@IgorCarron blogs recent applications of compressive sensing and matrix factorisation every week. (Compressive sensing solves underdetermined systems of equations, for example trying to fill in missing data, by L₁-norm minimisation.) This week: reverse-engineering biochemical pathways and complex systems analysis. (Source: … Continue reading
May 28, 2012
Tagged adjacency matrix, applied mathematics, biochemistry, biology, chemistry, complex networks, compressed sensing, compressive sensing, dynamical systems, graph theory, Igor Carron, L₁ norm, matrices, matrix algebra, matrix factorisation, matrix factorization, networks, synthetic biology, time series, topography
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Once you’re comfortable with 2-arrays and 2-matrices, you can move up a dimension or two, to 4-arrays or 4-tensors. You can move up to a 3-array / 3-tensor just by imagining a matrix which “extends back into the blackboard”. Like … Continue reading
Tagged 4-D, array, data, linear transformations, matrices, matrix, matrix algebra, object orientation, object-oriented programming, R, tensor
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Linear Transformations will take you on a Trip Comparable to that of Magical Mushroom Sauce, And Perhaps cause More Lasting Damage Long after I was supposed to “get it”, I finally came to understand matrices by looking at the above … Continue reading
Tagged algebra, eigenvector, eigenvectors, linear algebra, linear transformations, math, mathematics, maths, matrices, matrix algebra, matrix transformations, vector, vector calculus, vectors
In the loop quantum gravity approach, space-time is quantized by a procedure that encodes it in a discretized structure, consisting of spin networks and spin foams. A spin network consists of an oriented embedded graph in a 3-dimensional manifold with … Continue reading
February 18, 2011
Tagged art, general relativity, graph theory, group theory, groups, heroes, homotopy, loop quantum gravity, manifolds, math, mathematics, maths, matrices, matrix algebra, parallel transport, quantization, science, spacetime, special unitary group, spin foam, spin network, SU(2), tetrad, tetrads, vierbein, wizardry