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White Smoke Over Oxford?
Posted on December 10, 2015 by woit
I've stolen the title of this posting from Michael Harris, see his posting for a discussion of the same topic.
A big topic of discussion among mathematicians this week is the ongoing workshop at Oxford devoted to Mochizuki's claimed proof of the abc conjecture. For some background, see here. I first wrote about this when news arrived more than three years ago, with a comment that has turned out to be more accurate than I expected "it may take a very long time to see if this is really a proof."
While waiting for news from Oxford, I thought it might be a good idea to explain a bit how this looks to mathematicians, since I think few people outside the field really understand what goes on when a new breakthrough happens in mathematics. It should be made clear from the beginning that I am extremely far from expert in any of this mathematics. These are very general comments, informed a bit by some conversations with those much more expert.
What I'm very sure is not going to happen this week is "white smoke" in the sense of the gathered experts there announcing that Mochizuki's proof is correct. Before this can happen a laborious process of experts going through the proof looking for subtle problems in the details needs to take place, and that won't be quick.
The problem so far has been that experts in this area haven't been able to get off the ground, taking the first step needed. Given a paper claiming a proof of some well-known conjecture that no one has been able to prove, an expert is not going to carefully read from the beginning, checking each step, but instead will skim the paper looking for something new. If no new idea is visible, the tentative conclusion is likely to be that the proof is unlikely to work (in which case, depending on circumstances, spending more time on the paper may or may not be worthwhile). If there is a new idea, the next step is to try and understand its implications, how it fits in with everything else known about the subject, and how it may change our best understanding of the subject. After going through this process it generally becomes clear whether a proof will likely be possible or not, and how to approach the laborious process of checking a proof (i.e. which parts will be routine, which parts much harder).
Mochizuki's papers have presented a very unusual challenge. They take up a large number of pages, and develop an argument using very different techniques than people are used to. Experts who try and skim them end up quickly unable to see their way through a huge forest of unrecognizable features. There definitely are new ideas there, but the problem is connecting them to known mathematics to see if they say something new about that. The worry is that what Mochizuki has done is create a new formalism with all sorts of new internal features, but no connection to the rest of mathematics deep enough and powerful enough to tell us something new about that.
Part of the problem has been Mochizuki's own choices about how to explain his work to the outside world. He feels that he has created a new and different way of looking at the subject, and that those who want to understand it need to start from the beginning and work their way through the details. But experts who try this have generally given up, frustrated at not being able to identify a new idea powerful enough in its implications for what they know about to make the effort worthwhile. Mochizuki hasn't made things easier, with his decision not to travel to talk to other experts, and with most of the activity of others talking to him and trying to understand his work taking place locally in Japan in Japanese, with little coming out of this in a form accessible to others.
It's hard to emphasize how incredibly complex, abstract and difficult this subject is. The number of experts is very small and most mathematicians have no hope of doing anything useful here. What's happening in Oxford now is that a significant number of experts are devoting the week to their best effort to jointly see if they can understand Mochizuki's work well enough to identify a new idea, and together start to explore its implications. The thing to look for when this is over is not a consensus that there's a proof, but a consensus that there's a new idea that people have now understood, one potentially powerful enough to solve the problem.
About this, I'm hearing mixed reports, but I can say that some of what I'm hearing is unexpectedly positive. It now seems quite possible that what will emerge will be some significant understanding among experts of a new idea. And that will be the moment of a real breakthrough in the subject.
Update: Turns out the "unexpectedly positive" was a reaction to day 3, which covered pre-IUT material. Today, when things turned to the IUT stuff, it did not go well at all. See the link in the comments from lieven le bruyn to a report from Felipe Voloch. Unfortunately it now looks quite possible that the end result of this workshop will be a consensus that the IUT part of this story is just hopelessly impenetrable.
Update: Brian Conrad has posted here a long and extremely valuable discussion of the Oxford workshop and the state of attempts to understand Mochizuki's work. He makes clear where the fundamental problem has been with communication to other mathematicians, and why this problem still remains even after the workshop. The challenge going forward is to find a way to address it.
37 Responses to White Smoke Over Oxford?
Eric Weinstein says:
Thanks for this post. I think what is so confusing about this situation actually comes from how many mathematicians portray the field (at least to the outside world). In this fantasy description, mathematics is a uniquely objective subject and the only thing that matters is the proof. To my mind, Mochizuki is taking this portrayal quiet literally. In so he is revealing to the wider world what many Mathematicians are reluctant to admit to the public if not themselves.
In fact, the mathematical literature is very human in that it is filled with ambiguous statements, logical gaps, wrong proofs, attribution errors. With that said, there is *something* objective about it. In general, when well regarded(1) people from well known research institutions(2) with little history of making big false claims(3) are willing to write up something explicit(4) which is not too long(5) in roughly familiar terminology(6) in English/French/Russian or other major languages(7) and talk about their work to experts in seminars(8), they trigger a process that produces a level of scrutiny which is usually equal to the task of validating the claim in a matter of days to months. There is also the perverse requirement that the author not develop too much deeply original thinking(0) on her or his way to a proof if this process is to complete quickly.
Now, the problem here is that Mochizuki is pushing enough on various parts of 0-8 that it exposes what mathematicians know but are not always happy to admit: that the field, if it is objective, is not objective in the simple way conveyed to the world. Rather there is an economics of mathematics, a politics of math, and numerous failure modes of math which dominate the short run. In fact many senior mathematicians are of two minds where they know that the field is somehow completely objective and non-objective.
As a former insider turned outsider, I personally think this situation is terrific. In one simple stroke, Mochizuki has showed us that the field is driven by incentives, culture, and human failing. I hope that this proof is correct so that in the second act, he can show us that after the politics, recriminations, and resistance, the field usually ends up with something pretty close to objective truth. Over the long run things are much better, at least as far as the proofs are concerned (if not always the narrative and attribution.)
lieven le bruyn says:
The mood appears to have changed today. Felipe Voloch's daily update is just in :
ABC day 4 : https://plus.google.com/106680226131440966362/posts/LLHPN3QLoqX
Something opposite – Math Quartet Joins Forces on Unified Theory at Quanta: https://www.quantamagazine.org/20151208-four-mathematicians/
Jeffrey M says:
My two cents, as a mathematician, Peter has the process for this kind of thing exactly right. I watched it happen with Perelman's proof of Thurston's geometrization conjecture. I was at a conference maybe a week after it was released, and various experts in the field were there (my field is pretty close) – they had already been working on it feverishly the whole time. And they already were saying it looked likely to hold up. Of course that was a very different set up, since Perelman was doing work which followed in the footsteps of Hamilton (who teaches with Peter at Columbia), and basically what he did was to figure out a way to get through the wall which Hamilton hit. This seems way different, unprecedented more or less. I'm trying to think of a case where there was a completely new way of approaching something, and no one could understand, and I can't. Plenty of times someone comes up with a really new way to look at things, but it's always the case that people catch on pretty quickly, at least the examples I can think of.Usually, if a bunch of very good mathematicians look at something, and tell you it doesn't make any sense, it actually doesn't make any sense.
Rubbernecker says:
1) Its basically in an entirely new sub field and its incredibly rare for someone to move from one area to another
2) At least four people already understand a relatively young theory
3) No mathematician understands the vast majority of extant proofs
Is it maybe not that big a deal if experts working in other areas never understand this proof?
Rubbernecker,
This is supposed to be part of arithmetic algebraic geometry, and say new things about that subject. Many of the people at the workshop are among the best arithmetic algebraic geometers in the world.
What went wrong yesterday is that two of the four people (Mok, Hoshi) who supposedly understand IUT were unable to explain it to anyone else. A third (Yamashita) will try today, but his talks were supposed to assume material from the other two.
Yes, few people understand the details of many complicated proofs. As I was trying to explain here, that's not what's going on. What the experts are trying to find is a new idea that says something about arithmetic algebraic geometry.
The danger here is that IUT is a subject disconnected from the rest of mathematics. If you spend more time studying it, you will learn lots of new definitions, be able to prove lots of theorems relating them, but learn nothing new about other mathematics.
Chris W. says:
Opposite indeed. That's an inspiring story—another great article from Quanta.
RandomPaddy says:
The Scottish legal system has a verdict which may be applicable in this case: Not Proven.
The stark contrast between this conjecture and the recent, say, Polymath projects is glaring.
Michael Hutchings says:
Eric Weinstein: Your comment seems to imply that there is resistance to Mochizuki's work due to non-objective factors. There are of course various heuristics (usually with good reasons) which mathematicians use in deciding whether it is worthwhile for them to invest large amounts of time trying to understand something new. In Mochizuki's case, we have a conference of leading experts, including more than one fields medalist, getting together for a week to do their best to understand his work. One can't really say that his work isn't getting a fair hearing.
Thanks for this. I do not mean to imply that Mochizuki is running into something untoward. I mean to imply that we do a disservice to mathematics when we confuse the objective nature of the underlying subject matter with the way in which humans attempt to do mathematics. I don't mind the heuristics if they are recognized not to be fundamental truths.
Of course there is a resistance here. He is (to the best of my understanding) not bending over backward to decrease the burden on the proof checkers. I would find that annoying were I an expert in this field. But I would never pretend that math is uniquely objective as a profession. Proofs may be objective, but proof checking is not.
Let me make an analogy. In computer software, there is a difference between a code review done by a subjective human doing their best and a code review done by the compiler. What I find at turns amusing and annoying is when mathematicians pretend to be compilers. The compiler doesn't care about commenting code properly. It doesn't see whether a style guide has been adhered to or whether readability mattered to the developer. It just compiles or it fails.
Mochizuki seems not to care particularly for decreasing the burden on his proof checkers. For the subset of those proof checkers who are open about how prone to error and delay this process is, I believe he is acting sub-optimally and should be pushed to be more helpful. But, for those mathematicians who pretend that the profession is blind to all but the objective truth….I think this is a splendid reveal. No compiler takes this long.
What I was trying to get at in my posting is that "proof checking" isn't really what this is about (at some later date "proof checking" comes into play, but other things have to happen first: you can't sensibly check a proof you don't understand). What mathematicians actually do is something much less mechanical, trying to individually embody understanding of mathematical ideas, and share this understanding as a community. The problem here is that Mochizuki is not successfully communicating mathematical ideas to the rest of the community. "What we've got here is failure to communicate…" Why this is happening is a fascinating question, involving both the standard ways the community operates, as well as some very unusual special features of this case. I don't actually know of any other comparable example, and also it's not at all clear where this is going to end up.
sdf says:
Mochizuki has made minimal effort to engage with the community at large. In that case, workshops of this sort set a dangerous precedent. Simply the fact that he has already demonstrated that he is a first rate mathematician means that we should take this thing seriously without a real and proper involvement is silly. Until he begins making more of an effort it should be ignored. And the description given by Veloch of Kuehne's talk on day 2 shows, I think, that this thing is an embarrassment to the organisers and to Oxford by proxy.
jsm says:
There appears to be a black hole: if someone understands Mochizuki, then he can't be understood by anyone else.
Gavrilov says:
"The danger here is that IUT is a subject disconnected from the rest of mathematics."
This is not unprecedented. In 1968, P. S. Novikov and Adian published a
(negative) solution of the famous Burnside problem. The proof was more then 300 pages long, which is impressive but not unheard of even in 1960s. Its peculiarity is
that it does not use any standard methods; the authors pretty much developed a whole new theory from scratch.
Not being an expert, I can't say to what degree this theory (extremely hard to master)
is detached from the rest of mathematics. But it looks like this far it has only been used in a very narrow area of research, more or less close to the original problem.
Admittedly, the "Bernside theory" is built on a rather elementary basis, while Mochizuki started from the height of arithmetic geometry, but I would not call it a radical difference.
If the analogy, and the proof itself, is correct, then eventually we will see half a dozen of experts in this theory who understand it, while the rest of mathematicians, even from close fields, won't bother. Not terribly promising, but we do not always have what we dream of, in life or in mathematics.
Chris Austin says:
Under an earlier post, a commenter said that Mochizuki is a family name associated with the samurai class.
A Scientific American article, "Japanese Temple Geometry," by Tony Rothman, with assistance from Hidetoshi Fukagawa, May 1, 1998, says that during Japan's period of national seclusion, (1639 – 1854), there was a tradition in which samurai and others would prove mathematical theorems, usually about Euclidean geometry, and inscribe them on delicately colored wooden tablets called sangaku, and hang them under the roofs of temples, as an offering to the ancestors. Perhaps Mochizuki views his work in this spirit.
Timothy Gowers says:
I am a complete outsider to this area, but it seems to me that a very important thing that is lacking is some kind of story that explains why Mochizuki's machinery might be appropriate for proving the ABC conjecture. If I contrast it with another area I don't understand — Grothendieck-style algebraic geometry — the latter comes out far more favourably (in this one respect — I'm not talking about the fact that it has obviously been checked by thousands of mathematicians), because there are all sorts of accounts of how the more abstract way of looking at varieties is a fruitful thing to do. I know that if I did want to learn it, I wouldn't be told that I had to become comfortable with a vast array of complicated definitions before any benefits fed back into what I already know about.
The case with Perelman was again very different: I don't understand his proof at all, but I did understand accounts for the non-expert that explained about Ricci flow and what it was supposed to achieve.
What I would want to see from Mochizuki and his followers is a baby result that can be proved by his methods, that points the way towards more complicated ones.
math_lambda says:
On this Mathoverflow page Minhyong Kim, who is one of the organizers, has just written the following :
Update (12 December, 2015): I've written a brief summary of the Oxford workshop on IUTT rather rapidly, so as to save people the trouble of circulating rumours. This seemed to be a reasonable place to put it. All errors in it are my own: http://people.maths.ox.ac.uk/kimm/papers/iutt=clay.pdf
vmarko says:
That link seems to be broken (also on the mathoverflow page)?
Best, 🙂
Peter Shor says:
The link is probably only temporarily broken … Kim explains it in MathOverflow; he took it down while getting permission to quote Mochizuki.
Gowers,
There are cases when it is impossible. The Novikov-Adian theory I mentioned
is an example of a huge machinery designed specifically for an extremely
difficult but very narrow target, which is difficult to use for anything else.
No baby results there.
As I know nothing about IUT I can't say if it is the case, but it may be
a possibility.
Gavrilov, that's very interesting, but it raises an obvious question. If the only way to hit a narrow target is via a huge, elaborate, and seemingly irrelevant theoretical apparatus that has no other applications, then how does anybody discover that apparatus in the first place? There must be some story. The least Mochizuki could do is tell us that story. What is the story in the Novikov-Adian case? It cannot be that, just for fun, they developed an incredibly complicated theory and then observed to their great surprise that it solved precisely one interesting problem. Sometimes the story is that a theory is developed for another purpose but turns out to be useful for the given problem, but you imply that that is not the case for the the Novikov-Adian theory.
I realize that your point is that there aren't baby results along the way. Maybe I should generalize my requirement and say that there should be a path from not understanding the theory at all to understanding it completely that does not require huge leaps of faith that there is some point to what one is learning.
Klas M. says:
I'm far from an expert on the Burnside problem but describing the proof as isolated and without baby results does not seem correct to me. As I have understood it Novikov and Aidan set out to understand and classify periodic words and cancellation in groups and as a result of that work could prove that there are infinite Burnside groups. So before they got to their famous result they also had relevant "smaller" results.
Gowers, you ask questions I would like to know the answers myself.
Apparently, the idea of a solution first came to Novikov in 1950s, but
I do not know how far it was from the final theory, and what was the *story*.
Much less what is the path "from not understanding the theory at all to
understanding it completely" in this case.
These are interesting questions, but probably they could only be answered by an expert.
