A model-trust region algorithm utilizing a quadratic interpolant

AbstractA new model-trust region algorithm for problems in unconstrained optimization and nonlinear equations utilizing a quadratic interpolant for step selection is presented and analyzed. This is offered as an alternative to the piecewise-linear interpolant employed in the widely used “double dogleg” step selection strategy. After the new step selection algorithm has been presented, we offer a summary, with proofs, of its desirable mathematical properties. Numerical results illustrating the efficacy of this new approach are presented

A Derivative in Need: Rescuing U.S. Security-Based Swaps from the Race to the Bottom

Over the past 30 years, the development and proliferation of new financial instruments has provided investors with fresh and innovative methods to gain exposure to foreign markets, hedge investments, and capitalize on speculation opportunities. These “derivatives” have increased the interconnectedness of investors all over the globe, and in particular, the derivative known as the “security-based swap” has facilitated cross-border investments that were previously impracticable, yet greatly sought after. These financial advancements came at a price, however, and in 2007 and 2008, a lack of regulation over derivatives that led to a global financial crisis and spurred a widespread public desire for increased scrutiny over derivatives and those who use them. The United States responded by enacting the Dodd-Frank Wall Street Reform and Consumer Protection Act, which, among other things, established a new regulatory framework for derivatives, including security-based swaps. In the United States today, developments in both the legislative and judicial arenas following Dodd-Frank have come to a head, and the synergy between the two has resulted in an environment that is hostile to investors in security-based swaps. The result is a shift of these investments out of the United States and into foreign, less regulated markets, which thereby preserves the type of risks that Dodd-Frank was intended to mitigate. This note explains the benefits of security-based swaps while tracking these legislative and judicial developments, and it suggests a two-pronged solution for encouraging security-based swap investment within the United States while guarding against systemic financial risk. First, it calls for the abandonment of the economic reality test used by a court in the Southern District of New York as a means of evaluating the applicability of U.S. securities laws to actions involving derivatives. Second, it urges global coordination of financial regulatory regimes. Together these changes will afford U.S. security-based swap investors the ability to avail themselves of U.S. securities laws without the need for governmental intervention, while also establishing a baseline, blanket level of global financial regulation that will safeguard against systemic risk

A Derivative in Need: Rescuing U.S. Security-Based Swaps from the Race to the Bottom

Over the past 30 years, the development and proliferation of new financial instruments has provided investors with fresh and innovative methods to gain exposure to foreign markets, hedge investments, and capitalize on speculation opportunities. These “derivatives” have increased the interconnectedness of investors all over the globe, and in particular, the derivative known as the “security-based swap” has facilitated cross-border investments that were previously impracticable, yet greatly sought after. These financial advancements came at a price, however, and in 2007 and 2008, a lack of regulation over derivatives that led to a global financial crisis and spurred a widespread public desire for increased scrutiny over derivatives and those who use them. The United States responded by enacting the Dodd-Frank Wall Street Reform and Consumer Protection Act, which, among other things, established a new regulatory framework for derivatives, including security-based swaps. In the United States today, developments in both the legislative and judicial arenas following Dodd-Frank have come to a head, and the synergy between the two has resulted in an environment that is hostile to investors in security-based swaps. The result is a shift of these investments out of the United States and into foreign, less regulated markets, which thereby preserves the type of risks that Dodd-Frank was intended to mitigate. This note explains the benefits of security-based swaps while tracking these legislative and judicial developments, and it suggests a two-pronged solution for encouraging security-based swap investment within the United States while guarding against systemic financial risk. First, it calls for the abandonment of the economic reality test used by a court in the Southern District of New York as a means of evaluating the applicability of U.S. securities laws to actions involving derivatives. Second, it urges global coordination of financial regulatory regimes. Together these changes will afford U.S. security-based swap investors the ability to avail themselves of U.S. securities laws without the need for governmental intervention, while also establishing a baseline, blanket level of global financial regulation that will safeguard against systemic risk

