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Backflow is a cross between a casual-style action game and a multiplayer strategy game for mobile phones. In the game you take control of the waste disposal infrastructure for a city. It's your job to make sure each type of waste goes to the right place.

By flipping switches on pipe intersection points you direct the flow of waste to processing facilities at the bottom of the screen. Send recyclables to the right bins and they'll be converted into resources that you can use to upgrade your system, but put things in the wrong place and you'll increase the pollution in your city. Keep pollution low and your city will grow, but if it gets out of control your citizens will leave in droves! As your city grows in population, waste comes out faster and more frequently, and upgrades become more and more important. Trade resources with other players to make sure you can keep upgrading.

Try and build the biggest city you can without getting buried in the garbage!

Learning classifier decision boundaries and an informative two-dimensional linear subspace jointly through variational level set methods and optimization on the Stiefel manifold. The two classes of measurements, the black + markers and the magenta x markers are eight-dimensional. Only the first two dimensions are informative for classification: the points are separable by an ellipse in those two dimensions. The other six dimensions are independent Gaussian noise. Starting from a random initialization for a two-dimensional subspace, and a poor initialization for a decision boundary, t method converges to the plane of the first two dimensions and an elliptical decision boundary that separates the two classes. The blue line is the decision boundary. The green polygon outlines the projection of an eight-dimensional hypercube onto two dimensions using the current dimensionality reduction mapping. When aligned to two dimensions, the polygon is a square. Visit http://lids.mit.edu/research/project-highlights/classification-and-dimensionality.html for more information.

Knowledge Harvesting with the Mel King Fellows

As magic and ephemeral as they may seem, soap bubbles are a magnificent example of precise mathematics, physics and chemistry at work. This video lesson explores the science that explains soap bubbles, as well as the application of this knowledge to other areas, such as architecture and biology.

Video profile of the Pedal Thresher, an adaptive, pedal-operated multi-grain thresher, as invented by the Teen Technology InvenTeam from Bridgewater, New Jersey.

For more information about the Lemelson-MIT Program, visit web.mit.edu/invent

For more information about the InvenTeam initiative, visit web.mit.edu/inventeams