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Education & Academic

Announcement: Our First CBM Country

I'm very excited to announce that computerbasedmath.org has found the first country ready for our completely new kind of math education: it's Estonia. (...and here’s the press release). I thought Estonia could be first. They are very active on using technology (first to publish cabinet decisions immediately online, first to include programming in their mainstream curriculum), have ambition to improve their (already well respected) STEM aptitude and lack the dogma and resistance to change of many larger countries. There aren't so many countries with all those characteristics. In our first Estonia project we will work with them to rewrite key years of school probability and statistics from scratch. This is an area that's just crazy to do without a computer, even harmful. It's an area that's only come to the fore since computers because it only makes sense with lots of data. No-one in real life does these hand analyses or works with only 5 data points, so why do we make our students? Why get students emulating what computers do so much better (computing) rather than concentrate on imaginative thinking, analysis and problem-solving that students ought to be able to do so much better even than today's computers?
Conrad Wolfram
Education & Academic

Centennial of Markov Chains

On January 23, 1913 of the Julian calendar, Andrey A. Markov presented for the Royal Academy of Sciences in St. Petersburg his analysis of Pushkin's Eugene Onegin. He found that the sequence of consonants and vowels in the text could be well described as a random sequence, where the likely category of a letter depended only on the category of the previous or previous two letters. At the time, the Russian Empire was using the Julian calendar. The 100th anniversary of the celebrated presentation is actually February 5, 2013, in the now used Gregorian calendar. To perform his analysis, Markov invented what are now known as "Markov chains," which can be represented as probabilistic state diagrams where the transitions between states are labeled with the probabilities of their occurrences.
Oleksandr Pavlyk, Senior Kernel Developer, Algorithms R&D
Education & Academic

The Ultimate Univariate Probability Distribution Explorer

In this blog post, we want to report some work in progress that might interest users of probability and statistics and also those who wonder how we add new knowledge every day to Wolfram|Alpha. Since the beginning in 1988, Mathematica knew not only elementary functions (sqrt, exp, log, etc.) but many special functions of mathematical physics (such as the Bessel function K and the Riemann Zeta function) and number theoretical functions. All together, Mathematica knows now more than 300 such functions. The Wolfram Functions Site lists 300,000+ formulas and identities for these functions. And, based on Mathematica's algorithmic computation capabilities and the Functions Site's identities, most of this knowledge is now easily accessible in Wolfram|Alpha. For example, relation between sin(x) and cos(x), series representations of the Beta function, relation between BesselJ(n, x) and AiryAi(x), differential equation for ellipticF(phi, m), and examples of complicated indefinite integrals containing erf. But Wolfram|Alpha also knows about many special functions that are not in Mathematica because they are less common or less general. For instance, haversine(x), double factorial binomial(2n, n), Dickman rho(10/3), BesselPolynomialY[6, x], Conway's base 13 function(4003/371293), and Goldbach function(1000). Mathematica 7 knew 42 probability distributions; Mathematica 9 knows over 130 (parametric) probability distributions. Based on Mathematica, Wolfram|Alpha can answer a lot of queries about these distributions, such as characteristic function of the hyperbolic distribution or variance of the binomial distribution with p = 1/3, and give general overview pages for queries such as Student's t distribution or Gumbel distribution.
Oleg Marichev, Integration & Special Function Developer, Wolfram|Alpha Scientific Content Michael Trott, Chief Scientist, Wolfram|Alpha Scientific Content
Design & Visualization

Image Quality Analysis with Mathematica

With Mathematica, you can bring new ideas into focus. No one knows that better than Fritz Lebowsky. He's a senior principal engineer who does image-quality-related algorithm development for STMicroelectronics, a global manufacturer of electronics and semiconductors with advanced image processing technologies. Thanks to Mathematica's advanced programming language and computational power, Lebowsky is seeing major advancements in his image processing development work, with his latest color imaging project set to double performance while reducing cost by half. About the development, he says, "For the very first time in my research career I could combine several simple non-linear functions/dimensions to overcome some fundamental weaknesses in today's linear mathematics applied to image processing."
Wolfram Blog Team
Education & Academic

