We show how to speed up Karmarkar's linear programming algorithm for the case of multicommodity flows. The special structure
of the constraint matrix is exploited to obtain an algorithm for the multicommodity flow problem which requires O(s3.5v2.5eL) arithmetic operations, each operation being performed to a precision of O (L) bits. Herev is the number of vertices ande is the number of edges in the given network,s is the number of commodities, andL is bounded by the number of bits in the input. We obtain a speed up of the order of (e0.5/v0.5)+(e2.5/v2.5s2) over Karmarkar's modified algorithm which is substantial for dense networks. The techniques in the paper can also be used
to speed up any interior point algorithm for any linear programming problem whose constraint matrix is structurally similar
to the one in the multicommodity flow problem.
Research supported by a fellowship from the Shell Foundation.
Research supported by NSF under grant NSF DCR-8404239. 相似文献
Various boronic acids were treated with a rhodium (I) catalyst enabling their 1,4-conjugate addition to unprotected maleimide. The scope of the reaction was explored to include both electron-rich and electron poor boronic acids. These reactions were also performed in the microwave resulting in reduced reaction times and improved efficiencies. Additionally, substrates that were recalcitrant under conventional conditions were successfully reacted under microwave conditions. The reaction worked satisfactorily with boronic acids having a free OH or NH group. 相似文献
We considered the following natural conjecture: For every sorting algorithm every key will be involved in(logn) comparisons for some input. We show that this is true for most of the keys and prove matching upper and lower bounds. Every sorting algorithm for some input will involven–n/2+1 keys in at leastlog2n comparisons,>0. Further, there exists a sorting algorithm that will for every input involve at mostn–n
/c keys in greater thanlog2n comparisons, wherec is a constant and>0. The conjecture is shown to hold for natural algorithms from the literature. 相似文献
Halloysite nanotubes (HNTs) filled 80/20 (wt/wt) polypropylene (PP)/acrylonitrile butadiene styrene (ABS) blends and its composites in presence and absence of dual compatibilizer (polypropylene grafted maleic anhydride (PP-g-MA), and styrene-ethylene, butylene-styrene triblock copolymer grafted with maleic anhydrite (SEBS-g-MA)) have been prepared using twin screw extruder followed by injection moulding. Significant refinements in dispersed ABS droplets diameter and interparticle distance between dispersed ABS droplets were observed in case of HNTs filled 80/20 (wt/wt) PP/ABS blends and its composites in presence of PP-g-MA and SEBS-g-MA. This has resulted in significant enhancement in tensile and impact properties of HNTs filled 80/20 (wt/wt) PP/ABS blends and its composites in presence of PP-g-MA and SEBS-g-MA. Refinement in morphology of dispersed ABS phase results in decrease in crystallinity of HNTs filled 80/20 (wt/wt) PP/ABS blends and its composites in presence of PP-g-MA and SEBS-g-MA. In addition, HNTs act as heterogeneous nucleating agent for the growth of PP crystals, and hence crystallization rate of HNTs filled 80/20 (wt/wt) PP/ABS blends and its composites in presence and absence of PP-g-MA and SEBS-g-MA increases. Thermal stability also increases in case of HNTs filled 80/20 (wt/wt) PP/ABS blends and its composites in presence and absence of PP-g-MA and SEBS-g-MA. 相似文献
In this work, we show the advantages of label-free, tridimensional mass spectrometry imaging using dual beam analysis (25 keV Bi3+) and depth profiling (20 keV with a distribution centered at Ar1500+) coupled to time of flight secondary ion mass spectrometry (3D-MSI-TOF-SIMS) for the study of A-172 human glioblastoma cell line treated with B-cell lymphoma 2 (Bcl-2) inhibitor ABT-737. The high spatial (~250 nm) and high mass resolution (m/Δm ~10,000) of TOF-SIMS permitted the localization and identification of the intact, unlabeled drug molecular ion (m/z 811.26 C42H44ClN6O5S2– [M – H]–) as well as characteristic fragment ions. We propose a novel approach based on the inspection of the drug secondary ion yield, which showed a good correlation with the drug concentration during cell treatment at therapeutic dosages (0–200 μM with 4 h incubation). Chemical maps using endogenous molecular markers showed that the ABT-737 is mainly localized in subsurface regions and absent in the nucleus. A semiquantitative workflow is proposed to account for the biological cell diversity based on the spatial distribution of endogenous molecular markers (e.g., nuclei and cytoplasm) and secondary ion confirmation based on the ratio of drug-specific fragments to molecular ion as a function of the therapeutic dosage.
