Definition 1. Riemannian gradient The Riemannian gradient ∇f(U) of f at point U ∈ Od is the matrix UΩ, where Ω ∈ Skew(d), Ωji = −Ωij = ∇ijf(U), 1 ≤ i < j ≤ d is the directional derivative as defined in Eq. 1 of the main text, and Ωii = 0. The norm of the Riemannian gradient ||∇f(U)|| = Tr(∇f(U)∇f(U) ) = ||Ω||fro. Definition 2. A point U∗ ∈ Od is asymptotically stable with respect to Algorithm 1...

A quantitative theory of directional mutation pressure proposed in 1962 explained the wide variation of DNA base composition observed among different bacteria and its small heterogeneity within individual bacterial species. The theory was based on the assumption that the effect of mutation on a genome is not random but has a directionality toward higher or lower guanine-plus-cytosine content of...

We propose to study a novel pharmacovigilance problem for mining directional effects of high-order drug interactions on an adverse drug event (ADE). Our goal is to estimate each individual risk of adding a new drug to an existing drug combination. In this proof-of-concept study, we analyzed a large electronic medical records database and extracted myopathy-relevant case control drug co-occurren...

In general the audible sound has the characteristics of spreading, however the ultrasound is directional. This study used amplitude-modulating technique for an array of 8 ultrasonic transducers to produce directional audible sound beam. In this study sound field distribution for the directional audible sound beam has been investigated. The effect of different weightings varied with different fr...

directional simulation, among techniques for reliability analysis of engineering structures, is well known. in this context, directional simulation in load space, because of the considerable advantages of lower dimension of working space, is of considerable interest. as is expected due to structural resistance variability, the location of the relevant limit state(s) is no longer constant and mu...

1. A model for retinal directional selectivity postulates that GABAergic inhibition of responses to motions in the null (anti-preferred) direction underlies this selectivity. An alternative model postulates that besides this inhibition, there exists an asymmetric, nicotinic acetylcholine (ACh) input from starburst amacrine cells. It is possible for the latter but not the former model that stimu...

The dynamics of a spontaneous downconversion process with the idler mode coupled to an auxiliary mode is analysed. Depending on the presence or absence of nonlinear phase mismatch, a Zeno or anti–Zeno effect is found. This behavior is understood by using the dressed modes picture of the device. A possibility to achieve a quasi–phase– matching by careful adjustment of coupling strength is pointe...

Directional water transport fabrics can proactively transfer moisture from the body. They show great potential in making sportswear and summer clothing. While moisture transfer has been previously reported, heat transfer in directional water transport fabrics has been little reported in research literature. In this study, a directional water transport fabric was prepared using an electrosprayin...

Herein we demonstrate that switchable, spontaneous, directional-transport ability to both water and oil fluids can be created on fabric materials through wet-chemistry coating and successive UV irradiation treatment. When the fabric showed directional transport to a liquid, it prevented liquids of higher surface tension from penetration, but allowed liquids of lower surface tension to permeate,...