Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction

In this paper it is shown that, under the assumption of thelogarithmic distribution of numbers, floating-point additionand subtraction can result in overflow or underflow with alarmingfrequency—a frequency that increases rapidly with machinespeed unless the range of the exponent is also increased. Ifnumbers are assumed to be distributed in accordance with Sweeney's(1965) experiments, then severe loss of significance occurswith large probability in floating point subtraction. Theseresults have implications for computer design and lead to thesuggestion of a long word format which will reduce the risksto acceptable levels.     

MODELING THE DYNAMICS OF FISHERY STOCK RECOVERY: IMPLICATIONS FOR THE ASSESSMENT OF NATURAL RESOURCE DAMAGES

ABSTRACT. During the restoration planning phase of the natural resource damage assessment (NRDA) process, potential injuries to natural resources and services are evaluated in terms of the nature, degree and extent of injury so that the need for and scale of restoration actions can be ascertained. Injuries are quantified by comparing the condition of the injured natural resource relative to baseline (pre‐injury) conditions. The “Type A” procedures are used to quantify damages from smaller spills and rely on a standardized methodology and computer model to calculate injury and value of damages. In this model, fishery stock changes from injuries and resulting changes in user participation are not treated as dynamic. If true stock growth and re‐growth are indeed dynamic, then the Type A model is likely underestimating fishery losses. The purpose of this paper is to illustrate the potential for such underestimation by comparing simulated stock and harvest losses under dynamic treatment and a static treatment that more closely represents the way stock and service losses are estimated under the current NRDA process.     

An Information Theoretic Approach to Regulation Systems

Based on the work of Enegell(1985), a novel approach to theanalaysis of control systems by means of information-theoreticalconcepts is presented. Using results from rate-distortion theory,the requisite variety of the regulator necessary for a certianperformance is derived. This theory is used to analyse feedbackregulation systems, in particular, the Minimum Variance Controllaw for linear systems with a quadratic performance criterion.The main result of this paper has implications for the evaluationof L-bounds on analytic functions.     

AN ESR STUDY OF THE VISIBLE LIGHT PHOTOCHEMISTRY OF GILVOCARCIN V

Photolysis of gilvocarcin (GV) at 405 nm in argon saturated dimethylsulfoxide (DMSO) or 50% DMSO-water solutions in the presence of the sodium salt of 3,5-dibromo-2,6-dideutero-4-nitrosobenzene sulfonic acid (DBNBS-d2) generates the CH3-DBNBS-d2.spin adduct. It is postulated that this spin adduct is produced by photoreduction of DMSO by GV and the consequent formation and trapping of the generated methyl radicals. Gilvocarcin V also photoreduces oxygen and methyl viologen with quantum yields of 0.019 and 0.0012 respectively. The quantum yield for singlet oxygen formation by GV in DMSO, determined by measuring the rate of production of the nitroxyl radical produced by the reaction of 2,2,6,6-tetramethylpiperidinol with singlet oxygen, was found to be 0.15. Thus, GV photochemistry proceeds by both Type I and Type II pathways which could contribute to the reported GV phototoxicity in biological systems.     

CLEANING A RIVER: AN ANALYSIS OF VOLUNTARY JOINT ACTION

Abstract River pollution creates negative externalities to downstream water users. In this paper, we analyze how voluntary joint action of water users can improve pollution abatement when optimal treatment cannot be enforced. We model a transboundary pollution game with a unidirectional pollutant flow. Players are identical except for their location along the river. We find that, surprisingly, the location of coalition members has no impact on coalition stability. Location does, however, affect overall welfare. The more upstream the members of the coalition are, the higher is the overall welfare because the positive externalities of cleaning accrue to a larger number of downstream water users.     

