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programming language called #Formura , which allows scientists to develop sophisticated programming code when performing simulations on supercomputers with distributed memory. http://www.riken.jp/en/pr/topics/2017/20170117_1/
 
A new paradigm for supercomputer programming
Researchers from the RIKEN Advanced Institute for Computational Science (AICS), Chiba University, Kobe University, Kyoto University, and Fujitsu have developed a programming language, called #Formura , which allows scientists to develop sophisticated programming code when performing simulations on supercomputers with distributed memory.

" Stencil computationis a type of program, typically used for simulations, that involves computing short-range interactions between arrays. It is used in a wide range of applications such as weather simulations, earthquake simulations, metallurgy, and image processing. However, writing computer code to perform such simulations on supercomputers is extremely tedious both in terms of the writing and the fine-tuning of code. In particular, such applications can be extremely memory-intensive, therefore on powerful modern processors, which have limited memory bandwidth, the imbalance between processor speed and memory bandwidth has recently become a major headache for supercomputing applications.

The development of Formura—a feat that gave the group a position as finalists for the prestigious ACM Gordon Bell Award this year—makes possible the automatic generation of elegant programming codes for running stencil computation on supercomputers, while requiring scientists only to give the mathematical concepts to be used in the simulation. In the paper, titled “Simulations of Below-Ground Dynamics of Fungi: 1.184 Pflops Attained by Automated Generation and Autotuning of Temporal Blocking Codes ,” the group describes the new language and how it was used, on the powerful K computer, to perform simulations of the growth of mycorrhiza—networks of plant roots colonized by underground fungi.
According to Takayuki Muranushi of RIKEN AICS, the first author of the paper, the work represents a first step towards freeing computational scientists from the burden of programming and optimization, allowing them to concentrate on studying their own application problems. “We are very happy to have been chosen as finalists for this work,” he says. “One thing I'd like to say is that creating a custom programming language is not too difficult, and is a lot of fun. I am grateful to all the research in computer science that made this possible, and to all the people that allowed me to focus on this challenging and time-consuming task.”
article source : http://www.riken.jp/en/pr/topics/2017/20170117_1/






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Folgen und Reihen IV Alternierende Folgen. Alternierende Folgen · Der alternierende Faktor bei explizit definierten Folgen · Der alternierende Faktor bei rekursiv definierten Folgen. Folgen und Reihen V Arithmetische Folgen und Reihen. Inhalt zum Kapitel · Info-Seite · Arithmetische Folgen ...
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Variable Base Constant Power Series

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In this paper, what is said is that although an Ordinary Differential Equation can not be solved in general, as Poincaré affirmed, it is possible in general to give explicit solutions to the cycles of an ODE by means of its reprensentation as a Fourier series and to detect cycles As isolated points of a Hilbert space: https://www.researchgate.net/publication/260163204_An_equivalency_to_the_second_part_of_Hilberts_16th_problem?ev=prf_pub
Here is an example of this:
Https://www.researchgate.net/publication/264861771Solucion_explicita_al_cilo_de_la_ecuacion_de_van_der_Pol_de_tercer_grado_provisional?ev=prf_pub
In the case of the van der Pol equation.
We are on the way to approach Hilbert's problem XVI
Find over 100+ million publications, 11+ million researchers and 1 million answers to research questions. ResearchGate is a network dedicated to science and research. Connect, collaborate and discover scientific publications, jobs and conferences. All for free.
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Charlotte Larras's profile photo
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I guess there are no mathematicians at the Nasa ! thank-you very much for the moronic comment.
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You don't need much to post a good one. I just take from books and documentaries. I use my teachers and other remembrances too.
just put one and one together. Nothing new anymore. Believe someone did it all before.

Ecclesiastes 1:1-11
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Appreciate if anyone can provide a worked example of Benfords law.
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Hugo A. G. V. Rosa (Sr. X)'s profile photoPeter Marshall's profile photo
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Thanks all, I've used the resources provided and applied Benford`s successfully.
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Unas notas de trabajo sobre la hipótesis de Riemann:
https://www.researchgate.net/publication/261358702_Sobre_la_hipotesis_de_Riemann
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David Cole's profile photo
 
¡La hipótesis de Riemann es verdad!
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Robert Jacobson
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Research  - 
 
 
Mathematicians Aaron Broussard, Martin Malandro, and Abagayle Serreyn have cracked the code for the optimal video game multi-jump, a normal jump followed by additional jumps initiated in midair without the aid of a platform, to determine the highest achievable jump, and have described strategies human players or AI can use in real time to select successful multi-jumps in real time. Their results (doi) are published in the December issue of The American Mathematical Monthly . From the paper's introduction:

A multi-jump is a finite sequence of jumps where the first jump is initiated from the ground and the rest are initiated in midair. The number of jumps in a multi-jump is the length of the multi-jump, so a double jump is a multi-jump of length two. Several video games, such as Chair Entertainment Group(R)’s Shadow Complex(TM) and Nintendo(R)’s Super Smash Bros.(TM) Melee, feature triple jumps or multi-jumps of even longer length. _

_The basic problem we consider in this paper is the following. Suppose that a character in a two-dimensional side-scrolling video game wishes to use a multi-jump to jump to the right from a fixed starting point across a gap and land on a fixed platform. ...We therefore assume that the character has a known finite sequence of jump arcs available to her and faces the problem of selecting when to jump in midair, i.e., to switch from the arc of one jump to the next, so as to land on the platform. ...

