Sharp nonasymptotic bounds on the norm of random matrices with independent entries

We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that $$\mathbf{E}\Vert X\Vert \lesssim\max_i\sqrt{\sum_jb_{ij}^2}+\max _{ij}\vert b_{ij}\vert \sqrt{\log n}.$$ This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general sub-Gaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm. The proofs are based on a combination of the moment method and geometric functional analysis techniques. As an application, we show that our bounds immediately yield the correct phase transition behavior of the spectral edge of random band matrices and of sparse Wigner matrices. We also recover a result of Seginer on the norm of Rademacher matrices.Comment: Published at http://dx.doi.org/10.1214/15-AOP1025 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Musical Actions of Dihedral Groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.Comment: 27 pages, 11 figures. To appear in the American Mathematical Monthly

On the nature of the AGILE galactic transient sources

The Italian gamma-ray satellite AGILE has recently reported the detection of some variable high-energy sources likely of galactic origin. These sources do not have any obvious counterpart at lower energies. We propose that these sources are produced in proton-dominated jets of galactic microquasars. We develop a model for microquasar jets that takes into account both primary leptons and protons and all relevant radiative processes, including secondary particle emission and gamma-ray attenuation due to pair creation in the jet. We obtain spectral energy distributions that correspond to what is observed by AGILE, with most of the power concentrated between 100 MeV and 10 GeV and reaching luminosities of $10^{34-35}$ erg s$^{-1}$. We make detailed spectral predictions that can be tested by the Fermi gamma-ray telescope in the immediate future. We conclude that hadronic jets in galactic accreting sources can be responsible for the variable unidentified gamma-ray sources detected by AGILE.Comment: 4 pages, 2 figures. Accepted for publication in Astronomy & Astrophysics (Letters

Effects of formation properties in one-proton radioactivity

It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from a microscopic description of the decay process. In this way we explain the systematics of proton emission half-lives. At the same time the formation probability is shown to be a useful quantity to determine the deformation property of the mother nucleus.Comment: 5 pages, 5 figues, 2 tables, printer-friendly version, submitted to Phys. Rev.

Ensuring a More Evidence-based Policy for Basic Education

Can the Philippines achieve its goal on two key international commitments--the Millennium Development Goals (MDGs) on Education and the Education for All (EFA) Initiative--for the achievement of education for everyone? A closer look at the figures would show that the country may be at risk of not achieving its goal of attaining universal primary education by 2015. Given this scenario, the authors suggest that the government should intensify its efforts in improving basic education by having evidence-based policies and actions. In particular, they note that the Department of Education (DepEd) should be required to have a sound monitoring and evaluation system to regularly assess the conditions of basic education.basic education, millennium development goal (MDG), education indicators, monitoring and evaluation

Explaining Aviation Safety Incidents Using Deep Temporal Multiple Instance Learning

Although aviation accidents are rare, safety incidents occur more frequently and require a careful analysis to detect and mitigate risks in a timely manner. Analyzing safety incidents using operational data and producing event-based explanations is invaluable to airline companies as well as to governing organizations such as the Federal Aviation Administration (FAA) in the United States. However, this task is challenging because of the complexity involved in mining multi-dimensional heterogeneous time series data, the lack of time-step-wise annotation of events in a flight, and the lack of scalable tools to perform analysis over a large number of events. In this work, we propose a precursor mining algorithm that identifies events in the multidimensional time series that are correlated with the safety incident. Precursors are valuable to systems health and safety monitoring and in explaining and forecasting safety incidents. Current methods suffer from poor scalability to high dimensional time series data and are inefficient in capturing temporal behavior. We propose an approach by combining multiple-instance learning (MIL) and deep recurrent neural networks (DRNN) to take advantage of MIL's ability to learn using weakly supervised data and DRNN's ability to model temporal behavior. We describe the algorithm, the data, the intuition behind taking a MIL approach, and a comparative analysis of the proposed algorithm with baseline models. We also discuss the application to a real-world aviation safety problem using data from a commercial airline company and discuss the model's abilities and shortcomings, with some final remarks about possible deployment directions

Increased amino acid turnover and myofibrillar protein breakdown in advanced cancer are associated with muscle weakness and impaired physical function

Muscle wasting in cancer negatively affects physical function and quality of life. This study investigates amino acid metabolism and the association with muscle mass and function in patients with cancer.In 16 patients with advanced cancer undergoing chemotherapy and 16 healthy controls, we administered an intravenous pulse and prime of stable amino acid tracers. We took blood samples to measure the Rate of appearance (Ra), whole body production (WBP), clearance (Cl), and post absorptive whole body net protein breakdown (WBnetPB). Plasma amino acid concentrations and enrichments were analysed by LC-MS/MS. We assessed muscle mass, handgrip/leg/respiratory muscle strength and reported physical activity, quality of life, and physical function.Muscle strength was lower in cancer patients than in healthy controls. Total and limb muscle mass, reported physical activity and WBnetPB were comparable. WBP and Cl of tau-methylhistidine, leucine, glutamine and taurine were higher in cancer patients as well as glycine Cl. Amino acid metabolism was correlated with low muscle mass, strength, physical function and quality of life.Myofibrillar protein breakdown and production of amino acids involved in muscle contractility are up regulated in patients with cancer undergoing chemotherapy and related to muscle weakness and reduced physical outcomes

Development of New Taro Varieties through Breeding

The production of new crop varieties through hybridization is the only stable method of crop improvement. As a program, crop improvement through breeding has been a major project of most research centers and institutes. An example of the value of plant breeding was demonstrated by the release of IR-8 or "miracle rice" by the International Rice Research Institute in the mid-1960's. Other crops like corn and wheat had similar dramatic and valuable contributions. In Hawaii, new variety development has been and continues to be an important and well supported program of the Hawaiian Sugar Planters Association. Although taro is considered to be one of the oldest cultivated crops, there has virtually been no research program aimed at improving the varieties existing throughout the world. Because of the importance of taro as a commercial and staple crop in Hawaii and many countries in Asia and the Pacific area, an organized crop improvement program through breeding should be established and supported. Some of the advantages, problems, and general method of hybridizing taro are discussed