scholarly journals Removal Lemmas with Polynomial Bounds

2019 ◽  
Author(s):  
Lior Gishboliner ◽  
Asaf Shapira
Keyword(s):  
Sufficient Conditions ◽  
Extremal Problems ◽  
Natural Question ◽  
Negative Results ◽  
Global Properties ◽  
Graph Properties ◽  
Graph Property ◽  
Almost All ◽  
Polynomial Bounds ◽  
Removal Lemma

Abstract A common theme in many extremal problems in graph theory is the relation between local and global properties of graphs. One of the most celebrated results of this type is the Ruzsa–Szemerédi triangle removal lemma, which states that if a graph is $\varepsilon $-far from being triangle free, then most subsets of vertices of size $C(\varepsilon )$ are not triangle free. Unfortunately, the best known upper bound on $C(\varepsilon )$ is given by a tower-type function, and it is known that $C(\varepsilon )$ is not polynomial in $\varepsilon ^{-1}$. The triangle removal lemma has been extended to many other graph properties, and for some of them the corresponding function $C(\varepsilon )$ is polynomial. This raised the natural question, posed by Goldreich in 2005 and more recently by Alon and Fox, of characterizing the properties for which one can prove removal lemmas with polynomial bounds. Our main results in this paper are new sufficient and necessary criteria for guaranteeing that a graph property admits a removal lemma with a polynomial bound. Although both are simple combinatorial criteria, they imply almost all prior positive and negative results of this type. Moreover, our new sufficient conditions allow us to obtain polynomially bounded removal lemmas for many properties for which the previously known bounds were of tower type. In particular, we show that every semi-algebraic graph property admits a polynomially bounded removal lemma. This confirms a conjecture of Alon.

scholarly journals Structure and Supersaturation for Intersecting Families

10.37236/7683 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
József Balogh ◽  
Shagnik Das ◽  
Hong Liu ◽  
Maryam Sharifzadeh ◽  
Tuan Tran
Keyword(s):  
Main Tool ◽  
Extremal Problems ◽  
Typical Structure ◽  
Combinatorial Objects ◽  
Minimum Number ◽  
Vertex Set ◽  
Intersecting Families ◽  
Almost All ◽  
Removal Lemma

The extremal problems regarding the maximum possible size of intersecting families of various combinatorial objects have been extensively studied. In this paper, we investigate supersaturation extensions, which in this context ask for the minimum number of disjoint pairs that must appear in families larger than the extremal threshold. We study the minimum number of disjoint pairs in families of permutations and in $k$-uniform set families, and determine the structure of the optimal families. Our main tool is a removal lemma for disjoint pairs. We also determine the typical structure of $k$-uniform set families without matchings of size $s$ when $n \ge 2sk + 38s^4$, and show that almost all $k$-uniform intersecting families on vertex set $[n]$ are trivial when $n\ge (2+o(1))k$.

scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

scholarly journals Comparing the host galaxies of different type supernovae

2015 ◽  
Vol 11 (S319) ◽  
pp. 139-139
Author(s):  
Y. C. Liang ◽  
X. Shao ◽  
M. Dennefeld ◽  
X. Y. Chen ◽  
L. Zhou ◽  
...  
Keyword(s):  
Stellar Mass ◽  
Significant Fraction ◽  
Host Galaxies ◽  
Global Properties ◽  
Different Types ◽  
Type Ia ◽  
Total Light ◽  
Stellar Masses ◽  
Almost All ◽  
Cross Matching

AbstractWe compare the host galaxies of 902 supernovae, including Type Ia, II and Ibc, which are selected by cross-matching the Asiago Supernova Catalog with the SDSS DR7. We further selected 213 galaxies by requiring the light fraction of spectral observations > 15%, which could represent well the global properties of the galaxies. The diagrams related to Dn(4000), HδA, stellar masses, SFRs and specific SFRs for the SNe hosts show that almost all SNe II and most of SNe Ibc occur in SF galaxies. A significant fraction of SNe Ia occurs in AGNs and Absorp galaxies. These results are compared with those of the 689 comparison galaxies where the SDSS fiber captures < 15% of the total light. These comparison galaxies appear biased towards higher 12+log(O/H) (~0.1dex) at a given stellar mass, suggesting the aperture effect should be kept in mind when the properties of the hosts for different types of SNe are discussed.