For those who are interested, I have found a nice piece about the solution
of the general Burnside problem on Mathoverflow, by Mark Sapir.
http://mathoverflow.net/questions/48184/a-synopsis-of-adyan-s-solution-to-the-general-burnside-problem
In particular, it is said that there is no "short description" of Novikov-Adian work.
Yatima says:
Thank you Chris Austin for the sangaku reference. That was an interesting read:
"Many of the problems are elementary and can be solved in a few lines; they are not the kind of work a professional mathematician would publish. Fukagawa has found a tablet from Mie Prefecture inscribed with the name of a merchant. Others have names of women and children—12 to 14 years of age. Most, according to Fukagawa, were created by the members of the highly educated samurai class. A few were probably done by farmers; Fukagawa recalls how about 10 years ago he visited the former cottage of mathematician Sen Sakuma (1819–1896), who taught wasan (native Japanese mathematics) to the farmers in nearby villages in Fukushima Prefecture. Sakuma had about 2,000 students….
The best answer, then, to the question of who created temple geometry seems to be: everybody. On learning of the sangaku, Fukagawa came to understand that, in those days, many of the Japanese loved and enjoyed math, as well as poetry and other art forms."
Sorry Peter for the off-topic posting. Please remove if inappropriate.
Gowers, using your terminology from "Two cultures",
the work of Novikov and Adian is much closer in spirit to problem solving then
to theory building. This is why there is, apparently, no way to describe it in two words.
There are other examples of this sort, although less extreme, such as the Feit-Thompson theorem.
(But probably there are reasons to call this work a new theory, albeit an odd one,
and not a huge collection of tricks. It may be systematic in its own way.)
My point is that when you are focused on a single extremely difficult problem,
then no matter where you started, you have an (unfortunate) chance of producing something as incomprehencible as the Novikov-Adian proof.
David Roberts says:
@Tim Gowers
I think Mochizuki *has* been telling the story of how he came to think of his ideas, and how one should think of his work as approaching the solution: by analogy with other theorems and so on. The problem is that this other, existing, body of work requires something that doesn't exist in the arithmo-geometric world, and this is what his theory is designed to give, at the expense of catapulting out of the usual techniques and objects.
The problem is, there's too much analogy ("alien arithmetic structures" and so on) and less middle-ground explanation before one gets to pages and pages of definitions. I think Lieven le Bruyn did a great job of working through what a Frobenioid is, in a simple and known case. Such unpacking is something Mochizuki didn't do; clearly somebody or some collection of somebodies needs to go back to the precursor papers and fill in all the worked examples that are absent. This is for me the clearest way forward, and how to approach the massive wall of definitions with something like a climbing strategy.
Rh L says:
I think Mochizuki has attempted to tell the story of how he came to develop his ideas in the slightly more expository piece, A Panoramic Overview of Inter-universal Teichmuller Theory, available on his website:
http://www.kurims.kyoto-u.ac.jp/~motizuki/Panoramic%20Overview%20of%20Inter-universal%20Teichmuller%20Theory.pdf
As far as I can tell, and this is with the caveat that I could be very wrong in such a brief space, this grew from Mochizuki's proof of a conjecture of Grothendieck in anabelian geometry. One of the first things he seemed to have done, after proving Grothendieck's conjecture, was to build an analogue of Hodge theory for Arakelov geometry, which he called Hodge-Arakelov theory and wrote about in papers in 1999 and 2002.
In the introduction to Panorama, he characterised the current theory as the result of trying to overcome the difficulties of applying scheme-theoretic Hodge-Arakelov theory to diophantine geometry. The resulting theory appears to be (in part) a theory of non-scheme-theoretic deformations, i.e. a theory that presumably involves geometric structures that go beyond schemes.
random reader says:
(Rh L) "[he built] an analogue of Hodge theory for Arakelov geometry, which he called Hodge-Arakelov theory and wrote about in papers in 1999 and 2002. "
That's strange, because it would have been more important than proving ABC if he had succeeded. Building a working machinery that unifies Hodge theory with its number theoretic analogue (etale cohomology and site, l-adic Galois representations) has been a central goal in algebraic geometry for the past 50 years. It would have been the news of the millenium had somebody done this.
The more limited goal of building a more adelic Arakelov geometry, has been around since the late 1970's, and also considered very important. It is a fearsomely technical subject in ways that run in a different and much less algebraic direction than anything Mochizuki is known to have published or studied. If he had surmounted the difficulties (1) at all, and even better, (2) using his methods that don't rely on heavy doses of modern differential geometry and analysis, that would be considered a titanic achievement. It would have been noticed and recognized in the past 15 years.
That comes to one of the weird points about the Mochizuki ABC papers: where in those documents is there any of the hardcore analysis that one would expect, relating the very general algebra to the analytic number theory problem that is ABC? One would expect at least a page or two (or fifty) of grungy estimates and hard analysis at least for getting a weak form of ABC that might be boosted to full ABC by more algebraic arguments. Mochizuki does seem to use the latter, but there isn't much sign of hard analysis in his papers, and one should be able to find it just by skimming if it's there. This is a question that must have come up in various forms at the Oxford conference — where is the hard work being done? — and it would be a big confidence builder if the believers would just point to the locations in Mochizuki's papers where the analytic-number-theory part of the action takes place. The idea that it can be black-boxed into a few lines of analysis and 500 pages of algebra doesn't sound right.
Having said that, I think the sociological concerns about not leaving Japan to explain the proof, the papers not having been refereed, etc, have been overplayed. The papers contain plenty of motivation and exposition that is illuminating apart from the stated goal of proving ABC. They are quite discursive compared to anything else in the field of arithmetic geometry, which has more than its share of long dense papers, and are not in the impenetrable dense theorem-proof style.
(can't get the formatting to work when posting with firefox, sorry about that.)
@David Roberts, thanks for the nice words. I only "checked" one paper as a non-specialist, got stuck and then discovered the wealth hidden in the Arakelov bit. Just the same, if a student would hand in Fobenioids1 as a paper, she'd have to rewrite it seriously.
Sad to see that some refer to my blog as criticising Mochizuki (or even calling his work 'nonsense'), most recently at "Todeszone der Mathematik". I'm just getting tired of his lack of interest in reaching out.
Also sad to see that Minhyong Kim did not (yet) put his report on last week's Mochizuki-Fest in Oxford back online. I learned a lot from it. Anyway, luckily there's always the mysterious @math_jin Twitter account to repost images of 'lost' files.
As my own 'lost' blog is getting more hits recently I've put a little story online about the Log Lady and the Frobenioid of Z. It's about the Arakelov bit, but probably only digestible if you did see Twin Peaks, the log lady, and Norma at the Double R Diner, way back then…
Brian Conrad says:
@random reader: The "hard analysis" you're looking for is contained entirely in the known equivalence (from several decades back) between Szpiro's Conjecture for elliptic curves and the ABC Conjecture when each is formulated over general number fields (proof going via consideration of Frey curves associated to an ABC triple and a robust variation of the ground field).
Everything Mochizuki is doing is focused on proving Szpiro's Conjecture for all elliptic curves over all number fields. Moreover, it is in the nature of the method that his main work is in the case of elliptic curves satisfying certain auxiliary local and global properties that necessitate working over a somewhat large number field (and the general case is then deduced by a very short argument); in particular, his method does not work directly over Q in the main parts.
For the same reason, one cannot get some insight into Mochizuki's methods by trying to unravel what they are saying in the context of some of the other known concrete consequences, since his entire proof takes place in the setting of Szpiro's Conjecture (whose link to the known consequences via ABC goes through long-known arguments which treat Szpiro's Conjecture as a black box).
It is somewhat akin to the fact that Wiles' proof of Fermat's Last Theorem works not with the Fermat equation, nor even with elliptic curves over Q (for which general modularity in the semistable case was sufficient to apply to hypothetical Frey curves), but rather with Galois representations and modular forms, which in turn admit powerful operations having no interpretation in terms of elliptic curves (let alone the Fermat equation).
That is, one cannot get insight into Wiles' method by thinking solely about the more concrete framework of elliptic curves (because spaces of weight-2 modular forms with a given level generally have Hecke eigenvalues that are not rational, so not all eigenforms in the space are related to elliptic curves).
Brian Conrad,
thanks very much for the comment. Good to see the big guns weighing in here.
I don't see how Szpiro and ABC differ here, or how the lack of visible hard analysis is comparable to Wiles' proof of Fermat's Last Theorem.
In Wiles' work on FLT, the analytic objects he was showing to exist were known to have a rigid algebraic description with rich properties, and conjectured to satisfy a relatively precise (Langlands) equivalence between the algebraic and analytic sides of the coin. Wiles made a breakthough on the Galois (algebraic) side and consequences on the automorphic (analytic) one flowed, but this transfer of results was not itself the novelty of his work. The relations to analysis and the automorphic side of Langlands philosophy were, if vague memory serves, encapsulated in the use of some results from Tunnell's work on icosahedral(?) representations. Correct me if that's wrong, it is surely in your line of expertise and not mine. But the point is that a sufficiently precise translation to the non-analytic setting was already known and Wiles used it, maybe with some new twists, but the main action was in the algebraic theory, deformation of Galois representations, the commutative algebra of Hecke rings, and the patching argument with auxiliary primes.
It is a reasonable and important question to understand what Wiles' proof does at the level of concrete objects such as coefficients of modular forms, since he is ultimately proving an existence theorem for concrete objects and it is a bit outre if there is no way to describe in principle how the machinery unpacks to some sort of complicated manipulation of those objects. Asking the equivalent about Mochizuki's work does not strike me as a form of confusion or category error, but a basic conceptual point that (if answered) would clarify what is happening in his papers.
Returning to Mochizuki's proof and the absence of visible hard analysis there:
Both the Szpiro conjecture and ABC are analytic conjectures, one about numerical invariants of elliptic curves and the other about invariants of pairs of integers (or infinite families of either type of object, and the extension to number fields). In both cases one would expect a proof to include some sort of nontrivial estimation process involving inequalities, real/complex/harmonic analysis, L-functions, differential equations, etc to take place in order to obtain conclusions. Mochizuki works with some version of theta functions, which (maybe in a different setting) were known for a long time to have a more algebraic description, so to an extent there is an algebraization of the things to be proved, but I am not aware of any purely algebraic statement that is known to imply ABC or Szpiro or Vojta conjectures. His papers do involve some estimates, but rather short ones that make up very very little of the content of the papers. This is not the distribution of labor one (or this one commenter) would expect in a paper that purports to accomplish an amazing feat in what is ultimately analytic number theory.
In brief, even taking Szpiro/ABC equivalence as a black box, which might or might not contain a lot of hard analysis, it's hard to see how the Szpiro part can then be proved without lots of additional hard analysis. Perhaps Mochizuki shows that there is so much uniformity in the way the elliptic curve invariants vary, that easy estimates will do. But even this would require some strong results interconnecting the algebra and the analysis and at some point estimates seem likely to intervene.
@random reader:
Perhaps I was unclear in the analogy I was trying to make. The aspect of the proof of FLT I was alluding to was just that even though the statement of most primary interest is about showing that a specific equation has no Q-solution or that a specific q-series with Q-coefficients is in fact a modular form, the actual context for the argument must take place (as you are aware) with Hecke operators acting on spaces with eigenvalues outside of Q and with Galois deformation rings, neither of which can be "interpreted" entirely in terms of an initial more concrete structure of interest (such as a Diophantine equation or a specific q-series or a specific elliptic curve over Q).
That is, it was just meant as an illustration of the well-known fact that to prove a theorem of interest about a concrete thing we may need to enlarge the scope of the problem and then could lose the ability to "interpret" the core ideas of the proof in terms of operations involving just the original concrete thing. An expert in analytic number theory asked me recently how to unravel Mochizuki's arguments in the context of some other concrete consequences, and I had given a related explanation for why that couldn't be done and that this isn't a danger sign at all, and so I tried to import the same explanation for my original reading of your question: I had mistakenly thought you were specifically asking about trying to see where in his arguments he is getting his hands dirty with estimates involving ABC-triples. You won't find it in that form because he never works with ABC-triples.
In the context of Szpiro's conjecture, he also doesn't apply IUT to any old elliptic curve, but has to assume several local and global properties which are always attained after a finite extension of the ground field with controlled degree. So it is an essential feature of his technique that he is permitting rather general ground fields, and in fact the conditions he needs can't ever be fulfilled over Q.
In the end he is going to aim to prove Szpiro (for a given epsilon, with elliptic curves satisfying some specific local and global properties) with a constant depending on the ground field only through its Q-degree, so it is kosher for him to making extensions of controlled degree in the middle of the argument. There is a separate "short" argument using Belyi maps that reduces the general case of Szpiro to the ones he actually handles in the IUT machinery, but this latter argument is a clever proof by contradiction that makes things ineffective roughly as in Roth's theorem.
To tell you where the "analysis" yielding an inequality should be found, I need to say something about what is going on in his method (for which I only have an impressionistic awareness based on some lectures at the Oxford workshop last week). He uses serious algebro-geometric constructions with p-adic theta functions to make cohomological constructions that encode some local numerical invariants arising in Szpiro's conjecture (for an E satisfying the local and global hypotheses alluded to above) in terms of a special kind of fibered category (arising from E – {0}) called a Frobenioid. This encoding involves a controlled ambiguity after accounting for variation of choices made in the construction (i.e., what is intrinsic is not a specific cohomology class, but rather a certain coset by a controlled subgroup of an ambient cohomology group on a certain fundamental group). The full force of Mochizuki's work on the anabelian properties of hyperbolic curves is used to show that everything which just happened can be expressed in terms entirely intrinsic to a Frobenioid without any reference to the original elliptic curve.
The purpose of encoding number-theoretic data (with controlled error) in terms of Frobenioids appears to be that Frobeniods admit additional intrinsic operations (such as a weak version of "Frobenius maps") which one can't express in terms of the original geometric objects (such as punctured elliptic curves). By analyzing how the cohomological constructions interact with those operations (this involves introducing yet more abstract notions, such as "Hodge theaters") eventually after a lot of work he arrives at two bounded domains in an R-vector space, one domain inside the other, and comparing their volumes (which have to be computed!) gives the desired logarithmic form of the inequality with an "error term" (arising from various ambiguities in the constructions) that is the desired uniform constant if one can exert sufficiently precise control on it uniformly in the original elliptic curve. So it is in this final step of computing volumes with an "error term" that your sought-after "hard analysis" should be found.
But the constant obtained in that way isn't the one for Szpiro's Conjecture (for a given epsilon) for all elliptic curves over number fields of controlled degree! It is only suitable for elliptic curves satisfying a specific list of local and global properties. To bootstrap this back to general elliptic curves over an original number field of interest, one needs to go through a proof by contradiction as mentioned above, so in the end the final constant is ineffective (but depends on just epsilon and the Q-degree of the original ground field). So one recovers Mordell but not effective Mordell.
Wow, I didn't expect my comment to have sparked off such an excellent discussion.
@Brian Conrad: Thank you for the illuminating comments and for the excellent notes on the Oxford IUT Workshop you've posted here (via the "mysterious" @math_jin):
http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/
@Lieven le Bruyn: I've also very much appreciated your expository work on Frobenioids. Thank you for pointing out the @math_jin account, it would seem to be very useful at this stage.
@random reader: I was going to chime in on your comment to my remark on Hodge-Arakelov theory, but I think Brian Conrad has addressed that in his notes, i.e. that what was produced in the earlier papers would not have lived up to your expectation of what a "Hodge-Arakelov theory" would be. I think Mochizuki had said as much in the introduction that I was paraphrasing.
For those following comments here, but not updates, you should be reading Brian Conrad's report on the workshop here
Commenting because I can, and because it's not true that people don't read old comment threads[1]: they are an important source of a) historical information b) inside information. The number of times I've searched for things mathematical and found blog discussions on it that I found excellent…
I also wanted to comment on the mathbabe thread after it was closed, to prove up-to-date links for people trawling the interwebs for the history of this interesting episode.
[1] Sure it was a generalisation: I had assumed though that old comment threads were closed to prevent spam. The suggestion of starting a new blog to continue the discussion baffles me.
David Roberts,
The main reason is because of spam, but more specifically because after a certain period the ratio of non-spam/spam comments becomes quite small, and the great majority of traffic to the postings is spambots trying to break in.


