Anisotropy in Inflation with Non-minimal Coupling

We study a new anisotropic inflation model, with an inflaton field nonminimally coupled with the gravity and a vector field. We find that the anisotropic attractor solution exists not only in the weak curvature coupling limit, but more interestingly in the strong curvature coupling limit as well. We show that in the strong curvature coupling limit, the contribution from the anisotropy is greatly suppressed.Comment: V2, 12 pages, 3 figures, numerical analysis adde

California Almond Yield Prediction at the Orchard Level With a Machine Learning Approach.

California's almond growers face challenges with nitrogen management as new legislatively mandated nitrogen management strategies for almond have been implemented. These regulations require that growers apply nitrogen to meet, but not exceed, the annual N demand for crop and tree growth and nut production. To accurately predict seasonal nitrogen demand, therefore, growers need to estimate block-level almond yield early in the growing season so that timely N management decisions can be made. However, methods to predict almond yield are not currently available. To fill this gap, we have developed statistical models using the Stochastic Gradient Boosting, a machine learning approach, for early season yield projection and mid-season yield update over individual orchard blocks. We collected yield records of 185 orchards, dating back to 2005, from the major almond growers in the Central Valley of California. A large set of variables were extracted as predictors, including weather and orchard characteristics from remote sensing imagery. Our results showed that the predicted orchard-level yield agreed well with the independent yield records. For both the early season (March) and mid-season (June) predictions, a coefficient of determination (R 2) of 0.71, and a ratio of performance to interquartile distance (RPIQ) of 2.6 were found on average. We also identified several key determinants of yield based on the modeling results. Almond yield increased dramatically with the orchard age until about 7 years old in general, and the higher long-term mean maximum temperature during April-June enhanced the yield in the southern orchards, while a larger amount of precipitation in March reduced the yield, especially in northern orchards. Remote sensing metrics such as annual maximum vegetation indices were also dominant variables for predicting the yield potential. While these results are promising, further refinement is needed; the availability of larger data sets and incorporation of additional variables and methodologies will be required for the model to be used as a fertilization decision support tool for growers. Our study has demonstrated the potential of automatic almond yield prediction to assist growers to manage N adaptively, comply with mandated requirements, and ensure industry sustainability

Optimality of Graphlet Screening in High Dimensional Variable Selection

Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row has relatively few large coordinates (diagonals of G are normalized to 1). The sparsity in G naturally induces the sparsity of the so-called graph of strong dependence (GOSD). We find an interesting interplay between the signal sparsity and the graph sparsity, which ensures that in a broad context, the set of true signals decompose into many different small-size components of GOSD, where different components are disconnected. We propose Graphlet Screening (GS) as a new approach to variable selection, which is a two-stage Screen and Clean method. The key methodological innovation of GS is to use GOSD to guide both the screening and cleaning. Compared to m-variate brute-forth screening that has a computational cost of p^m, the GS only has a computational cost of p (up to some multi-log(p) factors) in screening. We measure the performance of any variable selection procedure by the minimax Hamming distance. We show that in a very broad class of situations, GS achieves the optimal rate of convergence in terms of the Hamming distance. Somewhat surprisingly, the well-known procedures subset selection and the lasso are rate non-optimal, even in very simple settings and even when their tuning parameters are ideally set