Using Graphing Calculators to Integrate Mathematics and Science

The computational, graphing, statistical and programming capabilities of today’s graphing calculators make it possible for teachers and students to explore aspects of functions and investigate real-world situations in ways that were previously inaccessible because of computational constraints. Many of the features of graphing calculators can be used to integrate topics from mathematics and science. Here we provide a few illustrations of activities that use the graphing, parametric graphing, regression, and recursion features of graphing calculators to study mathematics in science contexts

Constraints on the radio loud/radio quiet dichotomy from the fundamental plane

The fundamental plane for black hole activity constitutes a tight correlation between jet power, X-ray luminosity, and black hole mass. Under the assumption that a Blandford-Znajek-type mechanism, which relies on black hole spin, contributes non-negligibly to jet production, the sufficiently small scatter in the fundamental plane shows that black hole spin differences of $\mid$$\Delta$a$\mid \sim$1 are not typical among the active galactic nuclei population. If $-$ as it seems $-$ radio loud and radio quiet objects are both faithful to the fundamental plane, models of black hole accretion in which the radio loud/radio quiet dichotomy is based on a spin dichotomy of a$\sim$1/a$\sim$0, respectively, are difficult to reconcile with the observations. We show how recent theoretical work based on differences in accretion flow orientation between retrograde and prograde, accommodates a small scatter in the fundamental plane for objects that do have non-negligible differences in black hole spin values. We also show that the dichotomy in spin between the most radio loud and the most radio quiet involves $\mid$$\Delta$a$\mid \approx$0. And, finally, we show how the picture that produces compatibility with the fundamental plane, also allows one to interpret other otherwise puzzling observations of jets across the mass scale including 1) the recently observed inverse relation between radio and X-rays at higher Eddington ratios in both black hole X-ray binaries as well as active galactic nuclei and 2) the apparent contradiction between jet power and black hole spin observed in X-ray hard and transitory burst states in X-ray binaries.Comment: 8 pages, 1 figure, accepted in MNRA

Lightweight LCP Construction for Very Large Collections of Strings

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several applications, especially in biological contexts. Nowadays, the input data for many problems are big collections of strings, for instance the data coming from "next-generation" DNA sequencing (NGS) technologies. In this paper we present the first lightweight algorithm (called extLCP) for the simultaneous computation of the longest common prefix array and the Burrows-Wheeler transform of a very large collection of strings having any length. The computation is realized by performing disk data accesses only via sequential scans, and the total disk space usage never needs more than twice the output size, excluding the disk space required for the input. Moreover, extLCP allows to compute also the suffix array of the strings of the collection, without any other further data structure is needed. Finally, we test our algorithm on real data and compare our results with another tool capable to work in external memory on large collections of strings.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The final version of this manuscript is in press in Journal of Discrete Algorithm

INSURANCE LAW—COLLATERAL SOURCE REDUCTIONS IN CONNECTICUT: HOW INSURANCE “WRITEOFFS” NOW LEADS TO WINDFALL JUDGMENTS – AN ANALYSIS OF THE MARCIANO DECISION AND ITS IMPACT

The purpose of the tort compensation system is to make an injured party whole; no less, but no more. With that concept in mind, Connecticut first codified its “collateral source” reduction rules in 1985, which were designed to prevent an injured party from obtaining a “double recovery” of economic damages already paid to the injured party, or paid on the injured party’s behalf through an outside source, such as insurance.1 In Marciano v. Jimenez, however, the Connecticut Supreme Court interpreted section 52-225a to declare that when “any” right of reimbursement or subrogation exists to any portion of the claimed economic damages, there should be no collateral source reduction.2 As a result of this precedent, trial courts now routinely deny collateral source reductions in an overbroad manner. As of today, in any case involving the presence of a lien placed on the lawsuit for medical expenses paid, such as in cases with plaintiffs covered by Medicare or Medicaid, the Marciano decision has been interpreted to require the denial of any collateral source reduction. This includes the portions of the bill that were contractually written off by the provider and were never incurred by plaintiff. Judicial interpretation of section 52-225a in this manner, however, is inapposite with the legislative intent behind the statute’s enaction. A plaintiff’s recovery of financial damages for medical expenses that were never incurred or owed is the type of windfall benefit section 52225a was designed to avoid. In light of such harsh results, the Marciano decision needs to be rectified upon reconsideration of the decision by the Connecticut Supreme Court or through legislative action

Application of ERTS-1 data to the protection and management of New Jersey's coastal environment

ERTS-1 imagery is being used by the New Jersey Department of Environmental Protection (NJDEP) to develop information products that will assist the state in optimally managing its coastal resources and in allocating funds. Interviews with NJDEP personnel have identified significant problem areas in the coastal zone, and the types of remote sensor derived information products that can be used in real-time decision making. Initial analyses of imagery from several successive ERTS-1 orbits have shown the extent, predominant drift, and dispersion characteristics of waste disposal in coastal New Jersey waters. Imagery (MSS Bands 4 and 5) for several orbits, shows that New-York Harbor tidal discharge extending as far south as Long Branch, New Jersey

Local behavior of p-harmonic Green's functions in metric spaces

We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality

The Sub-Eddington Boundary for the Quasar Mass–Luminosity Plane: A Theoretical Perspective

By exploring more than sixty thousand quasars from the Sloan Digital Sky Survey Data Release 5, Steinhardt & Elvis discovered a sub-Eddington boundary and a redshift-dependent drop-off at higher black hole mass, possible clues to the growth history of massive black holes. Our contribution to this special issue of Universe amounts to an application of a model for black hole accretion and jet formation to these observations. For illustrativepurposes,we include~100,000 data points from the Sloan Digital Sky Survey Data Release 7 where the sub-Eddington boundary is also visible andpropose a theoretical picture that explains these features. By appealing to thin disk theory and both the lower accretion efficiency and the time evolution of jetted quasars compared to non-jetted quasars in our “gap paradigm”, we explain two features of the sub-Eddington boundary. First, we show that a drop-off on the quasar mass-luminosity plane for larger black hole mass occurs at allredshifts. But the fraction of jetted quasars is directly related to the merger function in thisparadigm, which means the jetted quasar fraction drops with decrease in redshift, which allows us to explain a second feature of the sub-Eddington boundary, namely a redshift dependence of the slope of the quasar mass-luminosity boundary at high black hole mass stemming from a change in radiative efficiency with time. We are able to reproduce the mass dependence of, as well as the oscillating behavior in, the slope of the sub-Eddington boundary as a function of time. The basic physical idea involves retrograde accretion occurring only for a subset of the more massive black holes,which implies that most spinning black holes in our model are prograde accretors.In short, this paper amounts to a qualitative overview of how a sub-Eddington boundary naturally emerges in the gap paradigm