Provided the platform is reachable by a multi-jump, we give strategies for solving this problem on the fly for both player-controlled and artificial intelligence (AI)-controlled characters. In the simplest situation all jumps available to the character are equal and fully concave (Definition 5). In this situation we give a simple strategy (the line method) that is usable by both players and AI. In our experience the majority of games featuring multi-jumps are covered by this situation. We give two further strategies for AI-controlled characters in more-complicated situations. Our first AI strategy is very general, in that it applies to any collection of standard jump functions (Definition 1). We also give a faster (less computationally intensive) AI strategy for collections of standard jump functions whose derivative inverses are known and computable exactly.
Mathematicians Aaron Broussard, Martin Malandro, and Abagayle Serreyn have cracked the code for the optimal video game multi-jump, a normal jump followed by additional jumps initiated in midair without the aid of a platform, to determine the highest achievable jump, and have described strategies hum...
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Babai, a professor at the University of Chicago, had presented in late 2015 what he said was a “quasi-polynomial” algorithm for graph isomorphism. source https://www.quantamagazine.org/20170105-graph-isomorphism-retraction/
 
The theoretical computer scientist László Babai has retracted a claim that amazed the computer science community when he made it just over a year ago. In November 2015, he announced that he had come up with a “ quasi-polynomial ” algorithm for graph isomorphism, one of the most famous problems in theoretical computer science. While Babai’s result has not collapsed completely — computer scientists still consider it a breakthrough — its central claim has been found, after a year of close scrutiny, to contain a subtle error.

“In Laci Babai, you have one of the most legendary and fearsome theoretical computer scientists there ever was, and in graph isomorphism, one of the most legendary and fearsome problems,” wrote Scott Aaronson, a theoretical computer scientist at the University of Texas, Austin, in an email. “A year ago, Laci threw an unbelievable knockout punch at [graph isomorphism], and now the problem itself seems to have gotten off the mat and thrown a counterpunch.”

The graph isomorphism problem asks for an algorithm that can spot whether two graphs — networks of nodes and edges — are the same graph in disguise. For decades, this problem has occupied a special status in computer science as one of just a few naturally occurring problems whose difficulty level is hard to pin down.

Roughly speaking, most computer science problems fall into one of two broad categories. There are “easy” problems, the ones that can be solved in a polynomial number of steps — if the size of the problem is denoted by n, the number of steps grows as, for example, n2 or n3. These problems can (generally) be solved efficiently on a computer. And there are “hard” problems, for which the best known algorithm takes an exponential (such as 2n ) number of steps — far too many for a computer to carry out efficiently. Only a handful of natural problems, including graph isomorphism, seem to defy this dichotomy; computer scientists have struggled for decades to figure out just where graph isomorphism belongs.
read more the article written By Erica Klarreich :
https://www.quantamagazine.org/20170105-graph-isomorphism-retraction/





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Find the radius of circle.
Shaded area =56 square cm
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Sambo Umaru's profile photoJürgen Weiß's profile photo
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There can be a crux in it with result of r=5 cm maybe
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An old post about a delayed differential equation governing the distribution of primes using probability heuristics alone

Q'(x) = - Q(x) Q( √x ) / x

http://babaksjournal.blogspot.com/2008/07/differential-equation-estimating.html
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Very interesting 90 min video about the future of pure mathematics and the role of computers for pure mathematics:

https://www.youtube.com/watch?v=psSyM1zp82k&feature=youtu.be
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Zac Bergart

Research  - 
 
 
Math Difficulties May Reflect Problems in a Crucial Learning System in the Brain
Children differ substantially in their mathematical abilities. In fact, some children cannot routinely add or subtract, even after extensive schooling. Yet the causes of these problems are not fully understood. Now, two researchers, at Georgetown University Medical Center and Stanford University, have developed a theory of how developmental “math disability” occurs.

The article, in a special issue on reading and math in Frontiers in Psychology, proposes that math disability arises from abnormalities in brain areas supporting procedural memory. Procedural memory is a learning and memory system that is crucial for the automatization of non-conscious skills, such as driving or grammar. It depends on a network of brain structures, including the basal ganglia and regions in the frontal and parietal lobes.

The procedural memory system has previously been implicated in other developmental disorders, such as dyslexia and developmental language disorder, say the study’s senior researcher, Michael T. Ullman, PhD, professor of neuroscience at Georgetown.

“Given that the development of math skills involves their automatization, it makes sense that the dysfunction of procedural memory could lead to math disability. In fact, aspects of math that tend to be automatized, such as arithmetic, are problematic in children with math disability. Moreover, since these children often also have dyslexia or developmental language disorder, the disorders may share causal mechanisms,” he says.  

Source:
https://gumc.georgetown.edu/news/math-difficulties-may-reflect-problems-in-a-crucial-learning-system-in-the-brain

Journal article:
http://journal.frontiersin.org/article/10.3389/fpsyg.2016.01318/full

#neuroscience   #mathdifficulties   #memory   #learning   #brainstructure  
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Plz m apna roll number bhool giya ho plz koi help kar do
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Una idea para concretar la conjetura de Polya Hilbert y así lograr resolver la hipótesis de Riemann: https://www.researchgate.net/publication/251518664_La_conjetura_de_Hilbert-Polya_y_una_propuesta_de_generalizacion
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