Herein we report the de novo design and synthesis of a geometrically flexible bis-indole carboxamide and a constrained derivative, as a novel class of small molecule scaffold that exhibits high stabilization potential for DNA G-quadruplex sequences associated with the promoters of c-kit2 and c-myc. 相似文献
The synthesis of multi‐substituted dibenzo[b,d]furan derivatives 7a‐b and 11a‐b from readily available starting materials is described. These compounds are important intermediates for synthesis of molecules having wide therapeutic applications. 相似文献
We report bis-phenylethynyl amide derivatives as a potent G-quadruplex binding small molecule scaffold. The amide derivatives were efficiently prepared in 3 steps by employing Sonogashira coupling, ester hydrolysis and a chemoselective amide coupling. Ligand-quadruplex recognition has been evaluated using a fluorescence resonance energy transfer (FRET) melting assay, surface plasmon resonance (SPR), circular dichroism (CD) and (1)H nuclear magnetic resonance (NMR) spectroscopy. While most of the G-quadruplex ligands reported so far comprise a planar, aromatic core designed to stack on the terminal tetrads of a G-quadruplex, these compounds are neither polycyclic, nor macrocyclic and have free rotation around the triple bond enabling conformational flexibility. Such molecules show very good binding affinity, excellent quadruplex:duplex selectivity and also promising discrimination between intramolecular promoter quadruplexes. Our results indicate that the recognition of the c-kit2 quadruplex by these ligands is achieved through groove binding, which favors the formation of a parallel conformation. 相似文献
A sensitive (method detection limit, 2.0 microg As L(-1)) colorimetric determination of trace As(v) and As(iii) concentrations in the presence of soluble phosphorus (P) concentrations in soil/water extracts is presented. The proposed method modifies the malachite green method (MG) originally developed for P in soil and water. Our method relies upon the finding that As(iii) and As(v) do not develop the green color during P analysis using the MG method. When an optimum concentration of ascorbic acid (AA) is added to a sample containing up to 15 times P > As (microM) concentrations, the final sample absorbance due to P will be equal to that of As(v) molecules. The soluble As concentration can then be quantified by the concentration difference between the mixed oxyanion (As + P) absorbance (proposed method) and the MG method absorbance that measures only P. Our method is miniaturized using a 96-well microplate UV-VIS reader that utilizes minute reagent and sample volumes (120 and 200 microL sample(-1), respectively), thus, minimizing waste and offering flexibility in the field. Our method was tested in a suite of As-contaminated soils that successfully measured both As and P in soil water extracts and total digests. Mean% As recoveries ranged between 84 and 117%, corroborating data obtained with high-resolution inductively-coupled plasma mass-spectrometry. The performance of the proposed colorimetric As method was unaffected by the presence of Cu, Zn, Pb, Ni, Fe, Al, Si, and Cr in both neutral and highly-acidic (ca. pH 2) soil extracts. Data from this study provide the proof of concept towards creating a field-deployable, portable As kit. 相似文献
Let a bounded full dimensional polytope be defined by the systemAxb whereA is anm × n matrix. Letai denote theith row of the matrixA, and define theweighted analytic center of the polytope to be the point that minimizes the strictly convex barrier function –
i=1mwi ln(aiTx –bi). The proper selection of weightswi can make any desired point in the interior of the polytope become the weighted analytic center. As a result, the weighted analytic center has applications in both linear and general convex programming. For simplicity we assume that the weights are positive integers.If some of thewi's are much larger than others, then Newton's method for minimizing the resulting barrier function is very unstable and can be very slow. Previous methods for finding the weighted analytic center relied upon a rather direct application of Newton's method potentially resulting in very slow global convergence. We present a method for finding the weighted analytic center that is based on the scaling technique of Edmonds and Karp and is an enhancement of Newton's method. The scaling algorithm runs in
iterations, wherem is the number of constraints defining the polytope andW is the largest weight given on any constraint. Each iteration involves taking a step in the Newton direction and its complexity is dominated by the time needed to solve a system of linear equations.Supported by the Campus Research Board, University of Illinois at Urbana-Champaign.Supported by the National Science Foundation under Grants CCR-9057481 and CCR-9007195. 相似文献