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The blade cut pretty effectively and did effectively on the couple of minor prying jobs it had to perform.
{{cleanup|reason=Should be using the &lt;ref&gt;-tags; an expert might need to check if the refs support the text|date=March 2012}}
[[Image:CheiPageRank.png|thumb|280px| Nodes with links in the plane of PageRank and CheiRank]]
 
The '''CheiRank''' is an [[Eigenvalues and eigenvectors|eigenvector]] with a maximal real eigenvalue of the [[Google matrix]] <math> G^* </math> constructed for a directed network with the inverted directions of links. It is similar to the [[PageRank]] vector, which ranks the network nodes in average proportionally to a number of incoming links being the maximal eigenvector of the [[Google matrix]] <math> G </math> with a given initial direction of links. Due to inversion of link directions the '''CheiRank''' ranks the network nodes in average proportionally to a number of outgoing links. Since each node belongs both to '''CheiRank''' and [[PageRank]] vectors the ranking of information flow on a directed network becomes '''two-dimensional'''.  
 
==Definition==
[[Image:CheiRank1.jpg|thumb|280px|  Fig1. Distribution of procedure calls of Linux Kernel network  in the plane of PageRank probability <math> x = \log_{10} P_i </math> and CheiRank probability <math> y = \log_{10} {P}^*_i </math> for Linux version 2.6.32 with matrix size <math> N=285509 </math> at <math> \alpha=0.85</math>, color shows the density of nodes with white for maximum and blue for minimum, black space has no nodes  (from [7])]]
 
For a given directed network the Google matrix is constructed in the way described in the article [[Google matrix]]. The [[PageRank]] vector  is the eigenvector with the maximal real eigenvalue <math> \lambda=1 </math>. It was introduce in [1] and is discussed in the article [[PageRank]]. In a similar way  the CheiRank is the eigenvector with the maximal real eigenvalue of the matrix <math> G^* </math> built in the same way as <math> G </math> '''but''' using inverted direction of links in the initially given adjacency matrix.   Both matrices <math> G </math> and <math> G^* </math> belong to the class of Perron–Frobenius operators and according to the [[Perron–Frobenius theorem]] the CheiRank <math> P^*_i </math> and PageRank <math> P_i </math> eigenvectors have nonnegative components which can be interpreted as probabilities [2,3]. Thus all <math> N </math> nodes <math> i </math> of the network can be ordered in a decreasing probability order with ranks <math> K^*_i, K_i </math> for CheiRank and PageRank <math> P^*_i, P_i </math> respectively. In average the PageRank probability <math> P_i </math> is proportional to the number of ingoing links with <math> P_i \propto 1/{K_i}^\beta </math> [4,5,6]. For the World Wide Web (WWW) network the exponent <math> \beta =1/(\nu-1) \approx 0.9 </math> where <math> \nu \approx 2.1</math> is the exponent for ingoing links distribution [4,5]. In a similar way the CheiRank probability is in average proportional to the number of outgoing links with
<math> P^*_i \propto 1/{K^*_i}^{\beta^*} </math> with
<math> \beta^* =1/(\nu^*-1) \approx 0.6 </math> where <math> \nu^* \approx 2.7 </math> is the exponent for outgoing links distribution of the WWW [4,5]. The CheiRank was introduced for the procedure call network of Linux Kernel software in [7], the term itself was used in [8]. While the PageRank highlights very well known and popular nodes, the CheiRank highlights very communicative nodes. Top PageRank and CheiRank nodes have certain analogy to authorities and hubs appearing in the [[HITS algorithm]] [9] but the HITS is query dependent while the rank probabilities <math> P_i </math> and <math> P^*_i </math> classify all nodes of the network. Since each node belongs both to CheiRank and PageRank we obtain a two-dimensional ranking of network nodes. It should be noted that there had been early studies of PageRank in networks with inverted direction of links [10,11]  but the properties of two-dimensional ranking had not be analyzed in detail.
 
[[Image:CheiRank2.jpg|thumb|280px|  Fig2.  Dependence of probability of PageRank <math> P </math>  (red curve) and CheiRank <math> P^* </math> (blue curve) on the corresponding rank indexes <math> K </math> and <math> K^* </math>. The straight dashed lines show the power law dependence with the slope <math> \beta=0.92; 0.57 </math>  respectively,  corresponding to <math> \beta=1/(\nu-1) </math> (from [8])]]
 
==Examples==
An example of nodes distribution in the plane of PageRank and CheiRank is shown in Fig.1 for the procedure call network of Linux Kernel software taken from [7].
 
