The Dual JL Transforms and Superfast Matrix Algorithms

We call a matrix algorithm superfast (aka running at sublinear cost) if it involves much fewer flops and memory cells than the matrix has entries. Using such algorithms is highly desired or even imperative in computations for Big Data, which involve immense matrices and are quite typically reduced to solving linear least squares problem and/or computation of low rank approximation of an input matrix. The known algorithms for these problems are not superfast, but we prove that their certain superfast modifications output reasonable or even nearly optimal solutions for large input classes. We also propose, analyze, and test a novel superfast algorithm for iterative refinement of any crude but sufficiently close low rank approximation of a matrix. The results of our numerical tests are in good accordance with our formal study.Comment: 36.1 pages, 5 figures, and 1 table. arXiv admin note: text overlap with arXiv:1710.07946, arXiv:1906.0411

Transient Binding and Dissipation in Cross-Linked Actin Networks

In contrast with entangled actin solutions, transiently cross-linked actin networks can provide highly elastic properties while still allowing for local rearrangements in the microstructure-on biological relevant time scales. Here, we show that thermal unbinding of transient cross-links entails local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the viscoelastic response of an isotropically cross-linked actin network by experimentally tuning the off rate of the transiently cross-linking molecules, their density, and the solvent viscosity. We reproduce the measured frequency response by a semiphenomenological model that is predicated on microscopic unbinding events

Composite study of aerosol export events from East Asia and North America

We use satellite observations of aerosol optical depth (AOD) from the Moderate Resolution Imaging Spectrometer (MODIS) together with the GEOS-Chem global chemical transport model to contrast export of aerosols from East Asia and North America during 2004–2010. The GEOS-Chem model reproduces the spatial distribution and temporal variations of Asian aerosol outflow generally well, although a low bias (−30%) is found in the model fine mode AOD, particularly during summer. We use the model to identify 244 aerosol pollution export events from E. Asia and 251 export events from N. America over our 7-year study period. When these events are composited by season, we find that the AOD in the outflow is enhanced by 50–100% relative to seasonal mean values. The composite Asian plume splits into one branch going poleward to the Arctic in 3–4 days, with the other crossing the Pacific Ocean in 6–8 days. A fraction of the aerosols is trapped in the subtropical Pacific High during spring and summer. The N. American plume travels to the northeast Atlantic, reaching Europe after 4–5 days. Part of the composite plume turns anticyclonically in the Azores High, where it slowly decays. Both the Asian and N. American export events are favored by a dipole structure in sea-level pressure anomalies, associated with mid-latitude cyclone activity over the respective source regions. This dipole structure during outflow events is a strong feature for all seasons except summer, when convection becomes more important. The observed AOD in the E. Asian outflow exhibits stronger seasonality, with a spring maximum, than the N. American outflow, with a broad spring/summer maximum. The large spring AOD in the Asian outflow is the result of enhanced sulfate and dust aerosol concentrations, but is also due to a larger export efficiency of sulfate and SO<sub>2</sub> from the Asian boundary layer relative to the N. American boundary layer. While the N. American sulfate outflow is mostly found in the lower troposphere (1–3 km altitude), the Asian sulfate outflow occurs at higher altitudes (2–6 km). In the Asian outflow 42–59% of the sulfate column is present above 2 km altitude, with only 24–35% in the N. American outflow. We link this to the factor of 2–5 lower precipitation in the warm conveyor belts (WCB) of midlatitude cyclones over E. Asia compared to N. America. This relative lack of precipitation makes Asian WCB very efficient for injecting aerosols in the middle troposphere

Superfast Refinement of Low Rank Approximation of a Matrix

Low rank approximation (LRA) of a matrix is a hot subject of modern computations. In application to Big Data mining and analysis the input matrices are usually so immense that one must apply superfast algorithms, which only access a tiny fraction of the input entries and involve much fewer memory cells and flops than an input matrix has entries. Recently we devised and analyzed some superfast LRA algorithms; in this paper we extend a classical algorithm of iterative refinement of the solution of linear systems of equations to superfast refinement of a crude but reasonably close LRA; we also list some heuristic recipes for superfast a posteriori estimation of the errors of LRA and support our superfast refinement algorithm with some superfast heuristic recipes for a posteriori error estimation of LRA and with superfast back and forth transition between any LRA of a matrix and its SVD. Our algorithm of iterative refinement of LRA is the first attempt of this kind and should motivate further effort in that direction, but already our initial tests are in good accordance with our formal study.Comment: 12.5 pages,, 1 table and 1 figur

QCD Matter Thermalization at RHIC and LHC

Employing the perturbative QCD inspired parton cascade, we investigate kinetic and chemical equilibration of the partonic matter created in central heavy ion collisions at RHIC and LHC energies. Two types of initial conditions are chosen. One is generated by the model of wounded nucleons using the PYTHIA event generator and Glauber geometry. Another is considered as a color glass condensate. We show that kinetic equilibration is almost independent on the chosen initial conditions, whereas there is a sensitive dependence for chemical equilibration. The time scale of thermalization lies between 1 and 1.5 fm/c. The final parton transverse energy obtained from BAMPS calculations is compared with the RHIC data and is estimated for the LHC energy.Comment: 8 pages, 10 figures, plenary talk at International Conference on Strangeness in Quark Matter 2008, Beijing, China, October 6-10, 200