Search for Supermassive Black Hole Binaries in the Sloan Digital Sky Survey Spectroscopic Sample

Supermassive black hole (SMBH) binaries are expected in a Lambda CDM cosmology given that most (if not all) massive galaxies contain a massive black hole at their center. So far, however, direct evidence for such binaries has been elusive. We use cross-correlation to search for temporal velocity shifts in the MgII broad emission lines of 0.36 < z < 2 quasars with multiple observations in the Sloan Digital Sky Survey. For ~ 10^9 Msun BHs in SMBH binaries, we are sensitive to velocity drifts for binary separations of ~ 0.1 pc with orbital periods of ~100 years. We find seven candidate sub-pc--scale binaries with velocity shifts > 3.4 sigma ~ 280 km/s, where sigma is our systematic error. Comparing the detectability of SMBH binaries with the number of candidates (N < 7), we can rule out that most 10^9 Msun BHs exist in ~ 0.03-0.2 pc scale binaries, in a scenario where binaries stall at sub-pc scales for a Hubble time. We further constrain that < one-third of quasars host SMBH binaries after considering gas-assisted sub-pc evolution of SMBH binaries, although this result is very sensitive to the assumed size of the broad line region. We estimate the detectability of SMBH binaries with ongoing or next-generation surveys (e.g., BOSS, Subaru Prime Focus Spectrograph), taking into account the evolution of the sub-parsec binary in circumbinary gas disks. These future observations will provide longer time baselines for searches similar to ours and may in turn constrain the evolutionary scenarios of SMBH binaries.Comment: Resubmitted to ApJ after referee's comments. 21 pages, 9 figure

Oh Deer! Analyzing the Impact of RIT Expansion and Development on White-tailed Deer (Odocoileus Virginianus) and Vehicle Collisions from 1993-2014

Increases in both human and deer populations, combined with habitat loss, habitat fragmentation, and decreased predation, have led to increases in deer-vehicle collisions (DVCs). The development of RIT over the past 20 years mimics typical urban/suburban development patterns, with documented deer-vehicle collisions. This research examines deer-vehicle collisions in regards to campus development, notably Park Point, to determine whether collisions are increasing or decreasing and to evaluate landscape variables that might be contributing factors. Data from 1993-2014, contributed by the RIT Campus Safety Office and the Monroe County Sheriff Office are modelled using ArcGIS software. This research builds on a previous research project and includes data collection via a social media survey. Findings show that strike counts are down, and that the areas of focus have shifted more toward the south. People are currently seeing more deer toward the south side of campus, indicating that the deer are possibly shifting their habitat preferences toward the south side of campus, which identifies several potential focus areas for RIT. It is recommended that RIT’s Facilities Management Services consider adding speed bumps or an alternative method such as flashing lights to alert drivers when deer are in the area along the southern loop to reduce driver speed and reduce the possibility of a deer strike in this area

Attributing a probability to the shape of a probability density

We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue that the simplest form of that method suffers from the same difficulties that inhibit level accuracy of Silverman's bandwidth-based test for modality: the conditional distribution of the bootstrap form of a density estimator is not a good approximation to the actual distribution of the estimator. This difficulty is less pronounced if the density estimator is oversmoothed, but the problem of selecting the extent of oversmoothing is inherently difficult. It is shown that the optimal bandwidth, in the sense of producing optimally high sensitivity, depends on the widths of putative bumps in the unknown density and is exactly as difficult to determine as those bumps are to detect. We also develop a second approach to ascribing a probability to shape, using Muller and Sawitzki's notion of excess mass. In contrast to the context just discussed, it is shown that the bootstrap distribution of empirical excess mass is a relatively good approximation to its true distribution. This leads to empirical approximations to the likelihoods of different levels of ``modal sharpness,'' or ``delineation,'' of modes of a density. The technique is illustrated numerically.Comment: Published at http://dx.doi.org/10.1214/009053604000000607 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chirplet approximation of band-limited, real signals made easy

