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- Loic Giot, Joel S. Bader, +46 authors Jonathan Rothberg
- Science
- 2003

Drosophila melanogaster is a proven model system for many aspects of human biology. Here we present a two-hybrid-based protein-interaction map of the fly proteome. A total of 10,623 predicted transcripts were isolated and screened against standard and normalized complementary DNA libraries to produce a draft map of 7048 proteins and 20,405 interactions. Aâ€¦ (More)

- Maxim Braverman, OGNJEN MILATOVIC, Mikhail Shubin
- 2002

We obtain several essential self-adjointness conditions for the SchrÃ¶dinger type operator HV = D D + V , where D is a first order elliptic differential operator acting on the space of sections of a hermitian vector bundle E over a manifold M with positive smooth measure dÎ¼, and V is a Hermitian bundle endomorphism. These conditions are expressed in terms ofâ€¦ (More)

- Maxim Braverman
- 2008

We propose a refinement of the Ray-Singer torsion, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. Given a closed, oriented manifold of odd dimension with fundamental group Î“, the refined torsion is a complex valued, holomorphic function defined for representations of Î“ which are close to the spaceâ€¦ (More)

- Maxim Braverman
- 2008

Let D be a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Let v : M â†’ g = LieG be an equivariant map, such that the corresponding vector field on M does not vanish outside of a compact subset. These data define an element of K-theory of the transversal cotangent bundle to M . Hence, byâ€¦ (More)

- Maxim Braverman
- 1999

Let M be an oriented even-dimensional Riemannian manifold on which a discrete group Î“ of orientation-preserving isometries acts freely, so that the quotientX = M/Î“ is compact. We prove a vanishing theorem for a half-kernel of a Î“-invariant Dirac operator on a Î“-equivariant Clifford module overM , twisted by a sufficiently large power of a Î“-equivariant lineâ€¦ (More)

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are nondegenerate in the sense of R.Bott), and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismutâ€™s modification of the Witten deformation of the deâ€¦ (More)

- Maxim Braverman
- 2008

We introduce a new canonical trace on odd class logarithmic pseudo-differential operators on an odd dimensional manifold, which vanishes on a commutators. When restricted to the algebra of odd class classical pseudo-differential operators our trace coincides with the canonical trace of Kontsevich and Vishik. Using the new trace we construct a newâ€¦ (More)

We study the zeta-regularized determinant of a non self-adjoint elliptic operator on a closed odd-dimensional manifold. We show that, if the spectrum of the operator is symmetric with respect to the imaginary axis, then the determinant is real and its sign is determined by the parity of the number of the eigenvalues of the operator, which lie on theâ€¦ (More)

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that thisâ€¦ (More)

- Maxim Braverman
- 1998

Let X be a smooth projective variety acted on by a reductive group G. Let L be a positive G-equivariant line bundle over X. We use a Witten type deformation of the Dolbeault complex of L, introduced by Tian and Zhang, to show, that the cohomology of the sheaf of holomorphic sections of the induced bundle on the Mumford quotient of (X, L) is equal to theâ€¦ (More)