Twice-Ramanujan Sparsifiers

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs. In particular, we prove that for every $d>1$ and every undirected, weighted graph $G=(V,E,w)$ on $n$ vertices, there exists a weighted graph $H=(V,F,\tilde{w})$ with at most \ceil{d(n-1)} edges such that for every $x \in \R^{V}$, $$x^{T}L_{G}x \leq x^{T}L_{H}x \leq (\frac{d+1+2\sqrt{d}}{d+1-2\sqrt{d}})\cdot x^{T}L_{G}x$$ where $L_{G}$ and $L_{H}$ are the Laplacian matrices of $G$ and $H$, respectively. Thus, $H$ approximates $G$ spectrally at least as well as a Ramanujan expander with $dn/2$ edges approximates the complete graph. We give an elementary deterministic polynomial time algorithm for constructing $H$

Financial Accounting Case Studies

This thesis was completed in the 2021-2022 academic year and is comprised of eleven accounting case studies. The topics from these cases vary widely and are not strictly focused on accounting. Examples of this includes cases done on the twenty-year anniversary of 9/11, the ramifications of COVID-19 on Pfizer, and having to interview a local business owner. We also completed cases concerning the city we wanted to intern in as well as an excel certification course. Following the conclusion of case 5, me and several other honors students worked together to complete the next six cases which involved analyzing International Paper. Topics we wrote on include the business structure of International Paper, audit risks facing the company and its controls, tax saving strategies, advisory opinions on the company’s operations, and an assessment of cyber-security and other large threats facing the company. Even though no one in the group had taken either tax or audit, these cases allowed us to have our first exposure to these topics. After completing these cases, we put together the papers into a PowerPoint presentation which was then presented in front of several accounting professionals from different firms. When our class was not working on a case, we had several speakers from different accounting firms speak to us. These interactions allowed us to get a head start on recruiting as well as make meaningful connections

CD-ROM publication of the Mars digital cartographic data base

The recently completed Mars mosaicked digital image model (MDIM) and the soon-to-be-completed Mars digital terrain model (DTM) are being transcribed to optical disks to simplify distribution to planetary investigators. These models, completed in FY 1991, provide a cartographic base to which all existing Mars data can be registered. The digital image map of Mars is a cartographic extension of a set of compact disk read-only memory (CD-ROM) volumes containing individual Viking Orbiter images now being released. The data in these volumes are pristine in the sense that they were processed only to the extent required to view them as images. They contain the artifacts and the radiometric, geometric, and photometric characteristics of the raw data transmitted by the spacecraft. This new set of volumes, on the other hand, contains cartographic compilations made by processing the raw images to reduce radiometric and geometric distortions and to form geodetically controlled MDIM's. It also contains digitized versions of an airbrushed map of Mars as well as a listing of all feature names approved by the International Astronomical Union. In addition, special geodetic and photogrammetric processing has been performed to derive rasters of topographic data, or DTM's. The latter have a format similar to that of MDIM, except that elevation values are used in the array instead of image brightness values. The set consists of seven volumes: (1) Vastitas Borealis Region of Mars; (2) Xanthe Terra of Mars; (3) Amazonis Planitia Region of Mars; (4) Elysium Planitia Region of Mars; (5) Arabia Terra of Mars; (6) Planum Australe Region of Mars; and (7) a digital topographic map of Mars

Physical mechanisms of interface-mediated intervalley coupling in Si

The conduction band degeneracy in Si is detrimental to quantum computing based on spin qubits, for which a nondegenerate ground orbital state is desirable. This degeneracy is lifted at an interface with an insulator as the spatially abrupt change in the conduction band minimum leads to intervalley scattering. We present a theoretical study of the interface-induced valley splitting in Si that provides simple criteria for optimal fabrication parameters to maximize this splitting. Our work emphasizes the relevance of different interface-related properties to the valley splitting.Comment: 4 pages, revised versio

Flexural behavior of web elements with openings

INTRODUCTION The purpose of this phase of the research has been to investigate the flexural behavior of C-shaped members with web openings. Three common industry standard C-sections were tested as outlined in the first progress report. The web openings were located at 24 inches on center as illustrated in Fig. 1. Each test specimen was subjected to two point loads until the ultimate flexural strength of the member was obtained. This report summarizes the test procedure and results of the research to date

Flexural behavior of web elements with openings

INTRODUCTION The purpose of this research project has been to investigate the flexural behavior of C-shaped members with web openings. Three common industry standard C-sections have been studied as summarized in the First and Second Progress Reports. To date two testing sequences have been completed. Test sequence No.1 investigated sections with web openings fabricated from nominally low yield strength material. Test sequence No.2 examined sections both with and without web openings. Specimens in test sequence No. 2 have nominally higher yield strengths. This report summarizes the test procedure and results of the research to date

Transcranial Doppler Based Cerebrovascular Reactivity Indices in Adult Traumatic Brain Injury: A Scoping Review of Associations With Patient Oriented Outcomes.

