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Semantic enrichment of textual data is the operation of linking mentions 1 with the entities they refer to, and the subsequent enrichment of such entities with the background knowledge about them available in one or more knowledge bases (or in the entire web). Information about the context in which a mention occurs, (e.g., information about the time, the(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract We consider the nonlinear stochastic heat equation in one dimension. Under some conditions on the nonlinearity, we show that the "peaks" of the solution are rare, almost fractal like. We also provide an upper bound on the length of the "islands", the regions of large values. These results are(More)
  • Nicos Georgiou, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu
  • 2015
Consider an infinite system ∂tut(x) = (L ut)(x) + σ(ut(x))∂tBt(x) of interacting Itô diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity σ. We will show that, locally in time, the solution behaves as a collection of(More)
We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat(More)
  • Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu, Academica Sinica
  • 2012
We consider a family of nonlinear stochastic heat equations of the form ∂tu = Lu + σ(u) ˙ W , where ˙ W denotes space-time white noise, L the generator of a symmetric Lévy process on R, and σ is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure u0. Tight a priori bounds on the(More)
— Visual sensing for robotics has been around for decades, but our understanding of a timing model remains crude. By timing model, we refer to the delays (processing lag and motion lag) between " reality " (when a part is sensed), through data processing (the processing of image data to determine part position and orientation), through control (the(More)
The recent outburst of context-dependent knowledge on the Semantic Web (SW) has led to the realization of the importance of the quads in the SW community. Quads, which extend a standard RDF triple, by adding a new parameter of the 'context' of an RDF triple, thus informs a reasoner to distinguish between the knowledge in various contexts. Although this(More)