Why TeX math search is more relevant now than ever
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Sojka, Petr
TeX is around 30 years old, and was conceived and written before the advent of MathML, not to mention the Internet. At that time the idea of indexing and searching mathematics was just a futuristic idea. When people jumped on the Google bandwagon, it was predicted that old technologies such as TeX mark-up for math would disappear in time (it is not used for tokenization and indexing properly). The advent of the Internet and \acro{W3C} brought mark-up and global search to the attention of the public. Somehow it was acceptable again. The recent move to the semantic search and MathML has brought renewed attention to the need of unambiguous canonical math representation in texts.
 Well, hopefully I will try to have some more content. As you may have noticed, I borrowed the title from Kave and I will try to answer it actually. So it's a very wide tag and our previous Skawe and Karl and many others have already come with this. Why Tecmas? It also has been talked about, Ross, Rishi and others convince us that Tecmas is the selling point of our tools and Tec and the compact logical expression notation Tec offered is now used throughout the words and it's like by any mathematicians you may think of. So formula is of hundreds of words and Tecmas wins here. But why Tecmas search? Well, nobody has mentioned it here and it's badly needed, however. Searching is a crucial part of accessibility when you have lots of lots of your PDS and you want to access it the most natural and usual ways to search it. And this is no different for mathematics. Why should it? So my honest opinion is that Tecmas search is really a must for when working with lots of data and working with digital library of mathematics, which is actually the project I am now involved in. The logo below when in frame of it we have thought a little more about it and tried to answer the question of the title. Well, one possible answer is because of the G as G as Google and globalization and it's sexy, right? So we have about 100 million pages of peer reviewed mathematics around and the ambition is to search it. It fits on the disk of your notebook and why on earth we shouldn't be able to search it even with formula in it. And well, that's the tasks we were thinking about and the gate to this knowledge is search. Digital library without math or search is an oxymoron. For pure text and keyword based search it's solved problem. You use Google every day and it's supported by review databases like Central Blood so one can say it's success. However, have you tried to search some formula on Google or in other system? There are not many systems that allow it so I would qualify that it's failure so far. So what we can do with that? It's to support that's needed. I come up with some examples. Adding ability to search for formulas in textual search may actually disambiguate and narrow your documents and narrow the search so that you actually find what you are looking for and sometimes the only difference that you can use is actually the formula. So for instance, it's possible that Kabe might be looking for some data for his talk in the whole river valley database of all types of articles ever which might be about my rough estimate is five number digit. I have told VDF people they said they have around 40 or 50,000 articles with Dan Viste and one could search that all within microseconds even with formulas. I have another really examples. Research might be working in some area of differential equations and the types of the equation might be differentiated by the formula so putting a formula in the search is crucial for she or he. And language of mathematics is actually the same with some exceptions for all the natural languages. So having global search, let's say on Google one can use formulas to search all over the place and the differences in notations are there but it might be cope with as such. So our topic of this conference is eBook. Imagine you're on your iPad or in the examples of eBook. Imagine that you may search in it because you usually use it for reference purposes only. Imagine that you can search the formula you remember and want to look for. So the take-off message of this talk is yes, you actually can and we have tried it and we have done it and I will just show you and if time permits I will then make explanation what to do and how it was done. So giving Google question like Einstein, check Google actually does the answer pizza Einstein which is not relevant usually what you are in for. So, what our system actually does? So when you put the query Einstein and his formula in your search box and you press the button which means you search for it, it does a lot of work, it converts it to mathematical, then it converts it into canonized mathematical, some canonical representation of it and then here you are, you have the results with the search terms, these will be the questions. Here then you can take in and go to see the real papers here and you end up in corner. So, how is it done? It is topic for the rest of the talk so I have 15 minutes to describe how it is done and how it works. So when we cope with this problem, we started with review of available solutions, we spoke to Google scholar people because we wanted to search the metadata, at least metadata of the articles on Google scholar and as mathematics is often even in the titles of papers, Google scholar does a bad job in it. There were other attempts by some publishers, for instance Springer offers latex search but it works on the text, literal text of the text mass cut out of their sources and as such it is deemed to fail because one never knows what offer has typed when writing the formula. Every formula has a zillion of ways how it can be entered and typed. So this is not