Background: Disruption in cerebrovascular reactivity following traumatic brain injury (TBI) is a known phenomenon that may hold prognostic value and clinical relevance. Ultimately, improved knowledge of this process and more robust means of continuous assessment may lead to advances in precision medicine following TBI. One such method is transcranial Doppler (TCD), which has been employed to evaluate cerebrovascular reactivity following injury utilizing a continuous time-series approach. Objective: The present study undertakes a scoping review of the literature on the association of continuous time-domain TCD based indices of cerebrovascular reactivity, with global functional outcomes, cerebral physiologic correlates, and imaging evidence of lesion change. Design: Multiple databases were searched from inception to November 2020 for articles relevant to the association of continuous time-domain TCD based indices of cerebrovascular reactivity with global functional outcomes, cerebral physiologic correlates, and imaging evidence of lesion change. Results: Thirty-six relevant articles were identified. There was significant evidence supporting an association with continuous time-domain TCD based indices and functional outcomes following TBI. Indices based on mean flow velocity, as measured by TCD, were most numerous while more recent studies point to systolic flow velocity-based indices encoding more prognostic utility. Physiologic parameters such as intracranial pressure, cerebral perfusion pressure, Carbon Dioxide (CO2) reactivity as well as more established indices of cerebrovascular reactivity have all been associated with these TCD based indices. The literature has been concentrated in a few centres and is further limited by the lack of multivariate analysis. Conclusions: This systematic scoping review of the literature identifies that there is a substantial body of evidence that cerebrovascular reactivity as measured by time-domain TCD based indices have prognostic utility following TBI. Indices based on mean flow velocities have the largest body of literature for their support. However, recent studies indicate that indices based on systolic flow velocities may contain the most prognostic utility and more closely follow more established measures of cerebrovascular reactivity. To a lesser extent, the literature supports some associations between these indices and cerebral physiologic parameters. These indices provide a more complete picture of the patient's physiome following TBI and may ultimately lead to personalized and precise clinical care. Further validation in multi-institution studies is required before these indices can be widely adopted clinically

The impact of hypertonic saline on cerebrovascular reactivity and compensatory reserve in traumatic brain injury: an exploratory analysis.

BACKGROUND: Intravenous hypertonic saline is utilized commonly in critical care for treatment of acute or refractory elevations of intracranial pressure (ICP) in traumatic brain injury (TBI) patients. Though there is a clear understanding of the general physiological effects of a hypertonic saline solution over long periods of time, smaller epoch effects of hypertonic saline (HTS) have not been thoroughly analyzed. The aim of this study was to perform a direct evaluation of the high-frequency response of HTS on the cerebrovascular physiological responses in TBI. METHODS: We retrospectively reviewed our prospectively maintained adult TBI database for those with archived high-frequency cerebral physiology and available HTS treatment information. We evaluated different epochs of physiology around HTS bolus dosing, comparing pre- with post-HTS. We assessed for changes in slow fluctuations in ICP, pulse amplitude of ICP (AMP), cerebral perfusion pressure (CPP), mean arterial pressure (MAP), cerebrovascular reactivity (as measured through pressure reactivity index (PRx)), and cerebral compensatory reserve (correlation (R) between AMP (A) and ICP (P)). Comparisons of mean measures and percentage time above clinically relevant thresholds for the physiological parameters were compared pre- and post-HTS using descriptive statistics and Mann-Whitney U testing. We assessed for subgroups of physiological responses using latent profile analysis (LPA). RESULTS: Fifteen patients underwent 69 distinct bolus infusions of hypertonic saline. Apart from the well-documented decrease in ICP, there was also a reduction in AMP. The analysis of cerebrovascular reactivity response to HTS solution had two main effects. For patients with grossly impaired cerebrovascular reactivity pre-HTS (PRx > + 0.30), HTS bolus led to improved reactivity. However, for those with intact cerebrovascular reactivity pre-HTS (PRx < 0), HTS bolus demonstrated a trend towards more impaired reactivity. This indicates that HTS has different impacts, dependent on pre-bolus cerebrovascular status. There was no significant change in metrics of cerebral compensatory reserve. LPA failed to demonstrate any subgroups of physiological responses to HTS administration. CONCLUSIONS: The direct decrease in ICP and AMP confirms that a bolus dose of a HTS solution is an effective therapeutic agent for intracranial hypertension. However, in patients with intact autoregulation, hypertonic saline may impair cerebral hemodynamics. These findings regarding cerebrovascular reactivity remain preliminary and require further investigation