1,224 research outputs found
Packing Odd Walks and Trails in Multiterminal Networks
No full textLet G be an undirected network with a distinguished set of terminals T ⊆ V(G) and edge capacities cap: E(G) → ℝ_+. By an odd T-walk we mean a walk in G (with possible vertex and edge self-intersections) connecting two distinct terminals and consisting of an odd number of edges. Inspired by the work of Schrijver and Seymour on odd path packing for two terminals, we consider packings of odd T-walks subject to capacities cap.
First, we present a strongly polynomial time algorithm for constructing a maximum fractional packing of odd T-walks. For even integer capacities, our algorithm constructs a packing that is half-integer. Additionally, if cap(δ(v)) is divisible by 4 for any v ∈ V(G)-T, our algorithm constructs an integer packing.
Second, we establish and prove the corresponding min-max relation.
Third, if G is inner Eulerian (i.e. degrees of all nodes in V(G)-T are even) and cap(e) = 2 for all e ∈ E, we show that there exists an integer packing of odd T-trails (i.e. odd T-walks with no repeated edges) of the same value as in case of odd T-walks, and this packing can be found in polynomial time.
To achieve the above goals, we establish a connection between packings of odd T-walks and T-trails and certain multiflow problems in undirected and bidirected graphs
New Exact and Approximation Algorithms for the Star Packing Problem in Undirected Graphs
No full textBy a T-star we mean a complete bipartite graph K_{1,t} for some t <= T. For an undirected graph G, a T-star packing is a collection of node-disjoint T-stars in G.
For example, we get ordinary matchings for and packings of paths of length 1 and 2 for . Hereinafter we assume that T >= 2.
Hell and Kirkpatrick devised an ad-hoc augmenting algorithm that finds a T-star packing covering the maximum number of nodes. The latter algorithm also yields a min-max formula.
We show that T-star packings are reducible to network flows, hence the above problem is solvable in time (hereinafter n denotes the number of nodes in G, and m --- the number of edges).
For the edge-weighted case (in which weights may be assumed positive) finding a maximum -packing is NP-hard. A novel 9/4 T/(T + 1)-factor approximation algorithm is presented.
For non-negative node weights the problem reduces to a special case of a max-cost flow. We develop a divide-and-conquer approach that solves it in O(m sqrt(n) log(n)) time. The node-weighted problem with arbitrary weights is more difficult. We prove that it is NP-hard for T >= 3 and is solvable in strongly-polynomial time for T = 2
Faster Algorithms for Half-Integral T-Path Packing
No full textLet G = (V, E) be an undirected graph, a subset of vertices T be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O(mn^1/2 log(n^2/m)/log(n))-time algorithm (hereinafter n := |V|, m := |E|).
Now let us consider the fractional relaxation, i.e. allow T-path packings with arbitrary nonnegative real weights. It is known that there always exists a half-integral solution, that is, one only needs to assign weights 0, 1/2, 1 to maximize the total weight of T-paths. It is also known that an optimum half-integral packing can be found in strongly-polynomial time but the actual time bounds are far from being satisfactory.
In this paper we present a novel algorithm that solves the half-integral problem within O(mn^1/2 log(n^2/m)/log(n)) time, thus matching the complexities of integral and half-integral versions
Liftings for noncomplete probability spaces
No full textThe current state of knowledge concerning liftings for noncomplete probability spaces is discussed. This is a somewhat expanded version of the author's talk given at the 1991 Summer Conference on General Topology and Applications in Honor of Mary Ellen Rudin and Her Work.PT: S; CR: BURKE MR, IN PRESS P AM MATH S BURKE MR, 1991, ISRAEL J MATH, V73, P33 BURKE MR, 1992, ISRAEL J MATH, V79, P289 CARLSON T, THEOREM LIFTING CHRISTENSEN JPR, 1974, TOPOLOGY BOREL STRUC FREMLIN DH, 1989, HDB BOOLEAN ALGEBRAS, P877 INOESCUTULCEA A, 1966, 5TH P BERK S MATH ST, V2 IONESCUTULCEA A, 1967, CONTRIBUTIONS PROB 1, P63 IONESCUTULCEA A, 1969, TOPICS THEORY LIFTIN JECH TJ, 1978, SET THEORY JOHNSON RA, 1980, P AM MATH SOC, V80, P234 JUST W, IN PRESS T AM MATH S KUPKA J, 1983, INDIANA U MATH J, V32, P717 LOSERT V, 1983, LNM, V1080, P95 MAHARAM D, 1958, P AM MATH SOC, V9, P987 SHELAH S, 1983, ISRAEL J MATH, V45, P90 TALAGRAND M, 1982, P AM MATH SOC, V84, P379 VONNEUMANN J, 1931, CRELLES J MATH, V165, P109; NR: 18; TC: 0; J9: ANN N Y ACAD SCI; PG: 4; GA: BZ86BSource type: Electronic(1
PROBLEM OF A RATIO OF THE POINTS OF VIEW IN THE NOVEL “FOMA GORDEYEV” BY MAXIM GORKY
No full textVarious points of view of the characters of the novel “Foma Gordeyev” by Maxim Gorky come
to light and are analysed in the article, their complicated ratio supported by certain motives – work or business, dissociation, loneliness, enrichment and search of the place in life – is considered. It is proved that the
