Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits

Gravitational waves (GW) from eccentric binaries have intricate signals encoding important features about the location, creation and evolution of the sources. Eccentricity shortens the merger time, making the emitted GW statistically predominant in the observed data once detectors will reach the required sensitivity. We present a novel implementation of fully analytical GW templates from eccentric binary black hole (BBH) mergers within the \texttt{Wolfram Mathematica} software. We increase the accuracy by identifying and minimizing the possible source of errors. We start with an overview of the physics involved in eccentric mergers, then assemble the strain for the inspiral by employing up to six post-Newtonian (PN) corrections. We complete the eccentric inspiral with the quasi-circular Backwards one Body (BoB) merger model in frequency, amplitude and phase, then we build the hybrid GW strain for the whole evolution of the binary. For low eccentricity we reach coincidence in the overlap, with no ambiguity in the time interval, a remarkable improvement from the usual matching techniques. For high-eccentricity we compensate for the implicit quasi-circular assumption of the BOB approach, by introducing a small rescaling in amplitude. Our streamlined implementation is relevant for the new field of GW astronomy and is straightforward to understand, use and extend, offering researchers in the field a valuable open resource tool.Comment: 27 pages, 10 figures, accepted for publication in the International Journal of Modern Physics

Merging Black Holes: Assessing the Performance of Two Analytic Gravitational Waves Models

Merging black holes produce the loudest signal in the detectors. However, this is the most difficult signal to accurately predict with analytical techniques. Only computer simulations account for the nonlinear physics during the collision, but they are inherently complex, costly, and affected by numerical errors. In order to bypass this problem, two analytical models for the merger have been developed: the Implicit Rotating Source and the newer Backwards one Body. In this work, we assess the performance of the latter model by comparing it with the former model and with the numerical data, identifying its strengths and weaknesses. We start with a comparison of the analytical approximations for estimating the final black hole mass, spin, ringdown frequency and quality factor. We continue by implementing the models in a set of new Mathematica notebooks and calculating the waveforms. Our main finding reveals discrepancies in amplitude, but overall excellent accord in frequency. The newer model is comparable with the older and with the simulations, having the added advantage that it depends only indirectly on numerical data, it accounts for spin, and it offers a seamless fit with the analytical formalisms for the inspiral. By independently evaluating and testing those models, we not only bring evidence of their reproducibility, thus upholding high scientific standards, but we enable readers to evaluate our results themselves.Comment: 28 pages, 7 figure

Generalized Metric Repair on Graphs

Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. However, as real data sets are noisy, they often do not possess this fundamental property. For this reason, Gilbert and Jain [A. Gilbert and L. Jain, 2017] and Fan et al. [C. Fan et al., 2018] introduced the closely related sparse metric repair and metric violation distance problems. Given a matrix, representing all distances, the goal is to repair as few entries as possible to ensure they satisfy a metric. This problem was shown to be APX-hard, and an O(OPT^{1/3})-approximation was given, where OPT is the optimal solution size. In this paper, we generalize the problem, by describing distances by a possibly incomplete positively weighted graph, where again our goal is to find the smallest number of weight modifications so that they satisfy a metric. This natural generalization is more flexible as it takes into account different relationships among the data points. We demonstrate the inherent combinatorial structure of the problem, and give an approximation-preserving reduction from MULTICUT, which is hard to approximate within any constant factor assuming UGC. Conversely, we show that for any fixed constant ?, for the large class of ?-chordal graphs, the problem is fixed parameter tractable, answering an open question from previous work. Call a cycle broken if it contains an edge whose weight is larger than the sum of all its other edges, and call the amount of this difference its deficit. We present approximation algorithms, one depending on the maximum number of edges in a broken cycle, and one depending on the number of distinct deficit values, both quantities which may naturally be small. Finally, we give improved analysis of previous algorithms for complete graphs

Background Checks for Firearm Transfers, 2015 - Statistical Tables

Describes background checks for firearms transfers conducted in 2015 and presents estimates of firearm applications received and denied annually since the effective date of the Brady Act in 1994 through 2015. Statistical tables provide data on the number of firearm applications processed by the FBI and state and local agencies, number of applications denied, reasons for denial, and estimates of applications by jurisdiction and by each type of approval system. Findings are based on data from BJS's Firearm Inquiry Statistics program, which annually surveys state and local background checking agencies to collect information on firearm background check activity and combines this information with the FBI's National Instant Criminal Background Check System transaction data to generate national estimates.Highlights:Since the effective date of the Brady Act on February 28, 1994, through December 31, 2015, nearly 197 million applications for firearm transfers or permits were subject to background checks and more than 3 million applications (1.5%) were denied.Nearly 17 million applications for firearm transfers were received in 2015, up from an estimated 15 million in 2014.About 1.4% of the nearly 17 million applications for firearm transfers or permits in 2015 were denied: about 107,000 by the FBI and about 119,000 by state and local agencies.Among state agency reporters, denial rates in 2015 were 3.0% for purchase permits, 1.5% for instant checks, 1.1% for other approval checks, and 1.1% for exempt carry permits.Local agencies denied 4.2% of applications for purchase permit checks and 1.1% of applications for exempt carry permits

Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

We report exact analytical expressions locating the $0\to1$, $1\to2$ and $2\to4$ bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark-Sacker bifurcations occur, starting from a non-diagonal period-2 orbit. This result is the key to understand the onset of synchronization in networks of quadratic maps.Comment: 6 pages, 3 figures (1 in color), submitted to Physica

Treatment of Rheumatoid Arthritis with Marine and Botanical Oils: Influence on Serum Lipids

