Klivans A.,University of Texas at Austin |
Journal of Machine Learning Research | Year: 2013
We give the first polynomial-time algorithm for agnostically learning any function of a constant number of halfspaces with respect to any log-concave distribution (for any constant accuracy parameter). This result was not known even for the case of PAC learning the intersection of two halfspaces. We give two very different proofs of this result. The first develops a theory of polynomial approximation for log-concave measures and constructs a low-degree l1 polynomial approximator for sufficiently smooth functions. The second uses techniques related to the classical moment problem to obtain sandwiching polynomials. Both approaches deviate significantly from known Fourier-based methods, where essentially all previous work required the underlying distribution to have some product structure. Additionally, we show that in the smoothed-analysis setting, the above results hold with respect to distributions that have sub-exponential tails, a property satisfied by many natural and well-studied distributions in machine learning. © 2013 D.M. Kane, A. Klivans & R. Meka.
Hasan M.,Udai Pratap Autonomous College |
Singh D.K.,IAS |
Singh A.K.,IAS |
Singh A.K.,Krishi Bhavan
Indian Journal of Ecology | Year: 2014
Higher organic carbon, electrical conductivity, bulk density and growth attributes viz. plant height, tillerand dry matter were recorded in 50 % N through carpet waste + 50% N through urea + PSB + 20 kg S ha-1 and this treatment was significantly higher over all other treatments but which was at par with 50 % N through FYM + 50% N through urea + PSB + 20 kg S ha-1 at all stages of crop. Higher pH was recorded at 50 % N through carpet waste + 50% N through urea + PSB + 20 kg S ha-1 and minimum pH was recorded at control treatment. Maximum grain and straw yield were recorded (4.6 and 6.41 ha-1) with 50 % N through carpet waste + 50% N through urea + PSB + 20 kg S ha-1 and which was significantly superior to all others treatment. Nutrient uptake and nutrient available in soil were found in 50 % N through carpet waste + 50% N through urea + PSB + 20 kg S ha-1 and this treatment was significantly to all others treatment but which was at par with 50 % N through FYM + 50% N through urea + PSB + 20 kg S ha-1 at all stages of crop.
News Article | April 8, 2016
Netflix effect or not, the Internet Activity Survey (IAS) results revealed by The Australian Bureau of Statistics on April 6, clearly mark the world's, and not just the Australians, growing reliance on Internet data, as reflected in the 1.71 million terabytes of downloaded content between October and December 2015. That's a far cry from the days of dial-up Internet, which was a prominent feature in all Aussie households a decade ago. The need for a great data plan with superfast connectivity has now become the lifeblood of people globally. The Australian numbers may only serve as the mirror for the global requirement in the coming years that hints at an improved broadband infrastructure. The whopping figure of 1.71 million terabytes, as represented by the Bureau, shows a 23.5 percent jump from the three months of April to June of the same year, and a 50 percent increase from the last three months of 2014 – from 52,745 terabytes in 2014 to 90,693 terabytes in 2015. This increasing thirst for easily available downloadable content is obviously fuelled by providers like Netflix. After its launch in March 2015, Internet service providers like iiNet were already struggling to meet the stupendous rise in demand. Most families in Australia now have their devices – laptops, desktops, smartphones, smart TVs – all connected to the Internet, as each family member spends hours after work usually surfing the net or watching Netflix on individual devices. Currently, Netflix reportedly has 2.7 million subscribers, with Stan coming a not-so-close second with its 700,000 members. Telstra is yet another contributing factor to the overwhelming spike in data download, with their free data days, which just goes to show the country's downloading skills when given a chance. One such free-data Sunday showed that a single user managed to get through 1 terabyte of data. In other words, that's 10 seasons of Friends, 24 seasons of The Simpsons, six seasons of Game of Thrones, Xbox games, and Microsoft packages, which still leaves many more gigabytes of downloadable space. So when multiplied by 1.71 million, that's something to wrap your brain around with. Tony Cross, the chief architect of the National Broadband Network (NBN), says he, however, doesn't find anything "atypical" about the revealed statistics, as "occasionally we get something such as the Netflix effect which causes a bump in average download use, but once you smooth those bumps out, we expect that kind of growth rate – 30 to 40 per – to continue for many years to come." © 2016 Tech Times, All rights reserved. Do not reproduce without permission.
