Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio

The failure of the Tacoma Narrows Bridge

The Board of Engineers appointed by you to report on the Failure of the Tacoma Narrows Bridge have made a complete investigation of the design, the behaviour after completion and the failure of the structure. Our report covering this investigation follows

Cosmogenic \u3csup\u3e26\u3c/sup\u3eAl/\u3csup\u3e10\u3c/sup\u3eBe surface production ratio in Greenland

The assumed value for the cosmogenic 26Al/10Be surface production rate ratio in quartz is an important parameter for studies investigating the burial or subaerial erosion of long-lived surfaces and sediments. Recent models and data suggest that the production ratio is spatially variable and may be greater than originally thought. Here we present measured 26Al/10Be ratios for 24 continuously exposed bedrock and boulder surfaces spanning ~61–77°N in Greenland. Empirical measurements, such as ours, include nuclides produced predominately by neutron-induced spallation with percent-level contributions by muon interactions. The slope of a York regression line fit to our data is 7.3 ± 0.3 (1σ), suggesting that the 26Al/10Be surface production ratio exceeds the commonly used value of 6.75, at least in the Arctic. A higher 26Al/10Be production ratio has implications for multinuclide cosmogenic isotope studies because it results in greater modeled burial durations and erosion rates

CHERI: a research platform deconflating hardware virtualisation and protection

Contemporary CPU architectures conflate virtualization and protection, imposing virtualization-related performance, programmability, and debuggability penalties on software requiring finegrained protection. First observed in micro-kernel research, these problems are increasingly apparent in recent attempts to mitigate software vulnerabilities through application compartmentalisation. Capability Hardware Enhanced RISC Instructions (CHERI) extend RISC ISAs to support greater software compartmentalisation. CHERI’s hybrid capability model provides fine-grained compartmentalisation within address spaces while maintaining software backward compatibility, which will allow the incremental deployment of fine-grained compartmentalisation in both our most trusted and least trustworthy C-language software stacks. We have implemented a 64-bit MIPS research soft core, BERI, as well as a capability coprocessor, and begun adapting commodity software packages (FreeBSD and Chromium) to execute on the platform

Seventh international conference on time-resolved vibrational spectroscopy

The International Conference on Time-Resolved Vibrational Spectroscopy (TRVS) is widely recognized as the major international forum for the discussion of advances in this rapidly growing field. The 1995 conference was the seventh in a series that began at Lake Placid, New York, 1982. Santa Fe, New Mexico, was the site of the Seventh International Conference on Time-Resolved Vibrational Spectroscopy, held from June 11 to 16, 1995. TRVS-7 was attended by 157 participants from 16 countries and 85 institutions, and research ranging across the full breadth of the field of time-resolved vibrational spectroscopy was presented. Advances in both experimental capabilities for time-resolved vibrational measurements and in theoretical descriptions of time-resolved vibrational methods continue to occur, and several sessions of the conference were devoted to discussion of these advances and the associated new directions in TRVS. Continuing the interdisciplinary tradition of the TRVS meetings, applications of time-resolved vibrational methods to problems in physics, biology, materials science, and chemistry comprised a large portion of the papers presented at the conference

Determination of the (3x3)-Sn/Ge(111) structure by photoelectron diffraction

At a coverage of about 1/3 monolayer, Sn deposited on Ge(111) below 550 forms a metastable (sqrt3 x sqrt3)R30 phase. This phase continuously and reversibly transforms into a (3x3) one, upon cooling below 200 K. The photoemission spectra of the Sn 4d electrons from the (3x3)-Sn/Ge(111) surface present two components which are attributed to inequivalent Sn atoms in T4 bonding sites. This structure has been explored by photoelectron diffraction experiments performed at the ALOISA beamline of the Elettra storage ring in Trieste (Italy). The modulation of the intensities of the two Sn components, caused by the backscattering of the underneath Ge atoms, has been measured as a function of the emission angle at fixed kinetic energies and viceversa. The bond angle between Sn and its nearest neighbour atoms in the first Ge layer (Sn-Ge1) has been measured by taking polar scans along the main symmetry directions and it was found almost equivalent for the two components. The corresponding bond lengths are also quite similar, as obtained by studying the dependence on the photoelectron kinetic energy, while keeping the photon polarization and the collection direction parallel to the Sn-Ge1 bond orientation (bond emission). A clear difference between the two bonding sites is observed when studying the energy dependence at normal emission, where the sensitivity to the Sn height above the Ge atom in the second layer is enhanced. This vertical distance is found to be 0.3 Angstroms larger for one Sn atom out of the three contained in the lattice unit cell. The (3x3)-Sn/Ge(111) is thus characterized by a structure where the Sn atom and its three nearest neighbour Ge atoms form a rather rigid unit that presents a strong vertical distortion with respect to the underneath atom of the second Ge layer.Comment: 10 pages with 9 figures, added reference

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm