trial of Etanercept and Methotrexate with radiographic Patient Outcomes (TEMPO, Keystone et.al).
We demonstrate a new approach to classical fiber-fed spectroscopy. Our method is to use a photonic lantern that converts an arbitrary (e.g. incoherent) input beam into N diffraction-limited outputs. For the highest throughput, the number of outputs m
ust be matched to the total number of unpolarized spatial modes on input. This approach has many advantages: (i) after the lantern, the instrument is constructed from commercial off the shelf components; (ii) the instrument is the minimum size and mass configuration at a fixed resolving power and spectral order (~shoebox sized in this case); (iii) the throughput is better than 60% (slit to detector, including detector QE of ~80%); (iv) the scattered light at the detector can be less than 0.1% (total power). Our first implementation operates over 1545-1555 nm (limited by the detector, a 640$times$512 array with 20$mu$m pitch) with a spectral resolution of 0.055nm (R~30,000) using a 1$times$7 (1 multi-mode input to 7 single-mode outputs) photonic lantern. This approach is a first step towards a fully integrated, multimode photonic microspectrograph.
We use the 1+3 frame formalism to write down the evolution equations for spherically symmetric models as a well-posed system of first order PDEs in two variables, suitable for numerical and qualitative analysis.
In this paper, we address the problem of identifying protein functionality using the information contained in its aminoacid sequence. We propose a method to define sequence similarity relationships that can be used as input for classification and clu
stering via well known metric based statistical methods. In our examples, we specifically address two problems of supervised and unsupervised learning in structural genomics via simple metric based techniques on the space of trees 1)Unsupervised detection of functionality families via K means clustering in the space of trees, 2)Classification of new proteins into known families via k nearest neighbour trees. We found evidence that the similarity measure induced by our approach concentrates information for discrimination. Classification has the same high performance than others VLMC approaches. Clustering is a harder task, though, but our approach for clustering is alignment free and automatic, and may lead to many interesting variations by choosing other clustering or classification procedures that are based on pre-computed similarity information, as the ones that performs clustering using flow simulation, see (Yona et al 2000, Enright et al, 2003).
