Inspection games in arms control

An inspection game is a mathematical model of a situation in which an inspector verifies the adherence of an inspectee to some legal obligation, such as an arms control treaty, where the inspectee may have an interest in violating that obligation. The mathematical analysis seeks to determine an optimal inspection scheme, ideally one which will induce legal behavior, under the assumption that the potential illegal action is carried out strategically; thus a non-cooperative game with two players, inspector and inspectee, is defined. Three phases of development in the application of such models to arms control and disarmament may be identified. In the first of these, roughly from 1961 through 1968, studies that focused on inspecting a nuclear test ban treaty emphasized game theory, with less consideration given to statistical aspects associated with data acquisition and measurement uncertainty. The second phase, from 1968 to about 1985, involves work stimulated by the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). Here, the verification principle of material accountancy came to the fore, along with the need to include the formalism of statistical decision theory within the inspection models. The third phase, 1985 to the present, has been dominated by challenges posed by such far-reaching verification agreements as the Intermediate Range Nuclear Forces Agreement (INF), the Treaty on Conventional Forces in Europe (CFE) and the Chemical Weapons Convention (CWC), as well as perceived failures of the NPT system in Iraq and North Korea. In this connection, the interface between the political and technical aspects of verification is being examined from the game-theoretic viewpoint.     

The game for the speed of convergence in repeated games of incomplete information

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value v _∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to v _∞ (p) (and will converge from above to v _∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payoffs-to the value v _∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG _∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v _n (p)− v _∞ (p) is of the order of magnitude of . In that case the value of SG _∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛^∞={X _k }^∞ _k=1, one defines for each n : V _n (𝔛^∞) ≔E∑ⁿ _k=1 |X _k+1 − X _k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛^∞, V _n (𝔛^∞) can be of the order of magnitude of n ^1/2−ε, for arbitrarily small ε>0. Received January 1999/Final version April 2002     

Study of ion–solvent interactions and activation energy of LiBr in DMSO,H<Subscript>2</Subscript>O and DMSO–H<Subscript>2</Subscript>O mixtures at various temperatures

The Jones–Dole B coefficients of the electrolyte Lithium bromide (LiBr), reference salts tetra butyl ammonium tetra phenyl borate (BU₄NBPh₄), tetra butyl ammonium bromide (BU₄NBr), and potassium chloride (KCl) in dimethylsulfoxide (DMSO), water, and DMSO–water mixtures were obtained at different temperatures range from 25 to 45 °C For this, the relative viscosities were measured for Lithium bromide (LiBr) and reference salts in DMSO, water, and DMSO–water mixtures at above-mentioned temperatures. The B coefficients of these electrolytes were behaved as structure makers in DMSO, while in H₂O and DMSO–H₂O mixtures, the B-coefficient values were less positive showing the weak structure-making effect. Ionic viscosity B coefficients allow us to assess the behavior of ions in the solvent mixtures. In this study it was observed that all the values of ionic B coefficient of (Li⁺) were positive and small showing the weak structure-making effects. It was also observed that Br⁻ ions maintain negative B coefficient values in all DMSO–H₂O mixtures, except in 60% DMSO mole fraction. From this it can be concluded that Br⁻ ion behaved as a structure breaker in water and in all DMSO–H₂O mixtures except in 60% DMSO mole fraction mixtures. The low B _± values of alkali metal ions and Br⁻ ions in water are due to the breakdown of the tetrahedral structural of water and the formation of strongly structured solvated ion. It is also observed that the values of the energy of activation of the flow for LiBr are greater in DMSO–water mixtures and in pure water than in DMSO. This may be due the presence of a network of hydrogen bonds which cause the hindrance in the flow of the solution of LiBr in DMSO–water mixtures and in pure water than in DMSO.     

5-epi-Canadensene and other novel metabolites of Taxus canadensis

The Canadian yew distinguishes itself from other yews by the nature of its taxane metabolites. We are now reporting a new canadensene taxane whose stereochemistry is rigorously established. The three-dimensional structures of canadensene, 5-epi-canadensene and three other related bicyclic taxanes isolated from other yews were calculated using distance constraints derived from NMR data. The stereochemistry of the substituents, the polar acetate groups and the double bonds determine the 3D models. In addition, three new taxanes were also characterized and some biosynthetic speculations are presented.     

A duality theorem on a pair of simultaneous functional equations

Given P and Q convex compact sets in R^kandR^s, respectively, and u a continuous real valued function on P × Q, we consider the following pair of dual problems: Problem I—Minimize ? so that ?: $\text{P × Q → R}\text{and}\text{? ?}\text{Cav}{}_{\mathrm{p}}\text{Vex}{}_{\mathrm{q}}\text{×}\text{max}\text{(u, ?)}$. Problem II—Maximize g so that g: P × Q → R and g ? Vex_q × Cav_pmin(u, g). Here Cav_p is the operation of concavification of a function with respect to the variable p?P (for each fixed q?Q). Similarly, Vex_q is the operation of convexification with respect to q?Q. Maximum and minimum are taken here in the partial ordering of pointwise comparison: $\text{? ? g}\text{means}\text{?(p, q) ? g(p, q) ?(p, q) ? P × Q}$. It is proved here that both problems have the same solution which is also the unique simultaneous solution of the following pair of functional equations: (i) $\text{? =}\text{Vex}{}_{\mathrm{q}}\text{max}\text{(u, ?)}$. (ii) $\text{? =}\text{Cav}{}_{\mathrm{p}}\text{min}\text{(u, ?)}$. The problem arises in game theory, but the proof here is purely analytical and makes no use of game-theoretical concepts.     

Identification of a novel protein regulating microtubule stability through a chemical approach

To identify novel proteins regulating the microtubule cytoskeleton, we screened a library of purine derivatives using mitotic spindle assembly in Xenopus egg extracts as an assay. Out of a collection of 1561 compounds, we identified 15 that destabilized microtubules without targeting tubulin directly, resulting in small spindles. Affinity chromatography with one compound, named diminutol, revealed a potential target as NQO1, an NADP-dependent oxidoreductase. A role for NQO1 in influencing microtubule polymerization was confirmed through inhibition studies using known inhibitors and immunodepletion. Therefore, this chemical approach has identified a novel factor required for microtubule morphogenesis and cell division.     

Methyl 4-Carbomethoxy-3-Hydroxy-5-Methyl-Phenyl-Acetoacetate from the Disilylated Dianion of Methyl Acetoacetate

Recently, Chaley and Chan¹ reported a novel synthesis of methyl olivetolate (3a) from the annelation of 1,3-bis(trimethylsiloxy)-1-methoxybuta-1,3-diene (1) with the acid chloride 2a and titanium tetrachloride at room temperature. In view of their success, we attempted to apply this methodology for a convenient synthesis of isotopically labelled orsellinic acid in order to unravel its biosynthesis to cyclopentanoids.     

Formulation of Bayesian analysis for games with incomplete information

A formal model is given of Harsanyi's infinite hierarchies of beliefs. It is shown that the model closes with some Bayesian game with incomplete information, and that any such game can be approximated by one with a finite number of states of world.     

NMR study of solid and liquid aluminium

Knight shift and spin-lattice relaxation were accurately measured in solid and liquid aluminium from room temperature to 1100°C. The Knight shift in the solid exhibits a strong explicit temperature dependence. K(a), the reciprocal enhancement factor of the Korringa relation, is found to be temperature dependent, an effect which is unaccounted for by the present methods of calculating the susceptibility.