Shortcutting Planar Digraphs

1995 ◽  
Vol 4 (3) ◽  
pp. 287-315 ◽  
Author(s):  
Mikkel Thorup
Keyword(s):  
Transitive Closure ◽  
Maximum Distance ◽  
Constructive Proof ◽  
Open Question ◽  
Planar Digraph

This paper presents a constructive proof that for any planar digraph G on p vertices, there exists a subset S of the transitive closure of G such that the number of arcs in S is less than or equal to the number of arcs in G, and such that the diameter of G∪S is O(α(p, p)(log p)2). Here the diameter refers to the maximum distance from a vertex υ to a vertex w where (υ, w) is from the transitive closure of G – which is also the transitive closure of G ∪ S. This result provides support for the author's previous conjecture that such a set S achieving a diameter polylogarithmic in the number of vertices exists for any digraph. The result also adresses an open question of Chazelle, who did some related work on trees, and suggested the generalization to the planar cases.

scholarly journals Venn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice

10.37236/1755 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Jerrold Griggs ◽  
Charles E. Killian ◽  
Carla D. Savage
Keyword(s):  
Boolean Lattice ◽  
Constructive Proof ◽  
Existence Proof ◽  
Chain Decomposition ◽  
Venn Diagrams ◽  
Minimum Number ◽  
Symmetric Chain Decomposition ◽  
Open Question ◽  
Symmetric Chain

We show that symmetric Venn diagrams for $n$ sets exist for every prime $n$, settling an open question. Until this time, $n=11$ was the largest prime for which the existence of such diagrams had been proven, a result of Peter Hamburger. We show that the problem can be reduced to finding a symmetric chain decomposition, satisfying a certain cover property, in a subposet of the Boolean lattice ${\cal B}_n$, and prove that such decompositions exist for all prime $n$. A consequence of the approach is a constructive proof that the quotient poset of ${\cal B}_n$, under the relation "equivalence under rotation", has a symmetric chain decomposition whenever $n$ is prime. We also show how symmetric chain decompositions can be used to construct, for all $n$, monotone Venn diagrams with the minimum number of vertices, giving a simpler existence proof.

Mars: was There an Ancient Eden?

1997 ◽  
Vol 161 ◽  
pp. 203-218 ◽  
Author(s):  
Tobias C. Owen
Keyword(s):  
Positive Answer ◽  
Biogenic Elements ◽  
Habitable Zones ◽  
The Face ◽  
The Origin Of Life ◽  
Early Mars ◽  
Favorable Conditions ◽  
Open Question ◽  
Rocky Planets ◽  
Impact Erosion

AbstractThe clear evidence of water erosion on the surface of Mars suggests an early climate much more clement than the present one. Using a model for the origin of inner planet atmospheres by icy planetesimal impact, it is possible to reconstruct the original volatile inventory on Mars, starting from the thin atmosphere we observe today. Evidence for cometary impact can be found in the present abundances and isotope ratios of gases in the atmosphere and in SNC meteorites. If we invoke impact erosion to account for the present excess of129Xe, we predict an early inventory equivalent to at least 7.5 bars of CO2. This reservoir of volatiles is adequate to produce a substantial greenhouse effect, provided there is some small addition of SO2(volcanoes) or reduced gases (cometary impact). Thus it seems likely that conditions on early Mars were suitable for the origin of life – biogenic elements and liquid water were present at favorable conditions of pressure and temperature. Whether life began on Mars remains an open question, receiving hints of a positive answer from recent work on one of the Martian meteorites. The implications for habitable zones around other stars include the need to have rocky planets with sufficient mass to preserve atmospheres in the face of intensive early bombardment.

192: Tubularized Urethral Replacement: What is the Maximum Distance for Normal Tissue Regeneration?

2004 ◽  
Vol 171 (4S) ◽  
pp. 51-51
Author(s):  
Roger E. De Filippo ◽  
Hans G. Pohl ◽  
James J. Yoo ◽  
Anthony Atala
Keyword(s):  
Tissue Regeneration ◽  
Normal Tissue ◽  
Maximum Distance

On the Semantic Content of Grammatical Gender and Its Impact on the Representation of Human Referents

2010 ◽  
Vol 57 (5) ◽  
pp. 367-375 ◽  
Author(s):  
Lisa Irmen ◽  
Julia Kurovskaja
Keyword(s):  
Semantic Content ◽  
Grammatical Gender ◽  
Differential Effects ◽  
Gender Information ◽  
Masculine Role ◽  
Feminine Role ◽  
And Gender ◽  
Gender Categories ◽  
Open Question

Grammatical gender has been shown to provide natural gender information about human referents. However, due to formal and conceptual differences between masculine and feminine forms, it remains an open question whether these gender categories influence the processing of person information to the same degree. Experiment 1 compared the semantic content of masculine and feminine grammatical gender by combining masculine and feminine role names with either gender congruent or incongruent referents (e.g., Dieser Lehrer [masc.]/Diese Lehrerin [fem.] ist mein Mann/meine Frau; This teacher is my husband/my wife). Participants rated sentences in terms of correctness and customariness. In Experiment 2, in addition to ratings reading times were recorded to assess processing more directly. Both experiments were run in German. Sentences with grammatically feminine role names and gender incongruent referents were rated as less correct and less customary than those with masculine forms and incongruent referents. Combining a masculine role name with an incongruent referent slowed down reading to a greater extent than combining a feminine role name with an incongruent referent. Results thus specify the differential effects of masculine and feminine grammatical gender in denoting human referents.

