BGG resolutions via configuration spaces

We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik-Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the sl_2 Bernstein - Gelfand - Gelfand resolution as an Aomoto complex.Comment: Latex, 19 page

A2(2)A_{2}^{(2)} Gaudin model and its associated Knizhnik-Zamolodchikov equation

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.Comment: 20 pages,no figure, typos corrected, LaTe

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces

We show that the Hirzebruch-Milnor class of a projective hypersurface, which gives the difference between the Hirzebruch class and the virtual one, can be calculated by using the Steenbrink spectra of local defining functions of the hypersurface if certain good conditions are satisfied, e.g. in the case of projective hyperplane arrangements, where we can give a more explicit formula. This is a natural continuation of our previous paper on the Hirzebruch-Milnor classes of complete intersections.Comment: 15 pages, Introduction is modifie

The narrative self, distributed memory, and evocative objects

In this article, I outline various ways in which artifacts are interwoven with autobiographical memory systems and conceptualize what this implies for the self. I first sketch the narrative approach to the self, arguing that who we are as persons is essentially our (unfolding) life story, which, in turn, determines our present beliefs and desires, but also directs our future goals and actions. I then argue that our autobiographical memory is partly anchored in our embodied interactions with an ecology of artifacts in our environment. Lifelogs, photos, videos, journals, diaries, souvenirs, jewelry, books, works of art, and many other meaningful objects trigger and sometimes constitute emotionally-laden autobiographical memories. Autobiographical memory is thus distributed across embodied agents and various environmental structures. To defend this claim, I draw on and integrate distributed cognition theory and empirical research in human-technology interaction. Based on this, I conclude that the self is neither defined by psychological states realized by the brain nor by biological states realized by the organism, but should be seen as a distributed and relational construct

A millisecond pulsar in a stellar triple system

Gravitationally bound three-body systems have been studied for hundreds of years and are common in our Galaxy. They show complex orbital interactions, which can constrain the compositions, masses, and interior structures of the bodies and test theories of gravity, if sufficiently precise measurements are available. A triple system containing a radio pulsar could provide such measurements, but the only previously known such system, B1620-26 (with a millisecond pulsar, a white dwarf, and a planetary-mass object in an orbit of several decades), shows only weak interactions. Here we report precision timing and multi-wavelength observations of PSR J0337+1715, a millisecond pulsar in a hierarchical triple system with two other stars. Strong gravitational interactions are apparent and provide the masses of the pulsar (1.4378(13) Msun, where Msun is the solar mass and the parentheses contain the uncertainty in the final decimal places) and the two white dwarf companions (0.19751(15) Msun and 0.4101(3) Msun), as well as the inclinations of the orbits (both approximately 39.2 degrees). The unexpectedly coplanar and nearly circular orbits indicate a complex and exotic evolutionary past that differs from those of known stellar systems. The gravitational field of the outer white dwarf strongly accelerates the inner binary containing the neutron star, and the system will thus provide an ideal laboratory in which to test the strong equivalence principle of general relativity.Comment: 17 pages, 3 figures, 1 table. Published online by Nature on 5 Jan 2014. Extremely minor differences with published version may exis

Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems

We work out finite-dimensional integral formulae for the scalar product of genus one states of the group $G$ Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians building up the connection and quantizing the quadratic Hamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil

Heisenberg realization for U_q(sln) on the flag manifold

We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the $U_q(\widehat{sl_n})$ [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a reference added

Critical points and resonance of hyperplane arrangements

If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the resonance of y. For arrangements satisfying certain conditions, we show that if y is resonant in dimension p, then the critical set of F has codimension at most p. These include all free arrangements and all rank 3 arrangements.Comment: revised version, Canadian Journal of Mathematics, to appea

Cell transformation assays for prediction of carcinogenic potential: State of the science and future research needs

Copyright @ 2011 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.Cell transformation assays (CTAs) have long been proposed as in vitro methods for the identification of potential chemical carcinogens. Despite showing good correlation with rodent bioassay data, concerns over the subjective nature of using morphological criteria for identifying transformed cells and a lack of understanding of the mechanistic basis of the assays has limited their acceptance for regulatory purposes. However, recent drivers to find alternative carcinogenicity assessment methodologies, such as the Seventh Amendment to the EU Cosmetics Directive, have fuelled renewed interest in CTAs. Research is currently ongoing to improve the objectivity of the assays, reveal the underlying molecular changes leading to transformation and explore the use of novel cell types. The UK NC3Rs held an international workshop in November 2010 to review the current state of the art in this field and provide directions for future research. This paper outlines the key points highlighted at this meeting