way to go. There are many changes to face. There is heterogeneity of mass representation, notation, the semantics handling and there is no established and accepted user interface and pure language for mass so far. And there were several attempts to solve the problem. There was 7-digit NSF grant by design science some five years ago. It was not seen based essentially indexing and grants of presentation math model but the site is gone, it is lodging, restricting it and even though it was pioneering effort in converting to math model, the results are not seen. There is another project, it is EgoMass by our colleagues, it is web search engine capable of handling mass. They did another step, they brought the idea of formula, augmentation, alpha equivalence, algorithm and relevance calculation solved the problem. I have already spoke about latex search, reactive mass and DLMF digital library of mathematical functions are projects where the mass can be searched by their domain is limited so they are able to offer, they have the offering part under control so they can mark up the formulas according their indexing engines but this cannot be used in general global search. People in Bremen are using semantic approach, they are based on and so it is not real index but the problem is that you can have reasonable amount data disambiguate it with this level of semantic markup. So we have decided to build our own taking lessons from the previous unsuccessful attempts and we have built MIAs engine, mass indexing and searcher which is math-aware full text based search engine. It adds mathematical equation curing to the basic of textual ones. So in addition to standard terms you can have mass in the search query in the standard tech or AMS latex to be precise notation so ideally it should be directly compiled with AMS latex and then you get what you are informed. We had to cope with the duality of tech and mathematical formats. Mass is used by people and here technology means so on the offering side and on the curing side tech is the preferred way of writing and working. However on the software application side, program side, algorithm side the MAPHEM clearly wins all DTPs, all algebra systems allows you to copy and paste formula and integrate in another and put it into browser etc. and some DTP system including KOS are having MAPHEML and XML at its heart. So inevitably a system for searching mass has to cope with this duality. Another idea one should think of it in retrieval is that the indexing terms and the search terms do not necessarily be the strictly same. In text retrieval usually word stems are indexed instead of word forms so in check average word has 30 different word forms so that may help to squeeze the index and there are examples like in tech book don't typesets there are example of content invitation, concept invitation and actually there is not, there is a song but the offer of that song is not on the invitation but it appears in the index. So it's an example that these two are not necessarily strictly same. So the same idea applies for mass search so we have designed the search such that for a given formula we generate set of substitutes more and more general and similar representations of formula. Let's put in the index and there are certain. That's top level architecture of the system. The text plays a role here. Then in the bookman is taken by the handler and the text is strong and the mass takes special care to stop the process and special representation of mass is put into index so that the searcher then may use it and input to it takes similar processing the contents are connected to mass of our timeline and the mass of the search. More precisely during the indexing so that a plus b and b plus a do not have to be the same the two are identical to the index. All the indexing contents are as older so that only the two are identical so that only a plus b and b is in the index the same happens for in the current page. Then it's tokenized so that the representation of the four plans is more general. I mean three variables are numbered and term based on that. So two match as much similar formula as possible and to a small index as possible. Rather big machinery takes care before the terms appear in the index. Let me show it on an example. That's having x squared plus y plus y in the view. So ordering doesn't change it so x is less than y. Then the algorithms for uniformly takes place and several subformally is generated and they are unified, unificationized terms are created. So finally you end up with 16 terms that are put into the index with different weights according to the similarity to the original term. During searching the similar things happen. Two terms are generated. Now four terms are generated and two match the index and for these two the ranking scores are added for the documents. Here you can see more details how the weighting, that means how similar the index terms are to the formula. So this tree has 16 nodes and every list has its weight which is stored in the index too. It's built upon Lucene, latest Lucene as a plugin with Java and it's state of the art digital library stuff used in this space and those of other systems. So nothing new here and it can be directly used in a real system. For evaluation we have used ArcScive converted into the XML. It's about half million documents which were converted to XML plus MathML by our Bremen colleague, Professor Kolhaze and others. At the end of the day we had 158 million of input formulae and with the multiplication we have three billion terms in the index. We have managed to squeeze it into 47 gigabytes so it's still manageable on a modest computer. And for details you can look recent papers of mine and it's the homepage of the project is on this URL. It scales well. The response time is still under half a millisecond. The indexing