TY - JOUR
AB - We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.
AU - Tamas Hausel
AU - Rodríguez Villegas, Fernando
ID - 1460
IS - 3
JF - Inventiones Mathematicae
TI - Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz
VL - 174
ER -
TY - JOUR
AB - A complete mitochondrial (mt) genome sequence was reconstructed from a 38,000 year-old Neandertal individual with 8341 mtDNA sequences identified among 4.8 Gb of DNA generated from ∼0.3 g of bone. Analysis of the assembled sequence unequivocally establishes that the Neandertal mtDNA falls outside the variation of extant human mtDNAs, and allows an estimate of the divergence date between the two mtDNA lineages of 660,000 ± 140,000 years. Of the 13 proteins encoded in the mtDNA, subunit 2 of cytochrome c oxidase of the mitochondrial electron transport chain has experienced the largest number of amino acid substitutions in human ancestors since the separation from Neandertals. There is evidence that purifying selection in the Neandertal mtDNA was reduced compared with other primate lineages, suggesting that the effective population size of Neandertals was small.
AU - Green, Richard E
AU - Malaspinas, Anna-Sapfo
AU - Krause, Johannes
AU - Briggs, Adrian W
AU - Johnson, Philip L
AU - Caroline Uhler
AU - Meyer, Matthias
AU - Good, Jeffrey M
AU - Maricic, Tomislav
AU - Stenzel, Udo
AU - Prüfer, Kay
AU - Siebauer, Michael F
AU - Burbano, Hernän A
AU - Ronan, Michael T
AU - Rothberg, Jonathan M
AU - Egholm, Michael
AU - Rudan, Pavao
AU - Brajković, Dejana
AU - Kućan, Željko
AU - Gušić, Ivan
AU - Wikström, Mårten K
AU - Laakkonen, Liisa J
AU - Kelso, Janet F
AU - Slatkin, Montgomery
AU - Pääbo, Svante H
ID - 3307
JF - Cell
TI - A complete neandertal mitochondrial genome sequence determined by highhhroughput sequencing
VL - 134
ER -
TY - JOUR
AB - We develop a new method for estimating effective population sizes, Ne, and selection coefficients, s, from time-series data of allele frequencies sampled from a single diallelic locus. The method is based on calculating transition probabilities, using a numerical solution of the diffusion process, and assuming independent binomial sampling from this diffusion process at each time point. We apply the method in two example applications. First, we estimate selection coefficients acting on the CCR5-Δ32 mutation on the basis of published samples of contemporary and ancient human DNA. We show that the data are compatible with the assumption of s = 0, although moderate amounts of selection acting on this mutation cannot be excluded. In our second example, we estimate the selection coefficient acting on a mutation segregating in an experimental phage population. We show that the selection coefficient acting on this mutation is ~0.43.
AU - Jonathan Bollback
AU - York, Thomas L
AU - Nielsen, Rasmus
ID - 3435
IS - 1
JF - Genetics
TI - Estimation of 2Nes From Temporal Allele Frequency Data
VL - 179
ER -
TY - CONF
AB - Simulation and bisimulation metrics for stochastic systems provide a quantitative gen- eralization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative μ-calculus and related probabilistic logics.
We present algorithms for computing the metrics on Markov decision processes (MDPs), turn- based stochastic games, and concurrent games. For turn-based games and MDPs, we provide a polynomial-time algorithm based on linear programming for the computation of the one-step metric distance between states. The algorithm improves on the previously known exponential-time algo- rithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known bound for Markov chains. For the bisimulation kernel of the metric, which corresponds to probabilistic bisimulation, our algorithm works in time O(n4) for both turn-based games and MDPs; improving the previously best known O(n9 · log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be accomplished via a reduction to the theory of real closed fields, involving a
formula with three quantifier alternations, yielding O(|G|O(|G|5)) time complexity, improving the previously known reduction with O(|G|O(|G|7)) time complexity. These algorithms can be iterated
to approximate the metrics using binary search.
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Majumdar, Ritankar
AU - Raman, Vishwanath
ID - 3504
TI - Algorithms for game metrics
VL - 2
ER -
TY - JOUR
AB - Gene expression levels fluctuate even under constant external conditions. Much emphasis has usually been placed on the components of this noise that are due to randomness in transcription and translation. Here we focus on the role of noise associated with the inputs to transcriptional regulation; in particular, we analyze the effects of random arrival times and binding of transcription factors to their target sites along the genome. This contribution to the total noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional methods for plotting the variance vs. mean expression level. We argue that simple, universal models of noise dominated by transcription and translation are inconsistent with the embedding of gene expression in a network of regulatory interactions. Analysis of recent experiments on transcriptional control in the early Drosophila embryo shows that these results are quantitatively consistent with the predicted signatures of input noise, and we discuss the experiments needed to test the importance of input noise more generally.
AU - Gasper Tkacik
AU - Gregor, Thomas
AU - Bialek, William S
ID - 3734
IS - 7
JF - PLoS One
TI - The role of input noise in transcriptional regulation
VL - 3
ER -