Theory, computation, and application of exponential splines

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines

Survey of New Zealand farmer intentions and opinions, October-December 1986

This survey is the ninth major survey of New Zealand Farmer Intentions and Opinions. All have been aimed at providing policy makers and those in the agri-business sector in New Zealand with data on which they can formulate policies and planning. The surveys have been continued in response to demands from those who want data on what farmers are intending to do, what they are thinking on major issues, aspects of the financial side, and what are some of the factors that determine their input purchases. In this survey were inserted special questions on financial matters raised in earlier surveys. In addition some questions were included to ascertain some feelings and views of the rural sector on a range of issues including insurance, the News Media and Transport

An economic survey of New Zealand wheatgrowers : financial analysis, 1981-82

The purpose of this economic analysis is to provide financial data relating to those New Zealand wheatgrowing farms that participated in the 1981-82 wheat enterprise survey. The analysis was based upon the annual financial statements prepared for wheatgrowers by their accountants

Orthogonal Linear Regression in Roentgen Stereophotogrammetry

Rooted in aerial reconnaissance, mathematical photogrammetry has evolved into a mainstay of biomedical image processing. The present paper develops an algorithm for Roentgen stereophotogrammetry, a method of imaging musculoskeletal systems both static and dynamic, which incorporates a number of novel features employing techniques from projective geometry, orthogonal regression and least squares approximation. Theoretical and numerical evidence is presented of the efficacy of the proposed procedure

Implications of transient methane flux on associated biological communities in high-arctic seep habitats, Storbanken, Norwegian Barents sea

The continental margins of the Arctic Ocean basin contain methane seeps, where transient fluxes of seafloor methane are released due to the thermal dissociation of gas hydrates. An increase in shallow methane seeps identified over the past decade, potentially due to enhanced warming of the Arctic Ocean bottom water and associated destabilization of hydrate structure. Biological communities associated with methane release east of Svalbard in the Barents Sea (Storbanken Crater site, 76° 46.7′N, 35° 43.5′E, depths between 120 m–300 m depths) were investigated using towed camera imagery and ship-based platforms during a 2017 CAGE17-2 cruise on the RV Helmer Hanssen. We analyzed relationships among methane flux data, seafloor habitat characteristics, and biological community structure (i.e., presence and distribution of megafauna and expression of microbial mats) from a total of 14 surveys (6827 images and 40 multicore sediment cores) within the Storbanken Crater area and compared it to 2015 data. Unlike seep expressions at deeper sites (∼1200 m) in the Norwegian margin region, no seep-endemic, chemosynthetic-associated megafaunal species were observed at the shallow surveyed sites and all sites hosted similarly diverse communities of non-seep species, including commercially important fish and crustaceans. Methane concentrations did not markedly differ between the crater and non-crater sites. Rates of methane gas advection through sediments (in the form of flares) were relatively low and concentration of methane was even lower in porewater samples at the crater site. We present the first evidence of methane flare flux and intermittent microbial mat distribution with associated folliculinid ciliates, which suggests a long history of methane emissions and a transient seep environment in spatial and temporal flux. Together, this study presents a critical baseline on the temporal release of arctic methane and benthic biological communities to initiate temporal studies that identify future changes and predict the impact of climate chang

Probing color coherence effects in pp collisions at [Formula: see text].

A study of color coherence effects in pp collisions at a center-of-mass energy of 7[Formula: see text] is presented. The data used in the analysis were collected in 2010 with the CMS detector at the LHC and correspond to an integrated luminosity of 36 pb[Formula: see text]. Events are selected that contain at least three jets and where the two jets with the largest transverse momentum exhibit a back-to-back topology. The measured angular correlation between the second- and third-leading jet is shown to be sensitive to color coherence effects, and is compared to the predictions of Monte Carlo models with various implementations of color coherence. None of the models describe the data satisfactorily