takes place several hours. We went down from 23 hours to nine with threading and as it scales linearly one can use parallel Lucene implementation when you see that your query response time is too high. So it can easily be map produced and used by Google without problems. So here is the URL for the demo interface. You can go there, play with it as I have already shown and search using this three billion index. And the ideas I have already spoke about, we convert to presentation with Tralix but later ML or other converters might be used. We use the UUMC library for canonicalization of MAHMAL. We generate snippets containing the formulae and we use the docs on the web. And it's already integrated in the UDML system which is, the demo is also already up and running on demo.UDML.U if you may give it a try. I have brought some interviews about the project and some of you have already took it. I also have here some papers if you want to go into the details. So to sum up, well, for the content you should have the data and our people in Birmingham are doing PDF to latex converter. So from this we will have MAHMAL for indexing even from PDF where we do not have access to the sources. We have developed a copy package where the tech part of formula is put as a second layer in the PDF. So we suggest publishers use it so that it would be easier to index it with MAHS in the future. Well, there are plenty of other things to do on our to-do list. It's worth mentioning that the approaches can be used even for content MAHMAL. So in case your data has content MAHMAL, these might be as trees inserted in the index as well and used in the searches. So it does depend on your preprocessing and the technology framework allows for it. And, well, we may think of something like Sage to canonize the MAHMAL before indexing, but that's another story. So we think we have done some steps towards the mass search engine for a community of mathematicians and perhaps also users of stuff you are types of thing. It's already imploded in DML. I do have papers with details that were published in Springlink and ACM.dl in recent doc-ank proceedings. Those who want preference, I can give some. So that's not... I haven't done this work alone. Of course, most of the hard work was done by my students, Martin Lischka and Michal Ruzicka. It was done within the funding of UDML project. And I owe a lot to the offers and contributors of tools used and also Kave for permitting me to steal his tight land part of his abstract. Thank you. Thank you very much. Questions. Unusual. Boris has a question. The problem with mathematics in tech is that it's extensible. In AMS, Leitech can say in the beginning declare math operator and create my own operator for my own operations. My question is, will... would your system understand this and just use a new op in the conversion and work? Well, the system works when you are able to convert it into math ML. So, well, it's easily... and reach it... currently our products is configured for full AMS Leitech. It's easy to add new markup similarly as you add support for it, for tech for HD or whatever. On this side, it's fine. It's harder to extend it in math ML. You may have to wait for math ML 4 or whatever will support your new operators and the like. So, once it ends in visually descriptive, in visual... at least as visual appearance of your operators is capable to be described by math ML 3, presently it's math ML it will do. And given that your... given that the system configured for conversion from your tech markup. Right? Anjusha. It's great to hear about it, but the examples which we have seen... examples which we have seen, it is about very small expression. What about complicated expressions? That is one thing. Another thing is about... you said it is all depend on what math ML... it is depend on math ML if it could convert the formula. But if you can look at the tech file which is already having the mathematics in textual format and most of the journals they are also asked for the tech file. So, it is also possible to operate your thing on the tech file and the mathematical formula which is available there. Do you think so? Wow. So, first question reminds me the first one. Yeah. So, one... an ArchSyffe article happened to be one big... really big formula. It started with dollar and then all the text was the text inline text. And that would rather huge and it generated a lot of sub-formulas but well the system called with it. On average on ArchSyffe we have for one formula about 20 to 30 index terms. So, the ratio of 3 million to 158 million formula is about 30 or so. So, the expansion is by 30 it is linear, culpable with... so, I don't see any problem here. The second question was whether it is used zeblon the tech files, right? Wow. You mean the math ML is inside the tech files or no, no. Well, for that you simply put your tech as a query and it gets converted to math ML. It is the mass chunk within the dollar a cent then you can search or index it. So, it... we think that doing that on the tech notation level it's loss of time. It has been proven by latex search that it simply doesn't work. Mathematicians are saying they are not capable of searching... of finding anything there because the differences in one place clearly black kids or twice and spaces there and there. So, you cannot search what are... you can't find what are you looking for. Math ML is called the structure of the formula. So, that's much, much better. Hello. First sort of answer Boris's question. Yeah, it's a tricky thing because I'm talking about the abstract level. The ability to present your latex version with your own carefully constructed macro is actually part of mathematical communication. So, math ML sort of ought to be capturing that. But if you think about the presentation math ML it's not at all clear what you should... because