Spectral Analysis of the Supreme Court

The focus of this paper is the linear algebraic framework in which the spectral analysis of voting data like that above is carried out. As we will show, this framework can be used to pinpoint voting coalitions in small voting bodies like the United States Supreme Court. Our goal is to show how simple ideas from linear algebra can come together to say something interesting about voting. And what could be more simple than where our story begins— with counting

High Performance Magnetic Bearings for Aero Applications

Several previous annual reports were written and numerous papers published on the topics for this grant. That work is not repeated here in this final report. Only the work completed in the final year of the grant is presented in this final report. This final year effort concentrated on power loss measurements in magnetic bearing rotors. The effect of rotor power losses in magnetic bearings are very important for many applications. In some cases, these losses must be minimized to maximize the length of time the rotating machine can operate on a fixed energy or power supply. Examples include aircraft gas turbine engines, space devices, or energy storage flywheels. In other applications, the heating caused by the magnetic bearing must be removed. Excessive heating can be a significant problem in machines as diverse as large compressors, electric motors, textile spindles, and artificial heart pumps

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

GenTAC registry report: Gender differences among individuals with genetically triggered thoracic aortic aneurysm and dissection

Previous data suggest women are at increased risk of death from aortic dissection. Therefore, we analyzed data from the GenTAC registry, the NIH‐sponsored program that collects information about individuals with genetically triggered thoracic aortic aneurysms and cardiovascular conditions. We performed cross‐sectional analyses in adults with Marfan syndrome (MFS), familial thoracic aortic aneurysm or dissection (FTAAD), bicuspid aortic valve (BAV) with thoracic aortic aneurysm or dissection, and subjects under 50 years of age with thoracic aortic aneurysm or dissection (TAAD <50 years). Women comprised 32% of 1,449 subjects and were 21% of subjects with BAV, 34% with FTAAD, 22% with TAAD <50 years, and 47% with MFS. Thoracic aortic dissections occurred with equal gender frequency yet women with BAV had more extensive dissections. Aortic size was smaller in women but was similar after controlling for BSA. Age at operation for aortic valve dysfunction, aneurysm or dissection did not differ by gender. Multivariate analysis (adjusting for age, BSA, hypertension, study site, diabetes, and subgroup diagnoses) showed that women had fewer total aortic surgeries (OR = 0.65, P  < 0.01) and were less likely to receive angiotensin converting enzyme inhibitors (ACEi; OR = 0.68, P  < 0.05). As in BAV, other genetically triggered aortic diseases such as FTAAD and TAAD <50 are more common in males. In women, decreased prevalence of aortic operations and less treatment with ACEi may be due to their smaller absolute aortic diameters. Longitudinal studies are needed to determine if women are at higher risk for adverse events. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97193/1/35836_ftp.pd

Discriminatory changes in circulating metabolites as a predictor of hepatocellular cancer in patients with MAFLD

Introduction: The burden of metabolic (dysfunction) associated fatty liver disease (MAFLD) is rising mirrored by an increase in hepatocellular cancer (HCC). MAFLD and its sequelae are characterized by perturbations in lipid handling, inflammation, and mitochondrial damage. The profile of circulating lipid and small molecule metabolites with the development of HCC is poorly characterized in MAFLD and could be used in future studies as a biomarker for HCC. Methods: We assessed the profile of 273 lipid and small molecule metabolites by ultra-performance liquid chromatography coupled to high-resolution mass spectrometry in serum from patients with MAFLD (n = 113) and MAFLD-associated HCC (n = 144) from six different centers. Regression models were used to identify a predictive model of HCC. Results: Twenty lipid species and one metabolite, reflecting changes in mitochondrial function and sphingolipid metabolism, were associated with the presence of cancer on a background of MAFLD with high accuracy (AUC 0.789, 95% CI: 0.721–0.858), which was enhanced with the addition of cirrhosis to the model (AUC 0.855, 95% CI: 0.793–0.917). In particular, the presence of these metabolites was associated with cirrhosis in the MAFLD subgroup (p < 0.001). When considering the HCC cohort alone, the metabolic signature was an independent predictor of overall survival (HR 1.42, 95% CI: 1.09–1.83, p < 0.01). Conclusion: These exploratory findings reveal a metabolic signature in serum which is capable of accurately detecting the presence of HCC on a background of MAFLD. This unique serum signature will be taken forward for further investigation of diagnostic performance as biomarker of early stage HCC in patients with MAFLD in the future

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Orthotopic Liver Transplantation in an Adult with Cholesterol Ester Storage Disease

