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Brian Lu
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Well, since no one in the English-speaking world seems to have produced a Hitler meme YouTube video for iOS 7 yet, I decided to try my hand.  It's my first time trying a meme video, but I'm surprised how well it turned out.  Enjoy!

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Top 12 Gadgets that Changed the World

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Agora Tower in Taipei, TAIWAN

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Yesterday in Science - 4.5.13

Exhaled breath carries a molecular 'breathprint' unique to each individual
Researchers have shown that exhaled human breath contains a characteristic molecular "fingerprint". Stable, specific 'breathprints' unique to an individual exist and may have applications as diagnostic tools in personalized medicine. The scientists want to use this finding to diagnose diseases based on the chemical analysis of patient's exhaled breath, using highly sensitive and precise instrumental methods.➜

Scientists Decode Dreams With Brain Scans
It used to be that what happened in your dreams was your own little secret. But today scientists report for the first time that they've successfully decoded details of people's dreams using brain scans.➜

Astrophysics: Fire in the hole!
Will an astronaut who falls into a black hole be crushed or burned to a crisp? Quantum effects would turn the event horizon into a seething maelstrom of particles. Anyone who fell into it would hit a wall of fire and be burned to a crisp in an instant.➜

Less than 5% of the Universe is Visible Matter
Astrophysicists have announced the first results from NASA’s Alpha Magnetic Spectrophotometer and claimed they have found what could be considered evidence (an excess of positrons) of dark matter. Less than 5% of our universe is visible matter, the rest is either dark matter or dark energy.➜

Bumblebees use logic to find the best flowers
Despite their tiny brains, bees are smart enough to pick out the most attractive flowers by watching other bees and learning from their behaviour. By using simple logic, they see which coloured flowers are the most popular, and conclude that those of the same colour must also contain lots of energy-rich nectar.➜

New camera system creates high-resolution 3-D images from up to a kilometer away
A standard camera takes flat, 2-D pictures. To get 3-D information, such as the distance to a far-away object, scientists can bounce a laser beam off the object and measure how long it takes the light to travel back to a detector. The technique, called time-of-flight (ToF), is already used in machine vision, navigation systems for autonomous vehicles, and other applications, but many current ToF systems have a relatively short range and struggle to image objects that do not reflect laser light well.➜

Here's a nice sum up of the last week in science by +Mark Bruce ➜

#onkarssciencebulletin #scienceeveryday   #science  

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Smale's problems are a list of eighteen unsolved problems in mathematics that was proposed by Steve Smale in 1998, and republished in 1999. Smale composed this list in reply to a request from Vladimir Arnold, then president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of Hilbert's problems that had been published at the beginning of the 20th century.

Finding strongly polynomial algorithms for linear programming is one of the “mathematical problems for the 21st century" according to Smale’s 9th problem: the linear programming problem

Linear programming, is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. 

In the book, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William J. Cook, it states linear programming is:
"an amazingly effective method for combining a large number of simple rules, satisfied by all tours, to obtain a single rule of the form 'no tour through this point set can be shorter than X.' The number X gives an immediate quality measure: if we can also produce a tour of length X then we can be sure that it is optimal."

The simplex algorithm, is a popular algorithm for linear programming. Mathematician George Dantzig provided an original example of this method by finding the best assignment of 70 people to 70 jobs to exemplify the usefulness of linear programming. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the simplex algorithm.

Will it ever happen that somebody proves that the simplex algorithm, with a particular pivoting rule, runs in polynomial time? A polynomial pivot rule would solve this problem in the affirmative. Well, a necessary prerequisite for this to happen is that we can work from any vertex (corner) to another prescribed vertex in a small number of steps along the polyhedron or polytope. So whether or not there exists a polynomial-time variant of the simplex method depends on the geometry of polyhedra (see the images).

Hirsch conjecture

Warren Hirsch conjectured in 1957 that, for any polyhedron defined by n inequalities (faces) in d dimensions, the length of the longest shortest path between any two vertices is at most n - d. When Francisco Santos announced his counterexample to the Hirsch conjecture in spring 2010, it sparked a flurry of activity examining the geometry and complexity of linear programming.

Santos gave three lectures, an 8 hour mini-course, on the Hirsch conjecture and the counter example. The three parts had the following entertaining titles:
Hirsch Wars Episode I: The Phantom Conjecture. This is mostly background and history, including the proofs of the two Klee-Walkup results on which his counter-example is based.
Hirsch Wars Episode II: Attack of the Prismatoids. The strong d-step Theorem and the construction of prismatoids in dimension 5 with large width.
Hirsch Wars Episodes III and IV: Revenge of the Linear Bound + A New Hope. The first part explores the asymptotics of counter-examples, and what we can (and cannot) expect from the prismatoid approach. The second part is about the diameter of simplicial complexes and more general objects, summing up some of the main results and ideas in the polymath3: The polynomial Hirsch Conjecture project.

For a more concise introduction see the talk Counter-examples to the Hirsch conjecture (;  it is targeted at a general mathematical audience and focuses more on the context of the Hirsch conjecture (linear programming, simplex method, history) than on the counter-example itself. Santos concludes that this counter example breaks a “psychological barrier”, but for applications it is absolutely irrelevant.

Finding a counterexample will be merely a small first step in the line of investigation related to the conjecture. (V. Klee and P. Kleinschmidt, 1987)

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Hyundai dreams up egg-shaped E4U personal transporter

Asian car manufacturers have been demoing Personal Mobility Vehicles (PMVs) for what seems like forever. They're usually fairly dull, but every once in a while a concept comes along that's earth-shatteringly good. Hyundai's E4U is one such concept. Looking like a bumblebee egg that fell into Tron's grid, the E4U moves by using a semisphere that constantly spins horizontally. The spinning semisphere is tilted to generate drive while two stabilizing wheels at the rear keep it moving straight. The technique is similar to how a helicopter steers — it tilts to move using its large horizontal rotor while using a vertically-mounted rotor for stability. It's not clear what exactly powers the E4U, but it seems unlikely to be gas.

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There are 11 ways to chop a pentagon into pieces by drawing lines between corners - lines that don't intersect.   For a square there are just 3 ways, and for a triangle there's just 1, using no lines at all.  

We can count the ways for a polygon with any number of corners, and we get these numbers:

1, 3, 11, 45 ,197, 903, 4279, 20793, 103049, …

These are called the Schröder–Hipparchus numbers, for an interesting reason.  Hipparchus was one of the best of the ancient Greek astronomers.   He lived around 100 BC, and he discovered the precession of the equinoxes, and invented the 'stereographic projection' - an important way to map a sphere on a plane. 

But Plutarch, a philosopher who lived two centuries later, said Hipparchus also showed that the number of “affirmative compound propositions” that can be made from ten “simple propositions” is 103049. 

See that number up there?

Nobody had a clue what Plutarch was talking about until 1994, when a grad student put the pieces together.  The story is in my blog article here:

and the story moves forwards even further in the comments.  I hope this is fun regardless whether you like simple easy math (chopping polygons into pieces), or heavy-duty sophisticated math (operads). 

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French newspaper to be delivered via drone!

A French newspaper company called Poste Groupe has announced on its blog the intention of delivering newspapers to residents of Auvergne, France, via drone. 

Specifically, they intend to use Parrot AR drones, which are controlled with iOS or Android phones or tablets. 

So what do you think? Visionary? Stupid? Early April Fool's joke?
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