Objective functions with redundant domains

Let (E,A) be a set system consisting of a finite collection A of subsets of a ground set E, and suppose that we have a function ϕ which maps A into some set S. Now removing a subset K from E gives a restriction A(K¯) to those sets of A disjoint from K, and we have a corresponding restriction ϕ|A(K¯) of our function ϕ. If the removal of K does not affect the image set of ϕ, that is Im(ϕ|A(X¯))=Im(ϕ), then we will say that K is a kernel set of A with respect to ϕ. Such sets are potentially useful in optimisation problems defined in terms of ϕ. We will call the set of all subsets of E that are kernel sets with respect to ϕ a kernel system and denote it by Kerϕ(A). Motivated by the optimisation theme, we ask which kernel systems are matroids. For instance, if A is the collection of forests in a graph G with coloured edges and ϕ counts how many edges of each colour occurs in a forest then Kerϕ(A) is isomorphic to the disjoint sum of the cocycle matroids of the differently coloured subgraphs; on the other hand, if A is the power set of a set of positive integers, and ϕ is the function which takes the values 1 and 0 on subsets according to whether they are sum-free or not, then we show that Kerϕ(A) is essentially never a matroid

Property Assessments and Information Asymmetry in Residential Real Estate

This paper presents a game theoretic model of property tax assessment that allows a tax appraiser to either choose a high or a low assessment. The owner either accepts or challenges this assessment. A ‘‘fixed effects’’ regression model is used to evaluate the differences in the assessed values of a sample of houses from Bexar County, Texas during 2000 and 2001. Where the owner of the house is identified as a state licensed property tax consultant, the assessed value, after adjusting for size, age, and other economic characteristics, ranged from a statistically robust 2.5% to 6.2% lower than neighboring houses.

Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66Ga.Comment: 15 pages, 8 figure

Implicit Liquidity Premiums in the Disposition of RTC Assets

The Resolution Trust Corporation (RTC) was created by congressional legislation passed in 1989, and was charged with, among other things, the orderly disposition of other real estate owned (OREO) property. Questions have been raised about how efficient and effective the RTC has been in achieved its congressional mandate. One of the issues resulting from the efficiency question involves the amount of discount the RTC realizes for a quick disposition of the property. This study utilizes data provided by the RTC concerning its sales to analyze the implicit liquidity premium resulting from disposing of OREO. The results of the study indicate what variables contribute to liquidity premiums. This paper's importance relies most heavily on the finding that realistic market adjustments in regulation, over time, helped to achieve a higher degree of liquidity for RTC real estate property sales. The findings of this paper confirm the legislative intent of FIRREA, which is to ensure that real estate properties acquired by the government are disposed of at the highest dollar value possible.

Sampling a Littoral Fish Assemblage: Comparison of Small-Mesh Fyke Netting and Boat Electrofishing

We compared small-mesh (4-mm) fyke netting and boat electrofishing for sampling a littoral fish assemblage in Muskegon Lake, Michigan. We hypothesized that fyke netting selects for small-bodied fishes and electrofishing selects for large-bodied fishes. Three sites were sampled during May (2004 and 2005), July (2005 only), and September (2004 and 2005). We found that the species composition of captured fish differed considerably between fyke netting and electrofishing based on nonmetric multidimensional scaling (NMDS). Species strongly associated with fyke netting (based on NMDS and relative abundance) included the brook silverside Labidesthes sicculus, banded killifish Fundulus diaphanus, round goby Neogobius melanostomus, mimic shiner Notropis volucellus, and bluntnose minnow Pimephales notatus, whereas species associated with electrofishing included the Chinook salmon Oncorhynchus tshawytscha, catostomids (Moxostoma spp. and Catostomus spp.), freshwater drum Aplodinotus grunniens, walleye Sander vitreus, gizzard shad Dorosoma cepedianum, and common carp Cyprinus carpio. The total length of fish captured by electrofishing was 12.8 cm (95% confidence interval ¼ 5.5– 17.2 cm) greater than that of fish captured by fyke netting. Size selectivity of the gears contributed to differences in species composition of the fish captured, supporting our initial hypothesis. Thus, small-mesh fyke nets and boat electrofishers provided complementary information on a littoral fish assemblage. Our results support use of multiple gear types in monitoring and research surveys of fish assemblages. Copyright by the American Fisheries Society 2007, Originally published in the North American Journal of Fisheries Management 27: 825-831, 2007

Searching for keV Sterile Neutrino Dark Matter with X-ray Microcalorimeter Sounding Rockets

High-resolution X-ray spectrometers onboard suborbital sounding rockets can search for dark matter candidates that produce X-ray lines, such as decaying keV-scale sterile neutrinos. Even with exposure times and effective areas far smaller than XMM-Newton and Chandra observations, high-resolution, wide field-of-view observations with sounding rockets have competitive sensitivity to decaying sterile neutrinos. We analyze a subset of the 2011 observation by the X-ray Quantum Calorimeter instrument centered on Galactic coordinates l = 165, b = -5 with an effective exposure of 106 seconds, obtaining a limit on the sterile neutrino mixing angle of sin^2(2 theta) < 7.2e-10 at 95% CL for a 7 keV neutrino. Better sensitivity at the level of sin^2(2 theta) ~ 2.1e-11 at 95\% CL for a 7 keV neutrino is achievable with future 300-second observations of the galactic center by the Micro-X instrument, providing a definitive test of the sterile neutrino interpretation of the reported 3.56 keV excess from galaxy clusters.Comment: 13 pages, 13 figures, submitted to Ap

Folding model analysis of alpha radioactivity

Radioactive decay of nuclei via emission of $\alpha$ particles has been studied theoretically in the framework of a superasymmetric fission model using the double folding (DF) procedure for obtaining the $\alpha$-nucleus interaction potential. The DF nuclear potential has been obtained by folding in the density distribution functions of the $\alpha$ nucleus and the daughter nucleus with a realistic effective interaction. The M3Y effective interaction has been used for calculating the nuclear interaction potential which has been supplemented by a zero-range pseudo-potential for exchange along with the density dependence. The nuclear microscopic $\alpha$-nucleus potential thus obtained has been used along with the Coulomb interaction potential to calculate the action integral within the WKB approximation. This subsequently yields microscopic calculations for the half lives of $\alpha$ decays of nuclei. The density dependence and the exchange effects have not been found to be very significant. These calculations provide reasonable estimates for the lifetimes of $\alpha$ radioactivity of nuclei.Comment: 7 pages including 1 figur

Contextual factors among indiscriminate or larger attacks on food or water supplies, 1946-2015

This research updates previous inventories of malicious attacks on food and water to include data from 1946 through mid-2015. A systematic search of news reports, databases and previous inventories of poisoning events was undertaken. Incidents that threatened or were intended to achieve direct harm to humans, and that were either relatively large (number of victims > 4 or indiscriminate in intent or realisation were included. Agents could be chemical, biological or radio-nuclear. Reports of candidate incidents were subjected to systematic inclusion and exclusion criteria as well as validity analysis (not always clearly undertaken in previous inventories of such attacks). We summarise contextual aspects of the attacks that may be important for scenario prioritisation, modelling and defensive preparedness. Opportunity is key to most realised attacks, particularly access to dangerous agents. The most common motives and relative success rate in causing harm were very different between food and water attacks. The likelihood that people were made ill or died also varied by food/water mode, and according to motive and opportunity for delivery of the hazardous agent. Deaths and illness associated with attacks during food manufacture and prior to sale have been fewer than those in some other contexts. Valuable opportunities for food defence improvements are identified in other contexts, especially food prepared in private or community settings