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High resolution video and images. This device is cointains a 1280 x 720 resolution camera.
Supports SD cards. Using micro sd cards this can record to cards are large as 32 GB, allowing an impressive 8 hours of high definition video storage.
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text:
Abu Dhabi to add 4,000 hotel rooms
An artists impression of the developed Saadiyat Island
THE Tourism Development & Investment Company (TDIC), the organisation charged with developing the tourism assets of the Abu Dhabi Tourism Authority (ADTA), is currently planning 15 projects in partnership with private investors, which will see up to 4,000 hotel rooms added to the UAE capital's hospitality portfolio within the next three years.
Addressing the Australian Business Group (ABIG) in Abu Dhabi, TDIC's chief executive, Lee Tabler, said: "We have around 15 projects already under discussion and construction with investors and announcements will be made over the next few months. In line with the Abu Dhabi Government's strategy, our approach is driven by an overwhelming desire for sustainable developments of environmental stewardship."
Tabler said TDIC has met with considerable success since its launch earlier this year with its flagship transformation of Saadiyat Island – the natural island lying just 500m offshore Abu Dhabi city. He also reiterated the emirate's partnership with the landmark Emirates Pearl resort, opposite the Emirates Palace and the Angsana brand of the award-winning Banyan Tree with running a boutique eco-resort in the Eastern mangroves area. Much more is to follow I can promise you as we work closely with private investors to scale up Abu Dhabi's tourism offering," he said.
Tabler told ABIG delegates that regionwide individual and corporate investors are keen to enter Abu Dhabi's emerging tourism and hospitality sectors perceiving them as having greater than ever investment returns.
"Business is booming in Abu Dhabi. Try and get hotel accommodation in this city and you will quickly see what I mean. The emirate is now recording some of the world's highest occupancy levels, according to a recent report by Deloittes – which, of course, means there's opportunity ahead.
"Tourism," said Tabler, "is being prioritised by the Abu Dhabi Government as part of its economic diversification strategy with ADTA targeting another 17,000 hotel rooms by 2015 to cope with its projection of three million tourists a year – an increase on the current one million visitors. The authority has approved investment packages for 4,000 new hotel rooms over the next three years."
Tabler said Abu Dhabi had achieved much since the formation 18 months ago of the ADTA. "Things are really on the move."

