Consolidation, technology, and the changing structure of banks' small business lending

The U.S. banking industry continues to consolidate, with large, complex banking organizations becoming more important. Traditionally, these institutions have not emphasized small business lending. On the other hand, technological advances, particularly credit scoring models, make it easier for banks to extend small business credit. To see what effects these influences might have generated on small business lending, David Ely and Kenneth Robinson explore the small business lending patterns at U.S. banks from 1994 through 1999. They find that larger banks are increasing their market share, most noticeably in the smallest segment of the small business loan market. The authors also present evidence that the size of the average small business loan has declined, especially at larger organizations, and that the gap in lending focus on the smallest small business loans has narrowed between small and large banks. These trends are consistent with increasing use of credit scoring models.Credit ; Credit scoring systems

The determinants of the wealth effects of banks' expanded securities powers

After several unsuccessful attempts by Congress to repeal Glass-Steagall restrictions on banks, the Federal Reserve more than doubled the revenue that commercial banking organizations' securities subsidiaries may earn from certain securities activities. The wealth effects associated with this event for a sample of publicly traded banking organizations are examined. We find evidence that indicates the revenue limit resulted in a less-than-optimal mix of activities for securities subsidiaries. However, subsequent merger activity that could have been generated by the revenue increase was not viewed favorably by investors.Securities

Probing Λ\LambdaCDM cosmology with the Evolutionary Map of the Universe survey

The Evolutionary Map of the Universe (EMU) is an all-sky survey in radio-continuum which uses the Australian SKA Pathfinder (ASKAP). Using galaxy angular power spectrum and the integrated Sachs-Wolfe effect, we study the potential of EMU to constrain models beyond $\Lambda$CDM (i.e., local primordial non-Gaussianity, dynamical dark energy, spatial curvature and deviations from general relativity), for different design sensitivities. We also include a multi-tracer analysis, distinguishing between star-forming galaxies and galaxies with an active galactic nucleus, to further improve EMU's potential. We find that EMU could measure the dark energy equation of state parameters around 35\% more precisely than existing constraints, and that the constraints on $f_{\rm NL}$ and modified gravity parameters will improve up to a factor $\sim2$ with respect to Planck and redshift space distortions measurements. With this work we demonstrate the promising potential of EMU to contribute to our understanding of the Universe.Comment: 15 pages (29 with references and appendices), 6 figures and 10 tables. Matches the published version. Minimal changes from previous versio

Fast Moment Estimation in Data Streams in Optimal Space

We give a space-optimal streaming algorithm with update time $O(log^2(1/\epsilon)loglog(1/\epsilon))$ for approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream up to a factor of $1 \pm \epsilon$. This provides a nearly exponential improvement over the previous space optimal algorithm of [Kane-Nelson-Woodruff, SODA 2010], which had update time $\Omega(1/\epsilon^2)$. When combined with the work of [Harvey-Nelson-Onak, FOCS 2008], we also obtain the first algorithm for entropy estimation in turnstile streams which simultaneously achieves near-optimal space and fast update time.Engineering and Applied Science

Probing Λ\LambdaCDM cosmology with the Evolutionary Map of the Universe survey

The Evolutionary Map of the Universe (EMU) is an all-sky survey in radio-continuum which uses the Australian SKA Pathfinder (ASKAP). Using galaxy angular power spectrum and the integrated Sachs-Wolfe effect, we study the potential of EMU to constrain models beyond $\Lambda$CDM (i.e., local primordial non-Gaussianity, dynamical dark energy, spatial curvature and deviations from general relativity), for different design sensitivities. We also include a multi-tracer analysis, distinguishing between star-forming galaxies and galaxies with an active galactic nucleus, to further improve EMU's potential. We find that EMU could measure the dark energy equation of state parameters around 35\% more precisely than existing constraints, and that the constraints on $f_{\rm NL}$ and modified gravity parameters will improve up to a factor $\sim2$ with respect to Planck and redshift space distortions measurements. With this work we demonstrate the promising potential of EMU to contribute to our understanding of the Universe.Comment: 15 pages (29 with references and appendices), 6 figures and 10 tables. Matches the published version. Minimal changes from previous versio

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Cosmology with the Highly Redshifted 21cm Line

In addition to being a probe of Cosmic Dawn and Epoch of Reionization astrophysics, the 21cm line at $z>6$ is also a powerful way to constrain cosmology. Its power derives from several unique capabilities. First, the 21cm line is sensitive to energy injections into the intergalactic medium at high redshifts. It also increases the number of measurable modes compared to existing cosmological probes by orders of magnitude. Many of these modes are on smaller scales than are accessible via the CMB, and moreover have the advantage of being firmly in the linear regime (making them easy to model theoretically). Finally, the 21cm line provides access to redshifts prior to the formation of luminous objects. Together, these features of 21cm cosmology at $z>6$ provide multiple pathways toward precise cosmological constraints. These include the "marginalizing out" of astrophysical effects, the utilization of redshift space distortions, the breaking of CMB degeneracies, the identification of signatures of relative velocities between baryons and dark matter, and the discovery of unexpected signs of physics beyond the $\Lambda$CDM paradigm at high redshifts.Comment: Science white paper submitted to Decadal 2020 surve

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure