Now the wars are over: The past, present and future of Scottish battlefields

Battlefield archaeology has provided a new way of appreciating historic battlefields. This paper provides a summary of the long history of warfare and conflict in Scotland which has given rise to a large number of battlefield sites. Recent moves to highlight the archaeological importance of these sites, in the form of Historic Scotland’s Battlefields Inventory are discussed, along with some of the problems associated with the preservation and management of these important cultural sites

Measurements of aerosol properties needed to infer backscatter characteristics in support of the NASA Doppler Lidar program

During the first year two areas of work were emphasized, analysis of aerosol data to provide improved estimates of backscatter over the Pacific ocean and development of a global model for backscatter at different wavelengths and preparation and planning for the aircraft flights of the GLOVE program. Significant progress was made in each of these areas. The analytical work is a continuation of the GAMETAG analysis, and was directed toward the development of a backscatter model for the Pacific Oceanic free troposphere. This has included a further evaluation of relationships between the optical effects at different wavelengths, a comparison of modeled optical effects at differing temporal resolutions, and an investigation of the effects of sampling on the modeled results. An initial investigation of the predictability of 9 to 10 micrometers Beta values from other data sets as well as some preliminary comparisons of the modeling results with experimental data. The comparison of the optical effects was extended to make the comparisons for different sets of time bases between 1 and 20 minutes

Inclusion of Experimental Information in First Principles Modeling of Materials

We propose a novel approach to model amorphous materials using a first principles density functional method while simultaneously enforcing agreement with selected experimental data. We illustrate our method with applications to amorphous silicon and glassy GeSe$_2$. The structural, vibrational and electronic properties of the models are found to be in agreement with experimental results. The method is general and can be extended to other complex materials.Comment: 11 pages, 8 PostScript figures, submitted to J. Phys.: Condens. Matter in honor of Mike Thorpe's 60th birthda

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Molecular Model of the Contractile Ring

We present a model for the actin contractile ring of adherent animal cells. The model suggests that the actin concentration within the ring and consequently the power that the ring exerts both increase during contraction. We demonstrate the crucial role of actin polymerization and depolymerization throughout cytokinesis, and the dominance of viscous dissipation in the dynamics. The physical origin of two phases in cytokinesis dynamics ("biphasic cytokinesis") follows from a limitation on the actin density. The model is consistent with a wide range of measurements of the midzone of dividing animal cells.Comment: PACS numbers: 87.16.Ka, 87.16.Ac http://www.ncbi.nlm.nih.gov/pubmed/16197254 http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2005.pd

V605 Aql: The Older Twin of Sakurai's Object

New optical spectra have been obtained with VLT/FORS2 of the final helium shell flash (FF) star, V605 Aql, which peaked in brightness in 1919. New models suggest that this star is experiencing a very late thermal pulse. The evolution to a cool luminous giant and then back to a compact hot star takes place in only a few years. V605 Aql, the central star of the Planetary Nebula (PN), A58, has evolved from T$_{eff}\sim$5000 K in 1921 to $\sim$95,000 K today. There are indications that the new FF star, Sakurai's Object (V4334 Sgr), which appeared in 1996, is evolving along a similar path. The abundances of Sakurai's Object today and V605 Aql 80 years ago mimic the hydrogen deficient R Coronae Borealis (RCB) stars with 98% He and 1% C. The new spectra show that V605 Aql has stellar abundances similar to those seen in Wolf-Rayet [WC] central stars of PNe with ~55% He, and ~40% C. The stellar spectrum of V605 Aql can be seen even though the star is not directly detected. Therefore, we may be seeing the spectrum in light scattered around the edge of a thick torus of dust seen edge-on. In the present state of evolution of V605 Aql, we may be seeing the not too distant future of Sakurai's Object.Comment: 12 pages, 1 figure, ApJ Letters in pres

Ergodicity, Decisions, and Partial Information

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that one may choose (under a mild integrability assumption) a decision strategy whose pathwise time-average loss is asymptotically smaller than that of any other strategy. The corresponding problem in the case of partial information proves to be much more delicate, however: if the process X is not observable, but decisions must be based on the observation of a different process Y, the existence of pathwise optimal strategies is not guaranteed. The aim of this paper is to exhibit connections between pathwise optimal strategies and notions from ergodic theory. The sequential decision problem is developed in the general setting of an ergodic dynamical system (\Omega,B,P,T) with partial information Y\subseteq B. The existence of pathwise optimal strategies grounded in two basic properties: the conditional ergodic theory of the dynamical system, and the complexity of the loss function. When the loss function is not too complex, a general sufficient condition for the existence of pathwise optimal strategies is that the dynamical system is a conditional K-automorphism relative to the past observations \bigvee_n T^n Y. If the conditional ergodicity assumption is strengthened, the complexity assumption can be weakened. Several examples demonstrate the interplay between complexity and ergodicity, which does not arise in the case of full information. Our results also yield a decision-theoretic characterization of weak mixing in ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page