redpajama_set_name: RedPajamaCommonCrawl


This hearing accessible, non-smoking room features one king sized bed. The room also has a visual alarm and notification devices for the doorbell or door knock and incoming phone calls.
The room features our clean and fresh Hampton bed, comfortable soft seating, an HDTV, microwave, mini-fridge and easy to operate alarm clock/radio. In the bathroom, you will enjoy a WaterPik shower head and bathtub or well lit shower (requested at check in if available). The free WiFi will help you stay connected while on the road. You'll also enjoy the convenience of having a coffeemaker with tea service and iron/ironing board in your room.
This mobility accessible, non-smoking room features one king-sized bed, and an accessible bathtub.
The room features comfortable soft seating, an HDTV, microwave, mini-fridge and easy to operate alarm clock/radio. The free WiFi will help you stay connected while on the road. You'll also enjoy the convenience of having a coffeemaker with tea service and iron/ironing board in your room.
This hearing accessible, non-smoking room features two queen-sized beds.
The room also has a visual alarm and notification devices for the doorbell or door knock and incoming phone calls. The room features our clean and fresh Hampton bed, comfortable soft seating, an HDTV, microwave, mini-fridge and easy to operate alarm clock/radio. In the bath, you will enjoy a WaterPik shower head and curved shower rod. The free WiFi will help you stay connected while on the road. You'll also enjoy the convenience of having a coffeemaker with tea service and iron/ironing board in your room.
This mobility accessible, non-smoking room features two queen-sized beds, and an accessible bathtub.
This mobility and hearing accessible, non-smoking room features two queen-sized beds, and an accessible roll-in shower.
The room also has a visual alarm and notification devices for the doorbell or door knock and incoming phone calls. The room features comfortable soft seating, an HDTV, microwave, mini-fridge and easy to operate alarm clock/radio. The free WiFi will help you stay connected while on the road. You'll also enjoy the convenience of having a coffeemaker with tea service and iron/ironing board in your room.


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text:
» Yaihara Fortis Santiago's blog
Cerebros Home | About |
Latina Science Outreach and Diversity Advocate Is Among 65 Inspiring Women in STEM Award Winners
Submitted by Yaihara Fortis Santiago on 17 August 2016 - 12:40pm
Dr. Mónica I. Feliú-Mójer, vice-director of Ciencia Puerto Rico
Dr. Mónica I. Feliú-Mójer, Vice-Director for Ciencia Puerto Rico (CienciaPR) and Science Outreach Program Manager for iBiology, has been selected to receive the 2016 Inspiring Women in STEM Award from INSIGHT Into Diversity magazine.
This award honors women who work to make a difference in the fields of science, technology, engineering, and mathematics (STEM). Dr. Feliú-Mójer will be featured, along with 64 other recipients, in the September 2016 issue of INSIGHT Into Diversity magazine, the largest and oldest diversity and inclusion publication in higher education.
"Dr. Feliú-Mójer has dedicated her life and work to mentoring and empowering women and underrepresented minorities to find success in STEM careers," said Dr. Giovanna Guerrero-Medina, CienciaPR 's Executive Director. "She has inspired countless numbers of people through her outreach work. All of us at Ciencia Puerto Rico are extremely proud of her."
Inspiring Women in STEM Award recipients were nominated by colleagues or mentees and selected by INSIGHT Into Diversity based on their efforts to inspire and encourage a new generation of young women to consider careers in STEM through mentoring, teaching, research, and successful programs and initiatives.
Ms. Yomarie Bernier, PhD Candidate at Turabo University in Puerto Rico and one of the students who has benefitted from Dr. Feliú-Mójer's mentoring, remarked: "Mónica has been a great role model and advisor to me and many other students. She motivates people with her charisma and passion for her work."
As Vice-director of CienciaPR, a non-profit that promotes STEM education and careers by engaging Latinx STEM professionals, Dr. Feliú-Mójer manages programs to strengthen the professional development of graduate students and connect them with role models and mentors and she leads the organization's science communication initiatives.
"This award is very special. I cherish the opportunity to pay it forward to future generations and honor the trailblazers on whose shoulders we all stand," said Dr. Feliú-Mójer. "I am humbled to be recognized for my work empowering young scientists, particularly young scientists of color, to make sure they develop the leadership skills they need succeed in their careers and also lift their communities as they climb."
Dr. Feliú-Mójer, who was born and raised in Puerto Rico and has a Ph.D. in Neurobiology from Harvard University, is an expert using culturally-relevant and experiential-based lessons to make science and scientific role models accessible to underserved audiences. She has helped edit and publish over 240 science articles for a general public and in 2013 was recognized with the Paul Shin Memorial Award from the Coalition for the Public Understanding of Science. Her work has been featured on international media outlets, such as Univisión, VOXXI, and Scientific American, among others.
In addition to working with CienciaPR, she is also Science Outreach Program Manager for iBiology, a UCSF-based non-profit organization that produces free educational online videos featuring the world's leading biologists.
"Dr. Feliú-Mójer's passion for making science as inclusive as possible through outreach, communication, and education has been both inspiring and motivating for us here at iBiology," said Dr. Sarah Goodwin, iBiology's Director. "The Inspiring Women in STEM award is a wonderful recognition of her commitment and dedication to improving access to science for all."
For more information about the 2016 Inspiring Women in STEM Award, please visit: http://www.insightintodiversity.com/wp-content/media/digitalissues/september2016/
Mujeres Inpiradoras
Insight into Diversity
Yaihara Fortis Santiago's blog
¡Regresa Semillas de Triunfo para niñas de 7mo a 9no grado!
Response for students and STEM educators to the emergency of COVID-19
Natural Disaster Response for STEM Educators in Puerto Rico: How to help?
Ideas para educadores: ¡Ciencia Boricua en la semana de la puertorriqueñidad!
H.R. 2528: STEM Opportunities Act of 2019
Scientific Organizations in PR
Learn more about scientifc organizations in Puerto Rico
Book: ¡Ciencia Boricua!


