We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates. We also address algorithmic issues, and describe the performance of a new computationally efficient test. This result is compared to a related hypothesis on the hardness of detecting satisfiability of...

In this lecture, we will perform a crude analysis of the performance of spectral partitioning algorithms in what are called stochastic block models or a planted partition model. The name you choose largely depends on your community and application. As we are especially interested today in partitioning, we will call it the planted partition model. In this model, we build a random graph that has ...

We study constraint satisfaction problems on the so-called planted random ensemble. We show that for a certain class of problems, e.g., graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the planted random ensemble. We study the structural phase transitions and the easy-hard-easy pattern in the average computational complexity. We also discuss th...

Ginkgo has been a mainstay of traditional Chinese medicine for more than 5000 years. Perhaps the ancient Taoist Monks had some vision of the future of Ginkgo as a brain and memory tonic when they planted it ceremonially in places of honor in their monasteries. They felt that this two lobed, fan-shaped leaf (biloba) represented the two phases of Yin and Yang in Taoist Philosophy. Ginkgo was plan...

Two soybean breeding lines (D82-2397A and J82-190) resistant to Heterodera glycines race 5 produced higher yields (P = 0.05) than the race 4-resistant cultivar Bedford for 2 years when planted in a field infested with H. glycines race 5 at Tiptonville, Tennessee. Yields were not different between D82-2397A and Bedford when planted in fields infested with race 3, race 9, or with no cyst nematode...

In this lecture we’ll explore Random Matrix Theory by exploring an application in network analysis. In particular, we’ll examine how Random Matrix Theory can be employed to develop an efficient randomized algorithm for finding planted cliques. In doing so, we will explore a general method for analyzing random graph problems with “planted” structure by treating them as a signal reconstruction pr...

A fundamental issue in clustering concerns one’s ability (and limitation) to detect clusters, assuming they are built-in to the model that generates the data [1, 4]. Results for the planted partition graph models suggest that clusters can be recovered with arbitrary accuracy if sufficient data (link density) is available [2]. More recently, this problem of cluster detectability has been address...

In the planted bisection model a random graph G(n, p+, p−) with n vertices is created by partitioning the vertices randomly into two classes of equal size (up to ±1). Any two vertices that belong to the same class are linked by an edge with probability p+ and any two that belong to different classes with probability p− < p+ independently. The planted bisection model has been used extensively to...

The authors attempted to estimate rice-planted areas using multi-temporal RADARSAT fine-mode and ERS1/SAR data in an early period of rice-planting season. The eastern part of Hiroshima City, HigashiHiroshima City, was selected as the test field, and three multi-temporal RADARSAT fine-mode images and ERS-1/SAR images, taken before and after rice-planting were used as the test data. From the firs...