Abstract. We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice [4] on the average height of planted plane trees, and results by Fulmek [9] and Katori et al. [14] on the expected value, respectively higher moments, of the height distribution of watermelons...

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general. For the case when all edges in the MRF carry the same symmetric, doubly stochastic potential, recent works have proposed to approximate BP by linearizing th...

Seedling establishment and survival on the Savannah River Site in South Carolina is being monitored as part of the Pen Branch Bottomland Restoration Project. Bottomland tree species were planted fi-om 1993-1995 across a hydrologic gradient which encompasses the drier upper floodplain corridor, the lower floodplain corridor and the continuously inundated delta. Twelve species were planted in the...

Rice and wheat are mainly planted in a row structure in China. Radiative transfer models have the potential to provide an accurate description of the bidirectional reflectance characteristics of the canopies of row-planted crops, but few of them have addressed the problem of row-planted structures. In this paper, a new 4SAIL-RowCrop model for row-planted rice and wheat canopies was developed by...

We consider the problem of finding planted bicliques in random matrices over GF [q]. That is, our input matrix is a GF [q]-sum of an unknown biclique (rank-1 matrix) and a random matrix. We study different models for the random graphs and characterize the conditions when the planted biclique can be recovered. We also empirically show that a simple heuristic can reliably recover the planted bicl...

Less than 10% of Minnesota’s hardwood forests remain after heavy logging in the 19 and early 20 centuries. In order to ensure that this ecosystem continues to be a part of Minnesota’s natural history, forest managers have begun practicing active and passive restoration. The composition of a remnant forest, planted forest, and an adjacent old-field in the St. Olaf College Natural Lands, was anal...

In Washington, over fifty percent of the wheat produced under rainfed conditions receives less than 300 mm of annual precipitation. Hence, a winter wheat-summer fallow cropping system has been established to obtain adequate moisture for winter wheat production. Current tilled fallow systems receive significant soil erosion through both wind and water. As a result, no-till chemical fallow system...

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...

We give a lower bound of Ω̃( √ n) for the degree-4 Sum-of-Squares SDP relaxation for the planted clique problem. Specifically, we show that on an Erdös-Rényi graph G(n, 1 2 ), with high probability there is a feasible point for the degree-4 SOS relaxation of the clique problem with an objective value of Ω̃( √ n), so that the program cannot distinguish between a random graph and a random graph wit...

Recently, several papers proving lower bounds for the performance of the Sum Of Squares Hierarchy on the planted clique problem have been published. A crucial part of all four papers is probabilistically bounding the norms of certain “locally random” matrices. In these matrices, the entries are not completely independent of each other, but rather depend upon a few edges of the input graph. In t...