Optimal Fuzzy Aggregation of Networks

This paper is concerned with the problem of fuzzy aggregation of a network with non-negative weights on its edges into a small number of clusters. Specifically we want to optimally define a probability of affiliation of each of the n nodes of the network to each of m < n clusters or aggregates. We take a dynamical perspective on this problem by analyzing the discrete-time Markov chain associated with the network and mapping it onto a Markov chain describing transitions between the clusters. We show that every such aggregated Markov chain and affiliation function can be lifted again onto the full network to define the so-called lifted transition matrix between the nodes of the network. The optimal aggregated Markov chain and affiliation function can then be determined by minimizing some appropriately defined distance between the lifted transition matrix and the transition matrix of the original chain. In general, the resulting constrained nonlinear minimization problem comes out to have continuous level sets of minimizers. We exploit this fact to devise an algorithm for identification of the optimal cluster number by choosing specific minimizers from the level sets. Numerical minimization is performed by some appropriately adapted version of restricted line search using projected gradient descent. The resulting algorithmic scheme is shown to perform well on several test examples

Markov State Models Based on Milestoning

Markov State Models (MSMs) have become the tool of choice to analyze large amounts of molec- ular dynamics data by approximating them as a Markov jump process between suitably predefined states. Here we investigate ”Core Set MSMs”, a new type of MSMs that builds on metastable core sets acting as milestones for tracing the rare event kinetics. We present a thorough analysis of Core Set MSMs based on the existing milestoning framework, Bayesian estimation methods and Transi- tion Path Theory (TPT). As a result, Core Set MSMs can now be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables. The performance of Core Set MSMs in comparison to standard MSMs is analyzed and illustrated on a model potential and the torsion angle dynamics of Alanine dipeptide

Nuclear energy density optimization: Shell structure

Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. In this work, we propose a new parameterization UNEDF2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDerS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parameterization UNEDF1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF2 parameterization is comparable with UNEDF1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parameterizations, the parameter confidence interval for UNEDF2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits and significant changes to the form of the functional are needed.Comment: 18 pages, 13 figures, 12 tables; resubmitted for publication to Phys. Rev. C after second review by refere

Síndrome de Turner: Relación entre Genotipo 45X0/46XY y los diferentes Fenotipos encontrados. Riesgo de desarrollo de Gonadoblastoma.

El Síndrome de Turner (ST) se caracteriza por disgenesia gonadal con amenorrea primaria, infantilismo sexual, talla baja y fenotipo femenino con múltiples anomalías congénitas. Es uno de los trastornos cromosómicos humanos más frecuentes; afecta a una niña por cada 2.500 recién nacidas vivas. El diagnóstico se basa en el reconocimiento clínico del cuadro, que debe ser confirmado mediante la práctica de un cariotipo. De acuerdo con los análisis citogenéticos, el 50-60% de los pacientes con ST tienen un cariotipo de 45, X. El resto, presentan aberraciones estructurales de uno de los cromosomas X o, más frecuentemente, un mosaicismo. La detección de un mosaicismo, conteniendo el cromosoma Y en el ST (45,X0/46XY), es de crucial importancia clínica, debido a que esta combinación se acompaña de un elevado riesgo de desarrollo de gonadoblastoma o de otro tumor gonadal; riesgo que ha sido estimado entre un 15-20%

Phylogenetic relationships and molecular evolution in uropeltid snakes (Serpentes: Uropeltidae): allozymes and albumin immunology

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73950/1/j.1095-8312.1990.tb00541.x.pd

Anticoagulation for non-valvular atrial aibrillation – towards a new beginning with ximelagatran

OBJECTIVES: Ximelagatran is a novel oral direct thrombin inhibitor. It has favorable pharmacodynamic properties, with a broad therapeutic range without the need for anticoagulation monitoring. We aimed to discover whether ximelagatran offers a genuine future replacement to warfarin for patients in persistent atrial fibrillation (AF). MATERIALS AND METHODS: We provide an evidence-based review of the relative merits and disadvantages of warfarin and aspirin. We subsequently present an overview of the evidence for the utility of ximelagatran in the treatment of AF. RESULTS: Adjusted dose warfarin is recommended over aspirin for patients in AF at high risk of future stroke. Some of this benefit is partially offset by the higher bleeding risks associated with warfarin therapy. The SPORTIF III and V studies have shown that ximelagatran is not inferior to warfarin in the prevention of all strokes in patients with AF (both persistent and paroxysmal). This benefit was partially offset by the finding of a significant elevation of liver transaminases (>3 × normal) in 6% of patients. CONCLUSIONS: Current data would suggest that ximelagatran might represent a future alternative to warfarin. The lack of need for anticoagulant monitoring has been partially offset by a need for regular monitoring of liver function. Further data from randomized clinical trials is clearly needed

Variational Approach to Molecular Kinetics

The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics

Bayesian molecular clock dating of species divergences in the genomics era

It has been five decades since the proposal of the molecular clock hypothesis, which states that the rate of evolution at the molecular level is constant through time and among species. This hypothesis has become a powerful tool in evolutionary biology, making it possible to use molecular sequences to estimate the geological ages of species divergence events. With recent advances in Bayesian clock dating methodology and the explosive accumulation of genetic sequence data, molecular clock dating has found widespread applications, from tracking virus pandemics, to studying the macroevolutionary process of speciation and extinction, to estimating a timescale for Life on Earth