[[Image:CheiRank3.jpg|thumb|280px|  Fig3. Density distribution of Wikipedia English articles (2009) in the plane of PageRank and CheiRank indexes <math> 0 < \ln K, \ln K^* < \ln N </math> shown by color with blue for minimum  and white for maximum (black for zero); green/red points show top 100 personalities from PageRank/CheiRank, yellow pluses show top 100 personalities from Hart's book, number of articles <math> N = 3282257 </math> (from [8])]]
 
The dependence of <math> P, P^* </math> on <math> K, K^* </math> for the network of hyperlink network  of Wikipedia English articles is shown in Fig.2 from [8]. The distribution of these articles in the plane of PageRank and CheiRank is shown in Fig.3 from [8]. The difference between PageRank and CheiRank is clearly seen from the names of Wikipedia articles (2009)  with highest rank. At the top of PageRank we have  1.United States, 2.United Kingdom, 3.France while for CheiRank we find 1.Portal:Contents/Outline of knowledge/Geography and places, 2.List of state leaders by year, 3.Portal:Contents/Index/Geography and places. Clearly PageRank selects first articles on a broadly known subject with a large number of ingoing links while CheiRank selects first highly communicative articles with many outgoing links. Since the articles are distributed in 2D they can be ranked in various ways corresponding to projection of 2D set on a line. The horizontal and vertical lines correspond to PageRank and CheiRank, 2DRank combines properties of CheiRank and PageRank as it is discussed in [8]. It gives top Wikipedia articles 1.India, 2.Singapore, 3.Pakistan.
 
The 2D ranking highlights the properties of Wikipedia articles in a new rich and  fruitful manner. According to the PageRank the top 100 personalities described in Wikipedia articles have in 5 main category activities: 58 (politics), 10 (religion),17 (arts), 15 (science), 0 (sport) and thus the importance of politicians is strongly overestimated. The CheiRank gives respectively 15, 1, 52, 16, 16 while for  2DRank one finds 24, 5, 62, 7, 2.
Such type of 2D ranking can find useful applications for various complex directed networks including the WWW.
 
CheiRank and PageRank naturally appear for the world trade network,
or [[international trade]],
where they and linked with export and import flows for a given country respectively [12].
 
Possibilities of development of two-dimensional search engines based on PageRank and CheiRank are considered in [13]. Directed networks can be characterized by the correlator between PageRank and CheiRank vectors: in certain networks this correlator is close to zero (e.g. Linux Kernel network)
while other networks have large correlator values (e.g. Wikipedia or university networks) [7,13].
 
==Simple network example==
[[Image:CheiRank4.jpg|thumb|240px|  Fig4. Example of directed network]]
[[Image:CheiRank5.jpg|thumb|240px|  Fig5. Related matrix <math> S </math>]]
[[Image:CheiRank6.jpg|thumb|240px|  Fig6. Related matrix <math> S^* </math>]]
A simple example of the construction of the Google matrices <math> G </math> and <math> G^* </math>, used for determination of the related PageRank and CheiRank vectors, is given below. The directed network example with 7 nodes is shown in Fig.4. The matrix <math> S </math>, built with the rules described
in the article [[Google matrix]], is shown in Fig.5;
the related Google matrix is <math> G=\alpha S + (1-\alpha)e e^{T}/N</math>
and the PageRank vector is the right eigenvector of <math> G </math>
with the unit eigenvalue (<math> G P=P</math>). In a similar way, to determine the CheiRank eigenvector all directions of links in Fig.4 are inverted,
then the matrix <math> S^* </math> is built,
according to the same rules applied for the network with inverted link
directions, as shown in Fig.6. The related Google matrix is
<math> G^*=\alpha S^* + (1-\alpha)e e^{T}/N</math> and the CheiRank vector
is the right eigenvector of <math> G^* </math>
with the unit eigenvalue (<math> G^* P^*=P^*</math>). Here <math> \alpha \approx 0.85 </math> is the damping factor taken at its usual value.
 
