1,657 research outputs found
Calogero-Moser systems and Hitchin systems
We exhibit the elliptic Calogero-Moser system as a Hitchin system of
G-principal Higgs pairs. The group G, though naturally associated to any root
system, is not semi-simple. We then interpret the Lax pairs with spectral
parameter of [dP1] and [BSC1] in terms of equivariant embeddings of the Hitchin
system of G into that of GL(N).Comment: 22 pages, Plain Te
Rank 2 Integrable Systems of Prym Varieties
A correspondence between 1) rank 2 completely integrable systems of Jacobians
of algebraic curves and 2) (holomorphically) symplectic surfaces was
established in a previous paper by the first author. A more general abelian
variety that occurs as a Liouville torus of integrable systems is a prym
variety associated to a triple (S,W,V) consisting of a curve S, a finite group
W of automorphisms of S and an integral representation V. Often W is a Weyl
group of a reductive group and V is the root lattice. We establish an analogous
correspondence between: i) Rank 2 integrable systems whose Liouville tori are
generalized prym varieties Prym(S_u,W,V) of a family of curves S_u, u in U. ii)
Varieties X of dimension 1+dim(V) with a W-action and an invariant V-valued
2-form. If V is one dimensional X is a symplectic surface. We obtain a rigidity
result: When the dimension of V is at least 2, under mild additional
assumptions, all the quotient curves are isomorphic to a fixed curve C.
This rigidity result imposes considerable constraints on the variety X: X
admits a W-invariant fibration to C and the generic fiber has an affine
structure modeled after V. Examples discussed include: Hitchin systems, reduced
finite dimensional coadjoint orbits of loop algebras, and principal bundles
over elliptic K3 surfaces.Comment: 53 page
Curve classes on irreducible holomorphic symplectic varieties
We prove that the integral Hodge conjecture holds for 1-cycles on irreducible
holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As
an application, we give a new proof of the integral Hodge conjecture for cubic
fourfolds.Comment: 15 page
Arbitrary finite intersections of doubling measures and applications
Using a wide array of machinery from diverse fields across mathematics, we
provide a construction of a measure on the real line which is doubling on all
-adic intervals for any finite list of , yet not doubling
overall. In particular, we extend previous results in the area, where only two
coprime numbers were allowed, by using substantially new ideas. In
addition, we provide several nontrivial applications to reverse H\"older
weights, weights, Hardy spaces, BMO and VMO function classes, and connect
our results with key principles and conjectures across number theory.Comment: 24 pages, 3 figure
Outcome of ATP-based tumor chemosensitivity assay directed chemotherapy in heavily pre-treated recurrent ovarian carcinoma
BACKGROUND: We wished to evaluate the clinical response following ATP-Tumor Chemosensitivity Assay (ATP-TCA) directed salvage chemotherapy in a series of UK patients with advanced ovarian cancer. The results are compared with that of a similar assay used in a different country in terms of evaluability and clinical endpoints. METHODS: From November 1998 to November 2001, 46 patients with pre-treated, advanced ovarian cancer were given a total of 56 courses of chemotherapy based on in-vitro ATP-TCA responses obtained from fresh tumor samples or ascites. Forty-four patients were evaluable for results. Of these, 18 patients had clinically platinum resistant disease (relapse < 6 months after first course of chemotherapy). There was evidence of cisplatin resistance in 31 patients from their first ATP-TCA. Response to treatment was assessed by radiology, clinical assessment and tumor marker level (CA 125). RESULTS: The overall response rate was 59% (33/56) per course of chemotherapy, including 12 complete responses, 21 partial responses, 6 with stable disease, and 15 with progressive disease. Two patients were not evaluable for response having received just one cycle of chemotherapy: if these were excluded the response rate is 61%. Fifteen patients are still alive. Median progression free survival (PFS) was 6.6 months per course of chemotherapy; median overall survival (OAS) for each patient following the start of TCA-directed therapy was 10.4 months (95% confidence interval 7.9-12.8 months). CONCLUSION: The results show similar response rates to previous studies using ATP-TCA directed therapy in recurrent ovarian cancer. The assay shows high evaluability and this study adds weight to the reproducibility of results from different centre
The blurring boundaries between synchronicity and asynchronicity:new communicative situations in work-related Instant Messaging
Instant messaging is one of the most popular communication technologies in virtual teams, enabling interactions to intertwine whole working days, thus creating the sense of copresence for team members who are geographically dispersed. Through close linguistic analyses of naturally occurring data from a virtual team, this article discusses the implications of two novel communicative situations enabled by instant messaging: presence information and the persistence of transcript. The preliminary findings of this study indicate that these new communicative situations require the flouting or rethinking of previously existing interactional norms and that communicative practices employed by the team members are not yet conventionalized/normalized, the expectations and interpretations of interactional rituals and timing vary highly, even within the same virtual team
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