you haven't got a macro language basically attached but it's something that the math ML group is certainly very much aware of. And it becomes really interesting when you're trying to do open math content. Math ML of course because that's really where you do have that information from the author and you either need to make it more explicit as I just suggested or have some nice heuristics for guessing what's going on. If he's using taking... Hello. But I just... more general is just a comment really that as I think implying and that's why I'm making it a bit more explicit. This is actually the start of a well coordinated and very big project that could be a very great importance to publishers and everybody if it all works the way that some very respectable people want it to shall we say. Well, thank you. Well, I agree and the converting from tech to math ML should take care of the peculiarities of authors markup and these are scientific papers so they are... they should appear on paper so on paper you should see the formula or commutative diagram so this should be expressed in some way in math ML at the end of the day. So of course authors are very creative so they will come up and broke something but they will not then be searched by this engine in future math ML so it might be motivation for there to stick to non-solutions. This is kind of the same level as you say authors are very inventive and especially in new fields they tend to invent new symbols or new terminology and this is something that is not yet standardized so the same concept could be represented by three or four different means. I guess the question is how do we get authors to be more standard? Well the answer is well we are doing hard to reach critical mass so that mathematicians will then go hopefully into udml.u as biologists are used to go to the central and they are looking the scientific papers there right who in biomedical domain who is not in public public central as is if it's wasn't published. So the dream is that udml will become such established site and then authors will be motivated to cope with the standards as then their stuff will be searchable there and more accessible and that would increase their page ranks etc. So that might be something for authors to be more compliant. One question we've gotten from some authors or other people is is there somewhere a list of what symbols are used in which areas of mathematics has this does anyone know of such a resource? Math society doesn't have any such thing and is not inclined to build one but if one exists I would love to know about it so if anybody does know about such a thing I'd be very appreciative. Final quick comment and we have to move on. Just a quick question to sort of counter Barbara as she's listening. Ross, thank you. I think my answer to that would be do you think that maths notation really has that property? We're not talking about physics notation here remember we're talking about maths notation. That's an open question. So I think part of the reason why it doesn't exist is because maths people don't think that way if you like or they use notation as you know in very strange ways. Thank you very much Pet. Thank you.
 Well, hopefully I will try to have some more content. As you may have noticed, I borrowed  the title from Kave and I will try to answer it actually. So it's a very wide tag and our  previous Skawe and Karl and many others have already come with this. Why Tecmas? It also  has been talked about, Ross, Rishi and others convince us that Tecmas is the selling point  of our tools and Tec and the compact logical expression notation Tec offered is now used  throughout the words and it's like by any mathematicians you may think of. So formula is  of hundreds of words and Tecmas wins here. But why Tecmas search? Well, nobody has mentioned  it here and it's badly needed, however. Searching is a crucial part of accessibility when you  have lots of lots of your PDS and you want to access it the most natural and usual ways  to search it. And this is no different for mathematics. Why should it? So my honest opinion  is that Tecmas search is really a must for when working with lots of data and working  with digital library of mathematics, which is actually the project I am now involved in.  The logo below when in frame of it we have thought a little more about it and tried to  answer the question of the title. Well, one possible answer is because of the G as G as  Google and globalization and it's sexy, right? So we have about 100 million pages of peer  reviewed mathematics around and the ambition is to search it. It fits on the disk of your  notebook and why on earth we shouldn't be able to search it even with formula in it.  And well, that's the tasks we were thinking about and the gate to this knowledge is search.  Digital library without math or search is an oxymoron. For pure text and keyword based  search it's solved problem. You use Google every day and it's supported by review databases  like Central Blood so one can say it's success. However, have you tried to search some formula  on Google or in other system? There are not many systems that allow it so I would qualify  that it's failure so far. So what we can do with that? It's to support that's needed.  I come up with some examples. Adding ability to search for formulas in textual search may  actually disambiguate and narrow your documents and narrow the search so that you actually  find what you are looking for and sometimes the only difference that you can use is actually  the formula. So for instance, it's possible that Kabe might be looking for some data for  his talk in the whole river valley database of all types of articles ever which might be  about my rough estimate is five number digit. I have told VDF people they said they have  around 40 or 50,000 articles with Dan Viste and one could search that all within microseconds  even with formulas. I have another really examples. Research might be working in some area  of differential equations and the types of the equation might be differentiated by the  formula so putting a formula in the search is crucial for she or he. And language of  mathematics is actually the same with some exceptions for all the natural languages.  So having global search, let's say on Google one can use formulas to search all over the  place and the differences in notations are there but it might be cope with as such. So  our topic of this conference is eBook. Imagine you're on your iPad or in the examples of  eBook. Imagine that you may search in it because you usually use it for reference purposes  only. Imagine that you can search the formula you remember and want to look for. So the  take-off message of this talk is yes, you actually can and we have tried it and we have  done it and I will just show you and if time permits I will then make explanation what  to do and how it was done. So giving Google question like Einstein, check Google actually  does the answer pizza Einstein which is not relevant usually what you are in for. So,  what our system actually does? So when you put the query Einstein and his formula in your  search box and you press the button which means you search for it, it does a lot of  work, it converts it to mathematical, then it converts it into canonized mathematical,  some canonical representation of it and then here you are, you have the results with the  search terms, these will be the questions. Here then you can take in and go to see the  real papers here and you end up in corner. So, how is it done? It is topic for the rest  of the talk so I have 15 minutes to describe how it is done and how it works. So when we  cope with this problem, we started with review of available solutions, we spoke to Google  scholar people because we wanted to search the metadata, at least metadata of the articles  on Google scholar and as mathematics is often even in the titles of papers, Google scholar  does a bad job in it. There were other attempts by some publishers, for instance Springer  offers latex search but it works on the text, literal text of the text mass cut out of their  sources and as such it is deemed to fail because one never knows what offer has typed when  writing the formula. Every formula has a zillion of ways how it can be entered and typed. So  this is not way to go. There are many changes to face. There is heterogeneity of mass representation,  notation, the semantics handling and there is no established and accepted user interface  and pure language for mass so far. And there were several attempts to solve the problem.  There was 7-digit NSF grant by design science some five years ago. It was not seen based  essentially indexing and grants of presentation math model but the site is gone, it is lodging,  restricting it and even though it was pioneering effort in converting to math model, the results  are not seen. There is another project, it is EgoMass by our colleagues, it is web search  engine capable of handling mass. They did another step, they brought the idea of formula,  augmentation, alpha equivalence, algorithm and relevance calculation solved the problem.  I have already spoke about latex search, reactive mass and DLMF digital library of mathematical  functions are projects where the mass can be searched by their domain is limited so they  are able to offer, they have the offering part under control so they can mark up the  formulas according their indexing engines but this cannot be used in general global search.  People in Bremen are using semantic approach, they are based on and so it is not real index  but the problem is that you can have reasonable amount data disambiguate it with this level  of semantic markup. So we have decided to build our own taking lessons from the previous  unsuccessful attempts and we have built MIAs engine, mass indexing and searcher which is  math-aware full text based search engine. It adds mathematical equation curing to the  basic of textual ones. So in addition to standard terms you can have mass in the search query  in the standard tech or AMS latex to be precise notation so ideally it should be directly  compiled with AMS latex and then you get what you are informed. We had to cope with the duality  of tech and mathematical formats. Mass is used by people and here technology means so on  the offering side and on the curing side tech is the preferred way of writing and working.  However on the software application side, program side, algorithm side the MAPHEM  clearly wins all DTPs, all algebra systems allows you to copy and paste formula and  integrate in another and put it into browser etc. and some DTP system including KOS are having MAPHEML  and XML at its heart. So inevitably a system for searching mass has to cope with this duality.  Another idea one should think of it in retrieval is that the indexing terms and the search terms  do not necessarily be the strictly same. In text retrieval usually word stems are indexed  instead of word forms so in check average word has 30 different word forms so that may help  to squeeze the index and there are examples like in tech book don't typesets there are  example of content invitation, concept invitation and actually there is not, there is a song  but the offer of that song is not on the invitation but it appears in the index. So it's an example  that these two are not necessarily strictly same. So the same idea applies for mass search  so we have designed the search such that for a given formula we generate set of substitutes  more and more general and similar representations of formula. Let's put in the index and there  are certain. That's top level architecture of the system. The text plays a role here.  