I suddenly started experiencing random pauses during a print. Was using an older version of Repertier server on a Pi 3. Version 7.something I think.
Was originally installed around march this year and was working fine until a few days ago. Seamed to happen shortly after my webcam feature disappeared.
Iv tried updating to the latest version, and it still happens.
If I plug the printer into my laptop and print from there it is okay, so must be the Pi or Repetier server that is causing the problems.
Any suggestions how to diagnose and fix the problem?
I tried the new pre-configured Pi SD image but couldn't get it to connect to my WiFi. Sounds like a common problem so I just went back to my original SD image and updated.
Yes, wifi is a bit broken in V5 and will be fixed with new update.
To diagnose it you would need to log a print and check at times when it happens. Typical I'd expect some communication errors when print pauses. For this some solutions depending on used firmware exist to solve them more quickly.
Just run a couple of prints, both had just one noticeable pause in them.
I searched logs for error and wait and these two popped up.
Not quite sure what to make of these. Any sugestions?
Checked my firmware settings (Repeteir firmware by the way), and I have the "Send "wait" when firmware is idle." option enabled.
Ill run a print from my laptop and see if i get the same "wait" commands.
Ran a 90 minute print from my laptop and no "Wait" in the log.
Definitely the Pi or Reptier server that is causing the problem.
Everything on the Pi is upto date. Ran the apt-get and apt-upgrade commands last night.
These 2 waits are no pause and are complete in accordance with the protocols. You see firmware is firing a row of ok followed by wait. So server had buffer full and correctly did not send new commands as "ok" was missing and as soon as it received "ok" it answered with moves. This can happen when a longer move prevents freing next "ok".
If exactly that time correlates with a pause it might be that server was paused by linux for some time intensive other job. But that is more or less impossible to detect afterwards. From 0.80.3 on it will therefore get a higher priority.
Iv not checked the exact times of the pauses, but I noticed two pause and there are two waits which seams to much of a coincident.
I checked the niceness parameter for repetier server using the top command and its at the minimum of -20 which as far as i know means the highest priority already.
There are a bunch of other command with nice = -20, but i don't know enough about software to know if this is normal or not, and if not what to do about them.
The command constantly at the top of list when im not printing, and using 1.6% cpu is mjpg streamer. Is this worth killing and trying a print without?
1.7% is nothing if you have 400% on pi 3, so that should not be the issue.
As you already have nice -20 you are using wheezy I guess. On Jessie it gets ignored with current release since I need to reduce limit before it works.
Other processes with -20 should be kernel processes also needing high priority.
Maybe run top on ssh console while printing to see what takes high cpu when hang happens, but would require fast reaction if it is just a short running process like a cron job doing some regular tasks like cleaning logs. As I said log show a possible delay in communication but also show server reacts immediatly after it gets the data. So is it a long move that delays because it blocks the input or is there a hang on communication for some unknown reason.
Hellow. Is there any update on the issue? im having the same problems as described here. Latest server version running it on a raspbery pi w zero on base install.
There is no general problem causing pauses. You need to check console if you experience communication errors which can cause this of course. Also make sure to not have too small gcode segments. With ping pong mode disabled you can normally send 300 lines per second without problems. If your model is so fine that it exceeds it the printer will also get problems getting to speed.
Does that mean that i need to set the input buffer size in the raptier to 16 as well?
I am connecting to it via an ESP3D via direct pin connectioon.
No, that is just how many moves marlin caches. The input buffer is most likely 127 byte long.
ESP3D - does that mean you use tcp/ip over wifi for communication? In that case you might get pauses if wifi gets interrupted. I'm not a big fan of using wifi for sending serial data as it is not stable enough especially if I look at my wifi network. Leases, other devices connecting, delays due to big data packets getting send. No idea what will happen there all the time.


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text:
TV3 est une chaîne de télévision publique catalane en Espagne. Appartenant au groupe Televisió de Catalunya, filiale du diffuseur public Corporació Catalana de Mitjans Audiovisuals, elle est la deuxième chaîne régionale établie dans le pays après la télévision basque ETB 1, et la première à diffuser exclusivement en catalan.

Cette chaîne généraliste accorde une place importante à l'information, au divertissement et à la culture régionale, et met l'accent sur le développement des productions en langue catalane. Leader en termes d'audience au niveau régional pendant près de treize ans (de 1997 à 2003 puis de 2009 à 2016) elle peut également être reçue en Andorre, dans le département français frontalier des Pyrénées-Orientales et dans une partie de l'Aragon. Une déclinaison à vocation internationale de la chaîne, TV3 CAT, est diffusée par voie hertzienne dans les îles Baléares, ainsi qu'en streaming sur internet et sur certains réseaux câblés et internet.

Televisió de Catalunya appart de TV3 possède aussi  de plus qui émettent aussi dans toute la Catalogne et en catalan : Esport 3 (uniquement consacré aux sports), El 33 (destiné à la diffusion de films documentaires), El super 3 (chaîne destinée à diffuser des programmes pour les enfants) et El 3/24 (uniquement diffusion de nouvelles et de programmes d'information).

Histoire
TV3 a commencé ses émissions d'essai le  (jour de la fête nationale de la Catalogne), mais ses émissions régulières ont commencé quelques mois plus tard, le . TV3 a été la première chaîne de télévision à être diffusée uniquement en catalan. En 1985, TV3 a étendu sa couverture à Andorre, en Catalogne Nord, et en communauté de Valence. Un an plus tard, TV3 a inauguré son nouveau siège, une installation de 4.5-hectares à Sant Joan Despí, près de Barcelone.

Depuis 1987, TV3 a diffusé une seconde chaîne audio sur presque toutes les séries et les films en langue étrangère avec l'audio d'origine du programme, d'abord en utilisant le système Zweikanalton, puis maintenant avec Nicam. Les séries et les films locaux sont habituellement diffusés en NICAM stéréo, bien que parfois une piste d'audiodescription pour les téléspectateurs aveugles et malvoyants est également disponible.

En 1988, TV3 a commencé un processus de décentralisation, d'abord avec des programmes de radiodiffusion avec de l'aranais pour le Val d'Aran et, un an plus tard, en ouvrant des bureaux à Tarragone, Gérone, et Lérida, et en créant les Telenoticies Comarques, un programme de nouvelles régionales diffusées simultanément dans quatre différentes éditions, une pour chacune des quatre provinces catalanes.

Programmes
TV3, en tant que service public, est une chaîne généraliste. Dans le domaine informatif, TV3 a trois éditions: les TN Migdia, TN Vespre, TN Comarques et TN Cap de Setmana, les nouvelles du matin dans leur quatrième chaîne uniquement consacrée aux nouvelles 3/24 et la première partie d'Els matins.

Ses premières émissions datent de 1983 ; certaines des plus populaires sont : Ventdelplà, Plats Bruts, Dinamita, El Cor de la Ciutat, Temps de Silenci, La Cosa Nostra, Les Teresines, Una Altra Cosa, Cracòvia,  Polònia ou Merlí.

Identité visuelle

Logos

Slogans
 2010–2013
 2013–2014 :
 2014–2015 :
 2015-2019 :
Depuis 2019 :

Siège
Le siège de Televisió de Catalunya est situé à Sant Joan Despí qui se trouve dans la province de Barcelone. Il est réparti dans plusieurs bâtiments où sont situés les bureaux de chaque chaîne, les centres de service et de contrôle, le centre de production audiovisuelle et le centre de production des services d'information.

TV3 dispose également d'un bureau central à Barcelone et de quatre centres de production à Gérone, Lleida, Tarragone et au Val d'Aran. En outre, elle possède des bureaux à Madrid, Bilbao, Perpignan et Valence, et a des correspondants à Andorre-la-Vieille, Bruxelles, Paris, Londres, Washington DC, Jérusalem et Pékin.

Audiences télévisuelles
Depuis 2009, TV3 est leader d'audiences en Catalogne.

L'audience moyenne annuelle est passée de  en 2007 à  en 2016.

En , la chaîne a atteint un pourcentage de  d'audience, ce qui l'a amenée à obtenir son maximum depuis , se plaçant huit points de La Sexta, qui occupait la deuxième place. TV3 s'est vue favorisée par le suivi informatif des conséquences du référendum du .

