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 Physical Theory of the Competition that Allows HIV to Escape from the Immune System

Competition within the immune system may degrade immune control of viral infections. We formalize the evolution that occurs in both HIV-1 and the immune system quasispecies. Inclusion of competition in the immune system leads to a novel balance between the immune response and HIV-1, in which the eventual outcome is HIV-1 escape rather than control. The analytical model reproduces the three stages of HIV-1 infection. We propose a vaccine regimen that may be able to reduce competition between T cells, potentially eliminating the third stage of HIV-1.Comment: 5 pages, 2 figures, to appear in Phys. Rev. Let

The stoichiometry of P2X2/6 receptor heteromers depends on relative subunit expression levels

Fast synaptic transmission involves the operation of ionotropic receptors, which are often composed of at least two types of subunit. We have developed a method, based on atomic force microscopy imaging to determine the stoichiometry and subunit arrangement within ionotropic receptors. We showed recently that the P2X(2) receptor for ATP is expressed as a trimer but that the P2X(6) subunit is unable to oligomerize. In this study we addressed the subunit stoichiometry of heteromers containing both P2X(2) and P2X(6) subunits. We transfected tsA 201 cells with both P2X(2) and P2X(6) subunits, bearing different epitope tags. We manipulated the transfection conditions so that either P2X(2) or P2X(6) was the predominant subunit expressed. By atomic force microscopy imaging of isolated receptors decorated with antiepitope antibodies, we demonstrate that when expression of the P2X(2) subunit predominates, the receptors contain primarily 2 x P2X(2) subunits and 1 x P2X(6) subunit. In contrast, when the P2X(6) subunit predominates, the subunit stoichiometry of the receptors is reversed. Our results show that the composition of P2X receptor heteromers is plastic and dependent on the relative subunit expression levels. We suggest that this property of receptor assembly might introduce an additional layer of subtlety into P2X receptor signaling

Optimal lower bounds for universal relation, and for samplers and finding duplicates in streams

In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \in\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that $x_i\neq y_i$. We prove that the randomized one-way communication complexity of this problem in the public coin model is exactly $\Theta(\min\{n,\log(1/\delta)\log^2(\frac n{\log(1/\delta)})\})$ for failure probability $\delta$. Our lower bound holds even if promised $\mathop{support}(y)\subset \mathop{support}(x)$. As a corollary, we obtain optimal lower bounds for $\ell_p$-sampling in strict turnstile streams for $0\le p < 2$, as well as for the problem of finding duplicates in a stream. Our lower bounds do not need to use large weights, and hold even if promised $x\in\{0,1\}^n$ at all points in the stream. We give two different proofs of our main result. The first proof demonstrates that any algorithm $\mathcal A$ solving sampling problems in turnstile streams in low memory can be used to encode subsets of $[n]$ of certain sizes into a number of bits below the information theoretic minimum. Our encoder makes adaptive queries to $\mathcal A$ throughout its execution, but done carefully so as to not violate correctness. This is accomplished by injecting random noise into the encoder's interactions with $\mathcal A$, which is loosely motivated by techniques in differential privacy. Our second proof is via a novel randomized reduction from Augmented Indexing [MNSW98] which needs to interact with $\mathcal A$ adaptively. To handle the adaptivity we identify certain likely interaction patterns and union bound over them to guarantee correct interaction on all of them. To guarantee correctness, it is important that the interaction hides some of its randomness from $\mathcal A$ in the reduction.Comment: merge of arXiv:1703.08139 and of work of Kapralov, Woodruff, and Yahyazade

Handgun carrying among white youth increasing in the United States: new evidence from the national survey on drug use and health 2002–2013

The objective of the present study was to examine trends and correlates of handgun carrying among adolescents ages 12–17 in the United States. Data was derived from the National Survey on Drug Use and Health (NSDUH) involving non-Hispanic White, African American, and Hispanic respondents ages 12–17 (n = 197,313) and spanning the years 2002–2013. Logistic regression was used to examine significance of trend year and correlates of previous 12-month handgun carrying. The overall self-reported prevalence of handgun carrying was 3.4%. The prevalence of handgun carrying during 2004–2005 was significantly higher for African-Americans (4.39%) compared to non-Hispanic Whites (3.03%). However, by 2012–2013, non-Hispanic Whites (4.08%) completely diverged and reported carrying handguns significantly more than both African-American (2.96%) and Hispanic (2.82%) youth. Male gender and a number of externalizing behaviors were significant correlates of handgun carrying; however, we also found evidence of differential correlates with regard to such factors as drug selling, parental affirmation, and income by race/ethnicity. To our knowledge, this is the largest study of handgun carrying among youth in the United States. Findings indicate that although at historically low levels handgun carrying is on the rise but only among non-Hispanic Whites. Differential correlates among racial/ethnic groups suggest prevention programming and policies may need modifications depending on group and geographic locale targeted.R25 DA030310 - National Institute on Drug Abuse at the National Institutes of Healt

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,

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,

Trends and correlates of substance use disorders among probationers and parolees in the United States 2002–2014

BACKGROUND: Substance use and crime/recidivism are irrevocably linked. We explore the nuances of this association by highlighting the prevalence, trends, and correlates of substance use dsorders in a large group of probationers/parolees. METHODS: We examined SUDs among probationers and parolees in the United States using data from the National Study on Drug Use and Health (NSDUH). Logistic regression models were computed to examine eight distinct outcomes: alcohol abuse, illicit drug abuse, marijuana/hashish abuse, comorbid alcohol and illicit drug abuse, alcohol dependence, illicit drug dependence, marijuana/hashish dependence, and comorbid alcohol and illicit drug dependence. RESULTS: Probationers/parolees have high prevalence rates across all SUDs categories and these trends have been relatively constant. Prevalence rates for alcohol abuse and dependence are two to six times higher than for marijuana and other illicit drug abuse and dependence. Key correlates of substance abuse for probationers/parolees include: age, gender, race/ethnicity, education, income, risk propensity, crime/violence measures, and comorbid substance abuse. Similar correlates were found for substance dependence, in addition to employment and mental health treatment. CONCLUSIONS: This study indicates that SUDs are higher among probationer/parolees as compared to their non-supervised counterparts − between four and nine times higher − and these levels have changed little in recent years. Effectively responding to SUDs in this population may enhance adherence to supervision requirements, prevent recidivism, and improve public safety. We may be better served using limited funds for further development of evidence-based policies and programs, such as drug courts, which demonstrate reductions in both drug use and recidivism

Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.