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Mathematics and Art - O'Reilly Radar - 1 views

  • Nikki Graziano's intriguing integration of mathematical curves into her photography sparked a Radar discussion about the relationship between mathematics and the real world. Does her work give insight into the nature of mathematics? Or into the nature of the world? And if so, what kind of insight? Mathematically, matching one curve to another isn't a big deal. Given N points, it's trivial to write an N+1 degree equation that passes through all of them. There are many more subtle ways of solving the same problem, with more aesthetically pleasing results: you can use sine functions, wavelets, square waves, whatever you want. Take out a ruler, measure some points, plug them into Mathematica, and in seconds you can generate as many curves as you like. So finding an equation that matches the curve of an artfully trimmed hedge is easy. The question is whether that curve tells us anything, or whether it's just another stupid math trick.
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C9 Lectures: Yuri Gurevich - Introduction to Algorithms and Computational Complexity, 1... - 0 views

  • In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields. (In more advanced or abstract settings, the instructions do not necessarily constitute a finite sequence, or even a sequence; see, for example, "nondeterministic algorithm".) Each algorithm is a list of well-defined instructions for completing a task. Starting from an initial state, the instructions describe a computation that proceeds through a well-defined series of successive states, eventually terminating in a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate randomness. [source = Bing Reference]
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F# in ASP.NET, mathematics and testing | .NET Zone - 0 views

  • Starting from Visual Studio 2010 F# is full member of .NET Framework languages family. It is functional language with syntax specific to functional languages but I think it is time for us also notice and study functional languages. In this posting I will show you some examples about cool things other people have done using F#.
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robots.net - New Model Mimics Human Vision Tasks - 1 views

  • Researchers at MIT’s McGovern Institute for Brain Research are working on a new mathematical model to mimic the human brain's ability to identify objects. The model can predict human performance on certain visual-perception tasks suggesting it’s a good indication of what's actually happening in the brain. Researchers are hoping the new findings will make their way into future object-recognition systems for automation, mobile robotics, and other applications.
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robots.net - Robots: Distributed Flight Array - 0 views

  • In its latest episode, the Robots Podcast interviews the lead researcher of the Distributed Flight Array and one of my colleagues at the ETH Zurich's IDSC, Raymond Oung. The Distributed Flight Array (DFA) is an aerial modular robot. Each individual module has a single, large propellor and a set of omniwheels to move around. Since a single propellor does not allow stable flight, modules move around to connect to each other. As shown in this video of the DFA, the resulting random shape then takes flight. After a few minutes of hovering the structure breaks up and modules fall back to the ground, restarting the cycle. As most projects at the IDSC, the DFA is grounded in rigorous mathematics and design principles and combines multiple goals: It serves as a real-world testbed for research in distributed estimation and control, it abstracts many of the real-world issues of the next generation of distributed multi-agent systems, and it provides an illustration for otherwise abstract concepts like distributed sensing and control to a general public. For more information on current work, future plans and real-world applications, read on or tune in!
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The Unheralded Benefits of the F# Programming Language « The Nomadic Developer - 0 views

  • As many long time readers know, I am an enthusiast of the F# programming language.  I make no apologies for the fact that, if you are developing software on the .NET platform, F# is one of the better choices you can make for numerous reasons.  It is one of the reasons I proudly contributed as a co-author to the book, Professional F# 2.0, which is being published by Wrox in October. Some of the oft cited benefits of F# are that, to distill them quickly, it is good at doing intensely mathematical operations, it is built for parallelism, and it is good at helping define domain specific languages.  Those benefits are so often cited by speakers on the F# speaker circuit that they pretty much seem cliche to me at this point (note, yours truly is proud to call himself a member of said circuit, and often gives this talk!)  As great as these features are, there are a couple features, that in my more mundane F# experiences, seem to stand out as things that “save my ass”, for lack of a better phrase, more often than not.
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Mercury Releases OpenSAL - Open Source Version of Scientific Algorithm Library | Milita... - 0 views

  • CHELMSFORD, MA.  October 7, 2010  Mercury Computer Systems, Inc. (NASDAQ: MRCY, www.mc.com), a trusted ISR subsystems provider, announced the availability of OpenSAL, an open source version of its award-winning Scientific Algorithm Library (SAL) for vector math acceleration. SAL is a high-throughput, low-latency signal processing library containing efficient algorithms with the fewest possible instructions and computing resources. OpenSAL provides a robust API, C code reference design and documentation for over 400 SAL math functions.
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Cleve's Corner - "Magic" Reconstruction: Compressed Sensing - MathWorks Newsletter - 1 views

  • When I first heard about compressed sensing, I was skeptical. There were claims that it reduced the amount of data required to represent signals and images by huge factors and then restored the originals exactly. I knew from the Nyquist-Shannon sampling theorem that this is impossible. But after learning more about compressed sensing, I’ve come to realize that, under the right conditions, both the claims and the theorem are true. The Nyquist-Shannon sampling theorem states that to restore a signal exactly and uniquely, you need to have sampled with at least twice its frequency. Of course, this theorem is still valid; if you skip one byte in a signal or image of white noise, you can’t restore the original. But most interesting signals and images are not white noise. When represented in terms of appropriate basis functions, such as trig functions or wavelets, many signals have relatively few non-zero coefficients. In compressed (or compressive) sensing terminology, they are sparse.
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Wolfram Blog : aMAZEing Image Processing in Mathematica - 1 views

  • A little over a mile from the Wolfram Research Europe Ltd. office, where I work, lies Blenheim Palace, which has a rather nice hedge maze. As I was walking around it on the weekend, I remembered a map solving example by Peter Overmann using new image processing features in an upcoming version of Mathematica. I was excited to apply the idea to this real-world example. Once back at my computer, I started by using Bing Maps to get the aerial photo (data created by Intermap, NAVTEQ, and Getmapping plc).
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Universal property of music discovered - 1 views

  • Researchers at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam have discovered a universal property of musical scales. Until now it was assumed that the only thing scales throughout the world have in common is the octave.
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How computers can mimic human 3-D vision | KurzweilAI - 1 views

  • Researchers at Purdue University have developed two new techniques for computer-vision technology that mimic how humans perceive three-dimensional shapes.The techniques, heat mapping and heat distribution, apply mathematical methods to enable machines to perceive three-dimensional objects by mimicking how humans perceive three-dimensional shapes by instantly recognizing objects no matter how they are twisted or bent, an advance that could help machines see more like people.
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