Notes et références

Voir aussi

Article connexe

 Canal Nou

Liens externes
 Portail de TV3.cat
 Chaîne YouTube de TV3

Televisió de Catalunya
Chaîne de télévision en Catalogne
Chaîne de télévision en catalan
Chaîne ou station de télévision fondée en 1983

redpajama_set_name: RedPajamaWikipedia


So I went past that puddle again today, on the bus again, and guess what, I photographed two more puddles in the same place - Duke of York Square, right at the Sloane Square end of Kings Road. I spotted the third one on the way back, and thought I'd missed photo-ing it, but when I got home I found that you can just about make out that one way behind the one I photoed properly, on the way.
I'm starting to rather like these damn things. At least they are different. Different because stupid, but different.
I am going to have to take a closer look at them. Maybe there are more that I have yet to observe. Expect lots of reflections in puddles photos, although I promise nothing.


text:
India ushering in rapid structural reforms to become USD 5 trillion economy by 2025: Piyush Goyal
 Addressing the Pravasi Bharatiya Diwas conference, the Commerce and Industry Minister said: "We are working simultaneously to bring about a quantum leap in our quality, in our productivity, in our efficiency, so that Indian Industry can truly expand our export basket, making it bigger, better and broader".
Rs 1,100 cr push for rubber plantation in northeast India
Industry body Automotive Tyre Manufactures Association (ATMA) will invest Rs 1,100 crore to undertake rubber plantation in additional 2,00,000 hectares of land in northeast India in the next five years, officials said on Wednesday.
Piyush Goyal thanks tyre makers for investing Rs 1,100 crore to set up plant in North East India
Assam's Industries and Commerce Minister Chandra Mohan Patowary called upon Chairmen cum Managing Directors of JK Tyre, Apollo Tyres, CEAT and MRF to come and invest in Assam as the state enjoys the geographical advantage of accessibility to ASEAN and South East Asian countries.
Govt paving way for entry of E-20 vehicles in 5 years
Sources said to push the move towards production, the government has also set up a committee of three Union ministers comprising Nitin Gadkari, Dharmendra Pradhan and Piyush Goyal.
Not just freight corridor, DFC a 'Dedicated For Country' scheme: Piyush Goyal
Goyal said the DFCs are the best example of Make in India and Aatmanirbhar Bharat. He said the DFC will play a role similar to what the river Ganga plays in terms of sustaining lives and livelihoods across its course.
India, Bangladesh should collaborate more in farm sector: Piyush Goyal
India has offered duty-free market access to Bangladesh in many products, including agri-exports, Goyal said and assured Bangladesh of complete cooperation in ensuring barrier-free trade between the countries.
India is seeing rapid recovery and progressing towards becoming a manufacturing hub: Piyush Goyal
"Under the mission of Atma Nirbhar Bharat, India is progressing rapidly to become a hub of manufacturing and expand our own role in the global economy," Goyal said, virtually addressing a conference hosted by the Institute of Chartered Accountants of India (ICAI) on Thursday.
DPIIT making genuine effort to provide single window system for approvals: Piyush Goyal
The commerce and industry ministry is making a "genuine" effort to set up a single-window system for approvals and clearances as it would help industry reduce their compliance burden, Union Minister Piyush Goyal said on Tuesday.
India witnessing V-shaped recovery, high FDI growth: Piyush Goyal
The minister said that FDI flows have been continuously growing and that in the April-September period, which is the first half, FDI inflows were about $40 billion, 13% higher than last year.
Startups to become backbone of India, promoting young entrepreneurs with new ideas: Piyush Goyal
"I have no doubt in my mind that that FICCI will be a part of our journey of a new India, of transforming India and building a more powerful India," said Goyal.
India asks EU to remove non-tariff barriers, standards to increase trade
"We will look for Sweden and EU to also opening its doors a little wider, removing some of the non-tariff barriers or standards which are very often unachievable for any country in the world almost other than Europe so that there I reciprocity in trade with Europe and Sweden and expand business on both sides," Goyal said.
Industry seeks clarity on RoDTEP, new FTAs, lower non-tariff barriers
In a meeting with commerce and industry minister Piyush Goyal on Monday, various industry associations also asked the government for clarity on the Remission of Duties and Taxes on Exported Products (RoDTEP) scheme as it is a reimbursement scheme and not an incentive scheme.
Create aggregation points for farm & MSME items, do minimal inspections: Piyush Goyal to states
Piyush Goyal has asked all states and Union Territories to create aggregation points for farm produce and products from micro, small and medium enterprises (MSMEs), move towards minimal inspections and truck stoppages, and establish logistics parks with truck parking and warehousing facilities.
GST framework is impacting engineering companies' exports: EEPC
The exporters had pointed out issues with the rule 96 (10) of the GST framework that is around taxation of goods and services meant for exports.
India's exports decline 18% in April-November period this fiscal: Commerce Secretary
"In 2020-21, April to November, there has been a decline of 17.84 per cent in our exports...If we exclude gems and jewellery and petroleum, then the decline is lower....In the sectors where economic activity is more meaningful in terms of value addition, there the decline is much lower," Commerce Secy said at the Board of Trade meeting.
Board of Trade meeting on Wednesday to discuss ways to boost exports, new foreign trade policy
The board, which includes members from public and private sector, advises the commerce and industry ministry on policy measures related to Foreign Trade Policy (FTP).
Government of India Scale Committee eyes $350-$380 billion in manufacturing value addition
A joint government-industry panel tasked with fast-tracking growth of the Indian manufacturing sector has identified opportunities to create $350-380 billion of local value addition in the coming decade.
Cabinet okays PLI scheme for 10 sectors including auto, telecom
To give an impetus to manufacturing sector, the Centre on Wednesday announced production linked incentive scheme for 10 sectors.
Restoration of India's GSP status, a small Indo-US trade deal to send very strong signal: Mukesh Aghi, USISPF
India is seeking exemption from high duties imposed by the US on some steel and aluminium products, resumption of export benefits to certain domestic products under the GSP, and greater market access for its products from sectors such as agriculture, automobile, automobile components and engineering.
Industries suffer Rs 22,000 crore loss due to suspension of goods trains: Sunder Sham Arora, Punjab minister
Punjab Industries and Commerce Minister Sunder Sham Arora appealed to Railways Minister Piyush Goyal to immediately resume operation of freight trains in the state. Industry representatives are meeting him and apprising him of problems being faced by them due to suspension of trains.


SESA is delighted to announce the publication of Ian Syson's The Game That Never Happened: The Vanishing History of Soccer in Australia. This is a pioneering cultural history of the game in Australia demonstrating that the game has been around as long as any of the other codes of football and is as foreign and domestic as any of them, yet lacks the recognition in the national story that it warrants.
The Game That Never Happenedfinishes where many other histories of Australian soccer have barely even started. It begins in the mid-nineteenth century and concludes between the two world wars, when the game suffers from a massive and perhaps crippling collapse. Australian soccer's prehistory and early history are vital but forgotten stories. If we are ever to domesticate what is still seen as a foreign game by many important historiographical, cultural and media narratives, this story needs to be told. The lie is that soccer is the game that never happened in Australia. That lie needs to be demolished.
Ian Syson is amongst a god-sent minority who are re-telling Australian soccer's historic truth while also challenging accepted notions of what it has supposedly meant to be Australian. Hitherto, the focus on soccer in Australia has skewed errantly towards 'the ethnics', a theme that has provided convenient fuel to the marginalisation inferno that has engulfed Australian soccer since the nineteenth century – except that 'the ethnics' weren't in Australia then. This is not to denounce the most profound impact of European migration on the game in this country since 1950, but it gives welcome oxygen to the ubiquity of Australian soccer since the very earliest days of the colonies' flirtations with football games. For soccer, where did it all go wrong? In the pages of this book we are starting seriously to tread the path to truth and reconciliation.
Ian Syson lectures in literary studies at Victoria University in Melbourne's west. He has researched the histories of Australian football codes for over a decade and has published many scholarly articles and newspaper reviews on Australian soccer.
The book will be launched in August and will be available from all good booksellers via Dennis Jones and Associates at an RRP of $29.95.
The lead picture has two SESA authors, Steve Horvat author of Accomplished Dreamsand Ian Syson with the latter's book at Sailors Rest on the Geelong waterfront in June 2018.