ratio of the characters’ points of view understood by the author as positions, from which events are considered, is among the bright artistic touches of early works of Maxim Gorky. This inclusion in the Fin de siècle
era, time of the overall overturn and of the new judgement of many concepts could be used in connection
with unwillingness of Maxim Gorky’s open expression of his author’s opinion. Composing a fancy plot, bringing heroes together, the
writer offers the sooth at the reader’s discretion rather than making emphases. The narrator’s voice is dominating, beginning and finishing the epic narration, at the same time only framing various points of view of the characters. The polyphony of the novel and the
thought-over ratio between the author, the storyteller and the heroes allowed Maxim Gorky creating gallery of living, spatial characters,
emphasising dramatic bases of the Russian life of the represented period and reducing all voices to a uniform denominator. The ratio
of the heroes’ points of view becomes one of the bases of the work’s composition and leads to understanding of the reasons of failures
of many characters. The author of the article analyses ways of introducing the speaking people’s images to the artistic text, emphasises
existence of the special sayings for all occasions in the text designed to influence the recipient by the offer of “wisdom formulas” to it,
only to be taken stock of by the reader. Most likely, the ratio of the points of view in the novel as a special device had, on the one hand,
already been preconditioned, and, on the other hand, could affect a peculiar mosaicity of the upcoming Maxim Gorky’s personal artistic
method. Moreover, features of the narration and substantial aspects of composition allow us saying that in the novel “Foma Gordeyev”,
Maxim Gorky creatively masters and actively uses findings of the Russian classics of the second half of the 19th century
170226 ELDER CARE EVENT BEARD 007
No full textProfessor Laura Olson, a member of the Political Science department at Lehigh, listens to her audience on Wednesday, Feb. 22, 2017 in Williams Hall. Olson is the author of "Elder Care Journey: A View from the Front Lines" (Maxim Beard/B&W Staff
170226 ELDER CARE EVENT BEARD 003
No full textProfessor Laura Olson, author of "Elder Care Journey: A View from the Front Lines", talks during a Brown Bag Series on Wednesday, Feb. 22, 2017 in Williams Hall. Olson is a professor of Political Science at Lehigh. (Maxim Beard/B&W Staff
170226 ELDER CARE EVENT BEARD 005
No full textProfessor Laura Olson, author of "Elder Care Journey: A View from the Front Lines", speaks during a Brown Bag Series on Wednesday, Feb. 22, 2017 in Williams Hall. Olson passionately discussed her personal experience with the long-term care system in the U.S. (Maxim Beard/B&W Staff
An RNA interference knock-down of nitrate reductase enhances lipid biosynthesis in the diatom Phaeodactylum tricornutum
No full textWhen diatoms are stressed for inorganic nitrogen they remodel their intermediate metabolism and redirect carbon towards lipid biosynthesis. However, this response comes at a significant cost reflected in decreased photosynthetic energy conversion efficiency and growth. Here we explore a molecular genetics approach to restrict the assimilation of inorganic nitrogen by knocking down nitrate reductase (NR). The transformant strain, NR21, exhibited about 50% lower expression and activity of the enzyme but simultaneously accumulated over 40% more fatty acids. However, in contrast to nitrogen-stressed wild-type (WT) cells, which grow at about 20% of the rate of nitrogen-replete cells, growth of NR21 was only reduced by about 30%. Biophysical analyses revealed that the photosynthetic energy conversion efficiency of photosystem II was unaffected in NR21; nevertheless, the plastoquinone pool was reduced by 50% at the optimal growth irradiance while in the WT it was over 90% oxidized. Further analyses reveal a 12-fold increase in the glutamate/glutamine ratio and an increase NADPH and malonyl-CoA pool size. Transcriptomic analyses indicate that the knock down resulted in changes in the expression of genes for lipid biosynthesis, as well as the expression of specific transcription factors. Based on these observations, we hypothesize that the allocation of carbon and reductants in diatoms is controlled by a feedback mechanism between intermediate metabolites, the redox state of the plastid and the expression and binding of transcription factors related to stress responses.Peer reviewe
Contribution of Citizen Science to Biodiversity Data Mobilization in Russia
No full textPresentation for TDWG 2020 - A Virtual Conference
Session: CO03, 22 October 2020
Conference Abstract: https://doi.org/10.3897/biss.4.59197
video: https://youtu.be/dOp6j69qxT4Presenting author: Maxim Shashko
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