Optimal approximate matrix product in terms of stable rank

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows. Here $\tilde{r}$ is the maximum stable rank, i.e. squared ratio of Frobenius and operator norms, of the two matrices being multiplied. This is a quantitative improvement over previous work of [MZ11, KVZ14], and is also optimal for any oblivious dimensionality-reducing map. Furthermore, due to the black box reliance on the subspace embedding property in our proofs, our theorem can be applied to a much more general class of sketching matrices than what was known before, in addition to achieving better bounds. For example, one can apply our theorem to efficient subspace embeddings such as the Subsampled Randomized Hadamard Transform or sparse subspace embeddings, or even with subspace embedding constructions that may be developed in the future. Our main theorem, via connections with spectral error matrix multiplication shown in prior work, implies quantitative improvements for approximate least squares regression and low rank approximation. Our main result has also already been applied to improve dimensionality reduction guarantees for $k$-means clustering [CEMMP14], and implies new results for nonparametric regression [YPW15]. We also separately point out that the proof of the "BSS" deterministic row-sampling result of [BSS12] can be modified to show that for any matrices $A, B$ of stable rank at most $\tilde{r}$, one can achieve the spectral norm guarantee for approximate matrix multiplication of $A^T B$ by deterministically sampling $O(\tilde{r}/\varepsilon^2)$ rows that can be found in polynomial time. The original result of [BSS12] was for rank instead of stable rank. Our observation leads to a stronger version of a main theorem of [KMST10].Comment: v3: minor edits; v2: fixed one step in proof of Theorem 9 which was wrong by a constant factor (see the new Lemma 5 and its use; final theorem unaffected

A genome-wide survey of segmental duplications that mediate common human genetic variation of chromosomal architecture.

Recent studies have identified a small number of genomic rearrangements that occur frequently in the general population. Bioinformatics tools are now available for systematic genome-wide surveys of higher-order structures predisposing to such common variations in genomic architecture. Segmental duplications (SDs) constitute up to 5 per cent of the genome and play an important role in generating additional rearrangements and in disease aetiology. We conducted a genome-wide database search for a form of SD, palindromic segmental duplications (PSDs), which consist of paired, inverted duplications, and which predispose to inversions, duplications and deletions. The survey was complemented by a search for SDs in tandem orientation (TSDs) that can mediate duplications and deletions but not inversions. We found more than 230 distinct loci with higher-order genomic structure that can mediate genomic variation, of these about 180 contained a PSD. A number of these sites were previously identified as harbouring common inversions or as being associated with specific genomic diseases characterised by duplication, deletions or inversions. Most of the regions, however, were previously unidentified; their characterisation should identify further common rearrangements and may indicate localisations for additional genomic disorders. The widespread distribution of complex chromosomal architecture suggests a potentially high degree of plasticity of the human genome and could uncover another level of genetic variation within human populations

Detection of Special Nuclear Material with High Purity Germanium (HPGe) and Mercuric Iodide (HgI\u3csub\u3e2\u3c/sub\u3e) Gamma Detectors

The Defense Threat Reduction Agency (DTRA) contracted for two gamma radiation detectors: mercuric iodide (HgI2) and electromechanically cooled (EMC) high purity germanium (HPGe) to support arms control inspection efforts. This project investigated whether these detectors could measure the quality and quantity of special nuclear material (SNM), particularly Pu-239 for the treaty verification mission. The project investigated two areas of detector capabilities: 1) HgI2 and HPGe detector performance necessary to characterize the quality of plutonium and the presence of shielding materials and 2) HgI2 and EMC HPGe detector performance degradation by high noise levels and EMC HPGe detector performance degradation caused by electromechanical-cooling. The first area studied the response functions of each of the detectors necessary to meet the detection objectives: measure the Pu-239/Pu 240 ratio to identify weapons grade plutonium and to identify a phony weapon. The second area of detector performance evaluated was the EMC HPGe detector\u27s cooling capabilities and its effect on the performance of the detector. The results show that neither of the detectors was ideally capable of supporting DTRA\u27s requirements. The HgI2 detector did not have sufficient efficiency or resolution to distinguish between Weapon Grade and Reactor Grade Plutonium. The EMC system suffered from grounding problems that degraded the resolution and efficiency. An initial study, evaluating the ability of detectors to determine the presence of a simulated tamper within the SNM physics package, showed great promise for identifying phony weapons

