Loop-fusion cohomology and transgression

`Loop-fusion cohomology' is defined on the continuous loop space of a manifold in terms of \vCech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that these cohomology groups, with coefficients in an abelian group, are isomorphic to those of the manifold and the transgression homomorphism factors through the isomorphism.Comment: 10 pages. v2 contains minor correction

Bigerbes

The bigerbes introduced here give a refinement of the notion of 2-gerbes, representing degree four integral cohomology classes of a space. Defined in terms of bisimplicial line bundles, bigerbes have a symmetry with respect to which they form 'bundle 2-gerbes' in two ways; this structure replaces higher associativity conditions. We provide natural examples, including a Brylinski-McLaughlin bigerbe associated to a principal G-bundle for a simply connected simple Lie group. This represents the first Pontryagin class of the bundle, and is the obstruction to the lifting problem on the associated principal bundle over the loop space to the structure group consisting of a central extension of the loop group; in particular, trivializations of this bigerbe for a spin manifold are in bijection with string structures on the original manifold. Other natural examples represent 'decomposable' 4-classes arising as cup products, a universal bigerbe on K(Z,4) involving its based double loop space, and the representation of any 4-class on a space by a bigerbe involving its free double loop space. The generalization to 'multigerbes' of arbitrary degree is also described.Comment: 56 pages. Version 2 includes the free loop version of the Brylinski-McLaughlin bigerbe and its relation to string structures, as well as a discussion of multigerbes of arbitrary orde

Comparison of Time Series and Random-Vibration Theory Site-Response Methods

The random-vibration theory (RVT) approach to equivalent-linear site-response analysis is often used to simulate site amplification, particularly when large numbers of simulations are required for incorporation into probabilistic seismic-hazard analysis. The fact that RVT site-response analysis does not require the specification of input-time series makes it an attractive alternative to other site-response methods. However, some studies have indicated that the site amplification predicted by RVT site-response analysis systematically differs from that predicted by time-series approaches. This study confirms that RVT site-response analysis predicts site amplification at the natural site frequencies as much as 20%-50% larger than time-series analysis, with the largest overprediction occurring for sites with smaller natural frequencies and sites underlain by hard rock. The overprediction is caused by an increase in duration generated by the site response, which is not taken into account in the RVT calculation. Correcting for this change in duration brings the RVT results within 20% of the time-series results. A similar duration effect is observed for the RVT shear-strain calculation used to estimate the equivalent-linear strain-compatible soil properties. An alternative to applying a duration correction to improve the agreement between RVT and time-series analysis is the modeling of shear-wave velocity variability. It is shown that introducing shear-wave velocity variability through Monte Carlo simulation brings the RVT results consistently within +/- 20% of the time-series results.Nuclear Regulatory Commission NRC-04-07-122Civil, Architectural, and Environmental Engineerin

An index theorem of Callias type for pseudodifferential operators

We prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic (scattering) metric, which have the form D + i \Phi, where D is elliptic pseudodifferential with Hermitian symbols, and \Phi is a Hermitian bundle endomorphism which is invertible at the boundary and commutes with the symbol of D there. The index of such operators is completely determined by the symbolic data over the boundary. We use the scattering calculus of R. Melrose in order to prove our results using methods of topological K-theory, and we devote special attention to the case in which D is a family of Dirac operators, in which case our theorem specializes to give families versions of the previously known index formulas.Comment: 18 pages, 1 figure. Revisions incorporated as suggested by referee report. To appear in the Journal of K-theor

„(Nie) trzymaj się ścieżki…” – przekształcenie baśni w thriller psychologiczny w grze komputerowej The Path

The aim of this paper is to prove that the narrative of the game The Path reverses the main properties of the fairy tale distinguished by the Russian structuralist Vladimir Propp. This results in the transformation of the game story’s genre from the fairy tale into that of the psychological thriller. The Russian scholar’s theory emphasises the role of characters of the narrative and their actions, which are significant components of the literary story, as well as the one that is told in the computer game. The study proves that the reversal of the functions and roles of dramatis personae in the game’s narrative results in the development of the elements characteristic for the psychological thriller in the game. The fact that this shift is fluent is an evidence that those two genres, although dissonant, have many common elements. The fairy tale and thriller are complementary – the latter reveals the hidden and suppressed aspects of the former.Celem artykułu jest próba analizy procesu transformacji baśni w thriller psychologiczny w grze komputerowej The Path. Punkt wyjścia do rozważań stanowi teoria strukturalna Vladimira Proppa, który poddał badaniom tradycyjne baśni, wyodrębniając ich elementy wspólne, takie jak funkcje i role postaci. Rosyjski strukturalista w swojej teorii jako kluczowe elementy opowieści uwypukla bohaterów i ich działania, istotne nie tylko z punktu widzenia teoretyków literatury, ale również badaczy podejmujących refleksję nad grami komputerowymi. Studium wykazuje, że funkcje i role bohaterów tradycyjnych baśni wyróżnione przez Proppa zostają w The Path zdeformowane: gra „schodzi” z wyznaczonej przez strukturę baśni ścieżki, tworząc lukę w gatunkowej przestrzeni, która zostaje wypełniona elementami właściwymi dla thrillera psychologicznego. Odwrócenie i deformacja funkcji oraz roli postaci baśniowych skutkuje przeobrażeniem opowiedzianej w grze historii w thriller. Owo przeobrażenie wydaje się niezwykle płynne dlatego, że baśń i thriller psychologiczny nie są całkowicie odmiennymi, wykluczającymi się gatunkami; przeciwnie – uzupełniają się wzajemnie. Drugi pokazuje i dopowiada to, co pierwszy przemilcza lub zataja