Functional linear regression that's interpretable

Regression models to relate a scalar $Y$ to a functional predictor $X(t)$ are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, $\beta(t)$, with $Y$ related to $X(t)$ through $\int\beta(t)X(t) dt$. Regions where $\beta(t)\ne0$ correspond to places where there is a relationship between $X(t)$ and $Y$. Alternatively, points where $\beta(t)=0$ indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of producing estimates of $\beta(t)$ that are exactly zero over regions with no apparent relationship and have simple structures over the remaining regions. Unfortunately, most fitting procedures result in an estimate for $\beta(t)$ that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this article we introduce a new approach which uses variable selection ideas, applied to various derivatives of $\beta(t)$, to produce estimates that are both interpretable, flexible and accurate. We call our method "Functional Linear Regression That's Interpretable" (FLiRTI) and demonstrate it on simulated and real-world data sets. In addition, non-asymptotic theoretical bounds on the estimation error are presented. The bounds provide strong theoretical motivation for our approach.Comment: Published in at http://dx.doi.org/10.1214/08-AOS641 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sparse regulatory networks

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses $L_1$ penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS350 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distributions

A key objective of the smart grid is to improve reliability of utility services to end users. This requires strengthening resilience of distribution networks that lie at the edge of the grid. However, distribution networks are exposed to external disturbances such as hurricanes and snow storms where electricity service to customers is disrupted repeatedly. External disturbances cause large-scale power failures that are neither well-understood, nor formulated rigorously, nor studied systematically. This work studies resilience of power distribution networks to large-scale disturbances in three aspects. First, a non-stationary random process is derived to characterize an entire life cycle of large-scale failure and recovery. Second, resilience is defined based on the non-stationary random process. Close form analytical expressions are derived under specific large-scale failure scenarios. Third, the non-stationary model and the resilience metric are applied to a real life example of large-scale disruptions due to Hurricane Ike. Real data on large-scale failures from an operational network is used to learn time-varying model parameters and resilience metrics.Comment: 11 pages, 8 figures, submitted to IEEE Sig. Pro

Plant preferential allocation and fungal reward decline with soil phosphorus: implications for mycorrhizal mutualism

Explaining the persistence of mutualism remains a challenge in ecology and evolutionary biology. The evolutionary stability of arbuscular mycorrhiza, a most widespread and ancient mutualistic association, is particularly intriguing because plants lack apparent mechanisms to prevent cheaters from gaining competitive advantages over cooperators. We developed a triple isotopic labeling method (14C, 32P, and 33P) within a split-root design to measure the exchange of carbon (C) and phosphorus (P) between the host plant and two mycorrhizal partners across a soil P gradient. Host plant preferentially allocated more C to the roots associated with the fungus delivering higher P per unit plant C, and the strength of preferential allocation decreased with increasing soil P availability. The host plant received more P per unit of allocated C from the better fungus and this advantageous exchange rate did not depend upon P availability. As a result, the level of preferential allocation was correlated with the differential delivery of P from the two fungi. Our findings suggest that plant preferential allocation to better mutualists can stabilize mutualisms in environments limiting in the traded resource, but as the availability of this resource increases, plant preferential allocation declines. This environmental dependence of preferential allocation generates predictions of declining levels in relative abundance of mutualistic fungi in high-resource environments

Adipocytes cause leukemia cell resistance to daunorubicin via oxidative stress response.

Adipocytes promote cancer progression and impair treatment, and have been shown to protect acute lymphoblastic leukemia (ALL) cells from chemotherapies. Here we investigate whether this protection is mediated by changes in oxidative stress. Co-culture experiments showed that adipocytes protect ALL cells from oxidative stress induced by drugs or irradiation. We demonstrated that ALL cells induce intracellular ROS and an oxidative stress response in adipocytes. This adipocyte oxidative stress response leads to the secretion of soluble factors which protect ALL cells from daunorubicin (DNR). Collectively, our investigation shows that ALL cells elicit an oxidative stress response in adipocytes, leading to adipocyte protection of ALL cells against DNR

An Experimental Syntactic Study of Binding: A Case Study of Korean Long-Distance Anaphor caki

PACLIC 23 / City University of Hong Kong / 3-5 December 200

The Impact of Research and Development on Economic Growth and Productivity in the US States

We estimate the impact of R&D on TFP and output in the private sector at the state level in the US from 1963 to 2007. R&D has a large effect on both output and TFP at the state level in the long run. The R&D elasticity in a state averages 0.056 to 0.143, implying returns to state GDP from R&D spending of 83% to 213%. There are also positive R&D spillovers, with 77% of the total returns accruing to other states. The R&D elasticities are either stable or increase slightly after 1993. The effects of R&D are dependent on the levels of human capital and development. States with more human capital have higher own- and other-R&D elasticities. States in the lowest tier of economic development have the least own-state R&D elasticity but the highest other-R&D elasticity. We discuss implications for policy in the US and in developing countries