Pseudo-Boolean function: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Kilom691
No edit summary
 
en>Legobot
m BOT: Dating templates: {{citation needed}} (2). Errors? stop me
Line 1: Line 1:
Make money online by selling your talents. Good music is always in demand and with today's technological advances, anyone with musical talent can make music and offer it for sale to a broad audience. By setting up your own website and using social media for promotion, you can share your music with others and [http://www.comoganhardinheiro101.com/?p=14 ganhe dinheiro] sell downloads with a free PayPal account. These suggestions ought to assist you in getting an income from the Internet. The more time you take to learn, the better prepared you will be when you begin. Search online for other articles to learn more so that you can make sure that you have financial success. <br><br><br>As you can see from the above article, anyone can make money in the online world when they have a good idea and solid tips to follow. If you have been reluctant in the past to use the internet [http://www.comoganhardinheiro101.com/?p=73 ganhar dinheiro pela internet] as a way to make money, you shouldn't have to worry any longer now that you read this article. Keep studying this topic, and soon you will see how it is possible to make money online.<br><br>for those able to guide them through their learning. Tutoring [http://www.comoganhardinheiro101.com/?p=18 como ficar rico] is also highly rewarding from a philanthropic standpoint.<br><br>After reading this article, you should be ready to start making some real cash online. All you have to do is to use the tips laid out here for you to use. You will find that making money online is easier than you thought, and that it is a real possibility for you. Thousands [http://www.comoganhardinheiro101.com/inicio/ ganhe dinheiro] of people across the country are now making online and loving every minute of it. Print this article out and keep it where you can see it and refer to it when necessary. Making money online is not an opportunity that you will want to miss. It's time for you to get started!<br><br>Start with your own passions. If you really want to make money online, you should pick a field that you're interested in. After all, you are going to spend a lot of time with it. If you're only trying forex because you heard it made a lot of money, for example, you're going to be bitterly [http://www.comoganhardinheiro101.com/?p=16 como conseguir dinheiro] [http://comoganhardinheiropelainternet.Comoganhardinheiro101.com/ disappointed] when you fail because you don't know anything about it. Now that you've read this guide, you now know tips on how to make money online. Use these tips for better cash flow. There are myriad opportunities to pad your pocket with online jobs. Soon, you could be raking it in.<br><br>Do you have a heart for customer service? If so, you can make money online answering phone calls for businesses. Additionally, you can make money by chatting online with a business's customer to help them solve problems and answer their questions. There are many customer service sites available including: LiveOps, [http://www.comoganhardinheiro101.com/ganhar-dinheiro-pela-internet-com-opcoes-binarias/ ganhar dinheiro] Working Solutions and ACD Direct. Now that you've read all of these great tips and tricks, you are primed to make some money online. Take your time as you begin to figure out what niche is right for you. Once you find your money making opportunity, build up your drive and start tackling it with passion!<br><br>When you are in a hurry to make money, reading about the topic may seem frustrating. The fact is that the more you know, the faster and better you will be at bringing in income. This article has given you the foundation you need, so build on it with  ganhar dinheiro experience and more learning. If you did [http://www.comoganhardinheiro101.com/ ganhe dinheiro na internet] not know you could make money online before now, you have been missing out. It is time to take control and make your own money online, too! The information given here should get you started. You will be surprised to learn just how many ways you can get started with online money making!<br><br>Now you know how to start your online revenue stream. Keep your focus and make smart choices and you are sure to be a success. Be patient, and in time you'll see some excellent income flowing. You just needed to be pointed in the right direction. [http://www.comoganhardinheiro101.com/?p=4 ganhe dinheiro na internet] These suggestions are methods that have worked for plenty of people and they can work for you, too. Anyone could make cash online, but you must keep learning if you desire to make money. Keep this in mind to get started as soon as possible.<br><br>While the Internet is a 24/7/365 kind of place, you can still make money thinking seasonally. After a major holiday, like Christmas, buy as much holiday decor and related items when they are on clearance. Save the merchandise for nine or ten months and then resell when demand is high again. Some families store entire [http://www.comoganhardinheiro101.com/?p=8 ganhar dinheiro] warehouses full of holiday yard inflatables for substantial profits a year later. You can now see, making money online is going to require some work. This piece ought to have proved useful, and you will ultimately get the results you want. Don't proceed hastily, and use what you've learned here to ensure success.<br><br>Write online to make money. There are quite a few legitimate companies that pay people to write articles online. You can find many different companies that will pay you to write different content with varying topics. If you enjoy writing, you should do research to look for companies  como ganhar dinheiro na internet that will pay you to write [http://www.comoganhardinheiro101.com/?p=10 ganhar dinheiro] online. Look for sources to write content for online venues. Article writing is very lucrative these days and you can take part in it. Understanding how to write and communicate well is key to this endeavor. Sharpen and hone your skills with writing and utilize this to pay big dividends to your online income.<br><br>Now that you've read this article, you know how to both find legitimate money making chances online and utilize them. It's possible to make money through the Internet these days. Be sure you think about what you have just read when you look for work online. Start your online [http://www.comoganhardinheiro101.com/?p=73 ganhe dinheiro] earning today by following the great advice discussed in this article. Earning money is not as hard as it may seem, you just need to know how to get started. By choosing to put your right foot forward, you are heading off to a great start earning money to make ends meet.<br><br>Make an interesting blog. Make posts on it regularly. By using social media site, you can attract new viewers to your page. Once it becomes popular, you could get daily advertisements on your website. When people click over to the advertiser's site, you'll get a commission. Never invest a [http://www.comoganhardinheiro101.com/ ganhar dinheiro] lot of money into any site that claims to offer you unlimited income opportunities. Chances are they will give you information you could have found yourself if you invested the time. This is true for online surveys as well as any other opportunities out there to make an additional income.<br><br>Whenever possible, buy in bulk and then sell individually to make money online. Buy collections of books, video games and music or collectibles. Then piece out the individual pieces one by one for multiple transactions to make the most possible money. Even consider buying on a site where something does not sell [http://www.comoganhardinheiro101.com/opcoes-binarias/ como ficar rico] too well to a site where it should, like buying collections of used books on eBay and selling them individually on Amazon. Freelance. Have much experience with a keyboard? Look to websites like oDesk. You do not even have to be a great writer. It can be daunting, but it can help you make some additional income.<br><br>You can see that making money online is very possible. You just need good information to point you in the right way. Just remember that you will need to put in time and effort on it. Nothing will be handed to you on a silver platter. However, if you put in the effort, you will reap your [http://www.comoganhardinheiro101.com/como-ganhar-dinheiro-pela-internet/ ganhando dinheiro na internet] rewards. You can be among those who profit from working online. Use the ideas that were just presented to you. Soon, you will discover that you are able to make a steady income. Start with the suggestions that are the easiest and build your way up to working on all kinds of tasks.<br><br>Getting paid money to work online isn't the easiest thing to do in the world, but it is possible. If this is something you wish to work with, then the tips presented above should have helped you. Take some time, do things the right way and then you can succeed. Now [http://www.comoganhardinheiro101.com/?p=8 ganhar dinheiro pela internet] you probably are able to see that it is possible to make money online. Whether you're just needing a little bit of income, or you may want a career, you can get these things done now that you know this information. Good luck and don't forget to give it your all!
''See [[homology (mathematics)|homology]] for an introduction to the notation.''
 
