Elliptic curve A catalog of elliptic curves. Region shown is [−3,3]2 (For a = 0 and b = 0 the function is not smooth and therefore not an elliptic curve.) Any elliptic curve can be written as a plane algebraic curve defined by an equation of the form: Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. An elliptic curve is not an ellipse: see elliptic integral for the origin of the term. Elliptic curves over the real numbers[edit] Graphs of curves y2 = x3 − x and y2 = x3 − x + 1 Although the formal definition of an elliptic curve is fairly technical and requires some background in algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only high school algebra and geometry. In this context, an elliptic curve is a plane curve defined by an equation of the form where a and b are real numbers. The group law[edit] its derivative.
How Many Friends Can Your Brain Handle? SAN DIEGO — Being a social butterfly just might change your brain: In people with a large network of friends and excellent social skills, certain brain regions are bigger and better connected than in people with fewer friends, a new study finds. The research, presented here Tuesday (Nov. 12) at the annual meeting of the Society for Neuroscience, suggests a connection between social interactions and brain structure. "We're interested in how your brain is able to allow you to navigate in complex social environments," study researcher MaryAnn Noonan, a neuroscientist at Oxford University, in England, said at a news conference. Basically, "how many friends can your brain handle?" Noonan said. [7 Personality Traits You Should Change] Scientists still don't understand how the brain manages human behavior in increasingly complex social situations, or what parts of the brain are linked to deviant social behavior associated with conditions like autism and schizophrenia.
A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography Elliptic Curve Cryptography (ECC) is one of the most powerful but least understood types of cryptography in wide use today. At CloudFlare, we make extensive use of ECC to secure everything from our customers' HTTPS connections to how we pass data between our data centers. Fundamentally, we believe it's important to be able to understand the technology behind any security system in order to trust it. To that end, we looked around to find a good, relatively easy-to-understand primer on ECC in order to share with our users. Be warned: this is a complicated subject and it's not possible to boil down to a pithy blog post. The dawn of public key cryptography Whitfield Diffie and Martin Hellman Modern cryptography is founded on the idea that the key that you use to encrypt your data can be made public while the key that is used to to decrypt your data can be kept private. A toy RSA algorithm The RSA algorithm is the most popular and best understood public key cryptography system. y2 = x3 + ax + b
You can increase your intelligence: 5 ways to maximize your cognitive potential | Guest Blog The views expressed are those of the author and are not necessarily those of Scientific American. "One should not pursue goals that are easily achieved. One must develop an instinct for what one can just barely achieve through one’s greatest efforts." While Einstein was not a neuroscientist, he sure knew what he was talking about in regards to the human capacity to achieve. Not so many years ago, I was told by a professor of mine that you didn’t have much control over your intelligence. Well, I disagreed. You see, before that point in my studies, I had begun working as a Behavior Therapist, training young children on the autism spectrum. One of my first clients was a little boy w/ PDD-NOS (Pervasive Developmental Delays-Not Otherwise Specified), a mild form of autism. He wasn’t the only child I saw make vast improvements in the years I’ve been a therapist, either. Although the data from those early studies showed dismal results, I wasn’t discouraged. What is "Intelligence"? 1. 2. 3. 4.
Two Generals' Problem Definition[edit] Positions of the armies. Armies A1 and A2 need to communicate but their messengers may be captured by army B. The thought experiment involves considering how they might go about coming to consensus. Yes, we will both attack at the agreed-upon time. Allowing that it is quite simple for the generals to come to an agreement on the time to attack (i.e. one successful message with a successful acknowledgement), the subtlety of the Two Generals' Problem is in the impossibility of designing algorithms for the generals to use to safely agree to the above statement. Illustrating the problem[edit] The first general may start by sending a message "Let us attack at 0900 on August 4." Knowing this, the second general may send a confirmation back to the first: "I received your message and will attack at 0900 on August 4." A solution might seem to be to have the first general send a second confirmation: "I received your confirmation of the planned attack at 0900 on August 4." Proof[edit]
How Technology Is Changing Our Brains A while back, Bill Keller of The New York Times stirred up a hornet’s nest when he wrote a column worrying that joining Facebook would have a debilitating effect on his 13 year-old daughter’s intellectual faculties. Technology advocates, including me, pounced. Now there are new studies out that seem to support his argument. One shows that using search engines decreases our memory and another suggests that GPS may atrophy our brains. Discovery magazine has collected a half-dozen similar examples on its site. I think the question itself is misplaced. What Makes An Expert? We come into the world not knowing much. We learn virtually everything that way, by combining low order patterns to form higher order ones. Experts define themselves by learning the highest order patterns through what Anders Ericsson, calls deliberate practice. In much the same way, surgeons spend years learning the patterns of the human body and experienced firemen become familiar with the patterns of burning buildings.
Making Makers | Learning Labs Together, Kids Learning Code, Maker Kids, TIFF and Toronto Public Library, have developed comprehensive, maker curriculum for educators who work in formal and informal learning environments with the objective of increasing Toronto youth access and engagement with advanced technology and digital tools! Our workshops and activities allow youth to create something with purpose, driven by their own vision and also empower teachers to be makers. We are hosting Train the Trainer Symposiums wherein the educators can learn how to run and modify activities by doing them. Toy Hacking at Maker Kids: Wednesday, Feb 12th from 8pm to 10pm (Download the module here and the materials here) Arduino Rovers at Maker Kids: Wednesday, Feb 19th from 8pm to 10pm (Download the module here and the materials here) Introduction to HTML & CSS at Kids Learning Code: Tuesday, Feb 25th from 6:30pm to 8:30pm (Download the module here and the materials here) Register here!
