A bound on the generalized competition index of a primitive matrix using Boolean rank

The competitive pressure of naturally regenerated European beech (Fagus sylvatica) saplings on planted pedunculate oak (Quercus robur) was investigated on two 1.8 ha permanent plots near Habsburg and Murten (Switzerland). The plots were established with the aim to test methods of artificial oak regeneration after large-scale windthrow. On both plots, 80 oaks exposed to varying levels of competitive pressure from at most 10 neighbouring beech trees were selected. The height of each oak as well as stem and branch diameters were measured. The competitive pressure was assessed using Schütz's competition index, which is based on relative tree height, crown overlap and distance from competing neighbours. Oak trees growing without or with only slight competition from beech were equally tall, while oaks exposed to moderate to strong competition were smaller. A threshold value for the competition index was found above which oak height decreased strongly. The stem and branch diameters of the oaks started to decrease even if the competition from beech was slight, and decreased much further with more competition. The oak stems started to become more slender even with only slight competition from beech. On the moderately acid beech sites studied here, beech grow taller faster than oak. Thus where beech is competing with oak and the aim is to maintain the oak, competitive pressure on the oak must be reduced at an early stage. The degree of the intervention should, however, take the individual competitive interaction into account, with more intervention if the competition is strong.

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Eurasian Competitive Capacity Turkey

International Conference on Eurasian Economies 2016 ◽

10.36880/c07.01743 ◽

2016 ◽

Author(s):

Hakkı Çiftçi ◽

Aliye Erşahinoğlu

Keyword(s):

Technological Development ◽

New Ventures ◽

Study Data ◽

Source Distribution ◽

Global Competition ◽

Competition Index ◽

Balanced Growth ◽

Innovative Management ◽

Energy Trade ◽

And Function

New ventures and creation of market awareness and industrial competition make competition as a prior concept. From this, evaluation of Eurasian competition capacity from the viewpoint of Turkey gains importance as an issue. Within the scope of EU 2020; 3 thematic priorities, 5 main targets, 7 initiatives were determined as a basis. This study that aims developing innovative management and achieving sustainable and more balanced growth with powerful innovative competition capacity, will take basic policies, which will create the competition capacity leans from Turkey to Eurasia, as a basis. This study also includes the analyses of sectoral competition capacity from Turkey to Eurasia as well as legal regulations, energy, trade, employment and geographical dimensions. As the method of this study, data regarding the indications of competition capacity over the last decade will be evaluated, deficiencies will be determined, source distribution will be directed, technological development functions will be achieved, efficient and function competition will be coordinated with the economic growth and a series of measurements will be taken and competition policies will be established in this regard. This study will also analyze the competition policies of Turkey and Eurasia and their objectives, efficiency and measurement of competition, general overview of Eurasian economies, global competition in Eurasian countries, index sequencing and scores in accordance with developed innovation in terms of Azerbaijan, Kazakhstan, Kyrgyzstan, Tajikistan and Turkey. Through the evaluation of rankings of Eurasian economies within Global Competition Index as well as the scores and Global Competition Report, the study will be concluded.

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The Economic Detection Instrument of the Netherlands Competition Authority: The Competition Index

SSRN Electronic Journal ◽

10.2139/ssrn.1992774 ◽

2012 ◽

Cited By ~ 1

Author(s):

Lilian Petit

Keyword(s):

The Netherlands ◽

Competition Authority ◽

Competition Index ◽

Detection Instrument

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On extremal matrices of second largest exponent by Boolean rank

Linear Algebra and its Applications ◽

10.1016/j.laa.2006.09.016 ◽

2007 ◽

Vol 422 (1) ◽

pp. 186-197 ◽

Cited By ~ 2

Author(s):

Bolian Liu ◽

Lihua You ◽

Gexin Yu

Keyword(s):

Boolean Rank

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A New Index Representing Individual Tree Competitive Status

Canadian Journal of Forest Research ◽

10.1139/x73-073 ◽

1973 ◽

Vol 3 (4) ◽

pp. 495-500 ◽

Cited By ~ 46

Author(s):

James A. Moore ◽

Carl A. Budelsky ◽

Richard C. Schlesinger

Keyword(s):

Spatial Distribution ◽

Strong Correlation ◽

Basal Area ◽

Tree Size ◽

Competition Index ◽

Individual Tree ◽

Silvicultural Practices ◽

Basal Area Growth ◽

Hardwood Species ◽

Area Growth

A new competition index, modified Area Potentially Available (APA), was tested in a complex unevenaged stand composed of 19 different hardwood species. APA considers tree size, spatial distribution, and distance relationships in quantifying intertree competition and exhibits a strong correlation with individual tree basal area growth. The most important characteristic of APA is its potential for evaluating silvicultural practices.

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Generalized competition index of primitive digraphs

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-017-0675-0 ◽

2017 ◽

Vol 33 (2) ◽

pp. 475-484

Author(s):

Li-hua You ◽

Fang Chen ◽

Jian Shen ◽

Bo Zhou

Keyword(s):

Competition Index ◽

Primitive Digraphs

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Non-negative integral matrices with given spectral radius and controlled dimension

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2021.93 ◽

2021 ◽

pp. 1-24

Author(s):

MEHDI YAZDI

Keyword(s):

Spectral Radius ◽

Positive Real Number ◽

Algebraic Integer ◽

Log P ◽

Irreducible Matrix ◽

Positive Real ◽

Shift Of Finite Type ◽

Primitive Matrix ◽

Integral Matrices ◽

Perron Number

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

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Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

ESAIM Probability and Statistics ◽

10.1051/ps/2019007 ◽

2019 ◽

Vol 23 ◽

pp. 797-802

Author(s):

Raphaël Cerf ◽

Joseba Dalmau

Keyword(s):

Markov Chain ◽

Probability Measure ◽

Branching Process ◽

Invariant Probability Measure ◽

Classical Formula ◽

Multitype Branching Process ◽

Primitive Matrix ◽

Watson Process

Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A, as well as of a multitype branching process with mean matrix e(A−I)t. These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.

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