Nodes on quintic spectrahedra

We classify transversal quintic spectrahedra by the location of 20 nodes on the respective real determinantal surface of degree 5. We identify 65 classes of such surfaces and find an explicit representative in each of them

Kernel method for nonlinear Granger causality

Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to reach a deeper comprehension of phenomena ranging from turbulent fluids to neural networks, as well as complex physiological signals. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.Comment: Revised version, accepted for publication on Physical Review Letter

Self Hardening Slurry Wall Installation by Hydromill at The Herbert Hoover Dike – An Innovative Solution

In 2007 the US Army Corps of Engineers classified the Herbert Hoover Dike in Florida as a DSAC 1 dam, and started the implementation of one of the largest dam rehabilitation projects in the nation. The construction of the cutoff wall is a key feature of this rehabilitation work to upgrade the dike to current dam safety criteria. The cutoff wall installation is currently being completed on Reach 1, which extends from Port Mayaca to Belle Glade, under a Multiple Task Order Contract based on performance specifications and stringent verification criteria. For the construction of the cutoff wall TREVIICOS selected the self-hardening slurry method. Since the cutoff wall is installed through a layer of highly variable limestone with UCS up to 14,000 psi, the excavation requires the use of the hydromill equipment. This is the first successful application of the hydromill technology with self-hardening slurry in a large scale project in the US. This paper presents the details of the method utilized, the quality control procedures, and the experience gained over seven miles of cutoff wall installed

The Velocity Dispersion Profile of the Remote Dwarf Spheroidal Galaxy Leo I: A Tidal Hit and Run?

(abridged) We present kinematic results for a sample of 387 stars located near Leo I based on spectra obtained with the MMT's Hectochelle spectrograph near the MgI/Mgb lines. We estimate the mean velocity error of our sample to be 2.4 km/s, with a systematic error of < 1 km/s. We produce a final sample of 328 Leo I red giant members, from which we measure a mean heliocentric radial velocity of 282.9 +/- 0.5 km/s, and a mean radial velocity dispersion of 9.2 +/- 0.4 km/s for Leo I. The dispersion profile of Leo I is flat out to beyond its classical `tidal' radius. We fit the profile to a variety of equilibrium dynamical models and can strongly rule out models where mass follows light. Two-component Sersic+NFW models with tangentially anisotropic velocity distributions fit the dispersion profile well, with isotropic models ruled out at a 95% confidence level. The mass and V-band mass-to-light ratio of Leo I estimated from equilibrium models are in the ranges 5-7 x 10^7 M_sun and 9-14 (solar units), respectively, out to 1 kpc from the galaxy center. Leo I members located outside a `break radius' (about 400 arcsec = 500 pc) exhibit significant velocity anisotropy, whereas stars interior appear to have isotropic kinematics. We propose the break radius represents the location of the tidal radius of Leo I at perigalacticon of a highly elliptical orbit. Our scenario can account for the complex star formation history of Leo I, the presence of population segregation within the galaxy, and Leo I's large outward velocity from the Milky Way. The lack of extended tidal arms in Leo I suggests the galaxy has experienced only one perigalactic passage with the Milky Way, implying that Leo I may have been injected into its present orbit by a third body a few Gyr before perigalacticon.Comment: ApJ accepted, 23 figures, access paper as a pdf file at http://www.astro.lsa.umich.edu/~mmateo/research.htm

A Positive Spin on a Negative Narrative: How the Media Portrays Fraternities and What Fraternities Can Do About It

As research on fraternity men largely focuses on misbehavior and criminal activity, no research examines the types of stories reported on by media outlets and whether these stories include fraternity voices or statements. Employing quantitative content analysis, this study examines 100 fraternity-related stories published by the ten newspaper websites most frequently visited by people in the United States. Findings suggest 12% of fraternity-related publications are positive in nature and tone, 36% of publications include official fraternity-issued statements, and 69% of all publications include official university-issued statements. Implications for practitioners and future research is addressed

Is Monotonicity in an IV and RD design testable? No, but you can still check it

Whenever treatment effects are heterogeneous and there is sorting into treatment based on the gain, monotonicity is a condition that both Instrumental Variable and fuzzy Regression Discontinuity designs have to satisfy for their estimand to be interpretable as a LATE. Angrist and Imbens (1995) argue that the monotonicity assumption is testable whenever the treatment is multivalued. We show that their test is informative if counterfactuals are observed. Yet applying the test without observing counterfactuals, as it is generally done, is not. Nevertheless, we argue that monotonicity can and should be investigated using a mix of economic intuition and data patterns, just like other untestable assumptions in an IV or RD design. We provide examples in a variety of settings as a guide to practice