1,446 research outputs found
Holomorphic symplectic geometry: a problem list
A list of open problems on holomorphic symplectic, contact and Poisson
manifolds
The Syntax of Korean Anaphora
From the earliest work on anaphora in transformational grammar, it has been assumed that the principles governing the organization of pronoun-antecedent'. relationships make reference to abstract features of structure. Accordingly, attempts to characterize the syntax of anaphora have exploited concepts ranging from command (Langacker 1966) and the cycle (Ross 1969) to K-command (Lasnik 1976), c-command (Reinhart 1981) and governing category (Chomsky 1981). In recent work (e.g., O'Grady 1983a, b), I have suggested that this type of approach is ill conceived and that the syntax of pronoun-antecedent relations can be better analyzed in terms of the interaction between word order and a single semantic contrast. The purpose of this paper is to show that the Korean anaphoric elements ku and caki lend themselves to a similar analysis
Modelling and analyzing adaptive self-assembling strategies with Maude
Building adaptive systems with predictable emergent behavior is a challenging task and it is becoming a critical need. The research community has accepted the challenge by introducing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. We recently proposed a conceptual framework for adaptation centered around the role of control data. In this paper we show that it can be naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model. Moreover, we exploit this model to specify and analyse a prominent example of adaptive system: robot swarms equipped with obstacle-avoidance self-assembly strategies. The analysis exploits the statistical model checker PVesta
On the Rozansky-Witten weight systems
Ideas of Rozansky and Witten, as developed by Kapranov, show that a complex
symplectic manifold X gives rise to Vassiliev weight systems. In this paper we
study these weight systems by using D(X), the derived category of coherent
sheaves on X. The main idea (stated here a little imprecisely) is that D(X) is
the category of modules over the shifted tangent sheaf, which is a Lie algebra
object in D(X); the weight systems then arise from this Lie algebra in a
standard way. The other main results are a description of the symmetric
algebra, universal enveloping algebra, and Duflo isomorphism in this context,
and the fact that a slight modification of D(X) has the structure of a braided
ribbon category, which gives another way to look at the associated invariants
of links. Our original motivation for this work was to try to gain insight into
the Jacobi diagram algebras used in Vassiliev theory by looking at them in a
new light, but there are other potential applications, in particular to the
rigorous construction of the (1+1+1)-dimensional Rozansky-Witten TQFT, and to
hyperkaehler geometry
Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type
Let X be a compact Kahler holomorphic-symplectic manifold, which is
deformation equivalent to the Hilbert scheme of length n subschemes of a K3
surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L)
vanishes and c_1(L) is primitive. Assume that the two dimensional subspace
H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex
coefficients, intersects trivially the integral cohomology. We prove that the
linear system of L is base point free and it induces a Lagrangian fibration on
X. In particular, the line-bundle L is effective. A determination of the
semi-group of effective divisor classes on X follows, when X is projective. For
a generic such pair (X,L), not necessarily projective, we show that X is
bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion
sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated
improvement to the exposition and corrected typos according to the referees
suggestions. To appear in the proceedings of the conference Algebraic and
Complex Geometry, Hannover 201
Feasibility of using microbeads with holographic barcodes to track DNA specimens in the clinical molecular laboratory
We demonstrate the feasibility of using glass microbeads with a holographic barcode identifier to track DNA specimens in the molecular pathology laboratory. These beads can be added to peripheral blood specimens and are carried through automated DNA extraction protocols that use magnetic glass particles. We found that an adequate number of microbeads are consistently carried over during genomic DNA extraction to allow specimen identification, that the beads do not interfere with the performance of several different molecular assays, and that the beads and genomic DNA remain stable when stored together under regular storage conditions in the molecular pathology laboratory. The beads function as an internal, easily readable specimen barcode. This approach may be useful for identifying DNA specimens and reducing errors associated with molecular laboratory testing
Symplectic involutions on deformations of K3^[2]
Let X be a Hyperk\"{a}hler variety deformation equivalent to the Hilbert
square on a K3 surface and let f be an involution preserving the symplectic
form. We prove that the fixed locus of f consists of 28 isolated points and 1
K3 surface, moreover the anti-invariant lattice of the induced involution on
H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting
of one such variety and a symplectic involution on it can be deformed into a
couple consisting of the Hilbert square of a K3 surface and the involution
induced by a Nikulin involution on the K3 surface.Comment: Final version, to appear on Central European Journal of Mathematic
- …