Distributed Lagrangian Methods for Network Resource Allocation

Motivated by a variety of applications in control engineering and information sciences, we study network resource allocation problems where the goal is to optimally allocate a fixed amount of resource over a network of nodes. In these problems, due to the large scale of the network and complicated inter-connections between nodes, any solution must be implemented in parallel and based only on local data resulting in a need for distributed algorithms. In this paper, we propose a novel distributed Lagrangian method, which requires only local computation and communication. Our focus is to understand the performance of this algorithm on the underlying network topology. Specifically, we obtain an upper bound on the rate of convergence of the algorithm as a function of the size and the topology of the underlying network. The effectiveness and applicability of the proposed method is demonstrated by its use in solving the important economic dispatch problem in power systems, specifically on the benchmark IEEE-14 and IEEE-118 bus systems

On the convergence rate of distributed gradient methods for finite-sum optimization under communication delays

Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems, due to the large scale of the data sets, the data and computation must be distributed over processors resulting in the need for distributed algorithms. In this paper, we consider a popular distributed gradient-based consensus algorithm, which only requires local computation and communication. An important problem in this area is to analyze the convergence rate of such algorithms in the presence of communication delays that are inevitable in distributed systems. We prove the convergence of the gradient-based consensus algorithm in the presence of uniform, but possibly arbitrarily large, communication delays between the processors. Moreover, we obtain an upper bound on the rate of convergence of the algorithm as a function of the network size, topology, and the inter-processor communication delays

Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays

This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled systems with time-varying delays. Next, we obtain the necessary and sufficient criteria which characterize the positivity of a mixed-order delay linear coupled system. Our main contribution is in Section 5. More precisely, by using a smoothness property of solutions to fractional differential equations and developing a new appropriated comparison principle for solutions to mixed-order delayed positive systems, we prove the attractivity of mixed-order non-homogeneous linear positive coupled systems with bounded or unbounded delays. We also establish a necessary and sufficient condition to characterize the stability of homogeneous systems. As a consequence of these results, we show the smallest asymptotic bound of solutions to mixed-order delay non-homogeneous linear positive coupled systems where disturbances are continuous and bounded. Finally, we provide numerical simulations to illustrate the proposed theoretical results

Direct measurements of DOCO isomers in the kinetics of OD+CO

Quantitative and mechanistically-detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analogue deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real-time, the branching and isomerization kinetics and absolute yields of all species in the OD+CO reaction are quantified as a function of pressure and collision partner.Comment: 19 pages, 4 figure

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Postharvest loss in the supply chain for vegetables – The case of chili and tomato in Viet Nam

AVRDC Publication 06-685Christian Genova II, Katinka Weinberger, Hoang Bang An, Dang Dinh Dam, Nguyen Thi Tan Loc, Le Nhu Thinh, Nguyen Thi Thanh Thu

Temperature-dependent magnetic particle imaging with multi-harmonic lock-in detection

Advances in instrumentation and tracer materials are still required to enable sensitive and accurate 3D temperature monitoring by magnetic particle imaging. We have developed a magnetic particle imaging instrument to observe temperature variations using MPI, and discuss resolution dependence on temperature and harmonic number. Furthermore, we present a low noise approach using lock-in detection for temperature measurement, and discuss implications for a new detection modality of MPI.Comment: 26 pages, 17 figure

Application of internal transcribed spacer (ITS) sequences for identifying Anoectochilus setaceus Blume in Thanh Hoa, Vietnam

Background. The term “DNA barcode” is used extensively in molecular taxonomy. Basically, this technique is based on the use of a DNA sequence (about 400–800 bp) as a standard to identify and determine the species relation of organisms quickly and accurately. Therefore, DNA barcodes not only help taxonomists in classifying and identifying species, but also improve their ability to control, understand and utilize biodiversity. In this study, the authors conducted identification of samples of Anoectochilus setaceus Blume collected in Thanh Hoa through the isolated sequence of ITS gene regions.Materials and methods. Total DNA was extracted from young leaves of A. setaceus samples using CTAB method. The ITS gene segment was amplified by PCR and sequenced. This genetic sequence was analyzed, compared and used to establish a phylogenetic tree using BioEdit, BLAST and DNASTAR programs.Results and conclusion. We isolated 4 sequences of the ITS gene region in 4 A. setaceus samples collected at Xuan Lien and Pu Luong of Thanh Hoa province; the ITS gene region was 667 nucleotide long. The findings identified the samples as the same species and showed 99% similarity to the ITS gene sequence of A. roxburghii (Wall.) Lindl. published in GenBank, GQ328774. This study also demonstrates that the method employing internal transcribed spacer (ITS) sequences is an effective tool to identify A. setaceus taxa