The Time Machine: A Simulation Approach for Stochastic Trees

In the following paper we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling (IS) and sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor (MRCA). However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this paper we propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface. The bias is investigated from a theoretical point of view. Results from simulation studies are also given to investigate the balance between loss of accuracy, saving in computing time and variance reduction.Comment: 22 Pages, 5 Figure

Mott insulators in strong electric fields

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.Comment: Revised and extended version: 26 pages, 5 figures, 1 tabl

Conformational Mechanics of Polymer Adsorption Transitions at Attractive Substrates

Conformational phases of a semiflexible off-lattice homopolymer model near an attractive substrate are investigated by means of multicanonical computer simulations. In our polymer-substrate model, nonbonded pairs of monomers as well as monomers and the substrate interact via attractive van der Waals forces. To characterize conformational phases of this hybrid system, we analyze thermal fluctuations of energetic and structural quantities, as well as adequate docking parameters. Introducing a solvent parameter related to the strength of the surface attraction, we construct and discuss the solubility-temperature phase diagram. Apart from the main phases of adsorbed and desorbed conformations, we identify several other phase transitions such as the freezing transition between energy-dominated crystalline low-temperature structures and globular entropy-dominated conformations.Comment: 13 pages, 15 figure

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Mediation in the Law Curriculum

Cited by Lord Neuberger in ‘Educating Future Mediators’ at the 4th Civil Mediation Council National Conference, May 201

Fluctuating fire regimes and their historical effects on genetic variation in an endangered shrubland specialist

The Pleistocene was characterized by worldwide shifts in community compositions. Some of these shifts were a result of changes in fire regimes, which influenced the distribution of species belonging to fire-dependent communities. We studied an endangered juniper–oak shrubland specialist, the black-capped vireo (Vireo atricapilla). This species was locally extirpated in parts of Texas and Oklahoma by the end of the 1980s as a result of habitat change and loss, predation, brood parasitism, and anthropogenic fire suppression. We sequenced multiple nuclear loci and used coalescence methods to obtain a deeper understanding of historical population trends than that typically available from microsatellites or mtDNA. We compared our estimated population history, a long-term history of the fire regime and ecological niche models representing the mid-Holocene, last glacial maximum, and last interglacial. Our Bayesian skyline plots showed a pattern of historical population fluctuation that was consistent with changing fire regimes. Genetic data suggest that the species is genetically unstructured, and that the current population should be orders of magnitude larger than it is at present. We suggest that fire suppression and habitat loss are primary factors contributing to the recent decline of the BCVI, although the role of climate change since the last glacial maximum is unclear at present

Mitochondrial phylogeography and demographic history of the Vicuña: implications for conservation

The vicuña (Vicugna vicugna; Miller, 1924) is a conservation success story, having recovered from near extinction in the 1960s to current population levels estimated at 275 000. However, lack of information about its demographic history and genetic diversity has limited both our understanding of its recovery and the development of science-based conservation measures. To examine the evolution and recent demographic history of the vicuña across its current range and to assess its genetic variation and population structure, we sequenced mitochondrial DNA from the control region (CR) for 261 individuals from 29 populations across Peru, Chile and Argentina. Our results suggest that populations currently designated as Vicugna vicugna vicugna and Vicugna vicugna mensalis comprise separate mitochondrial lineages. The current population distribution appears to be the result of a recent demographic expansion associated with the last major glacial event of the Pleistocene in the northern (18 to 22°S) dry Andes 14–12 000 years ago and the establishment of an extremely arid belt known as the 'Dry Diagonal' to 29°S. Within the Dry Diagonal, small populations of V. v. vicugna appear to have survived showing the genetic signature of demographic isolation, whereas to the north V. v. mensalis populations underwent a rapid demographic expansion before recent anthropogenic impacts

How Fitch-Margoliash Algorithm can Benefit from Multi Dimensional Scaling

Whatever the phylogenetic method, genetic sequences are often described as strings of characters, thus molecular sequences can be viewed as elements of a multi-dimensional space. As a consequence, studying motion in this space (ie, the evolutionary process) must deal with the amazing features of high-dimensional spaces like concentration of measured phenomenon

Lesson from the Stoichiometry Determination of the Cohesin Complex: A Short Protease Mediated Elution Increases the Recovery from Cross-Linked Antibody-Conjugated Beads

Affinity purification of proteins using antibodies coupled to beads and subsequent mass spectrometric analysis has become a standard technique for the identification of protein complexes. With the recent transfer of the isotope dilution mass spectrometry principle (IDMS) to the field of proteomics, quantitative analysesssuch as the stoichiometry determination of protein complexesshave become achievable. Traditionally proteins were eluted from antibody-conjugated beads using glycine at low pH or using diluted acids such as HCl, TFA, or FA, but elution was often found to be incomplete. Using the cohesin complex and the anaphase promoting complex/cyclosome (APC/C) as examples, we show that a short 15-60 min predigestion with a protease such as LysC (modified on-bead digest termed protease elution) increases the elution efficiency 2- to 3-fold compared to standard acid elution protocols. While longer incubation periodssas performed in standard on-bead digestionsled to partial proteolysis of the cross-linked antibodies, no or only insignificant cleavage was observed after 15-60 min protease mediated elution. Using the protease elution method, we successfully determined the stoichiometry of the cohesin complex by absolute quantification of the four core subunits using LC-SRM analysis and 19 reference peptides generated with the EtEP strategy. Protease elution was 3-fold more efficient compared to HCl elution, but measurements using both elution techniques are in agreement with