Object Persistence and Availability in Digital Libraries

We have studied object persistence and availability of 1,000 digital library (DL) objects. Twenty World Wide Web accessible DLs were chosen and from each DL, 50 objects were chosen at random. A script checked the availability of each object three times a week for just over 1 year for a total of 161 data samples. During this time span, we found 31 objects (3% of the total) that appear to no longer be available: 24 from PubMed Central, 5 from IDEAS, 1 from CogPrints, and 1 from ETD

Food Industry Mergers and Acquisitions Lead to Higher Labor Productivity

Processing plants in eight major food industries were highly productive before being acquired and they significantly improved their labor productivity afterward, Economic Research Service and U.S. Census Bureau researchers found in their analysis of Census data. The plant-level data on production inputs and costs provided a detailed picture of food-production facilities involved in mergers and acquisitions. The industries are meatpacking, meat processing, poultry slaughtering and processing, cheese making, fluid milk processing, flour milling, feed processing, and oilseed crushing. The analysis suggests that mergers and acquisitions contributed to the general improvement in labor productivity, echoing an earlier ERS study. Labor productivity is defined as output per worker.Mergers, acquisitions, labor productivity, consolidation, structural change, Agribusiness, Industrial Organization, Productivity Analysis,

Simple Analyses of the Sparse Johnson-Lindenstrauss Transform

For every n-point subset X of Euclidean space and target distortion 1+eps for 0l_2^m where f(x) = Ax for A a matrix with m rows where (1) m = O((log n)/eps^2), and (2) each column of A is sparse, having only O(eps m) non-zero entries. Though the constructions given for such A in (Kane, Nelson, J. ACM 2014) are simple, the analyses are not, employing intricate combinatorial arguments. We here give two simple alternative proofs of their main result, involving no delicate combinatorics. One of these proofs has already been tested pedagogically, requiring slightly under forty minutes by the third author at a casual pace to cover all details in a blackboard course lecture

Structural Change in the Meat, Poultry, Dairy and Grain Processing Industries

Consolidation and structural changes in the food industry have had profound impacts on firms, employees, and communities in many parts of the United States. Over 1972-92, eight important food industries underwent a structural transformation in which the number of plants declined by about one-third and the number of employees needed to staff the remaining plants dropped by more than 100,000 (20 percent). The number of plants in one other industry also dropped, but that industry added jobs. Economists generally attribute structural changes such as these to rising or falling demand and shifts in technology. This report examines consolidation and structural change in meatpacking, meat processing, poultry slaughter and processing, cheese products, fluid milk, flour milling, corn milling, feed, and soybean processing. Plant size and output per employee rose sharply in all industries, and even industries with rapidly growing demand—such as soybean processing and poultry slaughter/processing—used fewer plants. These findings suggest that technological change was the major force driving structural change.structural change, food processing, consolidation, grain processing, meat slaughter, dairy processing, Industrial Organization,

Effect of Food Industry Mergers and Acquisitions on Employment and Wages

Empirical analysis of mergers and acquisitions in eight important food industries suggests that workers in acquired plants realized modest increases in employment and wages relative to other workers. Results also show that mergers and acquisitions reduced the likelihood of plant closures while high relative labor costs encouraged plant shutdowns. These results differ from commonly held views that mergers and acquisitions lead to fewer jobs, wage cuts, and plant shutdowns.Food product industries, mergers and acquisitions, plant closures, Agribusiness, Industrial Organization,