624 research outputs found
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
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 R-matrix. We find the spectra and eigenvectors of the
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 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 , which
is written by the -difference operator on the flag manifold. We construct it
from the action of on the -symmetric algebra by the
Borel-Weil like approach. Our realization is applicable to the construction of
the free field realization for the [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
- …