Differential Game Theory Applied to a Model of the Arms Race

The arms race model of L. F. Richardson is considered within a differential game theoretic context. Five different approaches to the game are considered and the results compared. The particular model considered is a three nation arms race model which becomes a three player differential game. The five approaches to the game are the minimax, Nash, and Pareto approaches as well as two coalition approaches: C.P.O. (Coalitive Pareto Optimality) and N.C.O. (Nash Coalitive Optimality). Some suggestions are made for future research and some possible economic, social, and political implications of this work are considered.     

The flowing-afterglow technique,and approach to the study of polymer thermal degradation

We describe here a relatively new analytical method^1–3 for following the thermal reaction history of polymers by quantitatively detecting the evolution of gases and some volatiles by flowing-afterglow spectroscopy. The thermal and oxidative stability of common plastics in many industrial and defense applications is of wide interest. We have studied the evolution of moisture and carbon dioxide from Li₂CO₃/Orlon-filled diallyl phthalate (DAP) composites and have briefly examined the thermal stability of Estane 5703, a polyester-based thermoplastic polyurethane. The results of these preliminary studies have shown the utility of FLAG spectroscopy as a means toward our understanding polymer stability and lifetimes in specified environments. FLAG data, combined with differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) data, have extended our knowledge of Li₂CO₃/Orlon/DAP and Estane aging processes. The DAP composites evolve H₂O and CO₂ at near ambient temperatures, and we have described the kinetics of gas evolution and have attempted to describe the mechanism of thermal degradation. In the 25–120°C temperature range Estane 5703 evolves CO₂ as a decomposition product and some adsorbed moisture.     

Decision strategies that maximize the area under the LROC curve

For the 2-class detection problem (signal absent/present), the likelihood ratio is an ideal observer in that it minimizes Bayes risk for arbitrary costs and it maximizes the area under the receiver operating characteristic (ROC) curve [AUC]. The AUC-optimizing property makes it a valuable tool in imaging system optimization. If one considered a different task, namely, joint detection and localization of the signal, then it would be similarly valuable to have a decision strategy that optimized a relevant scalar figure of merit. We are interested in quantifying performance on decision tasks involving location uncertainty using the localization ROC (LROC) methodology. Therefore, we derive decision strategies that maximize the area under the LROC curve, A(LROC). We show that these decision strategies minimize Bayes risk under certain reasonable cost constraints. The detection-localization task is modeled as a decision problem in three increasingly realistic ways. In the first two models, we treat location as a discrete parameter having finitely many values resulting in an (L + 1) class classification problem. In our first simple model, we do not include search tolerance effects and in the second, more general, model, we do. In the third and most general model, we treat location as a continuous parameter and also include search tolerance effects. In all cases, the essential proof that the observer maximizes A(LROC) is obtained with a modified version of the Neyman-Pearson lemma. A separate form of proof is used to show that in all three cases, the decision strategy minimizes the Bayes risk under certain reasonable cost constraints.     

Heat-flow near a North Atlantic fracture zone

Fifteen new heat-flow measurements are reported, fourteen of which are located in or near a fracture zone near 43°N on the mid-Atlantic Ridge. These data, combined with earlier nearby measurements, show the fracture zone to have an observable, positive effect on the regional heat-flow field. A good correlation is observed between large near-bottom water potential temperature gradients and the occurrence of significant variations with depth in the measured rate of heat-flow. One measurement was taken in the Horseshoe abyssal plain west of Gibraltar and gave a value of 1.38 μcal/cm²s.     

Slip-System-Related Dislocation Study from <Emphasis Type="Italic">In-Situ</Emphasis> Neutron Measurements

A combined experimental/computational approach is employed to study slip-system-related dislocation-substructure formation during uniaxial tension of a single-phase, face-centered-cubic (fcc), nickel-based alloy. In-situ neutron-diffraction measurements were conducted to monitor the peak-intensity, peak-position, and peak-broadening evolution during a displacement-controlled, monotonic-tension experiment at room temperature. The measured lattice-strain evolution and the macrostress/macrostrain curves were used to obtain the material parameters required for simulating the texture development by a visco-plastic self-consistent (VPSC) model. The simulated texture compared favorably with experimentally-determined texture results over a range of 0 to 30 pct engineering strain. The grain-orientation-dependent input into the Debye-intensity ring was considered. Grains favorably oriented relative to the two detector banks in the geometry of the neutron experiment were indicated. For the favorably oriented grains, the simulated slip-system activity was used to calculate the slip-system-dependent, dislocation-contrast factor. The combination of the calculated contrast factor with the experimentally-measured peak broadening allows the assessment of the parameters of the dislocation arrangement within the specifically oriented grains, which has a quantitative agreement with the transmission-electron-microscopy results. This article is based on a presentation given in the symposium entitled “Neutron and X-Ray Studies for Probing Materials Behavior,” which occurred during the TMS Spring Meeting in New Orleans, LA, March 9–13, 2008, under the auspices of the National Science Foundation, TMS, the TMS Structural Materials Division, and the TMS Advanced Characterization, Testing, and Simulation Committee.

---

Verbal operant conditioning of hospitalized psychiatric patients.

In Exp. I, 81 male psychiatric patients were divided into 9 subgroups according to age and length of hospitalization. Plural nouns were reinforced by positive verbal feedback. Results were: (1) least chronic Ss increased their operant rates; (2) most chronic Ss did not; and (3) there was significant interaction with respect to age and chronicity. In Exp. II, 60 schizophrenics were divided into 6 subgroups with respect to length of hospitalization and mode of reinforcement, i.e., verbal, primary, or combination. Acute-type schizophrenics responded positively to all types of reinforcement. Chronics responded only to primary reinforcement and to the combination procedure. Mode of reinforcement was a significant variable affecting operant rate. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An information-theoretic approach to the written transmission of old English

Information theory offers a means for analyzing some constraints on the reading and copying process in Old English. Entropy for strings of various lengths offers a baseline measure of the uncertainty involved in transmission of Old English texts, while avoiding the pitfalls of applying models of modern reading to early medieval practice. Analysis of lengthy prose and verse texts in Old English revealed uniformly high values for entropy at all string lengths. High entropies may be the result of the language's irregular orthography, poetic koiné, and several dialects and imply that the language may have been easy to write but difficult to read. The low redundancy of the language which its high entropy values indicate suggests that the reader of Old English played an enhanced role in decoding a text and may provide an explanation for the high variability in the transmission of Old English verse.Katherine O'Brien O 'Keeffe is Professor of English at Texas A&M University and a co-director of its Interdisciplinary Group for Historical Literary Study.William Rundell is Professor of Mathematics at Texas A&M University.