Keith E. Gubbins: A celebration of statistical mechanics

We have used the density functional B3LYP method to study the effect of hydrogen bonds from the histidine ligand in various haem proteins to carboxyl groups or to the carbonyl backbone. Hydrogen bonds to carbonyl groups (encountered in globins and cytochromes, for example) have a small influence on the geometry and properties of the haem site. However, hydrogen bonds to a carboxyl group (encountered in peroxidases and haem oxidase) may have a profound effect. The results indicate that in the Fe³⁺ state, this leads to a deprotonation of the histidine ligand, whereas in the Fe²⁺ state, the proton involved in the hydrogen bond may reside on either histidine or the carboxylate group, depending on the detailed structure of the surroundings. If the histidine is deprotonated, the axial Fe-N bond length decreases by 0.15 Å, whereas the equatorial bond lengths increase. Moreover, the charge on iron and histidine is reduced, as is the spin density on iron. Most importantly, the energy difference between the high and intermediate spin states changes so that whereas the two spin states are degenerate in the Fe²⁺ state for the protonated histidine, they are degenerate for the Fe³⁺ state when it is deprotonated. This may facilitate the spin-forbidden binding of dioxygen and peroxide substrates, which takes place for the Fe²⁺ state in globins but in the Fe³⁺ state in peroxidases. The reduction potential of the haem group decreases when it hydrogen-bonds to a negatively charged group. The inner-sphere reorganization energy of the Fe²⁺/Fe³⁺ transition in a five-coordinate haem complex is ～30 kJ mol^?1, except when the histidine ligand is deprotonated without any hydrogen-bond interaction.     

Membrane capacitance: a non-local electroelastic treatment

The issue of membrane capacitance (C) is re-examined. The influence of fluctuations is studied using the non-local electroelastic model developed previously. The effect of undulations is compared with that due to voltage-induced thinning of the bilayer. It is shown that the undulatory contribution to the voltage dependence of C is significant at small surface tensions, but at higher tensions the role of compression becomes dominant. At all tensions, the effect of non-locality does not exceed 15–20% of the total undulatory contribution. The same results hold if ionic screening by the electrolyte (in a Poisson-Boltzmann approximation) is taken into consideration.     

THE INCOMPLETE‐INFORMATION SPLIT‐STREAM FISH WAR: EXAMINING THE IMPLICATIONS OF COMPETING RISKS

ABSTRACT. . It is now widely recognized that climactic regime shifts, which aperiodically alter a harvested fish stock's biomass and spatial distribution, may lead to distorted fisheries management decisions which negatively impact the fishery, both biologically and economically. This is particularly true for trans‐boundary migratory stocks, where optimal management relies on coordination among independent nation‐states. Unanticipated changes in stock distribution and abundance can upset expectations of national authorities, leading them to sanction inappropriate harvesting levels by their separately managed fleets targeting the same breeding fish stock. Our theoretical studies are based on a spatially‐distributed stochastic model, which we have called the “split‐stream model,‘ where two separately managed fleets harvest simultaneously at two separate sites. Our key assumption is that competing fleet managers, when harvesting noncooperatively, hold incomplete and asymmetric private information of current stock recruitment and spatial distribution. When subsequently negotiating to coordinate their harvests, they agree that they will share their information and then bargain over partition of the gains from their cooperation. This bargaining process takes into account the fleet's relative competitive strengths, particularly due to private information asymmetries. In this present article we introduce a more complex information structure than had been assumed in our earlier work (McKelvey and Golubtsov [2002], McKelvey, Miller and Golubtsov [2003], Mckelvey et al. [2004]). Specifically, both stock‐growth and stock‐split parameters vary stochastically and asynchronously. Thus, when harvesting noncooperatively, each fleet may possess private knowledge which is unavailable to the other. We examine the interplay of the harvesting game's information structure with other fishery characteristics, such as the fleets' economics and operating characteristics and their attitudes toward risk, to determine the implications of such structure for the outcome of the harvesting game. All of these changes are made to capture new conceptual phenomena and expand the range of applicability of the model.