Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Inter-collisional cutting of multi-walled carbon nanotubes by high-speed agitation

ArticleJOURNAL OF PHYSICS AND CHEMISTRY OF SOLIDS. 69(10): 2481-2486 (2008)journal articl

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Machine speed scaling by adapting methods for convex optimization with submodular constraints

In this paper, we propose a new methodology for the speed-scaling problem based on its link to scheduling with controllable processing times and submodular optimization. It results in faster algorithms for traditional speed-scaling models, characterized by a common speed/energy function. Additionally, it efficiently handles the most general models with job-dependent speed/energy functions with single and multiple machines. To the best of our knowledge, this has not been addressed prior to this study. In particular, the general version of the single-machine case is solvable by the new technique in O(n2) time

Lower and upper probabilities in the distributive lattice of subsystems

yesThe set of subsystems ∑ (m) of a finite quantum system ∑(n) (with variables in Ζ(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the ℓ(m | ρn) = Tr ((m) ρn ) (where (m) is the projector to ∑(m)) obeys a supermodularity inequality, and it is interpreted as a lower probability in the sense of the Dempster–Shafer theory, and not as a Kolmogorov probability. It is shown that the basic concepts of the Dempster–Shafer theory (lower and upper probabilities and the Dempster multivaluedness) are pertinent to the quantum formalism of finite systems

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Cyclic AMP Control Measured in Two Compartments in HEK293 Cells: Phosphodiesterase KM Is More Important than Phosphodiesterase Localization

The intracellular second messenger cyclic AMP (cAMP) is degraded by phosphodiesterases (PDE). The knowledge of individual families and subtypes of PDEs is considerable, but how the different PDEs collaborate in the cell to control a cAMP signal is still not fully understood. In order to investigate compartmentalized cAMP signaling, we have generated a membrane-targeted variant of the cAMP Bioluminiscence Resonance Energy Transfer (BRET) sensor CAMYEL and have compared intracellular cAMP measurements with it to measurements with the cytosolic BRET sensor CAMYEL in HEK293 cells. With these sensors we observed a slightly higher cAMP response to adenylyl cyclase activation at the plasma membrane compared to the cytosol, which is in accordance with earlier results from Fluorescence Resonance Energy Transfer (FRET) sensors. We have analyzed PDE activity in fractionated lysates from HEK293 cells using selective PDE inhibitors and have identified PDE3 and PDE10A as the major membrane-bound PDEs and PDE4 as the major cytosolic PDE. Inhibition of membrane-bound or cytosolic PDEs can potentiate the cAMP response to adenylyl cyclase activation, but we see no significant difference between the potentiation of the cAMP response at the plasma membrane and in cytosol when membrane-bound and cytosolic PDEs are inhibited. When different levels of stimulation were tested, we found that PDEs 3 and 10 are mainly responsible for cAMP degradation at low intracellular cAMP concentrations, whereas PDE4 is more important for control of cAMP at higher concentrations

A Fluorescent Chromatophore Changes the Level of Fluorescence in a Reef Fish

Body coloration plays a major role in fish ecology and is predominantly generated using two principles: a) absorbance combined with reflection of the incoming light in pigment colors and b) scatter, refraction, diffraction and interference in structural colors. Poikilotherms, and especially fishes possess several cell types, so-called chromatophores, which employ either of these principles. Together, they generate the dynamic, multi-color patterns used in communication and camouflage. Several chromatophore types possess motile organelles, which enable rapid changes in coloration. Recently, we described red fluorescence in a number of marine fish and argued that it may be used for private communication in an environment devoid of red. Here, we describe the discovery of a chromatophore in fishes that regulates the distribution of fluorescent pigments in parts of the skin. These cells have a dendritic shape and contain motile fluorescent particles. We show experimentally that the fluorescent particles can be aggregated or dispersed through hormonal and nervous control. This is the first description of a stable and natural cytoskeleton-related fluorescence control mechanism in vertebrate cells. Its nervous control supports suggestions that fluorescence could act as a context-dependent signal in some marine fish species and encourages further research in this field. The fluorescent substance is stable under different chemical conditions and shows no discernible bleaching under strong, constant illumination