8 Common Thinking Mistakes Our Brains Make Every Day and How to Prevent Them 12.3K Flares Filament.io 12.3K Flares × Get ready to have your mind blown. I was seriously shocked at some of these mistakes in thinking that I subconsciously make all the time. Especially as we thrive for continues self-improvement at Buffer, if we look at our values, being aware of the mistakes we naturally have in our thinking can make a big difference in avoiding them. Regardless, I think it’s fascinating to learn more about how we think and make decisions every day, so let’s take a look at some of these thinking habits we didn’t know we had. 1. We tend to like people who think like us. This is called confirmation bias. It’s similar to how improving our body language can actually also change who we are as people. Confirmation bias is a more active form of the same experience. Not only do we do this with the information we take in, but we approach our memories this way, as well. 2. This has to be one of my favorite thinking mistakes I came across. 3. 4. Well, no. 5. 6. 7. 8.
Massive Open Lab gets volunteers to beat computers in designing RNA Citizen science, the movement to draft non-specialists into areas of scientific research, doesn't require the volunteers to put on lab coats. In at least one case, scientists turned a prickly biochemical problem into a game and found that the gamers could typically beat the best computer algorithms out there. But all that work was done on cases where we already knew the answers, which was how we were able to measure the gamers' success. A consortium of researchers at Carnegie Mellon, Stanford, and Seoul National University put together what they called a Massive Open Laboratory. Once the tutorial is done, volunteers can start taking part in challenges like the one shown on top. At least, energetically stable based on calculations. In the first round, the current state-of-the-art software did a better job of designing RNA structures than the players did. From here, the researchers behind the Massive Open Lab plan on taking the work in two directions.
5 Strategies For Creating A Genius Mindset In Students How Can We Help Every Student Tap Their Inner Genius? by Zacc Dukowitz, Learnbop.com When we hear the word genius, certain people come immediately to mind—Albert Einstein in mathematics, or Warren Buffett in investing—but what exactly sets these people apart? It’s easy to simply shrug and say to ourselves, “Those people are just different. They have something most people don’t, and it’s as simple as that.” But the steps taken to arrive at a place of genius are actually more concrete, and have less to do with innate talent, than you might think. When it comes to cultivating intelligence, mindset is a huge factor. What is “Mindset”? Mindset refers to the beliefs you have about yourself and your basic qualities. Crucial opportunities for the application of good mindset habits occur in the classroom every day. And students who are—well, they may in fact be better positioned to become the next Einstein. The Characteristics of Genius Shifting Mindset 1) Change your Own Mindset 2) Change the Emphasis
Gamers beat algorithms at finding protein structures Today's issue of Nature contains a paper with a rather unusual author list. Read past the standard collection of academics, and the final author credited is... an online gaming community. Scientists have turned to games for a variety of reasons, having studied virtual epidemics and tracked online communities and behavior, or simply used games to drum up excitement for the science. But this may be the first time that the gamers played an active role in producing the results, having solved problems in protein structure through the Foldit game. According to a news feature on Foldit, the project arose from an earlier distributed computing effort called Rosetta@home. This is typically an energy minimization problem. It sounds simple, but with anything more than a short chain of amino acids, there are a tremendous number of potential configurations to be sampled in 3D space, which can bring powerful computers to their knees. Starting with algorithms, ending with brains
Study explains how the brain remembers pleasure and its implications for addiction | Kaleidoscope - UAB Campus News Key details of the way nerve cells in the brain remember pleasure are revealed in a study by UAB researchers published today in the journal Nature Neuroscience. Furthermore, the molecular events that form such “reward memories” appear to differ from those created by drug addiction, despite the popular theory that addiction hijacks normal reward pathways. Brain circuits have evolved to encourage behaviors proven to help our species survive by attaching pleasure to them. This study in rats supports the idea that the mammalian brain features several memory types, each using different circuits, with memories accessed and integrated as needed. “We believe reward memory may serve as a good model for understanding the molecular mechanisms behind many types of learning and memory,” said David Sweatt, Ph.D., chair of the UAB Department of Neurobiology, director of the Evelyn F. Natural pleasure versus addiction
Miniature bouncing tennis balls reveal cellular interiors I admit it, I love my job(s). I love doing science, and I love reporting science. In particular, I love it when my expectations are confounded, as they recently were in a paper I read. In this particular paper, I was expecting to see some nice results, not to learn anything truly new, since the authors have been working on this for a long time. What I found were results that are still a bit preliminary. Randomness generates a map Imagine that you want to explore a house. As you track the average location of the tennis balls, you map out the walls, beds, curtains, doors, and windows (the tennis balls that exit the window never return, as is often the case in real life). It turns out that you can do the same thing in a cell. It sounds great, but, in practice, you would be waiting a very long time to get that image. The key to this technique, though, is determining the particle position as accurately as possible as a function of time. A quantum locator The big deal comes from the prospects.