The Small-Is-Very-Small Principle

The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable cut, then it shows that the property has a very small witness: i.e. a witness below a given standard number. We draw various consequences from the central result. For example (in rough formulations): (i) Every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative w.r.t. formulas of complexity $\leq n$. (ii) Every sequential model has, for any $n$, an extension that is elementary for formulas of complexity $\leq n$, in which the intersection of all definable cuts is the natural numbers. (iii) We have reflection for $\Sigma^0_2$-sentences with sufficiently small witness in any consistent restricted theory $U$. (iv) Suppose $U$ is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential $V$ that locally inteprets $U$, globally interprets $U$. Then, $U$ is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations

Climatic and eustatic controls on the development of a Late Triassic source rock in the Jameson Land Basin, East Greenland

This work was undertaken as part of the continuing work of CASP in East Greenland. The sponsoring companies are thanked for their continued support of this work. Help in the field by T. Kinnaird and useful discussions with A. Whitham are gratefully acknowledged. The reviews of L. Clemmensen and an anonymous reviewer, and the input from S. Jones led to improvements to the original paper.Peer reviewedPostprin

Investigation of Light Scattering in Highly Reflecting Pigmented Coatings Quarterly Report, Feb. 1 - May 1, 1966

Monte Carlo method applied to pigment particle clusters, and relevance of Mie scattering function to reflected ligh

Investigation of light scattering in highly reflecting pigmented coatings Quarterly report, Nov. 1, 1965 - Feb. 1, 1966

Monte Carlo treatment to find light scattering parameters of metal filled, reflecting pigmented coating

Mixing Times in Quantum Walks on Two-Dimensional Grids

Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.Comment: 11 page

The Universal Cloud and Aerosol Sounding System (UCASS): a low-cost miniature optical particle counter for use in dropsonde or balloon-borne sounding systems

© Author(s) 2019. This work is distributed under the Creative Commons Attribution 4.0 License. An earlier version of this work was published in Atmospheric Measurement Techniques Discussions: https://dx.doi.org/10.5194/amt-2019-70.A low-cost miniaturized particle counter has been developed by The University of Hertfordshire (UH) for the measurement of aerosol and droplet concentrations and size distributions. The Universal Cloud and Aerosol Sounding System (UCASS) is an optical particle counter (OPC), which uses wide-angle elastic light scattering for the high-precision sizing of fluid-borne particulates. The UCASS has up to 16 configurable size bins, capable of sizing particles in the range 0.4–40 µm in diameter. Unlike traditional particle counters, the UCASS is an open-geometry system that relies on an external air flow. Therefore, the instrument is suited for use as part of a dropsonde, balloon-borne sounding system, as part of an unmanned aerial vehicle (UAV), or on any measurement platform with a known air flow. Data can be logged autonomously using an on-board SD card, or the device can be interfaced with commercially available meteorological sondes to transmit data in real time. The device has been deployed on various research platforms to take measurements of both droplets and dry aerosol particles. Comparative results with co-located instrumentation in both laboratory and field settings show good agreement for the sizing and counting ability of the UCASS.Peer reviewe

Analysis of stratospheric ozone, temperature, and minor constituent data

The objective of this research is to use available satellite measurements of temperature and constituent concentrations to test the conceptual picture of stratospheric chemistry and transport. This was originally broken down into two sub-goals: first, to use the constituent data to search for critical tests of our understanding of stratospheric chemistry and second, to examine constituent transport processes emphasizing interactions with chemistry on various time scales. A third important goal which has evolved is to use the available solar backscattered ultraviolet (SBUV) and Total Ozone Mapping Spectrometer (TOMS) data from Nimbus 7 to describe the morphology of recent changes in Antarctic and global ozone with emphasis on searching for constraints to theories. The major effort now being pursued relative to the two original goals is our effort as a theoretical team for the Arctic Airborne Stratospheric Expedition (AASE). Our effort for the AASE is based on the 3D transport and chemistry model at Goddard. Our goal is to use this model to place the results from the mission data in a regional and global context. Specifically, we set out to make model runs starting in late December and running through March of 1989, both with and without heterogeneous chemistry. The transport is to be carried out using dynamical fields from a 4D data assimilation model being developed under separate funding from this task. We have successfully carried out a series of single constituent transport experiments. One of the things demonstrated by these runs was the difficulty in obtaining observed low N2O abundances in the vortex without simultaneously obtaining very high ozone values. Because the runs start in late December, this difficulty arises in the attempt to define consistent initial conditions for the 3D model. To accomplish a consistent set of initial conditions, we are using the 2D photochemistry-transport model of Jackman and Douglass and mapping in potential temperature, potential vorticity space as developed by Schoeberl and coworkers

Satellite observation and mapping of wintertime ozone variability in the lower stratosphere

Comparison is made between 30 mbar ozone fields that are generated by a transport chemistry model utilizing the winds from the Goddard Space Flight Center stratospheric data assimilation system (STRATAN), observations from the LIMS instrument on Nimbus-7, and the ozone fields that result from 'flying a mathematical simulation of LIMS observations through the transport chemistry model ozone fields. The modeled ozone fields were found to resemble the LIMS observations, but the model fields show much more temporal and spatial structure than do the LIMS observations. The 'satellite mapped' model results resemble the LIMS observations much more closely. These results are very consistent with the earlier discussions of satellite space-time sampling by Salby

LaserTank is NP-complete

We show that the classical game LaserTank is $\mathrm{NP}$-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing $3$-SAT instances to LaserTank puzzles.Comment: 5 page

Microclimatological, Pedological, and Geomorphological Studies in the Western Tasersiaq Area, Greenland During Summer 1964

Final Report - 30 April 1964 -29 July 1965During the summer 1964, personnel of The Ohio State University Institute of Polar Studies conducted a field program in the Sukkertoppen Ice Cap area of southwest Greenland. The program included studies of soil and mass wasting in the Tasersiaq area immediately east of the ice cap, and studies of the microclimatology across the eastern edge of the ice cap. The results of this research program are contained in four parts. Part I, by Adolph Kryger, discusses the microclimatological (excluding radiation) results of observations taken at four stations, one at the base of the slope below the eastern edge of the Sukkertoppen Ice Cap, two intermediate ones on the slope, and one at the edge of the glacier. Part II, by Fritz Loewe, discusses the radiation observations. Both have related their observations to those at other permanent stations along the western Greenland coast. Part III, by K. R. Everett, presents the results of studies of mass-wasting and patterned ground phenomena. Part IV, by N. Holowaychuk and K. R. Everett, contains most of the results of the pedological studies. The report herein includes the discussion of soil morphology,chemistry, and classification.U.S. Army Natick Laboratories, Contract No. DA-19-129-AMC-301(N