==See also==
* [[PageRank]], [[HITS algorithm]], [[Google matrix]]
* [[Markov chains]], [[Transfer operator]], [[Perron–Frobenius theorem]]
* [[Information retrieval]]
* [[Web search engines]]
 
==References==
{{reflist}}
* {{Cite web
| last = [1] Brin S. |coauthors= Page L.
| publisher = Computer Networks and ISDN Systems v.30, p.107
| title =  The anatomy of a large-scale hypertextual Web search engine
|format= <!--None-->| year = 1998
| postscript = <!--None-->
}}
* {{cite book |last= [2] Langville|first= Amity N |coauthors= Carl Meyer|title= [[Google's PageRank and Beyond]] |publisher= [[Princeton University Press]] |year= 2006  |isbn= 0-691-12202-4 }}
* {{Cite web
| last = [3] Austin | first =  David
| publisher = AMS Feature Columns
| title =  How Google Finds Your Needle in the Web's Haystack
| url = http://www.ams.org/samplings/feature-column/fcarc-pagerank
|format= <!--None-->| year = 2008
| postscript = <!--None-->
}}
* {{Cite web
| last = [4] Donato D. |coauthors= Laura L., Leonardi S., Millozzi S.
| publisher = Eur. Phys. J. B v.38, p.239
| title =  Large scale properties of the Webgraph
|format= <!--None-->| year = 2004
| postscript = <!--None-->
}}
* {{Cite web
| last = [5] Pandurangan G. |coauthors= Ranghavan P., Upfal E.
| publisher = Internet Math. v.3, p. 1
| title =  Using PageRank to Characterize Web Structure
|format= <!--None-->| year = 2005
| postscript = <!--None-->
}}
* {{Cite web
| last = [6] Litvak N. |coauthors= Scheinhardt W.R.W, Volkovich Y.
| publisher = Lecture Notes in Computer Science, V.4936 p.72 {{doi|10.1007/978-3-540-78808-9}}
| title =  Probabilistic Relation between In-Degree and PageRank
|format= <!--None-->| year = 2008
| postscript = <!--None-->
}}
* {{Cite arxiv
| last = [7] Chepelianskii | first =  Alexei D.
| eprint = 1003.5455
| title = Towards physical laws for software architecture
| year = 2010
| postscript = <!--None-->
}}
* {{Cite web
| last = [8] Zhirov A.O. |coauthors= Zhirov O.V., Shepelyansky D.L.
| publisher = Eur. Phys. J. B v.77, p.523
| title =  Two-dimensional ranking of Wikipedia articles
|format= <!--None-->| year = 2010
| postscript = <!--None-->
}}
* {{Cite web
| last = [9] Kleinberg |first = Jon
| publisher = Journal of the ACM v.46(5), p.604
| title =  Authoritative sources in a hyperlinked environment
|format= <!--None-->| year = 1999
| postscript = <!--None-->
}}
* {{Cite web
| last = [10] Fogaras |first = D.
| publisher = Lecture Notes in Computer Science v.2877, p.65
| title =  Where to start browsing the web?
|format= <!--None-->| year = 2003
| postscript = <!--None-->
}}
* {{Cite web
| last = [11] Hrisitidis V. |coauthors= Hwang H., Papakonstantinou Y,
| publisher = ACM Trans. Database Syst. v.33, p.1
| title = Authority-based keyword search in databases
| format= <!--None-->| year = 2008
| postscript = <!--None-->
}}
* {{Cite arxiv
| last = [12] Ermann L. |coauthors= Shepelyansky D.L.
| eprint = 1103.5027
| title = Google matrix of the world trade network
| format= <!--None-->| year = 2011
| postscript = <!--None-->
}}
* {{Cite arxiv
| last = [13] Ermann L. |coauthors= Chepelianskii A.D., Shepelyansky D.L.
| eprint = 1106.6215
| title = Towards two-dimensional search engines
| format= <!--None-->| year = 2011
| postscript = <!--None-->
}}
 
==External links==
* [http://www.quantware.ups-tlse.fr/QWLIB/2drankwikipedia/ Two-dimensional ranking of Wikipedia articles]
* [http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank/ World trade: CheiRank versus PageRank]
* [http://www.quantware.ups-tlse.fr/QWLIB/dvvadi/ Towards two-dimensional search engines]
 
[[Category:Link analysis]]

Latest revision as of 22:04, 17 August 2014



Gerber On Sale New Knives & Gear Bear Grylls Series Camping Knives Fishing Knives Fixed Blades Folding Knives Gerber Flashlights Gerber Gator Hunting & Survival Kits Hunting Accessories Hunting Knives Multi-Tools Pocket Knives Saws & Axes Shovels & Spades Survival & Rescue