Traumatic brain injury (TBI) is a growing health concern in many occupations and disciplines. From amateur and professional athletes to soldiers and first responders, more and more people worldwide are at risk of sustaining TBIs and suffering potentially debilitating long-term effects. TBIs can happen anywhere, from battlefields to sports arenas, at home or on the road. Among both children and adults, falls are the leading cause of these impacts to the head, followed by blunt trauma, car crashes, and assaults. According to the U.S. Centers for Disease Control and Prevention (CDC), TBI incidents result in 2.2 million emergency room visits and cause more than 50,000 deaths nationwide every year. Even a seemingly minor brain injury can lead to long-term symptoms, such as difficulty concentrating, trouble organizing thoughts, fatigue, headaches, and memory loss. And, of course, it’s not only the injured individuals who are affected; TBI-related issues can also have lasting effects on families and communities. The issue has gained an even higher profile in recent years as more sports organizations, such as the National Football League and the National Collegiate Athletic Association, have adopted new policies, guidelines, and protocols in response to concerns about TBIs. The key to improvement lies in better understanding, preventing, and treating brain injuries. BlackBox Biometrics is contributing to that effort by developing advanced sensor systems that can instantly measure the unseen impact of concussive forces that can cause TBI. Among the company’s innovations is the Linx Impact Assessment System (IAS), a wearable device that fits inside a headband or skull cap to monitor athletes regardless of whether their sports require the use of helmets. (A recent episode of The Verge’s “Detours” series explores what’s at stake and how the technology works.) With its advanced technology, including microelectromechanical system (MEMS) accelerometers developed by Analog Devices, Inc. (ADI), Linx IAS can measure how hard, and how many times, athletes sustain impacts to the head. The accelerometers then send real-time data to a paired smartphone or tablet for analysis, for correlation to potential injury, or to fine-tune an athlete’s technique. The mobile application also includes a built-in sideline test that can help medical personnel decide whether to remove an athlete from play and/or seek medical attention. For use in dangerous environments, BlackBox Biometrics has also developed the Blast Gauge System, a three-gauge wearable set for first responders that measures exposure to blast overpressure—shock waves caused by explosions, the firing of weapons, sonic booms, and similar events. The Blast Gauge System is used by U.S. Special Forces, the FBI, and law-enforcement Special Weapons and Tactics (SWAT) teams to provide faster, more accurate treatment for people injured on the front lines. ADI’s MEMS components are essential to the success of the Linx monitoring system, says David Borkholder, BlackBox Biometrics’ chief technology officer. “ADI MEMS accelerometers provide high-g measurement capabilities with industry-leading sampling rates, enhancing the ability of the Blast Gauge System to accurately detect explosive and concussive events,” he explains. With multiple ADI MEMS inertial sensors, the system collects precise data measurements and relays them to the operator at the press of a button. Green, yellow, and red status LEDs provide instant triage data, and a micro–universal serial bus (USB) connection saves complete time-based data for later analysis by medical personnel. The ADI measurement sensors are based on multiaxis combinations of precision gyroscopes, accelerometers, magnetometers, and pressure sensors. The technology reliably senses and processes multiple degrees of freedom, even in highly complex applications and under dynamic conditions. As the industry leader in advanced sensor technology, ADI collaborates with and provides technologies for innovators such as BlackBox Biometrics, whose solutions positively affect lives and help redefine entire fields of study. ADI’s high-performance components and system solutions enable customers to develop products that are truly ahead of what’s possible.