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters

Applications of parametric and semi-parametric models for longitudinal data analysis

A wide range of scientific applications involve analyses of longitudinal data. Whether it is time or location, careful considerations need to be made when applying different statistical tools. One such challenge is to correctly estimate variance components in observed data. In this dissertation, I apply statistical tools to solve problems involving longitudinal data in the field of Biology, Healthcare and Networks. In the second chapter, I apply SSANOVA models to find regions in the genome that have a specific biological trait. We introduce a direct approach of estimating genomic longitudinal data of two different biological groups. Using SSANOVA we then produce a novel method to estimate the difference between the two groups and find regions (location or time) where this difference is biologically significant. In the third chapter, we analyze longitudinal network data using an overdispersed Poisson model. We build a network of musical writers yearly for a 42 year period. Using statistical models, we predict network level topology changes and find covariates that explain these changes. Network level characteristics used for this chapter include average node degree, clustering coefficient and network density. We also build a visualization tool using R-Shiny. The fourth chapter uses data partitioning to study the difference between insured patients and uninsured patients in health outcomes. There is a disparity in health outcomes depending on an individual's type of insurance. The level of risk for an injury is the longitudinal aspect of this dataset. We partition the data into four pre-defined risk categories and evaluate the disparity between insured and uninsured patients using logistic regression models

Microscopic calculations of double and triple Giant Resonance excitation in heavy ion collisions

We perform microscopic calculations of the inelastic cross sections for the double and triple excitation of giant resonances induced by heavy ion probes within a semicalssical coupled channels formalism. The channels are defined as eigenstates of a bosonic quartic Hamiltonian constructed in terms of collective RPA phonons. Therefore, they are superpositions of several multiphonon states, also with different numbers of phonons and the spectrum is anharmonic. The inclusion of (n+1) phonon configurations affects the states whose main component is a n-phonon one and leads to an appreacible lowering of their energies. We check the effects of such further anharmonicities on the previous published results for the cross section for the double excitation of Giant Resonances. We find that the only effect is a shift of the peaks towards lower energies, the double GR cross section being not modified by the explicity inclusion of the three-phonon channels in the dynamical calculations. The latters give an important contribution to the cross section in the triple GR energy region which however is still smaller than the experimental available data. The inclusion of four phonon configurations in the structure calculations does not modify the results.Comment: Revtex4, to be published in PR

FORCE PLATE RELIABILITY AND DYNAMICS FOR AMBULANCE VIBRATION SUPPRESSION

This Major Qualifying Project used experimental methods and mathematical analysis tools to determine the dynamic characteristics of a force plate design as a solution to attenuate harmful road-induced vibrations experienced in the patient-care compartment of an ambulance

On Bioelectric Algorithms

Cellular bioelectricity describes the biological phenomenon in which cells in living tissue generate and maintain patterns of voltage gradients across their membranes induced by differing concentrations of charged ions. A growing body of research suggests that bioelectric patterns represent an ancient system that plays a key role in guiding many important developmental processes including tissue regeneration, tumor suppression, and embryogenesis. This paper applies techniques from distributed algorithm theory to help better understand how cells work together to form these patterns. To do so, we present the cellular bioelectric model (CBM), a new computational model that captures the primary capabilities and constraints of bioelectric interactions between cells and their environment. We use this model to investigate several important topics from the relevant biology research literature. We begin with symmetry breaking, analyzing a simple cell definition that when combined in single hop or multihop topologies, efficiently solves leader election and the maximal independent set problem, respectively - indicating that these classical symmetry breaking tasks are well-matched to bioelectric mechanisms. We then turn our attention to the information processing ability of bioelectric cells, exploring upper and lower bounds for approximate solutions to threshold and majority detection, and then proving that these systems are in fact Turing complete - resolving an open question about the computational power of bioelectric interactions