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable

Die Europäische Union: eine neue Supermacht mit imperialen Ambitionen?

2005 ◽  
Vol 35 (139) ◽  
pp. 247-266 ◽  
Author(s):  
Hans-Jürgen Bieling
Keyword(s):  
World War Ii ◽  
Economic Crisis ◽  
Europäische Union ◽  
World War ◽  
Political Sovereignty ◽  
Military Conflicts ◽  
Imperial Power ◽  
International Role ◽  
Open Question ◽  
The Eu

Recent theoretical conceptions of imperialism may be useful correctives against idealising and harmonising views of international interdependency and co-operation. Analytically, however, they are not necessarily helpful. In terms of the EU, they do not really comprehend its particular international role. Despite improved financial and military capacities, the EU represents not yet an imperial power. Instead, it still pursues a rather hegemonic foreign policy approach due to internal economic restrictions, fragmented political sovereignty and the historical experiences of beneficial economic and political co-operation after World War II. Eventually, however, it remains an open question, whether the multilateralist, law-based and co-operative posture of the EU will prevail even under conditions of economic crisis and further military conflicts in the adjacent neighbourhood.

Tax competition and the activity of the regional tax policy

2020 ◽  
pp. 5-27
Author(s):  
S. M. Drobyshevsky ◽  
N. S. Kostrykina ◽  
A. V. Korytin
Keyword(s):  
Tax Competition ◽  
Tax Policy ◽  
Fiscal Federalism ◽  
Policy Instruments ◽  
Tax Incentives ◽  
Fiscal Autonomy ◽  
Tax Legislation ◽  
Tax Exemptions ◽  
Open Question ◽  
Regional Budgets

The problem of efficiency of regional tax expenditures is an actual issue of the fiscal policy and fiscal federalism in Russia. A large fiscal autonomy allows federal subjects to realize a more active tax policy to attract new investments. One cannot claim current fiscal powers of the Russian regions to be wide. However, not all the regions use even existing tax policy instruments. Moreover, out of the regions that use them only few provide incentives to stimulate investment decisions. Others use regional tax measures to support businesses that already have strong positions in the region. And it is an open question whether such tax incentives are efficient. On the other hand, an aggressive tax competition for investors can also be wasteful for regional budgets. In this paper, we calculate indicators that characterize the depth and scope of tax exemptions provided at the regional level. The calculations are based on the open tax statistics. Through the analysis of the tax legislation as well as the economic structure of selected regions, we reveal the inducements of their higher activity: federal regional tax policy, tax competition or benefits for budget-forming companies of the region.

From Deleuze and Guattari's Words to a Deleuzian Theory of Reading

2015 ◽  
Vol 9 (4) ◽  
pp. 529-557
Author(s):  
Daniel Haines
Keyword(s):  
Literary Criticism ◽  
Deleuze And Guattari ◽  
Transcendental Empiricism ◽  
Theory Of Reading ◽  
Open Question

While Deleuze and Guattari's passion for certain literature is well known, the nature of a ‘Deleuzian’ literary criticism remains an open question. However, most critics appear to agree that Deleuze and Guattari's comments on meaning and interpretation offer an ontological alternative to the textual focus of deconstruction. Through an interrogation of the difficult style of their books in relation to Plato, Nietzsche and Derrida, this paper offers a different reading of Deleuze and Guattari in relation to literary criticism. Despite appearances, transcendental empiricism and the project of ‘overturning Platonism’ provide a Deleuzian theory of reading that attends to textuality.

Luther or Erasmus ? An Open Question Still !

Moreana ◽  
1975 ◽  
Vol 12 (Number 45) (1) ◽  
pp. 71-74
Author(s):  
Randolph Klawiter
Keyword(s):  
Open Question

Sex determination and Y chromosome constitutive heterochromatin

2019 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
Abyt Ibraimov
Keyword(s):  
Sex Determination ◽  
Y Chromosome ◽  
Constitutive Heterochromatin ◽  
Sex Differentiation ◽  
Secondary Sexual Characteristics ◽  
Biological Meaning ◽  
Heterochromatin Block ◽  
Sexual Characteristics ◽  
Open Question ◽  
Efficient Elimination

In many animals, including us, the genetic sex is determined at fertilization by sex chromosomes. Seemingly, the sex determination (SD) in human and animals is determined by the amount of constitutive heterochromatin on Y chromosome via cell thermoregulation. It is assumed the medulla and cortex tissue cells in the undifferentiated embryonic gonads (UEG) differ in vulnerability to the increase of the intracellular temperature. If the amount of the Y chromosome constitutive heterochromatin is enough for efficient elimination of heat difference between the nucleus and cytoplasm in rapidly growing UEG cells the medulla tissue survives. Otherwise it doomed to degeneration and a cortex tissue will remain in the UEG. Regardless of whether our assumption is true or not, it remains an open question why on Y chromosome there is a large constitutive heterochromatin block? What is its biological meaning? Does it relate to sex determination, sex differentiation and development of secondary sexual characteristics? If so, what is its mechanism: chemical or physical? There is no scientifically sound answer to these questions.

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