This is a revised version of a post that originally appeared on the American Mathematical Society’s Joint Mathematics Meetings blog. Earlier this month, I attended the Joint Mathematics Meetings in Seattle. One of the reasons I enjoy going to the JMM is that I can get a feel for what is going on in parts of mathematics that I’m not terribly familiar with. This year, I attended two talks in a session called “mathematical information in the digital age,” that got me thinking about what mathematicians do. First, a confession: I went to the session because I like oranges. The first talk was by Thomas Hales, who is probably best known for his proof of the Kepler conjecture. In short, the conjecture says that the way grocers stack oranges is indeed the most efficient way to do it. The proof was a long case-by-case exhaustion, and Hales was not satisfied with a referee report that said the referee was 99% sure the proof was correct. So he did what any* mathematician would do: he took more than a decade to write and verify a formal computer proof of the result. I attended the talk because I figured there’s a small chance that any talk that mentions the Kepler conjecture might have oranges for the audience. Hales’ talk was called simply “Formal Proofs.” These are not proofs that are written using stuffy language, with every single step written out, but proofs that can be input into a computer and verified all the way down to the foundations of mathematics, whichever foundations one chooses. Hales began his talk with some examples of less-than-formal proofs, starting with a passage from William Thurston in which he used the phrase “subdivide and jiggle,” clearly not a rigorous way to describe mathematics. (Incidentally, Thurston also did mathematics with oranges. He would ask students to peel oranges to better understand 2- and 3-dimensional geometry.) Although I never met Thurston, I am one of his many mathematical descendants. his approach to mathematics, particularly his emphasis on intuition and imagination, has permeated the culture in my extended mathematical family and has had a great deal of influence on how I think about mathematics. That is why it was so refreshing for me to go to a talk where intuition wasn’t a primary focus. Hales was certainly not insinuating that Thurston was a bad mathematician. Thurston was only the first mathematician he used as an example of less-than-rigorously stated mathematics. A few slides later he mentioned the Bourbaki book on set theory. Yes, even that paragon of formal mathematics sucked dry of every drop of intuition, is not really full of formal proofs. Hales’ talk was a nice overview of the formal proof programs out there, some mathematical results that have been proved formally (including some that were already known), and a nice introduction to where the field is going. I’m particularly interested in learning more about the QED manifesto and FABSTRACTS, a service that would formalize the abstracts of mathematical papers, a much more tractable goal than formalizing an entire paper. The most amusing moment of the talk, at least to me, was a question from someone in the audience about the possibility of using a formal proof assistant to verify Mochizuki’s proof of the abc conjecture. Hales replied that with the current technology, you do need to understand the proof as you enter it, so there aren’t many people who can do it. The logical response: why doesn’t Mochizuki do it himself? Let’s just say I’m not holding my breath. The second talk I attended in the session was Michael Shulman’s called “From the nLab to the HoTT book.” He talked about both the nLab, a wiki for category theory, and the writing of the Homotopy Type Theory “research textbook,” a 600-page tome put together during an IAS semester about homotopy type theory, an alternative to set theory as a foundational system for mathematics. The theme of Shulman’s talk was “one size does not fit all,” either in the way people collaborate (contrasting the wiki and the textbook) or even in the foundations of mathematics (type theory versus set theory). I don’t know if it was intended, but I thought Shulman’s talk was an interesting counterpoint to Hales,’ most relevantly to me in the way it answered one of the questions Hales posed: why don’t more mathematicians use proof assistants? Beyond the fact that proof assistants are currently too unwieldy for many of us, Shulman’s answer was that we do mathematics for understanding, not just truth. He said what I was thinking during Hales’ talk, which was that to many mathematicians, using a formal proof assistant does not “feel like” mathematics. I am not claiming moral high ground here. It is actually something of a surprise to me that the prospect of being able to find and verify new truths more quickly is not more important to me. You never know what you’re going to get when you wander into a talk that is well outside your mathematical comfort zone. In my case, I didn’t end up with any oranges, but I got some interesting new-ti-me perspectives about how and why we prove.