The Kepler Problem: Orbit Cones and Cylinders

Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones

DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism

We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings

Stable-bounded subsets of Lα, and sample unboundedness of symmetric stable processes

AbstractLet Xt be the Levy symmetric stable process with index α ∈ [1, 2), and let C be a convex, symmetric subset of Lα[0, 1]. We prove that if C does not have compact closure then supƒϵC ¦∝01ƒ(t)dXt¦ is infinite with probability one. This extends a result of Dudley in the case α = 2

DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism

Abstract We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings

The Concordance Cosmic Star Formation Rate: Implications from and for the Supernova Neutrino and Gamma Ray Backgrounds

We constrain the Cosmic Star Formation Rate (CSFR) by requiring that massive stars produce the observed UV, optical, and IR light while at the same time not overproduce the Diffuse Supernova Neutrino Background as bounded by Super-Kamiokande. With the massive star component so constrained we then show that a reasonable choice of stellar Initial Mass Function and other parameters results in SNIa rates and iron yields in good agreement with data. In this way we define a `concordance' CSFR that predicts the optical SNII rate and the SNIa contribution to the MeV Cosmic Gamma-Ray Background. The CSFR constrained to reproduce these and other proxies of intermediate and massive star formation is more clearly delineated than if it were measured by any one technique and has the following testable consequences: (1) SNIa contribute only a small fraction of the MeV Cosmic Gamma-Ray Background, (2) massive star core-collapse is nearly always accompanied by a successful optical SNII, and (3) the Diffuse Supernova Neutrino Background is tantalizingly close to detectability.Comment: Improved discussion. Version accepted for publication in JCA

Oral rehydration versus intravenous therapy for treating dehydration due to gastroenteritis in children: a meta-analysis of randomised controlled trials

BACKGROUND: Despite treatment recommendations from various organizations, oral rehydration therapy (ORT) continues to be underused, particularly by physicians in high-income countries. We conducted a systematic review of randomised controlled trials (RCTs) to compare ORT and intravenous therapy (IVT) for the treatment of dehydration secondary to acute gastroenteritis in children. METHODS: RCTs were identified through MEDLINE, EMBASE, CENTRAL, authors and references of included trials, pharmaceutical companies, and relevant organizations. Screening and inclusion were performed independently by two reviewers in order to identify randomised or quasi-randomised controlled trials comparing ORT and IVT in children with acute diarrhea and dehydration. Two reviewers independently assessed study quality using the Jadad scale and allocation concealment. Data were extracted by one reviewer and checked by a second. The primary outcome measure was failure of rehydration. We analyzed data using standard meta-analytic techniques. RESULTS: The quality of the 14 included trials ranged from 0 to 3 (Jadad score); allocation concealment was unclear in all but one study. Using a random effects model, there was no significant difference in treatment failures (risk difference [RD] 3%; 95% confidence intervals [CI]: 0, 6). The Mantel-Haenzsel fixed effects model gave a significant difference between treatment groups (RD 4%; 95% CI: 2, 5) favoring IVT. Based on the four studies that reported deaths, there were six in the IVT groups and two in ORT. There were no significant differences in total fluid intake at six and 24 hours, weight gain, duration of diarrhea, or hypo/hypernatremia. Length of stay was significantly shorter for the ORT group (weighted mean difference [WMD] -1.2 days; 95% CI: -2.4,-0.02). Phlebitis occurred significantly more often with IVT (number needed to treat [NNT] 33; 95% CI: 25,100); paralytic ileus occurred more often with ORT (NNT 33; 95% CI: 20,100). These results may not be generalizable to children with persistent vomiting. CONCLUSION: There were no clinically important differences between ORT and IVT in terms of efficacy and safety. For every 25 children (95% CI: 20, 50) treated with ORT, one would fail and require IVT. The results support existing practice guidelines recommending ORT as the first course of treatment in appropriate children with dehydration secondary to gastroenteritis

Tax Rates and Corporate Decision-making

We survey companies and find that many use incorrect tax rate inputs into important corporate decisions. Specifically, many companies use an average tax rate (the GAAP effective tax rate, ETR) to evaluate incremental decisions, rather than using the theoretically correct marginal tax rate. We find evidence consistent with behavioral biases (heuristics, salience) and managers' educational backgrounds affecting these choices. We estimate the economic consequences of using the theoretically incorrect tax rate and find that using the ETR for capital structure decisions leads to suboptimal leverage choices and using the ETR in investment decisions makes firms less responsive to investment opportunities

Dyadic approximation of double integrals with respect to symmetric stable processes

Recently, Rosinski and Woyczynski have given necessary and sufficient conditions for the existence of the double integral with respect to a symmetric stable process of index [alpha] in [1, 2). In their approach the double integral is defined as an iterated Itô-type integral. We show here that it can also be defined as the limit of integrals of step functions and that the two approaches are equivalent. For many purposes this result reduces the study of double integrals to that of quadratic forms in independent stable random variables.multiple Wiener integral stochastic integration symmetric stable processes random quadratic forms p-summing maps radonifying maps