Explore the best tips and practices that can be used to increase the productivity of virtual teams.
A virtual team is a group of individuals who work across time, space and organizational boundaries with links strengthened by webs of communication technology.1 This type of team is becoming more and more popular due to the fact that with laptops, smartphones and internet connections, people can work from virtually anywhere. There are many benefits for organizations, including access to global talent and lower expenses for wages and office space.
In a recent survey, nearly 80% of highly qualified workers reported working always or frequently in virtual teams. However, most of these teams are not productive and successful and fail to meet their goals. On the other hand, the good news is that well-managed virtual teams are productive and successful, sometimes even more successful than the shared office space teams.
Having that in mind, let's discuss the best tips and practices that can be used to increase the productivity of virtual teams.
Communication is one of the most important things in virtual teams. It is usually less effective that the communication in traditional teams. Virtual teams face many difficulties in communication, such as time delays, common reference frames, differences of interpretation, and assurance of participation for remote team members.2 Nonverbal communication is also missing in virtual teams, and even more problems could potentially arise when some team members are co-located while others are in a different geographic location.
Communication needs to consider socio-emotional processes and challenges that arise in virtual teams due to its virtual nature. These processes are relationship building, cohesion (a sense of unity in a team) and trust.
If possible, the first team meeting should be face-to-face. As eye contact and body language help to develop interpersonal connections, face-to-face meetings can create a high level of trust between the team members. If live meeting is not possible, then use video chat instead.
Depending on the issue, different communication technologies should be used. Research has found that face-to-face meetings or phone calls are suitable for ambiguous tasks, managing conflicts, managing external resources, brainstorming and strategic talks. Electronic communication is more suitable for more structured tasks such as routine analysis, examining design tradeoffs and monitoring project status.
Timedoctor utilizes this tip in practice, where each team has their own chat room which is open at all times. The chat room should imitate chat between coworkers in office space, meaning that it should be used for both work-related and non-work-related stuff. However, make sure that these chat rooms are not distracting the team members and lowering their productivity too much.
Shared knowledge databases enable all team members to have access to the same information and to know that others have this information, too. This can solve many communication problems, as well as improve bonds between team members.
In virtual teams, team members are often located in different time zones. In order to eliminate communication time delays for crucial issues, it is important to determine a period when everyone is online and working and to schedule meetings during that time.
Virtual teams are usually composed of members from different cultures. These cultural differences could cause communication problems, so it is important to understand and accept them. There are many ways to do that. One way might be to ask each team member to introduce their country and culture by creating a short presentation.
In order to effectively manage a project, it is recommended to use project management software. There are many apps out there — test them and find out which one suits you best. For virtual teams, the best option is to manage projects in the cloud, as other team members can see their task list, deadlines and other important details. Other than that, most of the traditional project management tips apply. If you are interested in learning more about project management, read the project management series.
On every project, there will be documents that need to be read and/or edited by many people. Having a shared folder on Google Drive is the best option, as it allows both reading and editing the documents simultaneously. Also, some project management apps have file collaboration features.
Screen sharing software allows team members to share their screens. In case of a problem, it is useful that a person could see what team member is exactly doing. Some examples of these tools are Team viewer and Join.me.
Tracking work hours is important, especially if you are paying the team members on a per-hour basis. It is the project manager's tool that will ensure that everyone is present at work and that every team member is working as much as he should.
Tracking work hours can also be used to estimate how much time each team member needs to complete tasks and how accurate he or she is in time estimates.
It is also a good idea to create weekly or monthly reports and to provide bonuses for the most productive team members.
Team members working from home usually prefer flexible working hours. It is good to allow some flexibility, as they will work at times when they are most productive and when they have fewer distractions. However, determine a period when everyone has to be online and working. When everyone is present, it eliminates communication problems, such as time delays, and speeds up task completion in cases when a team member has to wait for a reply regarding a problem before he is able to continue working.
Virtual teams can be as effective as traditional teams. The goal of project manager is to apply the best management practices in order to achieve the project goals and meet the deadlines. Some of the tips and best practices are given above. If there are any tips and tricks that you have used and found effective, feel free to share them in the comments.


I like to try a variety of different chicken recipes, I always prefer to bake the chicken over frying and with the lower prices lately on chicken it makes purchasing in bulk portions that much better. Chicken was always a staple in my family household. Sundays always involved some form of chicken recipe that my parents would conjure up and they would also make sure to stick the chicken in the oven. The right spice mixture goes along way and makes sure that the chicken is never bland while it is baking.
I use a baking sheet to place all the chicken bites, don't forget to place some parchment paper over the baking sheet, as this keeps anything from sticking. This is a low calorie meal that you can serve with vegetables or even your favourite pasta. Panko bread crumbs was my choice for this recipe but you can usually regular bread crumbs if that is all you have. Have a ziploc bag handy for a cleaner mix of ingredients before you place it on the baking sheet. Kids will love these with a side dipping sauce of your choice.
2- Place the chicken in large bowl.
3- Whisk together the egg and mustard in a small bowl.
4- Pour the egg mixture over the chicken and stir to coat well.
5- Combine remaining ingredients in large resealable plastic bag, add chicken and shake to coat well.
6- Place chicken on baking sheet and bake for 30 minutes until sizzling.
I prefer baking my chicken 'bites' as well though every once in a while, a shallow fried chicken cutlet or schnitzel is a real treat. I wonder if one could make a Buffalo wing version of these bites. Love the flavours but find it crazy that chicken wings are usually more expensive to buy than boneless chicken breast on sale!!


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Home >> November 2008 Edition >> FEATURE - From Military to Corporate, True C3
FEATURE - From Military to Corporate, True C3
by Marc LeGare and Edward Topasna
CEO + Program Manager, Proactive Communications
The first decade of the 21st Century has offered satellite telecommunications providers plenty of lessons, challenges, and opportunities from the military customer. As the CEO of Proactive Communications, Inc. (PCI), I will address some of the broader implications for satellite telecommunications providers, lessons that we have learned over the past four years of increasing business. True Command, Control, and Communications (C3), from the military world to corporate environs, is a process whose time has come.
Lesson 1: The War On Terror
The two broadest lessons emerging from the long-term deployments of U.S. military and their support forces revolve around the close integration between military satcom and commercial satellite capacity and the use of satellite communications to jumpstart reconstruction efforts. It should come as no surprise not all of the military satcom requirements are met via their dedicated fleet of satellites. In fact, DISA reported in 2008 that the current mix of military to commercial satellite segment use was 20 to 80 percent and is projected to evolve in three to four years to five to 95 percent.
This should be good news to the commercial satcom (comsatcom) industry and an ongoing integration challenge for military communications planners. This integration effort will significantly influence network security, service delivery, and O&M (operations and management).
Lesson Two: Jumpstart Success + Satcom
The second learning opportunity, and one that PCI has experienced over the past four years, is the use of satellite telecommunications to jumpstart reconstruction efforts.
In any U.S. military campaign, we can expect enemy communications infrastructures to be targeted. Once U.S. forces liberate and occupy, reconstruction starts. For any number of practical and strategic reasons, creating a robust communications infrastructure is an important step in creating stability.
In Iraq, this was accomplished in support of the elections effort and was a significant, ongoing program for PCI. The Iraqi C2 Network (IC2N) was the Iraqi Government's largest satellite telecommunications network and spanned 258 nodes — every province and every major city. The original program did not specifically address transitioning the network to Government of Iraq (GoI) funding, but this did occur and was a strategic success for the USG.
All elections were supported with secure and non-secure voice and data. In fact, the network eventually became the largest secure Voice over IP (VoIP) network over satellite in the world. The ultimate goal for the GoI is to reduce their total cost of ownership by migrating to wireless, microwave, and fiber connectivity to maintain the integrity of their investment. Satellite telecommunications proved to be an invaluable tool in the Iraqi reconstructions effort.
The "20-80/5-95" paradigm presents some challenges to the industry. As the field soldier, airman, sailor, and marine become increasingly networked, real-time imagery and converged communications will increase the demand for more bandwidth. The challenge for milsatcom and comsatcom providers is how to increase throughput without the high investment costs of more satellites. We are seeing this process occur with DVB-S standards, network accelerators, and embedded compression devices. However, having this "free capacity" means an almost constant capital investment on the part of service providers. This will be a challenge to the industry in balancing investment strategies and constant technical change.
A second challenge is one we have seen in the military and is now appearing in the commercial arena — migrating from space segment provider to service provider. The customer, whether military or commercial, looks increasingly for companies that can deliver a communications network in an integrated fashion. Just as the military has seen radio, telephone, and VTC delivered over microwave and satellite, the same is now expected from the
commercial customer.
In the near future, advanced telecommunications providers will have the ability to provide a variety of communications services, including VoIP, radio, VTC, and surveillance. This will create a greater quality of service thereby placing more engineering requirements and necessitating the placement of more personnel in the field on the provider.
As a former war fighter and commander, I can very easily visualize PCI as a multifunctional theater communications brigade. For myself, this is a role reversal as well as an adaptation challenge.
Finally, these challenges offer real opportunities to satellite telecommunications companies who are nimble and aggressive. The first opportunity is the ability to deploy and support converged communications for customers. "Converged communications" can mean almost anything from the well-understood Cisco model of data, VoIP, and video, to the DISA concept of service delivery to the fringe.
The company that can design, deploy, and operate these converged networks will be the "go to" provider for communications requirements that also need satellite space segment for delivery. Customers may include the U.S. military, foreign governments, first responders, disaster assistance organizations, global corporations, or small/medium businesses that require links to global customer bases.
The diagram above depicts PCI's converged communications capabilities as demonstrated at the recent Department of Defense Interoperability Communications Exercise (DICE), an annual event sponsored by the Joint Forces Command and conducted by the Joint Interoperability Test Command. During DICE, PCI demonstrated that our SPaRTAN Communications on the Halt vehicle was able to interface and communicate with Army North (ARNORTH) and FEMA. PCI was able to conduct VTCs, VoIP calls, and email exchange with various Army units as well as federal and state emergency agencies.
ComSatCom Opportunities Ahead
We see the broader implications of command, control, and communications delivered over satellite to the military customer surfacing in other customer groups. Constrained capacity, growing demand, broader uses, converging networks, and technical complexity are providing insightful lessons, complex challenges, and real opportunities for satellite telecommunications companies.
Mr. LeGare became CEO of Proactive Communications, Inc. in 2006, after serving as the company's Chief Operating Officer and Operations Manager since 2003. Under Mr. LeGare's leadership as CEO, Proactive Communications has become the first U.S. company to work directly with the Iraqi Ministry of the Interior. Prior to joining PCI, Mr. LeGare was Senior Consultant and Operations Manager for Force XXI Battle Command Brigade of TRW/Northrop-Grumman. From 1981 to 1999, Mr. LeGare served various command and staff positions for the U.S. Army worldwide, including Battalion Commander from 1999 to 2001. LeGare earned a B.S. from the United States Military Academy, West Point, a Master of Science from the Air Force Institute of Technology, and a Master of Military Arts and Sciences from the School of Advanced Military Studies.
Mr. Topasna was brought into the company as a Program Manager in 2007. After serving for more than 20 years in the U.S. Army as a Signal Warrant Officer, he continued to work with the III Corps, G6 as Network Planner prior to joining PCI. Mr. Topasna served various Signal Battalions, Brigades, and Corps G6 staff positions for the U.S. Army worldwide as a Network Controller, Network Technician, and Network Planner. Mr. Topasna accompanied the 13th Corps Support Command to Iraq during Operation Iraqi Freedom II (OIF II).
About Proactive Communications
Proactive Communications, Inc. (PCI) is a 40 employee IT and Satellite Telecommunications Company with a world-wide footprint. It specializes in creating communications solutions in complex environments. Its telecommunications experience in Iraq and Afghanistan in 2003-2005, an invitation to get involved in Katrina Relief effort was offered. From that experience, PCI has branched out to communications solutions for first responders such as the Florida National Guard.


