Russian university's mathematicians help improve efficiency of data centers using Markov chains

RUDN University, situated in southwestern Moscow, mathematicians have created a model of maximum efficiency of data centers. It is based on a nontrivial Markov chain. In addition to the obvious practical applications of the results for the organization of servers and data centers, the theoretical part will be useful for the theory of queues and queuing, as well as for working with big data and neural networks. The study is published in the journal MathematicsCREDIT RUDN University{module In-article}

A data center is a system of servers, and their task is to provide supercomputing resources and disk space at the request of users. The higher the load, the more equipment is heating up. Servers may temporarily stop working if they overheat. The temperature level that corresponds to the overheating point is called the first critical level. The second is the level to which the temperature of the server must fall for it to resume (at least partially) the work.

These levels are different. For example, if each user loads the server so that the temperature of its processor grows by 0.1 degrees, and the first critical level is 100 degrees, the second critical level should be set no higher than 99.9 degrees. If to put above, the first request of the user will overheat the server again. In this case, the two critical levels should be located close enough to each other - if their difference is big, the server capacity will not be used completely. It is necessary to configure these levels so that the servers of the data center do not shut down constantly due to overheating and at the same time work with a full load.

RUDN University mathematicians Olga Dudina and Alexander Dudin were able to find a solution to the optimization problem, which allows ensuring that the servers work at full capacity and do not overheat. Its condition looks like this: depending on a random process that simulates the flow of users, place two critical levels to prevent overheating, but the computation power would be used to the maximum. At the same time, partial inactivity is allowed, that is, if the second critical temperature level is exceeded, some requests from users are rejected.

RUDN University mathematicians solved probabilistic equations for different values of critical levels. As a random process that simulates the arrival of users, RUDN University mathematicians used the Markov chain. The simplest example of such a chain is a random walk of a point along a straight line. Every second, a coin is tossed: if heads come up, the point moves 1 cm forward, if tails - ¬one centimeter back. Time is discrete in this process, that is, changes occur once a second, and the position of the point in the future depends only on its current position and the result of the coin toss.

To test the effectiveness of their method, RUDN University mathematicians conducted a numerical experiment that simulated the behavior of the server. Its results were evaluated using indicator E, a quality criterion that determines losses for denial of service to the user and overheating of equipment per unit of time. It turned out that the new method allows more than ten times - from 0.31 to 0.03 - to reduce the loss of the simulated server and significantly increase the efficiency of the data center.

Also, the Markov chain, which originated in the work of mathematicians, has some interesting properties. In addition to its applications in IT, their model will be useful in Queueing theory. This theory is necessary for solving queuing problems, working with big data and neural networks.

Goethe University astrophysicists win breakthrough prize to study blackholes

Professor Luciano Rezzolla and his team, together with 347 researchers from the worldwide Event Horizon Telescope Collaboration, have been awarded the Breakthrough Prize 2020 in recognition of their ground-breaking achievements

For their exceptional and fundamental achievements in capturing the first direct image of a black hole, researchers from the team headed by astrophysicist Professor Luciano Rezzolla of Goethe University, together with 347 scientists from the global Event Horizon Telescope Collaboration, will receive the Breakthrough Prize 2020, which comes with $ 3 million in prize money. With its 10 members, the Goethe University team is one of the largest in the entire collaboration, which comprises 140 institutions in total.

With the aid of eight radio telescopes around the world, to which meanwhile another three have been added, the scientists succeeded in capturing the first direct visual evidence of the supermassive black hole at the centre of the galaxy Messier 87 in April 2019. The prize will be distributed equally among all the co-authors of the corresponding scientific publications, and will be awarded on 3rd November.

beitragsbild black hole rezzolla 8925a{module In-article}
Luciano Rezzolla’s team made fundamental contributions to the theoretical interpretation of the results throughout all phases of the observations: using supercomputers, they simulated how material forms a ring-shaped disc as it orbits and is pulled into the black hole, and how the tremendous gravitation bends light rays around the black hole. It was also necessary to rule out various alternatives to black holes that are also compatible with the theory of relativity. “The confrontation of theory with observations is always a dramatic moment for a theoretical physicist. We were quite relieved, and also proud, that the observations matched our predictions so well,” states Luciano Rezzolla.

Goethe University President Professor Dr. Birgitta Wolff: “Together with Luciano Rezzolla and his team, we are delighted about this important global award. We warmly congratulate all of our colleagues who contributed to this achievement! We remember the enthusiasm of audience in the packed lecture hall on Campus Riedberg when Luciano Rezzolla and his colleagues from the European Consortium (Professor Michael Kramer from the Max Planck Institut für Radioastronomie in Bonn and Professor Heino Falcke from the Dutch Radboud University) first presented the results of their joint research at Goethe University on 17th April 2019. It was a celebration of the power of fascination emanating even from abstract science. I hope that further ground-breaking research will be forthcoming from this great global collaboration.”

Goethe University Vice-President Professor Simone Fulda, who is responsible for research, said: “We are proud to have played such a prominent role as Goethe University in a true scientific breakthrough of global significance and congratulate Luciano Rezzolla and his team for the outstanding achievements that led to it. Physics is an important research focal point that has shaped Goethe University’s research profile for many years.”

“It’s a great honour and an enormous gratification to see that the work done at Goethe University has received the highest recognition and has contributed to pushing the limits of our understanding of fundamental physics. It is also a fair recognition of what has ultimately been a team effort and hence a shared burden and challenge of many scientists across the world,” commented Luciano Rezzolla.