This dagger-like knife from Browning's Black Label line of tactical gear is this gallery's sharpest knife – on both sides! The Backlash is each perfectly symmetrical knife and completely balanced. Few knife designs have the penetrating energy and the rich history of the dagger. This double-edged fixed-blade has a hollow-ground 440 stainless steel blade with a titanium finish. The handle is built from CNC-machined black G10 material, and has a stainless steel pommel and hand guard. The molded polymer sheath, with its Tek-Lok belt clip, adjusts into various positions offering a range of carry choices. Use the Backlash as a boot knife, as a belt knife, or repair it to your backpack straps so you generally have a dagger at hand.

I got my 1st KaBar when I was 18. It was provided to me by my recruiter when I joined the Marines. Ever given that then, that knife had been with me virtually everywhere, such as my deployment to Iraq. The knife is sturdy and seriously stands up for its reputation. When I left the Marine Corps, i passed it on to 1 of my guys. Considering the fact that then, I've owned a lot of unique knives that are popular in the market, but i really feel like practically nothing can compare to this classic. Right after much consideration, I've decided obtain an additional 1.

A “lockback” performs like awith the added benefit of folding into the deal with for security and comfort. The lockback gets its name from the rocking lock plate visible on the back of the deal with. Opening the blade causes the rocker to lock against the blade, locking it open. To release the “lock,” simply push down on the rocker at the back of the handle. Closing generally calls for two hands, though there are 1-hand openers, which are best for activities like climbing where only one hand is free. Liner Locker – One particular-Hander

The SRK functions a 6-inch, AUS-8A stainless steel, teflon coated blade. The teflon coat eliminates the glare although at the exact same time, adds protection against corrosion. The blade itself is a clip point style with a three/16-inch thickness. A really powerful blade certainly! Best for detail tasks, general cutting, slicing, chopping, and skinning. Knife Mule is proud to announce that that their top rated ranked on line knife super shop has been continuing to add the quantity of higher top quality knife producers for customers. The dedicated client base of Knife Mule is going to be thrilled at the new selection of quite higher excellent prime notch knife producers and suppliers that will be featured on Knife Mule in the coming months. Stuff You Can Use A Massive Knife For

Combining excellent with lost expense, Cold Steel's Pendleton Lite Hunter counters the notion that to get the most effective, you spend far more. If you have any kind of inquiries regarding where and how you can utilize Best Pocket Knife Whittling (like this), you can contact us at the page. Cold Steel's budget fixed blade hunting knife won the 2010 "Best of the Ideal" Hunting Knife award from Field & Stream magazine. In this post I am going to be seeking at just 5 such knives that I own, but if you want to look at more options then Blade Reviews is a great place to commence This knife is a joy to use. The blade control is nice, the grip is strong and the mass of the knife lends to nice chopping. Of all the knives I tested, this knife excelled at no task and failed at none as nicely. – Spyderco Tenacious Black G-ten Handle Black Blade Knife – Much more Facts & Evaluations Fig 1. Gerber 31-001066 Bear Grylls Compact Length of blade five.25 “

You want to find a knife maker with a strong warranty, as there are some truly remarkable ones out there. Unconditional lifetime warranties are quite uncomplicated to locate in this solution market, so it would pretty much be stupid not to make a buy if the solution didn't have 1. Though some knives below $20 may well not have these great warranties, it would not be an low-cost replacement fee if anything were to come about. These tactical knives are once again quick to carry and manoeuvre. They could be easily concealed underneath shits and collars and becomes really handy in through emergency tactical scenarios. These have been utilized by the marines for decades and have been their trusted tool to classic combat over generations. Ideal Knife Awesome - OCT 8, 2013 The Knife Blade

Ontario Knives has teamed up with Jeff Randall of Randall Adventure and Coaching to created edge tools. The RAT-three is a compact fixed blade in the RAT line. The RAT-3 has a 3.5-inch D2 tool steel blade. D2 is a good steel for hardness and for influence resistance. D2 sharpens pretty nicely. D2 does have some corrosion troubles, but lots of makers use it. The RAT-3 has a textured epoxy coating on the blade for protection. The drop point blade has a smaller quantity of serrations at the rear of the blade. There is a finger choil and serrated thumb ramp for additional precise cutting or scraping jobs. The blade cut pretty effectively and did effectively on the couple of minor prying jobs it had to perform.

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