Determining the dimension of iterative Hessian transformation

The central mean subspace (CMS) and iterative Hessian transformation (IHT) have been introduced recently for dimension reduction when the conditional mean is of interest. Suppose that X is a vector-valued predictor and Y is a scalar response. The basic problem is to find a lower-dimensional predictor \eta^TX such that E(Y|X)=E(Y|\eta^TX). The CMS defines the inferential object for this problem and IHT provides an estimating procedure. Compared with other methods, IHT requires fewer assumptions and has been shown to perform well when the additional assumptions required by those methods fail. In this paper we give an asymptotic analysis of IHT and provide stepwise asymptotic hypothesis tests to determine the dimension of the CMS, as estimated by IHT. Here, the original IHT method has been modified to be invariant under location and scale transformations. To provide empirical support for our asymptotic results, we will present a series of simulation studies. These agree well with the theory. The method is applied to analyze an ozone data set.Comment: Published at http://dx.doi.org/10.1214/009053604000000661 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Idiopathic head tremor in english bulldogs

Idiopathic head tremor (IHT) syndrome is a recognized but poorly characterized movement disorder in English bulldogs (EBs). The data analyzed were collected via a detailed online questionnaire and video recordings. Thirty-eight percent of the population demonstrated IHT. The first presentation was early in life. There was no sex or neutered status predisposition. The condition disappeared with time in 50% of the cases. The direction of the head movement was vertical or horizontal. The number of episodes per day and the duration of the episodes were greatly variable. The majority of episodes occurred at rest. Most of the episodes were unpredictable. And there was no alteration of the mental status for most dogs during the episodes. Stress has been reported as a suspected trigger factor. IHT in EBs can be considered an idiopathic paroxysmal movement disorder

Effects of Isometric Handgrip Training in Patients With Peripheral Artery Disease: A Randomized Controlled Trial

BackgroundMeta‐analyses have shown that isometric handgrip training (IHT) can reduce brachial systolic and diastolic blood pressure (BP) by >6/4 mm Hg, respectively. However, whether IHT promotes these effects among patients with peripheral artery disease, who exhibit severe impairment in cardiovascular function, is currently unknown. This study aimed to evaluate the effects of IHT on the cardiovascular function of patients with peripheral artery disease. Methods and ResultsA randomized controlled trial with peripheral artery disease patients assigned to either the IHT or control group was conducted. The IHT group performed 3 sessions per week, for 8 weeks, of unilateral handgrip exercises, consisting of 4 sets of isometric contractions for 2 minutes at 30% of maximum voluntary contraction and a 4‐minute interval between sets. The control group received a compression ball in order to minimize the placebo effects, representing sham training. The primary outcome was brachial BP. The secondary outcomes were central BP, arterial stiffness parameters, cardiac autonomic modulation, and vascular function. The IHT program reduced diastolic BP (75 [10] mm Hg preintervention versus 72 [11] mm Hg postintervention), with no change in the control group (74 [11] mm Hg preintervention versus 74 [11] mm Hg postintervention), with this between‐group difference being significant (P=0.04). Flow‐mediated dilation improved in the IHT group (6.0% [5.7] preintervention versus 9.7% [5.5] postintervention), with no change in the control group (7.6% [5.5] preintervention versus 7.4% [5.1] postintervention), with this between‐group difference being significant (P=0.04). There was no change in other measured variables over the intervention period. ConclusionsIHT reduced brachial diastolic BP and improved local vascular function in patients with peripheral artery disease

Distributed Sparse Signal Recovery For Sensor Networks

We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naive distributed implementation of IHT would require global communication of every agent's full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the best-known distributed basis pursuit method

Localized shocks

We study products of precursors of spatially local operators, $W_{x_{n}}(t_{n}) ... W_{x_1}(t_1)$, where $W_x(t) = e^{-iHt} W_x e^{iHt}$. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in $t$. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.Comment: 23 pages plus appendices, 12 figures. v2: minor error in Appendix B corrected. v3: figure added to the introduction comparing the butterfly effect cone with the standard light con