As a collective, this year’s Breakthrough Prize laureates probed the galaxies to capture the first image of a black hole. The jury has found remarkable the achievements by combining telescope after synchronizing them with atomic clocks, producing a virtual telescope as large as the Earth, to obtain unprecedented resolution. The image of the supermassive black hole at the centre of the Messier 87 galaxy was obtained after painstakingly analysing the data with novel algorithms and techniques, and reveals a bright ring marking the point where light orbits the black hole, surrounding a dark region where light cannot escape the black hole’s

gravitational pull. The black hole shadow matched the expectations of Einstein’s theory of General Relativity.

Collaboration Director Shep Doeleman of the Harvard-Smithsonian Center for Astrophysics, who will accept the prize on behalf of the collaboration at the ceremony on 3rd November 2019, says: „We set out to see the unseeable, and we needed to build a telescope as large as the Earth to do it. It sounds like science fiction, but we assembled an incredible global team of experts and used the most advanced radio telescopes on the planet to make it a reality. This breakthrough prize celebrates a new beginning in our study of black holes.“

The “Breakthrough Prize Foundation” has prominent backers. Its founding members are Sergey Brin, Priscilla Chan and Mark Zuckerberg, Ma Huateng, Yuri und Julia Milner, and Anne Wojcicki.

University at Buffalo chemists predict new forms of superhard carbon

A study identifies dozens of new carbon structures that are expected to be superhard, including some that may be about as hard as diamonds

Superhard materials can slice, drill and polish other objects. They also hold potential for creating scratch-resistant coatings that could help keep expensive equipment safe from damage.

Now, science is opening the door to the development of new materials with these seductive qualities.

Researchers have used computational techniques to identify 43 previously unknown forms of carbon that are thought to be stable and superhard -- including several predicted to be slightly harder than or nearly as hard as diamonds. Each new carbon variety consists of carbon atoms arranged in a distinct pattern in a crystal lattice. CAPTION An illustration depicts three of 43 newly predicted superhard carbon structures. The cages colored in blue are structurally related to diamond, and the cages colored in yellow and green are structurally related to lonsdaleite.  CREDIT Credit: Bob Wilder / University at Buffalo, adapted from Figure 3 in P. Avery et al., npj Computational Materials, Sept. 3, 2019.{module In-article}

The study -- published on Sept. 3 in the journal npj Computational Materials -- combines computational predictions of crystal structures with machine learning to hunt for novel materials. The work is theoretical research, meaning that scientists have predicted the new carbon structures but have not created them yet.

"Diamonds are right now the hardest material that is commercially available, but they are very expensive," says University at Buffalo chemist Eva Zurek. "I have colleagues who do high-pressure experiments in the lab, squeezing materials between diamonds, and they complain about how expensive it is when the diamonds break.

"We would like to find something harder than a diamond. If you could find other materials that are hard, potentially you could make them cheaper. They might also have useful properties that diamonds don't have. Maybe they will interact differently with heat or electricity, for example."

Zurek, PhD, a professor of chemistry in UB College of Arts and Sciences, conceived of the study and co-led the project with Stefano Curtarolo, PhD, professor of mechanical engineering and materials science at Duke University.

The quest for hard materials

Hardness relates to a material's ability to resist deformation. As Zurek explains, it means that "if you try to indent a material with a sharp tip, a hole will not be made, or the hole will be very small."

Scientists consider a substance to be superhard if it has a hardness value of over 40 gigapascals as measured through an experiment called the Vickers hardness test.

All of the study's 43 new carbon structures are predicted to meet that threshold. Three are estimated to exceed the Vickers hardness of diamonds, but only by a little bit. Zurek also cautions that there is some uncertainty in the calculations.

The hardest structures the scientists found tended to contain fragments of diamond and lonsdaleite -- also called hexagonal diamond -- in their crystal lattices. In addition to the 43 novel forms of carbon, the research also newly predicts that a number of carbon structures that other teams have described in the past will be superhard.

Speeding up the discovery of superhard materials

The techniques used in the new paper could be applied to identify other superhard materials, including ones that contain elements other than carbon.

"Very few superhard materials are known, so it's of interest to find new ones," Zurek says. "One thing that we know about superhard materials is that they need to have strong bonds. Carbon-carbon bonds are very strong, so that's why we looked at carbon. Other elements that are typically in superhard materials come from the same side of the periodic table, such as boron and nitrogen."

To conduct the study, researchers used XtalOpt, an open-source evolutionary algorithm for crystal structure prediction developed in Zurek's lab, to generate random crystal structures for carbon. Then, the team employed a machine learning model to predict the hardness of these carbon species. The most promising hard and stable structures were used by XtalOpt as "parents" to spawn additional new structures, and so on.

The machine learning model for estimating hardness was trained using the Automatic FLOW (AFLOW) database, a huge library of materials with properties that have been calculated. Curtarolo's lab maintains AFLOW and previously developed the machine learning model with Olexandr Isayev's group at the University of North Carolina at Chapel Hill.

"This is accelerated material development. It's always going to take time, but we use AFLOW and machine learning to greatly accelerate the process," Curtarolo says. "The algorithms learn, and if you have trained the model well, the algorithm will predict the properties of material -- in this case, hardness -- with reasonable accuracy."

"You can take the best materials predicted using computational techniques and make them experimentally," says study co-author Cormac Toher, Ph.D., assistant research professor of mechanical engineering and materials science at Duke University.