Cholesterol ester storage disease (CESD) is a rare autosomal recessive lipid storage disorder associated with mutations of the gene encoding lysosomal acid lipase, manifestations of which include chronic liver disease and early atherosclerosis. Although normally presenting in childhood, severity is variable and the condition can occasionally remain undetected until middle age. Typical presentation is with asymptomatic hepatosplenomegaly and hyperlipidaemia, though the condition is probably underdiagnosed. Treatment is supportive and may include attention to cardiovascular risk factors. Phase I/II trials of enzyme replacement therapy are ongoing, but this approach remains experimental. We present the case of a 42-year-old woman diagnosed with CESD in childhood who ran an indolent course until re-presentation with cirrhotic hydrothorax. She underwent orthotopic liver transplantation but required re-transplantation for hepatic artery thrombosis. She remains well with excellent graft function 2 years later. Although atherosclerosis was apparent at assessment, and may have contributed to hepatic artery thrombosis, partial correction of the metabolic defect and restoration of liver function by transplantation together with ongoing medical therapy should permit reasonable survival over the longer term from both a liver and a vascular perspective. This is the first reported case of orthotopic liver transplantation for CESD in an adult, which was the only available option to improve survival. The case highlights the importance of monitoring patients with CESD through adulthood and suggests that liver replacement at a later stage may yet be indicated and remain of benefit

Cardiovascular Outcomes in Aortopathy: GenTAC Registry of Genetically Triggered Aortic Aneurysms and Related Conditions.

BACKGROUND: The GenTAC (Genetically Triggered Thoracic Aortic Aneurysm and Cardiovascular Conditions) Registry enrolled patients with genetic aortopathies between 2007 and 2016. OBJECTIVES: The purpose of this study was to compare age distribution and probability of elective surgery for proximal aortic aneurysm, any dissection surgery, and cardiovascular mortality among aortopathy etiologies. METHODS: The GenTAC study had a retrospective/prospective design. Participants with bicuspid aortic valve (BAV) with aneurysm (n = 879), Marfan syndrome (MFS) (n = 861), nonsyndromic heritable thoracic aortic disease (nsHTAD) (n = 378), Turner syndrome (TS) (n = 298), vascular Ehlers-Danlos syndrome (vEDS) (n = 149), and Loeys-Dietz syndrome (LDS) (n = 121) were analyzed. RESULTS: The 25% probability of elective proximal aortic aneurysm surgery was 30 years for LDS (95% CI: 18-37 years), followed by MFS (34 years; 95% CI: 32-36 years), nsHTAD (52 years; 95% CI: 48-56 years), and BAV (55 years; 95% CI: 53-58 years). Any dissection surgery 25% probability was highest in LDS (38 years; 95% CI: 33-53 years) followed by MFS (51 years; 95% CI: 46-57 years) and nsHTAD (54 years; 95% CI: 51-61 years). BAV experienced the largest relative frequency of elective surgery to any dissection surgery (254/33 = 7.7), compared with MFS (273/112 = 2.4), LDS (35/16 = 2.2), or nsHTAD (82/76 = 1.1). With MFS as the reference population, risk of any dissection surgery or cardiovascular mortality was lowest in BAV patients (HR: 0.13; 95% CI: 0.08-0.18; HR: 0.13; 95%: CI: 0.06-0.27, respectively). The greatest risk of mortality was seen in patients with vEDS. CONCLUSIONS: Marfan and LDS cohorts demonstrate age and event profiles congruent with the current understanding of syndromic aortopathies. BAV events weigh toward elective replacement with relatively few dissection surgeries. Nonsyndromic HTAD patients experience near equal probability of dissection vs prophylactic surgery, possibly because of failure of early diagnosis

Ensembl Genomes 2013: scaling up access to genome-wide data

Ensembl Genomes (http://www.ensemblgenomes.org) is an integrating resource for genome-scale data from non-vertebrate species. The project exploits and extends technologies for genome annotation, analysis and dissemination, developed in the context of the vertebrate-focused Ensembl project, and provides a complementary set of resources for non-vertebrate species through a consistent set of programmatic and interactive interfaces. These provide access to data including reference sequence, gene models, transcriptional data, polymorphisms and comparative analysis. This article provides an update to the previous publications about the resource, with a focus on recent developments. These include the addition of important new genomes (and related data sets) including crop plants, vectors of human disease and eukaryotic pathogens. In addition, the resource has scaled up its representation of bacterial genomes, and now includes the genomes of over 9000 bacteria. Specific extensions to the web and programmatic interfaces have been developed to support users in navigating these large data sets. Looking forward, analytic tools to allow targeted selection of data for visualization and download are likely to become increasingly important in future as the number of available genomes increases within all domains of life, and some of the challenges faced in representing bacterial data are likely to become commonplace for eukaryotes in future