In this paper we consider imprecise terrains, that is, triangulated terrains with a vertical error interval in the vertices. In particular, we study the problem of removing as many local extrema (minima and maxima) as possible from the terrain. We show that removing only minima or only maxima can be done optimally in O(n log n) time, for a terrain with n vertices. Interestingly, however, removi...

In the analysis of dynamic financial quantities such as stock prices, equity prices, etc., reasonable results are often obtained if we only consider local maxima (“peaks”) and local minima (“troughs”) and ignore all the other values. The empirical success of this strategy remains a mystery. In this paper, we provide a possible explanation for this success. 1 Formulation of the Problem Peak-and-...

In [40], it was shown that the following singularly perturbed Dirichlet problem 2∆u− u+ |u|p−1u = 0, in Ω, u = 0 on ∂Ω has a nodal solution u which has the least energy among all nodal solutions. Moreover, it is shown that u has exactly one local maximum point P 1 with a positive value and one local minimum point P 2 with a negative value and, as → 0, φ(P 1 , P 2 ) → max (P1,P2)∈Ω×Ω φ(P1, P2), ...

Abstract In this paper we describe I-Subdue, an extension to the Subdue graph-based data mining system. I-Subdue operates over sequentially received relational data to incrementally discover the most representative substructures. The ability to incrementally refine discoveries from serially acquired data is important for many applications, particularly as computer systems become more integrated...

Proof of Proposition 1: The off-equilibrium path beliefs imply that any price offer below M(w) is definitely rejected, and any price offer above M(w̄) is definitely accepted. Any price offer v between M(w) and M(w̄) leads F to believe that w = M−1(v), and he is indifferent between accepting and rejecting it, making it optimal for him to randomize his acceptance decision. Finally, when the randomi...

We show that two popular discounted reward natural actor-critics, NAC-LSTD and eNAC, follow biased estimates of the natural policy gradient. We derive the first unbiased discounted reward natural actor-critics using batch and iterative approaches to gradient estimation and prove their convergence to globally optimal policies for discrete problems and locally optimal policies for continuous prob...