Volumetric Rendering of Colliding Galaxies

The physics involved in simulating galaxy collisions can be extremely complex. The most accurate simulations take into account not just points representing stars, but also magnetic fields and invisible dark matter, as well as n-body interactions allowing the individual stars to interact with each other. These complex simulations are usually carried out on large-scale supercomputers over long periods of time. One of the more interesting aspects of galaxy collisions is that they can create density variations resulting in all kinds of emergent structure. Density waves can develop that lead to star formation from compressed gas clouds. A couple of years ago, I wrote a Demonstration that provides a simplified solution to galaxy collisions. This Demonstration is designed to run in real time inside a Manipulate, so the problem has been simplified by removing n-body interactions, dark matter, magnetic fields, and so on. Basically, it treats the two galaxies as large point masses with lots of massless test particles orbiting them. The test particles respond only to the two galaxy "centers." In a real galaxy collision, the chances of two stars getting close enough to each other to interact directly is very remote, so it's not too far of a stretch to ignore this effect for a first-order approximation. The more stars that are included in the simulation (by minimizing the star separation parameter), the more intricate the results (and the more computationally intense). In fact, as more stars are added, it becomes easier to see density variations where many test masses cluster together, but it still looks very discrete. Real galaxies, like the Milky Way, can have hundreds of billions of stars. Trying to carry out a point simulation with that many stars becomes a bit taxing on most home systems, and definitely exceeds the time constraints of a real-time dynamic tool like Manipulate. So how can we better visualize these density variations? I decided to try to modify my Demonstration to use one of the new features in Mathematica 9, namely volumetric rendering. This way, we can simulate the galaxy collisions with fewer numbers of points, but render the results as if there were billions of stars, resulting in a more realistic and informative visualization.
Jeff Bryant, Research Programmer, Wolfram|Alpha Scientific Content
Announcements & Events

Lab and Process Automation with Mathematica in Biotech Research

From the beginning, the founders of the biotechnology startup Emerald Therapeutics wanted to develop an ideal research platform that would allow for lab and process automation during experiments as well as easy communication of their findings. Brian Frezza, Emerald's Co-founder and Co-CEO, says Mathematica's flexible programming language and interactive notebook environment made it the clear choice. The company's scientists and engineers have a shared codebase in Mathematica, which allows them to use one platform for all of the tasks in their antiviral research workflow—from developing functions to processing and storing data, designing and managing experiments, presenting findings, and directly controlling lab instruments. In this video, Frezza takes us into the company's lab to show us the advantages of having Mathematica as the company's core platform, including how it's used to automate experiments.
Wolfram Blog Team
Education & Academic

Hunting for Turing Machines at the Wolfram Science Summer School

This year is the 100th birthday of Alan Turing, so at the 2012 Wolfram Science Summer School we decided to turn a group of 40 unassuming nerds into ferocious hunters. No, we didn't teach our geeks to take down big game. These are laptop warriors. And their prey? Turing machines! In this blog post, I'm going to teach you to be a fellow hunter-gatherer in the computational universe. Your mission, should you choose to accept it, is to FIND YOUR FAVORITE TURING MACHINE. First, I'll show you how a Turing machine works, using pretty pictures that even my grandmother could understand. Then I'll show you some of the awesome Turing machines that our summer school students found using Mathematica. And I'll describe how I did an über-search through 373 million Turing machines using my Linux server back home, and had it send me email whenever it found an interesting one, for two weeks straight. I'll keep the code to a minimum here, but you can find it all in the attached Mathematica notebook. Excited? Primed for the hunt? Let me break it down for you. The rules of Turing machines are actually super simple. There's a row of cells called the tape:
Paul-Jean Letourneau, Lead Computational Biology Developer, Algorithms R&D
Announcements & Events

Welcome, National Museum of Mathematics

I was just in New York City for the grand opening of the National Museum of Mathematics. Yes, there is now a National Museum of Mathematics, right in downtown Manhattan. And it’s really good—a unique and wonderful place. Which I’m pleased to say I’ve been able to help in various ways in bringing into existence […]

Stephen Wolfram
Products

Modeling in the Search for New Drugs—G-Protein-Coupled Receptors (GPCRs)

Explore the contents of this article with a free Wolfram SystemModeler trial. Yesterday, the Nobel Prize in Chemistry was awarded to Robert J. Lefkowitz and Brian K. Kobilka for having mapped how a family of cellular receptors called G-protein-coupled receptors (GPCRs) work. The Nobel Prize winners' research has proven to be very important in the development of novel therapeutic drugs—about 40–50% of all therapeutic drugs in use today are centered on GPCRs. The real beauty of GPCR-based response systems is that they include components that are used over and over again for the response to external signals in many kinds of cellular functions throughout our bodies. Sight, smell, and the adrenaline response are examples of these GPCR-mediated responses with physiologically important functions. Identifying new targets for therapeutic drug intervention includes analysis of the complex webs of signaling pathways and feedback systems in our cells, extending beyond the first event of a signal connecting with the GPCR on the cell surface, which is non-trivial. Lately the cost-effective practice of using mathematical models as an initial step for finding those elusive new targets, and also as a tool for understanding how other reactions of a cell might be affected by a new drug, has been growing. In this blog post we are going to use modeling and simulation in order to illustrate how the GPCR-based cellular response to an external signal can be modified. And by performing this analysis, I thought we should also see how we can find promising targets for therapeutic drug design, which are then aimed at either increasing or decreasing the response. Since the first two steps in the pathways are identical in most of the GPCR-based signal responses in a cell, we can freely choose a representative model. One such well understood signal response pathway that uses GPCR is the mating pheromone response in yeast, which we are here going to explore using Mathematica and Wolfram SystemModeler.
Mikael Forsgren, Senior Applications Engineer, SystemModeler
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