On construction of optimal mixed-level supersaturated designs

Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing $E(f_{\mathrm{NOD}})$- and $\chi^2$-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.Comment: Published in at http://dx.doi.org/10.1214/11-AOS877 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of product rate in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.Comment: 19 pages, 10 figure

Approximation algorithms for kk-submodular maximization subject to a knapsack constraint

In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the non-monotone case, we are the first to consider the knapsack problem and provide a greedy-type combinatorial algorithm with approximation ratio $\frac{1}{3}(1-e^{-3})\approx 0.317$

Spectral tracing of deuterium for imaging glucose metabolism.

Cells and tissues often display pronounced spatial and dynamical metabolic heterogeneity. Common glucose-imaging techniques report glucose uptake or catabolism activity, yet do not trace the functional utilization of glucose-derived anabolic products. Here we report a microscopy technique for the optical imaging, via the spectral tracing of deuterium (STRIDE), of diverse macromolecules derived from glucose. Based on stimulated Raman-scattering imaging, STRIDE visualizes the metabolic dynamics of newly synthesized macromolecules, such as DNA, protein, lipids and glycogen, via the enrichment and distinct spectra of carbon-deuterium bonds transferred from the deuterated glucose precursor. STRIDE can also use spectral differences derived from different glucose isotopologues to visualize temporally separated glucose populations using a pulse-chase protocol. We also show that STRIDE can be used to image glucose metabolism in many mouse tissues, including tumours, brain, intestine and liver, at a detection limit of 10 mM of carbon-deuterium bonds. STRIDE provides a high-resolution and chemically informative assessment of glucose anabolic utilization