Game interpretation of Kolmogorov complexity

The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation and showing that all "natural" properties are either true for all sufficiently powerful oracles or false for all sufficiently powerful oracles. This result is a simple consequence of Martin's determinacy theorem, but its proof is instructive: it shows how one can prove statements about Kolmogorov complexity by constructing a special game and a winning strategy in this game. This technique is illustrated by several examples (total conditional complexity, bijection complexity, randomness extraction, contrasting plain and prefix complexities).Comment: 11 pages. Presented in 2009 at the conference on randomness in Madison

Minimum energy path for the nucleation of misfit dislocations in Ge/Si(001) heteroepitaxy

A possible mechanism for the formation of a 90{\deg} misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial state and a final state with a 90{\deg} misfit dislocation is found using the nudged elastic band method. The initial path is generated using a repulsive bias activation procedure in a model system including 75000 atoms. The energy along the path exhibits two maxima in the energy. The first maximum occurs as a 60{\deg} dislocation nucleates. The intermediate minimum corresponds to an extended 60{\deg} dislocation. The subsequent energy maximum occurs as a second 60{\deg} dislocation nucleates in a complementary, mirror glide plane, simultaneously starting from the surface and from the first 60{\deg} dislocation. The activation energy of the nucleation of the second dislocation is 30% lower than that of the first one showing that the formation of the second 60{\deg} dislocation is aided by the presence of the first one. The simulations represent a step towards unraveling the formation mechanism of 90{\deg} dislocations, an important issue in the design of growth procedures for strain released Ge overlayers on Si(100) surfaces, and more generally illustrate an approach that can be used to gain insight into the mechanism of complex nucleation paths of extended defects in solids

Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace

We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the calculation. Performing the calculation through three loops yields the equations of motion up to five derivatives on the fieldstrengths, which upon integration gives the bosonic sector of the effective action for a single D-brane in trivial bulk background fields through four derivatives and to all orders in alpha'. Finally, the present calculation shows that demanding ultra-violet finiteness of the non-linear sigma-model can be reformulated as the requirement that the background is a deformed stable holomorphic U(1) bundle.Comment: 25 pages, numerous figure

Global standards of Constitutional law : epistemology and methodology

Just as it led the philosophy of science to gravitate around scientific practice, the abandonment of all foundationalist aspirations has already begun making political philosophy into an attentive observer of the new ways in which constitutional law is practiced. Yet paradoxically, lawyers and legal scholars are not those who understand this the most clearly. Beyond analyzing the jurisprudence that has emerged from the expansion of constitutional justice, and taking into account the development of international and regional law, the ongoing globalization of constitutional law requires comparing the constitutional laws of individual nations. Following Waldron, the product of this new legal science can be considered as ius gentium. This legal science is not as well established as one might like to think. But it can be developed on the grounds of the practice that consists in ascertaining standards. As abstract types of best “practices” (and especially norms) of constitutional law from around the world, these are only a source of law in a substantive, not a formal, sense. They thus belong to what I should like to call a “second order legal positivity.” In this article I will undertake, both at a methodological and an epistemological level, the development of a model for ascertaining global standards of constitutional law

Mapping Local Climate Zones for a Worldwide Database of the Form and Function of Cities

Progress in urban climate science is severely restricted by the lack of useful information that describes aspects of the form and function of cities at a detailed spatial resolution. To overcome this shortcoming we are initiating an international effort to develop the World Urban Database and Access Portal Tools (WUDAPT) to gather and disseminate this information in a consistent manner for urban areas worldwide. The first step in developing WUDAPT is a description of cities based on the Local Climate Zone (LCZ) scheme, which classifies natural and urban landscapes into categories based on climate-relevant surface properties. This methodology provides a culturally-neutral framework for collecting information about the internal physical structure of cities. Moreover, studies have shown that remote sensing data can be used for supervised LCZ mapping. Mapping of LCZs is complicated because similar LCZs in different regions have dissimilar spectral properties due to differences in vegetation, building materials and other variations in cultural and physical environmental factors. The WUDAPT protocol developed here provides an easy to understand workflow; uses freely available data and software; and can be applied by someone without specialist knowledge in spatial analysis or urban climate science. The paper also provides an example use of the WUDAPT project results

Formation and evolution of cosmic D-strings

We study the formation of D and F-cosmic strings in D-brane annihilation after brane inflation. We show that D-string formation by quantum de Sitter fluctuations is severely suppressed, due to suppression of RR field fluctuations in compact dimensions. We discuss the resonant mechanism of production of D and F-strings, which are formed as magnetic and electric flux tubes of the two orthogonal gauge fields living on the world-volume of the unstable brane. We outline the subsequent cosmological evolution of the D-F string network. We also compare the nature of these strings with the ordinary cosmic strings and point out some differences and similarities.Comment: Added discussion and reference

WUDAPT: Facilitating advanced urban canopy modeling for weather, climate and air quality applications

Environmental issues and impacts to society will be exacerbated with increased population, diminishing resources and the prospects for extreme weather events and climate changes. Current community-based models available for weather, climate and air quaity applications are powerful state-of-science modeling systems, which, with careful considerations, can be employed to address the impact of these issues fo urban areas. Given the complex and high degree of spatial inhomogeneity of the underlying surface area we will review mesh size, appropriate multi-scale science and morphological descriptions and their data requirements including unique city specific gridded morphology and material composition for their forecasting and climate applications. For this presentation, we discuss, describe and show examples from an ongoing but preliminary prototypic collaborative effort, whose design bases is to provide the experience and recommendations toward extending the scope of the National Urban Database and Access Portal Tools (NUDAPT) to worldwide coverage (WUDAPT). WUDAPT would thus provide requisite gridded data for urban applications of advanced forecast and climate models throughout the world. Strategically, the prototypic efforts will be designed to provide proven protocols for the facilitaton of the data gathering and processing based on available remote sensing and ground-based sampling. Tactically, we employ an iterative approach first obtaining coarse gridded Local Climate Zone (LCZ) classification derived from available Web-based products such as Google-Earth, and Landsat satellite magery. Further sub-class discretization of LCZs and the application of GeoWiki technology facilitates further refinements and ground truthing to yield the desired gridded building morphological distribution parameters and their material composition. Local experts would be encouraged to become involved to ensure factors unique to their area in the world would be incorporated. Finally, given that model applications may require data with different grid resolution we present an outline that employs the new and powerful Multiple Resolution Analyses scheme that can address this need within the scope of WUDAPT

Freak observers and the measure of the multiverse

I suggest that the factor $p_j$ in the pocket-based measure of the multiverse, $P_j=p_j f_j$, should be interpreted as accounting for equilibrium de Sitter vacuum fluctuations, while the selection factor $f_j$ accounts for the number of observers that were formed due to non-equilibrium processes resulting from such fluctuations. I show that this formulation does not suffer from the problem of freak observers (also known as Boltzmann brains).Comment: 6 pages, no figures; references adde