Latent protein trees

Unbiased, label-free proteomics is becoming a powerful technique for measuring protein expression in almost any biological sample. The output of these measurements after preprocessing is a collection of features and their associated intensities for each sample. Subsets of features within the data are from the same peptide, subsets of peptides are from the same protein, and subsets of proteins are in the same biological pathways, therefore, there is the potential for very complex and informative correlational structure inherent in these data. Recent attempts to utilize this data often focus on the identification of single features that are associated with a particular phenotype that is relevant to the experiment. However, to date, there have been no published approaches that directly model what we know to be multiple different levels of correlation structure. Here we present a hierarchical Bayesian model which is specifically designed to model such correlation structure in unbiased, label-free proteomics. This model utilizes partial identification information from peptide sequencing and database lookup as well as the observed correlation in the data to appropriately compress features into latent proteins and to estimate their correlation structure. We demonstrate the effectiveness of the model using artificial/benchmark data and in the context of a series of proteomics measurements of blood plasma from a collection of volunteers who were infected with two different strains of viral influenza.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS639 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum cohomology of flag manifolds and Toda lattices

We discuss relations of Vafa's quantum cohomology with Floer's homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of these conjectures, compute quantum cohomology algebras of the flag manifolds. The answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a Toda lattice.Comment: 35 page

Feedback from massive stars at low metallicities : MUSE observations of N44 and N180 in the Large Magellanic Cloud

Accepted for publication in MNRAS, 27 pages, 21 figuresWe present MUSE integral field data of two HII region complexes in the Large Magellanic Cloud (LMC), N44 and N180. Both regions consist of a main superbubble and a number of smaller, more compact HII regions that formed on the edge of the superbubble. For a total of 11 HII regions, we systematically analyse the radiative and mechanical feedback from the massive O-type stars on the surrounding gas. We exploit the integral field property of the data and the coverage of the HeII$\lambda$5412 line to identify and classify the feedback-driving massive stars, and from the estimated spectral types and luminosity classes we determine the stellar radiative output in terms of the ionising photon flux $Q_{0}$. We characterise the HII regions in terms of their sizes, morphologies, ionisation structure, luminosity and kinematics, and derive oxygen abundances via emission line ratios. We analyse the role of different stellar feedback mechanisms for each region by measuring the direct radiation pressure, the pressure of the ionised gas, and the pressure of the shock-heated winds. We find that stellar winds and ionised gas are the main drivers of HII region expansion in our sample, while the direct radiation pressure is up to three orders of magnitude lower than the other terms. We relate the total pressure to the star formation rate per unit area, $\Sigma_{SFR}$, for each region and find that stellar feedback has a negative effect on star formation, and sets an upper limit to $\Sigma_{SFR}$ as a function of increasing pressure.Peer reviewe

Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm

Skin effect with arbitrary specularity in Maxwellian plasma

The problem of skin effect with arbitrary specularity in maxwellian plasma with specular--diffuse boundary conditions is solved. A new analytical method is developed that makes it possible to to obtain a solution up to an arbitrary degree of accuracy. The method is based on the idea of symmetric continuation not only the electric field, but also electron distribution function. The solution is obtained in a form of von Neumann series.Comment: 7 pages, 2 figure

A First Look at the Auriga-California Giant Molecular Cloud With Herschel and the CSO: Census of the Young Stellar Objects and the Dense Gas

We have mapped the Auriga/California molecular cloud with the Herschel PACS and SPIRE cameras and the Bolocam 1.1 mm camera on the Caltech Submillimeter Observatory (CSO) with the eventual goal of quantifying the star formation and cloud structure in this Giant Molecular Cloud (GMC) that is comparable in size and mass to the Orion GMC, but which appears to be forming far fewer stars. We have tabulated 60 compact 70/160um sources that are likely pre-main-sequence objects and correlated those with Spitzer and WISE mid-IR sources. At 1.1 mm we find 18 cold, compact sources and discuss their properties. The most important result from this part of our study is that we find a modest number of additional compact young objects beyond those identified at shorter wavelengths with Spitzer. We also describe the dust column density and temperature structure derived from our photometric maps. The column density peaks at a few x 10^22 cm^-2 (N_H2) and is distributed in a clear filamentary structure along which nearly all the pre-main-sequence objects are found. We compare the YSO surface density to the gas column density and find a strong non-linear correlation between them. The dust temperature in the densest parts of the filaments drops to ~10K from values ~ 14--15K in the low density parts of the cloud. We also derive the cumulative mass fraction and probability density function of material in the cloud which we compare with similar data on other star-forming clouds.Comment: in press Astrophysical Journal, 201

Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

VLASSICK: The VLA Sky Survey in the Central Kiloparsec

At a distance of 8 kpc, the center of our Galaxy is the nearest galactic nucleus, and has been the subject of numerous key projects undertaken by great observatories such as Chandra, Spitzer, and Herschel. However, there are still no surveys of molecular gas properties in the Galactic center with less than 30" (1 pc) resolution. There is also no sensitive polarization survey of this region, despite numerous nonthermal magnetic features apparently unique to the central 300 parsecs. In this paper, we outline the potential the VLASS has to fill this gap. We assess multiple considerations in observing the Galactic center, and recommend a C-band survey with 10 micro-Jy continuum RMS and sensitive to molecular gas with densities greater than 10^4 cm^{-3}, covering 17 square degrees in both DnC and CnB configurations ( resolution ~5"), totaling 750 hours of observing time. Ultimately, we wish to note that the upgraded VLA is not just optimized for fast continuum surveys, but has a powerful correlator capable of simultaneously observing continuum emission and dozens of molecular and recombination lines. This is an enormous strength that should be fully exploited and highlighted by the VLASS, and which is ideally suited for surveying the center of our Galaxy.Comment: 13 pages, 3 figures, a White Paper submitted to provide input in planning the Very Large Array Sky Surve

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards