Impact of regularization on Spectral Clustering

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regularization parameter $\tau$ is large we show that the minimum degree assumption can potentially be removed. As a special case, for an SBM with two blocks, the results require the maximum degree to be large (grow faster than $\log n$) as opposed to the minimum degree. More importantly, we show the usefulness of regularization in situations where not all nodes belong to well-defined clusters. Our results rely on a `bias-variance'-like trade-off that arises from understanding the concentration of the sample Laplacian and the eigen gap as a function of the regularization parameter. As a byproduct of our bounds, we propose a data-driven technique \textit{DKest} (standing for estimated Davis-Kahan bounds) for choosing the regularization parameter. This technique is shown to work well through simulations and on a real data set.Comment: 37 page

Lossy Compression via Sparse Linear Regression: Performance under Minimum-distance Encoding

We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this structure is motivated by an analogous construction proposed recently by Barron and Joseph for communication over an AWGN channel. For i.i.d Gaussian sources and minimum-distance encoding, we show that such a code can attain the Shannon rate-distortion function with the optimal error exponent, for all distortions below a specified value. It is also shown that sparse regression codes are robust in the following sense: a codebook designed to compress an i.i.d Gaussian source of variance $\sigma^2$ with (squared-error) distortion $D$ can compress any ergodic source of variance less than $\sigma^2$ to within distortion $D$. Thus the sparse regression ensemble retains many of the good covering properties of the i.i.d random Gaussian ensemble, while having having a compact representation in terms of a matrix whose size is a low-order polynomial in the block-length.Comment: This version corrects a typo in the statement of Theorem 2 of the published pape

GOOD FOR WHOM? THE FRAMING OF CONFLICT IN POST-9/11 AMERICA, 2001-2004

This thesis explores the framing of conflict after the September 11, 2001 terrorist attacks, and more specifically, during President George W. Bush’s first term in office. Notions of American exceptionalism touched upon every facet of the nation’s response to the attacks, providing guidance, identity and resolve in the history of the Good War. The immediate tethering of Pearl Harbor and September 11 in the national discourse exemplified the foremost role that nostalgia would play in not only making sense of the attacks but devising a response to them. This thesis recovers what was lost to those destructive comforts in the collective memory. Indeed, the Bush administration, led by Bush and the unprecedentedly powerful Dick Cheney, saw opportunity in tragedy, and successfully used the fear and anger elicited by the attacks to extend the Bush Doctrine to Saddam Hussein’s Iraq. For Bush in particular, however, the war in Iraq was also a divine one — a self-professed mission from God. The conflict, he pledged, would liberate the Iraqi people from the barbarous Ba’ath regime and bring democracy to the Middle East. Images of American torture released from the Abu Ghraib prison, however, fiercely contradicted the president’s narrative. Time and again, the war on terrorism was framed as a good war. This thesis explains where that term came from, how it influenced the framing of conflict after the terrorist attacks, and who, ultimately, the war was good for

Lanthanide Luminescence and its Applications in Forensic Science

Lanthanide compounds, specifically those containing europium and terbium can exhibit luminescent properties when combined with ligands that promote this characteristic. Lanthanide luminescence has proven to have an array of useful applications, one of which is the formation of luminescent powders for exposure of latent fingerprints. The aim of this study was to synthesise a novel ligand to support luminescent character in europium and terbium compounds, and then dope these compounds in to talcum powder. This resulting powder would ideally give exposure of latent fingerprints that can then be enhanced, through excitation of the luminescent compounds dispersed in the powder. A novel (Me)₃CN(CH₂P(O)Ph₂)₂ ligand (p=o) was synthesised, and in turn was used to synthesis a range of Ln(β‐diketonate)₃(p=o) compounds. These compounds were assessed for potential luminescent activity, and doped into talcum powder. These powders were then appraised for their prospective use as latent fingerprint exposing agents. Through modification of a published procedure, the (Me)₃CN(CH₂P(O)Ph₂)₂ ligand was synthesised, and characterised by Electrospray Ionisation (ESI) Mass spectrometry, Nuclear Magnetic Resonance (NMR) spectroscopy, Infra‐red (IR) spectroscopy, melting point analysis and elemental analysis. With β‐diketonate ligands acetylacetone (acac) and thenoyltrifluoroacetone (tta), lanthanide metals lanthanum, europium and terbium and the (p=o) ligands a series of novel compounds were synthesised (Ln(β‐diketonate)₃(p=o)). These compounds were characterised by the methods listed above. Using the neutral ligands 1,10‐phenanthroline (phen) and 2,2‐bipyridine (bipy), a series of Eu/Tb(acac/tta)₃(phen/bipy) compounds were synthesised and doped into talcum powder, to investigate the effects on particle and structure character of the doped talcum powders. Talcum powder was also sonicated to investigate the effect of this on particle size, along with effect on use as a fingerprinting agent. Laser diffraction and Scanning Electron Microscopy studies informed of a notable decrease in particle size with sonication, and an increase in specific surface area. However the effect of this process on increasing exposure of latent fingerprints was deemed too insignificant to justify the procedure. The compounds Eu/Tb(acac/tta)₃(phen/bipy), (Eu/Tb(β‐diketonate)₃(p=o) and [H₂NMe₂]₃[Eu/Tb(2,6‐dpa)₃].2H₂O were investigated for luminescent activity. Fluorescence spectroscopy determined the dominant emission wavelengths from 254 nm and 312 nm excitation were at 510 nm and 625 nm respectively. The talcum powders, doped with the luminescent compounds were analysed for luminescent activity. Direct screening with an ultra‐violet (UV) lamp with emission wavelengths of 254 nm and 312 nm informed of the powders with the most intensely observed luminescent emissions. From these results, Eu(tta)₃(p=o), H₂NMe₂]₃[Eu(2,6‐ dpa)₃].2H₂O, Tb(acac)₃(p=o) and H₂NMe₂]₃[Tb(2,6‐dpa)₃].2H₂O were chosen as the most promising candidates for more in‐depth investigation of latent fingerprint exposure potential. Furthermore, it was determined that the novel (Me)₃CN(CH₂P(O)Ph₂)₂ ligand was successful as a neutral ligand for supporting luminescence. The powders were trialled by several variables, including surface, powder quantity, age of latent print, temperature, and the brush used to determine their effectiveness. Powders were compared to commercial Greenwop and Redwop fingerprint powders, as these were the most similar industrial samples in terms of use. Through trials in the laboratory and the police fingerprinting laboratory, it was determined that the doped talcum powders were inferior to the commercial “wop” samples in terms of latent print definition under UV conditions. However, the talcum powders had several useful applications, specifically the dual effect of exposing prints clearly under UV and non‐UV conditions. It was concluded the best application for the fingerprint powders was on smooth surfaces such as glass, with a gradual application of powder. Small amounts of powder gave more clarity under non‐UV print exposure, but higher quantities of powder were required to get ample luminescent intensity under UV conditions

Comparison of Training Models for Hearing Screening Personnel

Early identification of permanent hearing loss begins with the competency of the individuals completing a hearing screening in being able to identify children who are at-risk for hearing loss. The appropriate management of hearing healthcare for children, during the developmental period from birth to school age, requires these individuals to possess knowledge related to screenings, protocols, and follow-up, for children in need of additional diagnostic services. The Early Childhood Hearing Outreach (ECHO) Initiative was formulated by the National Center for Hearing Assessment and Management (NCHAM) as an extension to newborn hearing screening programs. The program focuses on assisting hearing screeners and healthcare providers who serve children birth to three years of age. In 2014, the Illinois State University ECHO Team began contracted services for the Illinois ECHO program. Its focus was to establish and provide an effective training model for otoacoustic emission hearing screenings using course curriculum supported by the ECHO Initiative. The current study assessed the validity of the ECHO Initiative curriculum. It further sought to compare didactic-based and practicum-based training models to determine if any significant differences in degree of knowledge acquisition or retention could be observed. While the curricular content of the ECHO program demonstrated a significant effect on knowledge acquisition, minimal differences between training models were identified. The data collected between training models helped to highlight functional implications for effective grant sponsorship. Relocation of service in conjunction with alternative delivery methods, as well as a review of Illinois mandated reporting forms, were discussed as a much-needed consideration for the future of the ECHO program within the state of Illinois

Sound Exposure Characterization for Faculty Musicians: A Hearing Loss Prevention Initiative

The primary aim of this project was to characterize the sound exposure of faculty musicians at a university music department, specifically for hearing loss prevention purposes. Sound measurements were obtained as a major portion of the project to calculate the risk for over-exposure to hazardous sound intensities. Excessive sound exposure can cause permanent injury to the human auditory system. This type of injury is diagnostically classified as noise-induced hearing loss and tinnitus. To verify risk-exposure status, dosimeters were used to sample a variety of accessible musician training environments. Sound samples obtained from personal noise dosimetry instrumentation were used to obtain common noise metrics, such as A-weighted decibel (dBA) intensity level, time-weighted average, and peak sound pressure level. During group rehearsals and private lessons, our measurements indicated that faculty musicians were exposed to sound levels in excess of 85dBA (the damage-risk criterion level used by most countries, except the United States). At times, students and faculty were exposed to sound intensities in excess of 90dBA. These surveillance samples were plotted and interpreted to provide appropriate recommendations for faculty musicians. To deliver hearing-loss prevention to all workers affected by hazardous sound, our national policies, hearing conservation programs, and hearing-health wellness should be revised and mandated for professional musicians