The Triangle Operator

We examine the averaging operator corresponding to the manifold in $\mathbb{R}^{2d}$ of pairs of points $(u,v)$ satisfying $|u| = |v| = |u - v| = 1$, so that $\{0,u,v\}$ is the set of vertices of an equilateral triangle. We establish $L^p \times L^q \rightarrow L^r$ boundedness for $T$ for $(1/p, 1/q, 1/r)$ in the convex hull of the set of points $\lbrace (0, 0, 0) ,\, (1, 0 , 1) ,\, (0, 1, 1) , \, ({1}/{p_d}, {1}/{p_d}, {2}/{p_d}) \rbrace$, where $p_d = \frac{5d}{3d - 2}$.Comment: 15 pages, discussion on the maximal variant expande

Self alignment techniques for strapdown inertial navigation systems with aircraft application

Self alignment techniques for strapdown inertial navigation systems for commercial aircraf

Trunk muscle activity during drop jump performance in adolescent athletes with back pain

It was with great interest we read the recently published article “Trunk Muscle Activity during Drop Jump Performance in Adolescent Athletes with Back Pain.” Investigating back pain (BP) in adolescents is commendable as there is growing evidence that for many, an experience of BP as early as 14 years of age may relate to ongoing pain in adulthood (Coenen et al., 2017). Indeed, the conventional narrative is changing as individual physical factors such as posture, use of schoolbags, and hypermobility are only weakly associated with adolescent BP. Rather, factors which predict BP at a young age are considered to be multi-dimensional and include gender, negative BP beliefs and poor mental health (O\u27Sullivan et al., 2017; Smith et al., 2017). Mueller et al. (2017) have focused on a single physical factor (trunk muscle activation patterns) drawing inferences regarding BP prevention and treatment. This article prompts consideration of three essential aspects regarding research design and interpretation of findings: 1. Interpreting results from cross-sectional designs 2. Interpreting pain-related differences in motor behavior 3. Translating and conveying scientific results to the end-user (patients, healthcare professionals and policy makers)

Consistent and High Rates of Gene Transfer Can Be Obtained Using Flow-Through Transduction over a Wide Range of Retroviral Titers

Overview summary Flow-through transduction provides a means by which high rates of gene transfer can occur without using high titers of virus vector. Reproducibly high numbers of transduced cells can be obtained with a wide range of virus titers, thus relaxing the requirement of set (high) titers within a transduction protocol. Incorporating flow-through transductions within clinical applications of gene therapy may also obviate the need for large volumes of high-titer virus produced by vector producer cell line cultures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63214/1/hum.1996.7.6-743.pd

Structural Kinetic Modeling of Metabolic Networks

To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit kinetic modeling based on differential equations is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a detailed and quantitative account of the dynamical capabilities of metabolic systems, without requiring any explicit information about the particular functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible, or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a systematic statistical exploration of the comprehensive parameter space. The method is applied to two paradigmatic examples: The glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.Comment: 14 pages, 8 figures (color