McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, i.e. locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large deviation principle is also derived for the McKean-Vlasov stochastic equations under those weak assumptions. The wide applications of main results are illustrated by various concrete examples such as the Granular media equations, Kinetic equations, distribution dependent porous media equations and Navier-Stokes equations, moreover, we could remove or relax some typical assumptions previously imposed on those models.Comment: 53 page

Like-sign Di-lepton Signals in Higgsless Models at the LHC

We study the potential LHC discovery of the Z1 KK gauge boson unitarizing longitudinal W+W- scattering amplitude. In particular, we explore the decay mode Z1->t tbar along with Z1-> W+W- without specifying the branching fractions. We propose to exploit the associated production pp-> W Z1, and select the final state of like-sign dileptons plus multijets and large missing energy. We conclude that it is possible to observe the Z1 resonance at a 5 sigma level with an integrated luminosity of 100 inverse fb at the LHC upto 650 GeV for a dominant WW channel, and 560 GeV for a dominant ttbar channel.Comment: 13 pages, 7 figure

Hidden Trends in 90 Years of Harvard Business Review

In this paper, we demonstrate and discuss results of our mining the abstracts of the publications in Harvard Business Review between 1922 and 2012. Techniques for computing n-grams, collocations, basic sentiment analysis, and named-entity recognition were employed to uncover trends hidden in the abstracts. We present findings about international relationships, sentiment in HBR's abstracts, important international companies, influential technological inventions, renown researchers in management theories, US presidents via chronological analyses.Comment: 6 pages, 14 figures, Proceedings of 2012 International Conference on Technologies and Applications of Artificial Intelligenc

Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbour interactions

By using the method of density-matrix renormalization-group to solve the different spin-spin correlation functions, the nearest-neighbouring entanglement(NNE) and next-nearest-neighbouring entanglement(NNNE) of one-dimensional alternating Heisenberg XY spin chain is investigated in the presence of alternating nearest neighbour interactions of exchange couplings, external magnetic fields and next-nearest neighbouring interactions. For dimerized ferromagnetic spin chain, NNNE appears only above the critical dimerized interaction, meanwhile, the dimerized interaction effects quantum phase transition point and improves NNNE to a large value. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighboring (NNN) interactions on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks NNE below and above critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always decreases NNE. The antiferromagnetic NNN interaction results to a larger value of NNNE in comparison to the case when the NNN interaction is ferromagnetic.Comment: 13 pages, 4 figures,. accepted by Chinese Physics B 2008 11 (in press