The gap in mortality between patients with rheumatoid arthritis (RA) and the general population (1.5–3.0 fold risk) is increasing. This disparity is attributable mainly to cardiovascular disease (CVD), as the CVD risk is comparable to patients with diabetes mellitus. The purpose of this study is to determine whether borage seed oil rich in gamma-linolenic acid, fish oil rich in eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), or the combination of both oils are useful treatments for dyslipidemia in patients with RA. We randomized patients into a double blind, 18 month trial. Mixed effects models were used to compare trends over time in serum lipids. No significant differences were observed between the three groups: All three treatment groups exhibited similar meaningful improvement in the lipid profile at 9 and 18 months. When all groups were combined, these treatments significantly reduced total and LDL-cholesterol and triglycerides, increased HDL-cholesterol, and improved the atherogenic index. All improvements observed at 9 months persisted at 18 months (P < 0.001 verses baseline). Conclusion. Marine and botanical oils may be useful treatment for rheumatoid arthritis patients who are at increased risk for cardiovascular disease compared to the general population

Treatment of Rheumatoid Arthritis with Marine and Botanical Oils: Influence on Serum Lipids (poster)

Background: Over the past 30 years substantial progress has been made in the medical and surgical management of patients with rheumatoid arthritis (RA). Despite this progress, there is an increasing gap in mortality between patients with RA (1.5-3.0 fold risk) and the general population. This disparity is mainly attributable to cardiovascular disease (CVD) as the CVD risk is comparable in RA patients as to patients with diabetes mellitus. Although the reasons for this gap are not entirely clear, the traditional risk of abnormalities in lipid profiles appears to be enhanced by a chronic increase in inflammatory cytokines, resulting in accelerated atherosclerosis. Study Objective: The object of this study was to determine the effect of marine (fish oil) and botanical oils (borage oil) on lipids (TC, HDL, LDL, TG), a risk factor for cardiovascular disease in patients with RA. The main outcome (to be presented elsewhere) was to determine whether a combination of borage seed oil rich in gammalinolenic acid (GLA) and fish oil rich in eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) is superior to either oil alone for the treatment of RA. Population and Setting: The study was an 18 month randomized, double-masked comparison of borage seed oil, fish oil, and the combination of both oils in RA patients with active synovitis. Intervention: Patients received 3.5 gm omega-3 fatty acids daily in a 2.1gm EPA/1.4 gm DHA ratio (7 fish oil and 6 sunflower oil capsules daily); or 1.8 gm /d GLA (6 borage oil and 7 sunflower oil capsules /d); or 7 fish oil and 6 borage oil capsules daily (combination therapy). Discussion: Rheumatoid Arthritis (RA) is a chronic systemic inflammatory disease. Mediators of inflammation and prothrombotic factors contribute to endothelial dysfunction and development of cardiovascular disease in RA patients. Marine and botanical oils represent an excellent primary or secondary therapy for improvement of the cardiovascular risk management in RA. Patients taking these oils exhibit significant additional reductions in total and LDL-cholesterol, triglycerides, the TC/HDL ratio, and in the atherogenic index, and experience a significant increase in HDL-cholesterol. All of these improvements in the lipid profile were seen after 9 months of therapy, and increased after 18 months of oils administration. The overall dropout rate was 51%, and was similar across groups: 25 in the borage oil group, 28 in the fish oil group, and 22 in the combination group. Reasons for dropout were mainly gastrointestinal distress (belching, bloating, diarrhea, nausea, cramping), or an inability to swallow the large number of rather sizable capsules. This can be ameliorated by freezing the capsules and reducing their size. Among those evaluated for this study, compliance was 100%, assessed by pill counts. Learning Outcome: All treatments were safe, thus treatment of RA patients with one or a combination of these or similar oils should prove useful for reduction of cardiovascular risk in RA patients

A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV

Benign Paroxysmal Positional Vertigo (BPPV) is a mechanical disorder of the vestibular system in which calcite particles called otoconia interfere with the mechanical functioning of the fluid-filled semicircular canals normally used to sense rotation. Using hydrodynamic models, we examine the two mechanisms proposed by the medical community for BPPV: cupulolithiasis, in which otoconia attach directly to the cupula (a sensory membrane), and canalithiasis, in which otoconia settle through the canals and exert a fluid pressure across the cupula. We utilize known hydrodynamic calculations and make reasonable geometric and physical approximations to derive an expression for the transcupular pressure $\Delta P_c$ exerted by a settling solid particle in canalithiasis. By tracking settling otoconia in a two-dimensional model geometry, the cupular volume displacement and associated eye response (nystagmus) can be calculated quantitatively. Several important features emerge: 1) A pressure amplification occurs as otoconia enter a narrowing duct; 2) An average-sized otoconium requires approximately five seconds to settle through the wide ampulla, where $\Delta P_c$ is not amplified, which suggests a mechanism for the observed latency of BPPV; and 3) An average-sized otoconium beginning below the center of the cupula can cause a volumetric cupular displacement on the order of 30 pL, with nystagmus of order $2^\circ$/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.Comment: 15 pages, 5 Figures updated, to be published in J. Biomechanic

Optimizing the vertebrate vestibular semicircular canal: could we balance any better?

The fluid-filled semicircular canals (SCCs) of the vestibular system are used by all vertebrates to sense angular rotation. Despite masses spanning seven decades, all mammalian SCCs are nearly the same size. We propose that the SCC represents a sensory organ that evolution has `optimally designed'. Four geometric parameters are used to characterize the SCC, and `building materials' of given physical properties are assumed. Identifying physical and physiological constraints on SCC operation, we find that the most sensitive SCC has dimensions consistent with available data.Comment: 4 pages, 3 figure