The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes

We study the Laplacian in deformed thin (bounded or unbounded) tubes in ?$\R^3$, i.e., tubular regions along a curve $r(s)$ whose cross sections are multiplied by an appropriate deformation function $h(s)> 0$. One the main requirements on $h(s)$ is that it has a single point of global maximum. We find the asymptotic behaviors of the eigenvalues and weakly effective operators as the diameters of the tubes tend to zero. It is shown that such behaviors are not influenced by some geometric features of the tube, such as curvature, torsion and twisting, and so a huge amount of different deformed tubes are asymptotically described by the same weakly effective operator

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

Stein structures: existence and flexibility

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure

The air-launched autonomous micro observer

Author Posting. © American Meteorological Society, 2022. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of the Atmospheric and Oceanic Technology 39(4), (2022): 491–502, https://doi.org/10.1175/jtech-d-21-0046.1.The Air-Launched Autonomous Micro Observer (ALAMO) is a versatile profiling float that can be launched from an aircraft to make temperature and salinity observations of the upper ocean for over a year with high temporal sampling. Similar in dimensions and weight to an airborne expendable bathythermograph (AXBT), but with the same capability as Argo profiling floats, ALAMOs can be deployed from an A-sized (sonobuoy) launch tube, the stern ramp of a cargo plane, or the door of a small aircraft. Unlike an AXBT, however, the ALAMO float directly measures pressure, can incorporate additional sensors, and is capable of performing hundreds of ocean profiles compared to the single temperature profile provided by an AXBT. Upon deployment, the float parachutes to the ocean, releases the air-deployment package, and immediately begins profiling. Ocean profile data along with position and engineering information are transmitted via the Iridium satellite network, automatically processed, and then distributed by the Global Telecommunications System for use by the operational forecasting community. The ALAMO profiling mission can be modified using the two-way Iridium communications to change the profiling frequency and depth. Example observations are included to demonstrate the ALAMO’s utility.This work was supported by the National Oceanographic and Atmospheric Administration under Grants NA13OAR4830233 (as part of CINAR Sandy Supplemental funding from the Disaster Relief Appropriations Act of 2013) and NA14OAR4320158 and by Office of Naval Research under Grants N0001416WX01384, N0001416WX01262, and N000141512293. ALAMO floats are commercially available from MRV Systems, LLC (https://www.mrvsys.com)

Distances from Stellar Kinematics for Peculiar Virgo Cluster Spiral Galaxies

We present distance estimates for eleven peculiar Virgo cluster spiral galaxies based on measurements of the stellar kinematics of their central 2 kpc. Stellar circular velocities were obtained using two-integral dynamical models. Distances were obtained by comparing, at each radius, the stellar circular velocities with synthetic H_alpha rotation curves derived from NIR Tully-Fisher relations.The results show that most of our galaxies are located within 4 Mpc of the core of the cluster. Three of these galaxies, previously classified as "low rotator galaxies" or with "Truncated/Compact" H_alpha radial distributions, have stellar kinematics-based distances that are discrepant with HI-based distances by at least 60%, and are likely to be located within the virial radius of the cluster. These discrepancies appear due to very truncated gas distributions plus non-circular gas motions or gas motions not in the plane of the stellar disk, perhaps as the result of gravitational interactions. Our results show that environmental effects can significantly reduce the measured HI linewidths for some disturbed cluster galaxies, thus affecting the accurate determination of distances based on gas kinematics methods.Comment: 33 pages, 11 figures, 4 tables, ApJ Accepte

Morphomic Malnutrition Score: A Standardized Screening Tool for Severe Malnutrition in Adults

BackgroundGranular diagnostic criteria for adult malnutrition are lacking.ObjectiveThis study uses analytic morphomics to define the Morphomic Malnutrition Score (MMS), a robust screening tool for severe malnutrition.MethodsThe study population (n = 643) consisted of 2 cohorts: 1) 124 emergency department patients diagnosed with severe malnutrition by a registered dietitian (RD) and an available computed tomography (CT) scan within 2 days of RD evaluation, and 2) 519 adult kidney donor candidates to represent a healthy cohort. Body composition markers of muscle area and abdominal adiposity were measured from patient CT scans using analytic morphomic assessment, and then converted to sexâ and ageâ adjusted percentiles using the Reference Analytic Morphomics Population (RAMP). RAMP consists of 6000 patients chosen to be representative of the general population. The combined cohort was then randomly divided into training (n = 453) and validation (n = 190) sets. MMS was derived using logistic regression. The model coefficients were transformed into a score, normalized from 0 to 10 (10 = most severe).ResultsSeverely malnourished patients had lower amounts of muscle and fat than kidney donors, specifically for dorsal muscle group area at the twelfth thoracic vertebral level (P  6.1 was accurate in determining nutrition diagnosis (82.1% sensitivity; 88.3% specificity; 85.2% balanced accuracy).ConclusionsMMS provides an evidenceâ based, granular assessment to distinguish severely malnourished adults from a healthy population.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146447/1/jpen1175.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146447/2/jpen1175_am.pd

Dark Energy and the quietness of the Local Hubble Flow

The linearity and quietness of the Local ($< 10 Mpc$) Hubble Flow (LHF) in view of the very clumpy local universe is a long standing puzzle in standard and in open CDM cosmogony. The question addressed in this paper is whether the antigravity component of the recently discovered dark energy can cool the velocity flow enough to provide a solution to this puzzle. We calculate the growth of matter fluctuations in a flat universe containing a fraction $\Omega_X(t_0)$ of dark energy obeying the time independent equation of state $p_X = w \rho_X$. We find that dark energy can indeed cool the LHF. However the dark energy parameter values required to make the predicted velocity dispersion consistent with the observed value $v_{rms}\simeq 40km/sec$ have been ruled out by other observational tests constraining the dark energy parameters $w$ and $\Omega_X$. Therefore despite the claims of recent qualitative studies dark energy with time independent equation of state can not by itself explain the quietness and linearity of the Local Hubble Flow.Comment: 4 pages, 3 figures, accepted in Phys. Rev. D. Minor corrections, one figure adde

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

The Hubble Space Telescope Key Project on the Extragalactic Distance Scale XXIV: The Calibration of Tully-Fisher Relations and the Value of the Hubble Constant

This paper presents the calibration of BVRIH$ Tully-Fisher relations based on Cepheid distances to 21 galaxies within 25 Mpc, and 23 clusters within 10,000 km/s. These relations have been applied to several distant cluster surveys in order to derive a value for the Hubble constant, H0, mainly concentrating on an I-band all-sky survey by Giovanelli and collaborators which consisted of total I magnitudes and 50% linewidth data for ~550 galaxies in 16 clusters. For comparison, we also derive the values of H0 using surveys in B-band and V-band by Bothun and collaborators, and in H-band by Aaronson and collaborators. Careful comparisons with various other databases from literature suggest that the H-band data, whose magnitudes are isophotal magnitudes extrapolated from aperture magnitudes rather than total magnitudes, are subject to systematic uncertainties. Taking a weighted average of the estimates of Hubble constants from four surveys, we obtain H0 = 71 +- 4 (random) +- 7 (systematic) km/s/Mpc. We have also investigated how various systematic uncertainties affect the value of H0 such as the internal extinction correction method used, Tully-Fisher slopes and shapes, a possible metallicity dependence of the Cepheid period-luminosity relation and cluster population incompleteness bias.Comment: 34 pages, 13 figure