Regular, Commutative, Maximal Semigroups of Quotients

1975 ◽  
Vol 18 (1) ◽  
pp. 99-104 ◽  
Author(s):  
Jurgen Rompke
Keyword(s):  
Commutative Semigroup ◽  
Regular Ring ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Necessary And Sufficient Conditions ◽  
Natural Question ◽  
Commutative Case ◽  
Ring Of Quotients ◽  
Singular Ideal ◽  
Necessary And Sufficient

A well-known theorem which goes back to R. E. Johnson [4], asserts that if R is a ring then Q(R), its maximal ring of quotients is regular (in the sense of v. Neumann) if and only if the singular ideal of R vanishes. In the theory of semigroups a natural question is therefore the following: Do there exist properties which characterize those semigroups whose maximal semigroups of quotients are regular? Partial answers to this question have been given in [3], [7] and [8]. In this paper we completely solve the commutative case, i.e. we give necessary and sufficient conditions for a commutative semigroup S in order that Q(S), the maximal semigroup of quotients, is regular. These conditions reflect very closely the property of being semiprime, which in the theory of commutative rings characterizes those rings which have a regular ring of quotients.

Hyponormal and essentially normal operators

1979 ◽  
Vol 83 (1-2) ◽  
pp. 123-132
Author(s):  
C. R. Putnam
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Principal Result ◽  
Hyponormal Operator ◽  
Essentially Normal ◽  
Normal Operators ◽  
Result Theorem ◽  
Almost All ◽  
Spectral Family

SynopsisLet T be a hyponormal operator on a Hilbert space, so that T*T – TT*≧ 0. Let T have the Cartesian representation T = H + iJ where H has the spectral family {Et} and suppose that EtJ − JEt is compact for almost all t on a Borei set α satisfying E(α) = I. The principal result (Theorem 3) is that under these hypotheses T must be normal. In case T is hyponormal and essentially normal some sufficient conditions are given assuring that, for a fixed t, EtJ − JEt is compact.

scholarly journals Regular and Irregular Performance Variation of Module String and Occurred Conditions for Potential Induced Degradation-Affected Crystalline Silicon Photovoltaic Power Plants

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4230 ◽  
Author(s):  
Jingsheng Huang ◽  
Yaojie Sun ◽  
He Wang ◽  
Junjun Zhang
Keyword(s):  
Power Plants ◽  
Crystalline Silicon ◽  
Sufficient Conditions ◽  
Ethyl Vinyl ◽  
Climate Conditions ◽  
Photovoltaic Power ◽  
Performance Variation ◽  
Current Voltage ◽  
Almost All ◽  
Necessary And Sufficient

Potential induced degradation (PID) leads to power degradation, and reduces durability and reliability of solar modules. However, this problem has not been thoroughly solved so far. The results from interlaboratory and field study show contradictory fault phenomenon for PID. In this paper, PID of crystalline silicon photovoltaic power plants distributed in various climate conditions was investigated. These photovoltaic power plants consist of two types of crystalline silicon solar modules, which cover almost all kinds of front glass, ethyl vinyl acetate (EVA) and backsheet available commercially. It was found that only a few of power plants were affected by PID. By measuring current voltage characteristics of PID-affected solar modules, the real faults phenomenon was uncovered and classified into regular and irregular power degradation in a module string. The results obtained in this work show that the negative potential caused by high system voltage and stacking faults are necessary and sufficient conditions for PID occurrence for the first time. The anomalous power degradation is related to the stacking fault, which appears randomly during the crystal growth.

scholarly journals A Note on the Speed of Hereditary Graph Properties

10.37236/644 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Vadim V. Lozin ◽  
Colin Mayhill ◽  
Victor Zamaraev
Keyword(s):  
Practical Importance ◽  
Bipartite Graphs ◽  
Hereditary Property ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs ◽  
Graph Properties ◽  
Graph Property ◽  
Vertex Set ◽  
Split Graphs ◽  
Hereditary Properties

For a graph property $X$, let $X_n$ be the number of graphs with vertex set $\{1,\ldots,n\}$ having property $X$, also known as the speed of $X$. A property $X$ is called factorial if $X$ is hereditary (i.e. closed under taking induced subgraphs) and $n^{c_1n}\le X_n\le n^{c_2n}$ for some positive constants $c_1$ and $c_2$. Hereditary properties with the speed slower than factorial are surprisingly well structured. The situation with factorial properties is more complicated and less explored, although this family includes many properties of theoretical or practical importance, such as planar graphs or graphs of bounded vertex degree. To simplify the study of factorial properties, we propose the following conjecture: the speed of a hereditary property $X$ is factorial if and only if the fastest of the following three properties is factorial: bipartite graphs in $X$, co-bipartite graphs in $X$ and split graphs in $X$. In this note, we verify the conjecture for hereditary properties defined by forbidden induced subgraphs with at most 4 vertices.

