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Sutton P.D.,Trinity College Dublin | Lotze J.,Trinity College Dublin | Lahlou H.,Trinity College Dublin | Fahmy S.A.,Nanyang Technological University | And 5 more authors.
IEEE Communications Magazine | Year: 2010

Iris is a software architecture for building highly reconfigurable radio networks. It has formed the basis for a wide range of dynamic spectrum access and cognitive radio demonstration systems presented at a number of international conferences between 2007 and 2010. These systems have been developed using heterogeneous processing platforms including generalpurpose processors, field-programmable gate arrays and the Cell Broadband Engine. Focusing on runtime reconfiguration, Iris offers support for all layers of the network stack and provides a platform for the development of not only reconfigurable point-to-point radio links but complete networks of cognitive radios. This article provides an overview of Iris, presenting the unique features of the architecture and illustrating how it can be used to develop a cognitive radio testbed. © 2006 IEEE. Source

Dougherty R.,Center for Communications Research | Freiling C.,California State University, San Bernardino | Zeger K.,University of California at San Diego
Proceedings of the IEEE | Year: 2011

Networks derived from matroids have played a fundamental role in proving theoretical results about the limits of network coding. In this tutorial paper, we review many connections between matroids and network coding theory, with specific emphasis on network solvability, admissible network alphabet sizes, linear coding, and network capacity. © 2006 IEEE. Source

Chow T.Y.,Center for Communications Research
Journal of Computer and System Sciences | Year: 2011

Razborov and Rudich have proved that, under a widely-believed hypothesis about pseudorandom number generators, there do not exist P/poly-computable Boolean function properties with density greater than 2-poly(n) that exclude P/poly. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory, because virtually all Boolean function properties used in existing lower bound proofs have the stated complexity and density. In this paper, we show that under the same pseudorandomness hypothesis, there do exist nearly-linear-time-computable Boolean function properties with only slightly lower density (namely, 2-q(n) for a quasi-polynomial function q) that not only exclude P/poly, but even separate NP from P/poly. Indeed, we introduce a simple, explicit property called discrimination that does so. We also prove unconditionally that there exist non-uniformly nearly-linear-time-computable Boolean function properties with this same density that exclude P/poly. Along the way we also note that by slightly strengthening Razborov and Rudich s argument, one can show that their "naturalization barrier" is actually a barrier to proving superquadratic circuit lower bounds, not just P/poly circuit lower bounds. It remains open whether there is a naturalization barrier to proving superlinear circuit lower bounds. © 2010 Elsevier Inc. All rights reserved. Source

Bringmann K.,University of Cologne | Li Y.,University of Cologne | Rhoades R.C.,Center for Communications Research
European Journal of Combinatorics | Year: 2014

In this paper, we provide an asymptotic for the number of row-Fishburn matrices of size n which settles a conjecture by Vit Jelínek. Additionally, using q-series constructions we provide new identities for the generating functions for the number of such matrices, one of which was conjectured by Peter Bala. © 2014 Elsevier Ltd. Source

News Article | January 25, 2016
Site: http://motherboard.vice.com/

Go is an old game where, broadly speaking, players take turns placing white and black pieces on a board in an attempt to surround the most empty territory on the playing field. The earliest known reference to it dates back to China in the 5th century B.C., which means people were playing it along the shores of the Yangtze before the Parthenon cast its shadow over Athens. At once simple and complex, it's known for the high degree of versatility its gridded playing surface offers, and for years—centuries, even—some players assumed the number of legal positions must be infinite on the game's standard 19x19 boards. But that's not exactly true, as computer scientist John Tromp revealed last week. There's just a friggin' lot of them. Specifically, Tromp discovered this is the number of legal ways you can use the board's 361 points with the black and white playing pieces and empty spaces: That's hardly the kind of thing you can figure out with pen and paper. As one Reddit user pointed out in reference to Tromp's earlier work, that's bigger than the total number of observable atoms in the universe. Tromp started the calculations back in March 6 of last year, with the help of staff and big servers at both the Institute for Advanced Study's School of Natural Sciences and the IDA's Center for Communications Research in Princeton, New Jersey, along with some help from Hewlett-Packard's Helion Cloud. "The software was developed mostly in 2005, so from then we had the ability to attempt it, but not the required hardware resources," Tromp tells me in an e-mail. "By 2007, we (me and Michal Koucký) were just able to compute the number of legal 17x17 positions, and that exhausted the resources available at the Dutch Centre for Mathematics and Computer Science where I worked." Want to double-check his work? Tromp provides the software he used on his github repository, but he cautions that you'll need "a beefy server with 15 TB of fast scratch diskspace, 8 to 16 cores, and 192 GB of RAM." Indeed, for years the available technology held him back, limiting him to calculating boards beneath 19x19 grid standard. The leap from 17x17 to 19x19 may not seem like much, but Tromp emphasizes that each increase in the board's dimensions demands a fivefold increase in the memory, time, and diskspace required. Tromp unsuccessfully tried to get "dozens" of companies, people, and institutions like Amazon and Google to sponsor his quest to borrow the hardware to calculate the results for a 19x19 board, but the winning ticket dropped in 2014 when fellow Dutchman Piet Hut, an astronomer at the Institute for Advanced Study, came through with an offer. After Tromp and friends achieved some notoriety for figuring out the number of legal positions on an 18x18 board, the right folks jumped on board for the final push. So after solving a mystery that's been unsolved for 2,500 years, what's next? Tromp tells me he plans to continue work on his "Cuckoo Cycle" proof-of-work system and solve large-scale Connect Four problems, but he's especially interested in improving his similar work on chess. Chess, though, is a different beast. Which leaves the question of why? "Having the ability to determine the state complexity of the greatest abstract board game, and not doing it, that just doesn't sit right with me," Tromp says. "Or, as the great mathematician Hilbert proclaimed, 'We must know — we will know!"

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