A smart, durable leather case for the DermLite DL4. Protects the DL4 from drops and scratches as well as making it easily portable.
This sleeve is designed to provide better grip and comfort whilst holding the DermLite DL4. The high-quality silicone protects the DL4 from drops and scratches, whilst still allowing easy access to the power button and charging port.


Emergency services hit out at the "disgraceful" minority of England fans who marked the team's passage to the World Cup semi-finals with disorder.
Some fans were filmed entering Swedish furniture store Ikea after the 2-0 quarter final win over Sweden, chanting "football's coming home", disrupting displays and throwing items around.
Sergeant Wayne Baker, with West Yorkshire Police, tweeted his disgust after pictures emerged of revellers dancing on top of an ambulance in central London.
"When I see behaviour like this it makes me anything but proud to be English .... You are a total disgrace. As for our National Football Team ... that does make me proud to be English!" he wrote.
London Ambulance Service published images of the damage to the vehicle.
"We're delighted with the result, but this has put a big dampener on the celebrations for us: while our officer attended a call nearby, this car was damaged in Borough High Street during the celebrations after the game, it's now off the road to be repaired," they wrote.
Emergency services urged people to share photos on social media to help them find people who damaged the car.
One woman who jumped up and down on the response car, and whose image was widely circulated, has been traced, according to Poplar Police.
"Fairly sure every single one of them will enjoy explaining to the courts why they thought damaging London Ambulance vehicles was the appropriate response to England winning," Tower Hamlets Police wrote on Twitter.
Meanwhile, West Midlands police said it took the most ever 999 calls in its history, logging 3276 in 24 hours owing to "a mix of the sun, World Cup, and alcohol".
A spokesman for the Met said there had not been a spike in call-outs, despite the hysteria following England's victory over Sweden.
The match was held on the same weekend as the London Pride Parade, Wireless Festival and British Summertime Hyde Park, which brought swathes of tourists to the capital.
Videos posted to social media saw huge crowds fill the streets in cities across the country after the team made it through to the World Cup semi-finals.
In Nottingham, a group of supporters were seen dancing on top of a bus shelter, while other clips from Manchester and Birmingham showed people on top of buses with their shirts off.
Footage from Clapham, south London, sees a fan plunge through a glass bus stop roof after leaping from the top of a double-decker bus.
In one video, a car can be seen with a smashed roof and windscreen in Nottingham.
A crowd of supporters were also filmed rushing into an Ikea store in Stratford, east London, dancing on the furniture and kicking items around.
"We are aware of a small group of fans celebrating the match result in one of our stores," an Ikea spokeswoman said.
"Being both British and Swedish, we were on the edge of our seats during the game and we would like to say 'Grattis!' (that's congratulations in Swedish) to the England team for getting through to the semi-finals."
England will meet Croatia in the semi-final on Wednesday evening.
They will play either France or Belgium in the final, held on Sunday, should they get there.


Delmas Colliery South Africa is located at Mpumalanga, South Africa. Location coordinates are: Latitude= -26.25921, Longitude= 28.82831. This infrastructure is of TYPE Coal_Mines and CATEGORY Fuels and Resources. .


maconit® is an Information Technology Staffing and Consulting firm based in Richmond, Virginia. Built on the foundation of establishing long term relationships in the Richmond IT community, maconit® has developed a candidate and employee focused approach. With a senior management staff, dedicated to addressing our candidates' career interests and goals, maconit® takes the time to get to know you, your background and most importantly, your career aspirations.
Can't find a news story? Don't worry, we didn't delete them, they are just tucked away somewhere safe.
Looking for more? We have many open jobs and are looking for people like you to fill them!
maconit® is a privately held corporation located in Richmond, VA. We are one of the most respected consulting and staffing firms in the area.
Our core values of hard work, respecting all people we work with and adhering to ethical business practices have allowed us to develop many strong long term relationships with our clients, employees and candidates.
maconit® is an IT staffing and consulting firm based in Richmond, VA. Our customers are comprised of small, mid-sized, and fortune 500 companies across all sectors of business and government.
Our philosophy of working with clients is similar to that of our candidates; we work hard to get to know your culture and business and build and maintain a long term relationship.
We pride ourselves in our business ethics, comprehensive recruiting process and the ability to deliver quality candidates to our valued clients.
Our senior recruiting staff is dedicated to finding the right candidate the first time. To achieve this, we meet with each of our candidates; perform technical screening, references and background checks and ensure they are a fit both technically and personally for your team!
Many companies actually give you more work to do by bombarding you with resumes. This is not what we consider service. We try to learn as much about your company and job requirements as possible in order to find the right candidate for you the first time.
We perform a very thorough interview process which includes an in-depth personal interview, technical testing and sound reference checks on all candidates.
If for any reason a hire from maconit® doesn't work out in the first 90 days, we will provide a replacement at no additional fee.
Depending on your needs, we can provide a staffing solution to custom fit your company. We provide direct hire staffing (fee based and contract), contract to hire and consulting services.
They actively seek and place some of the best consultants I have ever had the pleasure to work with.
maconit® believes that happy employees lead to satisfied clients. So, we invest in our consultants and provide the tools and support you require! Our employees enjoy a wide variety of benefits and exciting career opportunities.
maconit, Inc. expense form used to reimburse funds each month.
Please have your time sheet in every week by Monday at 11:00 AM.
maconit is a privately held corporation located in Richmond, VA. We are one of the most respected consulting and staffing firms in the area.
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Роберт Аршакович Атаян (; 7 ноября 1915, Тегеран, Пе́рсия — 5 марта 1994, Лос-Анджелес, США) — армянский и советский , , , , профессор. Кандидат искусствоведения (1955), заслуженный деятель искусств Армянской ССР (1961).

Биография
Сын поэта и прозаика Аршака Атаяна, брат художника Армена Атаяна.

В 1941 году окончил Ереванскую консепваторию по классу В. Г. Тальяна. Совершенствовался, как музыковед под руководством профессора Ленинградской консерватории Х. С. Кушнарёва.

С 1944 года — преподаватель Ереванской консерватории, с 1955 года — доцент консерватории по классу специальности и общей гармонии, профессор — с 1977 года, заведующий кафедрой теории музыки (1962—1974 и 1982—1986). Одновременно с 1948 года (с перерывами) работал в Институте искусств АН Армянской ССР.

Научная и творческая деятельность
Исследователь армянского музыкального фольклора (с 1951 года — участник и руководитель ряда фольклорных экспедиций), армянской нотописи. Признанный специалист по искусству Комитаса, составитель и редактор первого академического издания произведений Комитаса (т. 1-6, 1960-82; т. 7-12, 1997—2003; подготовил к печати Г. Геодакян), издания произведений М. Екмаляна («Хоровые и сольные песни», 1970). Главный редактор и автор статей в сборниках «Комитасакан» (вып. 1-2, 1969-82, на армянском языке).

Автор камерно-инструментальных и вокальных произведений, обработок армянской народной и гусанской музыки, средневековных тагов.

Избранные сочинения
 Учебник элементарной теории музыки (совм. с Т. Тер-Мартиросяном). Ереван, 1949, 3 изд., доп. 1962;
 Пособие по изучению новоармянской нотописи и ладов армянской народной песни. Ереван, 1950;
 Армен Тигранян (совм. с M. M. Мурадяном). Ереван, 1955;
 Армянские композиторы (совм. с А. Татевосяном и М. Мурадяном, на рус. яз.). Ереван, 1956;
 Обзор истории армянской музыки. XIX-XX вв. (Досоветский период), Шахвердян Александр Исаак, Атаян, Роберт Аршак, Ереван, «Айпострат», 1959.
 Музыкальная грамотность и песенник. Для начальной школы I-IV классов. Мирзаян М., Атаян Роберт Аршак, Ереван, Армтеусманхрат, 1958.
 Армянская хазовая нотопись. Вопросы изучения и расшифровки. Ереван, 1959;
 Гусан Аваси (на рус. яз.). М., 1962, также на арм. яз. Ереван, 1963;
 Комитас — собиратель и исследователь армянской народной песни (VII Международный конгресс антропологических и этнографических наук). М., 1952 (на рус. и франц. яз.);
 Армянская народная песня. М., 1965 (на рус. яз.);
 Армен Тигранян. М., 1966 (на рус. яз.);
 Komitas (творческий портрет композитора, на англ. яз.). Нью-Йорк, 1969;

Р. Атаян умер в Лос-Анджелесе. Похоронен в Ереване.

Литература
 Большая биографическая энциклопедия. 2009.
 Музыкальная энциклопедия. — М.: Советская энциклопедия, Советский композитор. Под ред. Ю. В. Келдыша. 1973—1982

Кандидаты искусствоведения
Авторы учебников
Преподаватели Ереванской консерватории
Выпускники Ереванской консерватории
Похороненные на Тохмахском кладбище


Imagine: $16 billion of local coastal property permanently underwater, including up to 30,000 homes. Property tax rolls slashed by more than $250 million. Tens of thousands of coastal jobs displaced or lost, cutting upwards of $161 billion from the Tampa Bay regional economy. Waterfront parks and infrastructure washed away or made obsolete.
"The Cost of Doing Nothing," a study released earlier this year by the Tampa Bay Regional Planning Council, paints a striking economic portrait of how rising sea levels might transform the area's economy by 2060 if Pinellas, Hillsborough, Pasco and Manatee county communities fail to take more measures to reduce their flood risk.
The idea behind the report? To equip local communities with a more tangible understanding of what may be at stake as seas rise.


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