scholarly journals Wiener-type invariants on graph properties

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 489-502
Author(s):  
Qiannan Zhou ◽  
Ligong Wang ◽  
Yong Lu
Keyword(s):  
Connected Graph ◽  
Sufficient Conditions ◽  
Graph Properties ◽  
Wiener Type ◽  
Simple Connected Graph

The Wiener-type invariants of a simple connected graph G = (V(G),E(G)) can be expressed in terms of the quantities Wf = ?{u,v}?V(G) f(dG(u,v)) for various choices of the function f (x), where dG(u,v) is the distance between vertices u and v in G. In this paper, we mainly give some sufficient conditions for a connected graph to be k-connected, ?-deficient, k-hamiltonian, k-edge-hamiltonian, k-path-coverable or satisfy ?(G)? k.

The Projective Antecedent of the Three Reflection Theorem

1991 ◽  
Vol 34 (2) ◽  
pp. 265-274
Author(s):  
F. A. Sherk
Keyword(s):  
Projective Geometry ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Metric Geometry ◽  
Natural Question ◽  
Complete Answer ◽  
Special Cases ◽  
Reflection Theorem ◽  
Necessary And Sufficient

AbstractA complete answer is given to the question: Under what circumstances is the product of three harmonic homologies in PG(2, F) again a harmonic homology ? This is the natural question to ask in seeking a generalization to projective geometry of the Three Reflection Theorem of metric geometry. It is found that apart from two familiar special cases, and with one curious exception, the necessary and sufficient conditions on the harmonic homologies produce exactly the Three Reflection Theorem.

Metronomic chemotherapy (MC) in the neoadjuvant setting: Results of two parallel feasibility trials in patients (pts) with HER2 positive (HER2+) and negative (HER2-) locally advanced breast cancer (LABC) (Traq-Me and TAME).

2012 ◽  
Vol 30 (27_suppl) ◽  
pp. 197-197
Author(s):  
Vanessa Petry ◽  
Alessandro Leal ◽  
Roberto J. Arai ◽  
Simone Marinho ◽  
Marcelo Paiva ◽  
...  
Keyword(s):  
Locally Advanced Breast Cancer ◽  
Locally Advanced ◽  
Pathologic Complete Response ◽  
Metronomic Chemotherapy ◽  
Complete Response ◽  
Cardiac Safety ◽  
Her2 Positive ◽  
Negative Results ◽  
Vegf Pathway ◽  
Almost All

197 Background: In a previous randomized trial (SWOG 0012), MC seemed to improve pCR rates compared to standard anthracycline/taxane neoadjuvant chemotherapy (NC). We aimed to evaluate the feasibility of MC with a taxane→anthracycline schedule, which has also been shown potentially superior to the reverse sequence [J Clin Oncol 28:15s, 2010 (suppl; abstr 548)]. We also aimed to establish the feasibility of MC in combination with trastuzumab. Methods: The original accrual goal was 25 HER2+ pts and 40 HER2- pts. HER2- pts received MC consisting of paclitaxel (100mg/m2) x8 weeks followed by doxorubicin (24mg/m2) x9 weeks combined with oral cyclophosphamide (100mg/day), without G-CSF. HER2+ pts also received trastuzumab (4 mg/kg followed by 2mg/kg) concurrently with the entire CT. Objectives: Primary: To evaluate the feasibility of these schedules (defined as a febrile neutropenia [FN] rate no higher than 10%). Secondary: cardiac safety and general tolerability; efficacy as measured by objective clinical, radiological and pathologic complete response (pCR). Results: Almost all pts were staged as III (TraQme 8/9 88% and MeTo 4/11 36%). The HER2+ cohort was prematurely closed after 2 (22%) pts developed G3 pneumonitis (during the metromonic phase). Both responded to medical treatment and recovered. One pt had G2 hand-foot skin reaction (HFS) and another had G2 mucositis. The HER2- cohort was also prematurely closed with only 11 pts because of high rates of mucocutaneous toxicity (G3 HFS in 36%, G3 rash in 9%) and also due to the recent SWOG0221 negative results. There were 2 (18%) cases of FN and 3 (27%) of G4 neutropenia in this cohort, but no cases of pneumonitis. 1/11(9%) HER2- and 5/9HER2+(55%) pts had a pCR. VEGF pathway-related biomarkers were collected and will be presented at a later date. Conclusions: The proposed MC schedules proved too toxic to be considered for further clinical development. In addition, MC resulted in unexpectedly high rates of severe pulmonary toxicity when given in combination with trastuzumab. HER2+ but not HER2- pts had an impressively high pCR rate.

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