Regulation: A View from Inside the Machine

This is a transcript of the keynote address virtually delivered by Hester M. Peirce at the symposium “Protecting the Public While Fostering Innovation and Entrepreneurship: First Principles for Optimal Regulation,” hosted at the University of Missouri School of Law on February 8, 2019. The transcript of this address was initially published on the official website of the Securities and Exchange Commission; it has been lightly edited to ensure readability and formatting continuity

Confrontation and conflict in the poetry of John Donne

In tracing the heritage of the concern over the relative values of the material and the immaterial, one can see that the problem was considerably significant in Medieval thought as a great deal of the philosophical writings of the Age were dedicated to the problem of the universals. The question of whether reality existed in the form or the particular, however, was not a speculation peculiar to the Middle Ages. The academic controversy, as far as one can determine, found its germination in the Hellenic tradition of Plato and Aristotle; a brief recall of its ancient history, then, would seem to be in order

P- and S- wave velocities of consolidated sediments from a seafloor seismic survey in the North Celtic Sea Basin, offshore Ireland

A geophysical survey was conducted over a hydrocarbon prospect in the North Celtic Sea Basin using a small array of ocean-bottom seismographs (OBSs). The purpose of this study was to determine the ratio of (P) compressional- to (S) shear-wave velocity of consolidated sedimentary rocks in order to constrain possible subsurface variations in pore-fluid content. The ratio of VP and VS- is known to be particularly sensitive to lithology, porosity and pore-fluid content, making it a useful parameter for evaluating hydrocarbon prospects. OBSs offer a relatively cheap and time-effective means of acquiring multi-component data compared with ocean-bottom cables. In this contribution, we demonstrate the ability of an OBS survey comprising three pairs of two OBSs spaced at 1.6 km to recover lateral variations in the VP/VS ratio. A key requirement of this type of study is that S-waves will be generated by mode conversions in the subsurface, since they cannot be generated in nor travel through fluids. In this survey, the contrast in physical properties of the hard seabed of the North Celtic Sea Basin provided a means of generating converted S-waves. Two-dimensional ray-tracing and forward modeling was used to create both VP and VS models along a profile crossing the Blackrock prospect in the North Celtic Sea Basin. These models comprise four layers and extend to a maximum depth of 1.1 km. The observed northward decrease in the VP/VS ratio at depths of 500-1000 m below the seafloor in the study area is interpreted to represent lateral variation in the amount of gas present in the pore space of Upper Cretaceous chalks and shales overlying the prospective reservoir

Dynamic model of fiber bundles

A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under non-vanishing stress always breaks down in the presence of noise. Revealed in particular is the characteristic time evolution that the system tends to resist the stress for considerable time, followed by sudden complete rupture. The critical stress beyond which the complete rupture emerges is also obtained

Dynamic model for failures in biological systems

A dynamic model for failures in biological organisms is proposed and studied both analytically and numerically. Each cell in the organism becomes dead under sufficiently strong stress, and is then allowed to be healed with some probability. It is found that unlike the case of no healing, the organism in general does not completely break down even in the presence of noise. Revealed is the characteristic time evolution that the system tends to resist the stress longer than the system without healing, followed by sudden breakdown with some fraction of cells surviving. When the noise is weak, the critical stress beyond which the system breaks down increases rapidly as the healing parameter is raised from zero, indicative of the importance of healing in biological systems.Comment: To appear in Europhys. Let

A random fiber bundle with many discontinuities in the threshold distribution

We study the breakdown of a random fiber bundle model (RFBM) with $n$-discontinuities in the threshold distribution using the global load sharing scheme. In other words, $n+1$ different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the $i-th$ class are uniformly distributed between the values $\sigma_{2i-2}$ and $\sigma_{2i-1}$ where $1 \leq i \leq n+1$. Moreover, there is a gap in the threshold distribution between $i-th$ and $i+1-th$ class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution (ASD), on the other hand, shows a non-universal, non-power law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary $n$ is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution ($n=1$), especially when the density and the range of threshold values of fibers belonging to strongest ($n+1$)-th class is kept identical in all the cases.Comment: 6 pages, 4 figures, Accepted in Phys. Rev.