Quiet Planting in the Locked Constraint Satisfaction Problems

We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and first and second moment considerations; in particular the connection with the reconstruction on trees appears to be crucial. Our main result is the location of the hard region in the planted ensemble. In a part of that hard region instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio

Optimal Testing for Planted Satisfiability Problems

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 of detection. Our analysis relies on the study of the number of satisfying assignments, for which we prove new results. We also address algorithmic issues, and give a computationally efficient test with optimal statistical performance. This result is compared to an average-case hypothesis on the hardness of refuting satisfiability of random formulas

Parallel Tempering for the planted clique problem

The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard method for the analysis of disordered models, the Parallel-Tempering (PT) algorithm, to the clique problem, showing numerically that its time-scaling in the hard region is indeed polynomial for the analyzed sizes. We also apply PT to a different but connected model, the Sparse Planted Independent Set problem. In this situation thresholds should be sharper and finite size corrections should be less important. Also in this case PT shows a polynomial scaling in the hard region for the recovery.Comment: 12 pages, 5 figure

Cereal Leaf Beetle (Coleoptera: Chrysomelidae) Influence of Seeding Rate of Oats on Populations

In field and greenhouse studies, more cereal leaf beetle [Oulema melanopus (Lin- naeus)] eggs and larvae were found per unit area on spring oats, Avena sativa L., planted either at intermediate (54 kg/ha) or high (136 kg/ha) seeding rates, than when planted at a lower seeding rate (14 kg/ha). However, there were fewer eggs and larvae per stem in plantings of the high or intermediate rates than in those of the lower rate. Oats should not be planted at less than the recommended rates in beetle-infested areas

When do two planted graphs have the same cotransversal matroid?

Cotransversal matroids are a family of matroids that arise from planted graphs. We prove that two planted graphs give the same cotransversal matroid if and only if they can be obtained from each other by a series of local moves.Comment: 12 pages, 7 figures; expository change

Tightness of the maximum likelihood semidefinite relaxation for angular synchronization

Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it recovers the true MLE. Most tightness proofs only apply to situations where the MLE exactly recovers a planted solution (known to the analyst). It is then sufficient to establish that the optimality conditions hold at the planted signal. In this paper, we study an estimation problem (angular synchronization) for which the MLE is not a simple function of the planted solution, yet for which the convex relaxation is tight. To establish tightness in this context, the proof is less direct because the point at which to verify optimality conditions is not known explicitly. Angular synchronization consists in estimating a collection of $n$ phases, given noisy measurements of the pairwise relative phases. The MLE for angular synchronization is the solution of a (hard) non-bipartite Grothendieck problem over the complex numbers. We consider a stochastic model for the data: a planted signal (that is, a ground truth set of phases) is corrupted with non-adversarial random noise. Even though the MLE does not coincide with the planted signal, we show that the classical semidefinite relaxation for it is tight, with high probability. This holds even for high levels of noise.Comment: 2 figure

Effect of Growing Season on Growth and Relation of Height and Above Ground Biomass of Avicennia Marina

Relation of height of seedling stands and above ground biomass is an important indicator of successful stand establishment and effectivity of carbon cycle which requires further study. This research aimed to study the growth level of Avicennia marina seedling planted in dry season and rainy season and to analyze the relation of mangrove stand height to above ground biomass of seedling for each season. This research was conducted through field experiment involving grouped random design including group of seedling plantation in dry season and rainy season with 40 replication for each group and 6 months of experiment period. Data collection including stand height above ground biomass, followed by data analysis on the relation of seedling height and above ground biomass. The result showed that the growth of mangrove stand planted in rainy season was better than those planted on dry season. Average height of mangrove Avicennia marina stand planted in dry season was 30,5 ± 7,3 cm while stand height of mangrove planted in rainy season was 42,7 ± 11,4 cm. Above ground biomass data showed the average of 4,1 ± 1,8 gr in the dry season treatment group and 6,6 ± 2,5 gr in the rainy season treatment group. Regression analysis on the relation of stand height and above ground biomass of Avicennia marina seedling showed that the above ground biomass was significantly affected by stand height both for dry season and rainy season treatments. But, there was a difference on the determination index and the coefficient of the effect on each treatment groups. The relation of stand height and above ground biomass was Y = 0.1871 X0.8832 with R2 = 0.2802 for the dry season group and Y = 0.0506 X1.2892 with R2 = 0.743 for the rainy season group.