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Analysis of explicit tau-leaping schemes for simulating chemically reacting systems
- Multiscale Model. Simul
"... Abstract. This paper builds a convergence analysis of explicit tau-leaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with state-dependent intensity. The stochast ..."
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Cited by 28 (6 self)
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Abstract. This paper builds a convergence analysis of explicit tau-leaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with state-dependent intensity. The stochastic differential equation form of the chemical master equation can be given via Poisson random measures. Based on this form, different types of tau-leaping schemes can be proposed. In order to make the problem well-posed, a modified explicit tau-leaping scheme is considered. It is shown that the mean square strong convergence is of order 1/2 and the weak convergence is of order 1 for this modified scheme. The novelty of the analysis is to handle the non-Lipschitz property of the coefficients and jumps on the integer lattice.
Degree Fluctuations and the Convergence Time of Consensus Algorithms
, 2012
"... We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus i ..."
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Cited by 6 (0 self)
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We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus is achieved within a given accuracy ɛ on n nodes in time B+4n3Bln(2n/ɛ). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give a simple proof of a result of Cao, Spielman, and Morse that the worst case convergence time becomes exponentially large in the number of nodes n under slight relaxation of the degree constancy assumption.
Liouville properties of plurisubharmonic functions
"... §0 Introduction. In this paper we will prove a Liouville theorem on smooth plurisubharmonic functions on a complete noncompact Kähler manifold with nonnegative bisectional curvature. Using this Liouville theorem we prove a splitting theorem for such manifolds as well as a gap theorem in terms of the ..."
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Cited by 4 (0 self)
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§0 Introduction. In this paper we will prove a Liouville theorem on smooth plurisubharmonic functions on a complete noncompact Kähler manifold with nonnegative bisectional curvature. Using this Liouville theorem we prove a splitting theorem for such manifolds as well as a gap theorem in terms of the curvature decay of such a manifold.
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, 2013
"... Measurement of heavy flavor electron flow in Au + Au collisions at sqrt(sNN) = 62.4 GeV ..."
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Measurement of heavy flavor electron flow in Au + Au collisions at sqrt(sNN) = 62.4 GeV
Ferromagnetism in a Realistic Two-Band Model: ∗ A Slave-Boson Study
, 2001
"... Using a slave boson representation of multi-band Hubbard models, we investigate a two-band model relevant to layered perovskites in the vicinity of half-filling. Beside the strong influence of the Hund’s rule coupling, we obtain that the phase diagram separates into two regions: a weak to moderate c ..."
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Using a slave boson representation of multi-band Hubbard models, we investigate a two-band model relevant to layered perovskites in the vicinity of half-filling. Beside the strong influence of the Hund’s rule coupling, we obtain that the phase diagram separates into two regions: a weak to moderate coupling region where the effective mass is weakly renormalized, and a strong coupling regime where it is strongly renormalized. The transition between these two regimes is very sharp. It takes place in a (vanishingly) small domain. A ferromagnetic instability in only found in the strongly correlated regime, and is triggered by the Hund’s rule coupling. The results are compared to La-doped layered ruthenates. PACS numbers: 71.10.Fd, 71.30.h, 74.70.Pq, 75.30.Kz. 1.
1Degree Fluctuations and the Convergence Time of Consensus Algorithms
"... We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus i ..."
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We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus is achieved within a given accuracy on n nodes in time B+4n3Bln(2n/). Because there is a direct relation between consensus algorithms in time-varying environments and inhomogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give a simple proof of a result of Cao, Spielman, and Morse that the worst case convergence time becomes exponentially large in the number of nodes n under slight relaxation of the degree constancy assumption. I.