Then in the bookman is taken by the handler and the text is strong and the mass takes special care  to stop the process and special representation of mass is put into index so that the searcher  then may use it and input to it takes similar processing the contents are connected to  mass of our timeline and the mass of the search. More precisely during the indexing so that  a plus b and b plus a do not have to be the same the two are identical to the index. All  the indexing contents are as older so that only the two are identical so that only a plus b  and b is in the index the same happens for in the current page. Then it's tokenized so  that the representation of the four plans is more general. I mean three variables are  numbered and term based on that. So two match as much similar formula as possible and to  a small index as possible. Rather big machinery takes care before the terms appear in the index.  Let me show it on an example. That's having x squared plus y plus y in the view. So ordering  doesn't change it so x is less than y. Then the algorithms for uniformly takes place and  several subformally is generated and they are unified, unificationized terms are created.  So finally you end up with 16 terms that are put into the index with different weights according  to the similarity to the original term. During searching the similar things happen. Two terms  are generated. Now four terms are generated and two match the index and for these two the  ranking scores are added for the documents. Here you can see more details how the weighting,  that means how similar the index terms are to the formula. So this tree has 16 nodes and  every list has its weight which is stored in the index too. It's built upon Lucene, latest  Lucene as a plugin with Java and it's state of the art digital library stuff used in this  space and those of other systems. So nothing new here and it can be directly used in a real  system. For evaluation we have used ArcScive converted into the XML. It's about half million  documents which were converted to XML plus MathML by our Bremen colleague, Professor  Kolhaze and others. At the end of the day we had 158 million of input formulae and with  the multiplication we have three billion terms in the index. We have managed to squeeze it  into 47 gigabytes so it's still manageable on a modest computer. And for details you can  look recent papers of mine and it's the homepage of the project is on this URL. It scales well.  The response time is still under half a millisecond. The indexing takes place several hours. We  went down from 23 hours to nine with threading and as it scales linearly one can use parallel  Lucene implementation when you see that your query response time is too high. So it can  easily be map produced and used by Google without problems. So here is the URL for the demo  interface. You can go there, play with it as I have already shown and search using this  three billion index. And the ideas I have already spoke about, we convert to presentation  with Tralix but later ML or other converters might be used. We use the UUMC library for  canonicalization of MAHMAL. We generate snippets containing the formulae and we use  the docs on the web. And it's already integrated in the UDML system which is, the demo is  also already up and running on demo.UDML.U if you may give it a try. I have brought some  interviews about the project and some of you have already took it. I also have here some  papers if you want to go into the details. So to sum up, well, for the content you should  have the data and our people in Birmingham are doing PDF to latex converter. So from this  we will have MAHMAL for indexing even from PDF where we do not have access to the sources.  We have developed a copy package where the tech part of formula is put as a second layer  in the PDF. So we suggest publishers use it so that it would be easier to index it with  MAHS in the future. Well, there are plenty of other things to do on our to-do list.  It's worth mentioning that the approaches can be used even for content MAHMAL. So in  case your data has content MAHMAL, these might be as trees inserted in the index as well  and used in the searches. So it does depend on your preprocessing and the technology framework  allows for it. And, well, we may think of something like Sage to canonize the MAHMAL before  indexing, but that's another story. So we think we have done some steps towards the  mass search engine for a community of mathematicians and perhaps also users of stuff you are  types of thing. It's already imploded in DML. I do have papers with details that were  published in Springlink and ACM.dl in recent doc-ank proceedings. Those who want preference,  I can give some. So that's not... I haven't done this work alone. Of course, most of the  hard work was done by my students, Martin Lischka and Michal Ruzicka. It was done within the  funding of UDML project. And I owe a lot to the offers and contributors of tools used  and also Kave for permitting me to steal his tight land part of his abstract. Thank you.  Thank you very much. Questions. Unusual. Boris has a question.  The problem with mathematics in tech is that it's extensible. In AMS, Leitech can say in  the beginning declare math operator and create my own operator for my own operations. My  question is, will... would your system understand this and just use a new op in the conversion  and work? Well, the system works when you are able to convert it into math ML. So, well,  it's easily... and reach it... currently our products is configured for full AMS Leitech.  It's easy to add new markup similarly as you add support for it, for tech for HD or whatever.  