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FSTTCS
2009
Springer
14 years 10 days ago
The Power of Depth 2 Circuits over Algebras
We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (ΣΠΣ) arithmetic circuit...
Chandan Saha, Ramprasad Saptharishi, Nitin Saxena
CORR
2007
Springer
144views Education» more  CORR 2007»
13 years 5 months ago
Distributing the Kalman Filter for Large-Scale Systems
This paper derives a near optimal distributed Kalman filter to estimate a large-scale random field monitored by a network of N sensors. The field is described by a sparsely con...
Usman A. Khan, José M. F. Moura
COMBINATORICS
2006
221views more  COMBINATORICS 2006»
13 years 5 months ago
Kernels of Directed Graph Laplacians
Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D - Q, sometimes referred to as the directed Laplacian. ...
John S. Caughman IV, J. J. P. Veerman
CDC
2010
IEEE
172views Control Systems» more  CDC 2010»
12 years 9 months ago
Electrical centrality measures for electric power grid vulnerability analysis
— This paper investigates measures of centrality that are applicable to power grids. Centrality measures are used in network science to rank the relative importance of nodes and ...
Zhifang Wang, Anna Scaglione, Robert J. Thomas
FOCS
2006
IEEE
13 years 11 months ago
On a Geometric Generalization of the Upper Bound Theorem
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Uli Wagner