'''Persistent homology''' is a method for computing topological features of a space at  different spatial resolutions. More persistent features are detected over a wide range of length and are deemed more likely to represent true features of the underlying space, rather than artifacts of sampling, noise, or particular choice of parameters. <ref>Carlsson, Gunnar (2009). "[http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/ Topology and data]". ''AMS Bulletin'' '''46(2)''', 255&ndash;308.</ref>
 
To find the persistent homology of a space, the space must first be represented as a [[simplicial complex]]. A distance function on the underlying space corresponds to a [[Filtration (mathematics)|filtration]] of the simplicial complex, that is a nested sequence of increasing subsets.  
 
Formally, consider a real-valued function on a simplicial complex <math>f:K \rightarrow \mathbb{R}</math> that is non-decreasing on increasing sequences of faces, so <math>f(\sigma) \leq f(\tau)</math> whenever <math>\sigma</math> is a face of <math>\tau</math> in <math>K</math>. Then for every <math> a \in \mathbb{R}</math> the [[sublevel set]] <math>K(a)=f^{-1}(-\infty, a]</math> is a subcomplex of K, and the ordering of the values of <math>f</math> on the simplices in <math>K</math> (which is in practice always finite) induces an ordering on the sublevel complexes that defines the filtration
: <math> \emptyset = K_0 \subseteq K_1 \subseteq \ldots \subseteq K_n = K </math>
When <math> 0\leq i \leq j \leq n</math>, the inclusion <math>K_i \hookrightarrow K_j</math> induces a [[group homomorphism|homomorphism]] <math>f_p^{i,j}:H_p(K_i)\rightarrow H_p(K_j)</math> on the [[simplicial homology]] groups for each dimension <math>p</math>. The <math>p^{th}</math> '''persistent homology groups''' are the images of these homomorphisms, and the <math>p^{th}</math> '''persistent [[Betti numbers]]''' <math> \beta_p^{i,j}</math> are the [[rank of a group|ranks]] of those groups.<ref>Edelsbrunner, H and Harel, J (2010). ''Computational Topology: An Introduction''. American Mathematical Society.</ref>
 
There are various software packages for computing persistence intervals of a finite filtration, such as [http://code.google.com/p/javaplex/ javaPlex], [http://www.mrzv.org/software/dionysus/ Dionysus], [http://www.sas.upenn.edu/~vnanda/perseus/index.html Perseus], [http://phat.googlecode.com/ PHAT], and the [http://cran.r-project.org/web/packages/phom/index.html phom] R package.
 
==References==
{{reflist}}
 
[[Category:Homology theory]]

Revision as of 13:01, 4 July 2013

See homology for an introduction to the notation.

Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of length and are deemed more likely to represent true features of the underlying space, rather than artifacts of sampling, noise, or particular choice of parameters. [1]

To find the persistent homology of a space, the space must first be represented as a simplicial complex. A distance function on the underlying space corresponds to a filtration of the simplicial complex, that is a nested sequence of increasing subsets.

Formally, consider a real-valued function on a simplicial complex that is non-decreasing on increasing sequences of faces, so whenever is a face of in . Then for every the sublevel set is a subcomplex of K, and the ordering of the values of on the simplices in (which is in practice always finite) induces an ordering on the sublevel complexes that defines the filtration

When , the inclusion induces a homomorphism on the simplicial homology groups for each dimension . The persistent homology groups are the images of these homomorphisms, and the persistent Betti numbers are the ranks of those groups.[2]

There are various software packages for computing persistence intervals of a finite filtration, such as javaPlex, Dionysus, Perseus, PHAT, and the phom R package.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  1. Carlsson, Gunnar (2009). "Topology and data". AMS Bulletin 46(2), 255–308.
  2. Edelsbrunner, H and Harel, J (2010). Computational Topology: An Introduction. American Mathematical Society.