On this side, it's fine. It's harder to extend it in math ML. You may have to wait for math  ML 4 or whatever will support your new operators and the like. So, once it ends in visually  descriptive, in visual... at least as visual appearance of your operators is capable to  be described by math ML 3, presently it's math ML it will do. And given that your...  given that the system configured for conversion from your tech markup. Right?  Anjusha. It's great to hear about it, but the examples which we have seen... examples  which we have seen, it is about very small expression. What about complicated expressions?  That is one thing. Another thing is about... you said it is all depend on what math ML...  it is depend on math ML if it could convert the formula. But if you can look at the tech  file which is already having the mathematics in textual format and most of the journals  they are also asked for the tech file. So, it is also possible to operate your thing on  the tech file and the mathematical formula which is available there. Do you think so?  Wow. So, first question reminds me the first one. Yeah. So, one...  an ArchSyffe article happened to be one big... really big formula. It started with dollar  and then all the text was the text inline text. And that would rather huge and it generated  a lot of sub-formulas but well the system called with it. On average on ArchSyffe we  have for one formula about 20 to 30 index terms. So, the ratio of 3 million to 158 million  formula is about 30 or so. So, the expansion is by 30 it is linear, culpable with... so,  I don't see any problem here. The second question was whether it is used zeblon the tech files,  right? Wow. You mean the math ML is inside the tech files or no, no. Well, for that you  simply put your tech as a query and it gets converted to math ML. It is the mass chunk  within the dollar a cent then you can search or index it. So, it... we think that doing  that on the tech notation level it's loss of time. It has been proven by latex search  that it simply doesn't work. Mathematicians are saying they are not capable of searching...  of finding anything there because the differences in one place clearly black kids or twice and  spaces there and there. So, you cannot search what are... you can't find what are you looking  for. Math ML is called the structure of the formula. So, that's much, much better.  Hello. First sort of answer Boris's question. Yeah, it's a tricky thing because I'm talking  about the abstract level. The ability to present your latex version with your own carefully  constructed macro is actually part of mathematical communication. So, math ML sort of ought to  be capturing that. But if you think about the presentation math ML it's not at all clear  what you should... because you haven't got a macro language basically attached but it's  something that the math ML group is certainly very much aware of. And it becomes really  interesting when you're trying to do open math content. Math ML of course because that's  really where you do have that information from the author and you either need to make  it more explicit as I just suggested or have some nice heuristics for guessing what's going  on. If he's using taking... Hello. But I just... more general is just a comment really that  as I think implying and that's why I'm making it a bit more explicit. This is actually the  start of a well coordinated and very big project that could be a very great importance to publishers  and everybody if it all works the way that some very respectable people want it to shall we say.  Well, thank you. Well, I agree and the converting from tech to math ML should take care of the  peculiarities of authors markup and these are scientific papers so they are... they should  appear on paper so on paper you should see the formula or commutative diagram so this should  be expressed in some way in math ML at the end of the day. So of course authors are very  creative so they will come up and broke something but they will not then be searched by this  engine in future math ML so it might be motivation for there to stick to non-solutions.  This is kind of the same level as you say authors are very inventive and especially  in new fields they tend to invent new symbols or new terminology and this is something that is not  yet standardized so the same concept could be represented by three or four different means.  I guess the question is how do we get authors to be more standard?  Well the answer is well we are doing hard to reach critical mass so that mathematicians will then go  hopefully into udml.u as biologists are used to go to the central and they are looking the scientific  papers there right who in biomedical domain who is not in public public central as is if it's  wasn't published. So the dream is that udml will become such established site and then  authors will be motivated to cope with the standards as then their stuff will be searchable  there and more accessible and that would increase their page ranks etc. So that might be  something for authors to be more compliant.  One question we've gotten from some authors or other people is is there somewhere a list of what  symbols are used in which areas of mathematics has this does anyone know of such a resource?  Math society doesn't have any such thing and is not inclined to build one but if one exists  I would love to know about it so if anybody does know about such a thing I'd be very appreciative.  Final quick comment and we have to move on.  Just a quick question to sort of counter Barbara as she's listening.  Ross, thank you. I think my answer to that would be do you think that maths notation really has that  property? We're not talking about physics notation here remember we're talking about maths notation.  That's an open question. So I think part of the reason why it doesn't exist is because maths people  don't think that way if you like or they use notation as you know in very strange ways.  Thank you very much Pet.  Thank you.
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