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inequalities - Is the Jaccard distance a distance? - MathOverflow
Steinhaus Transform
the referenced survey: http://kenclarkson.org/nn_survey/p.pdf

It's known that this transformation produces a metric from a metric. Now if you take as the base metric D the symmetric difference between two sets, what you end up with is the Jaccard distance (which actually is known by many other names as well).
q-n-a  overflow  nibble  math  acm  sublinear  metrics  metric-space  proofs  math.CO  tcstariat  arrows  reduction  measure  math.MG  similarity  multi  papers  survey  computational-geometry  cs  algorithms  pdf  positivity  msr  tidbits  intersection  curvature  convexity-curvature  intersection-connectedness  signum 
february 2017 by nhaliday
Orthogonal — Greg Egan
In Yalda’s universe, light has no universal speed and its creation generates energy.

On Yalda’s world, plants make food by emitting their own light into the dark night sky.
greg-egan  fiction  gedanken  physics  electromag  differential  geometry  thermo  space  cool  curiosity  reading  exposition  init  stat-mech  waves  relativity  positivity  unit  wild-ideas  speed  gravity  big-picture  🔬  xenobio  ideas  scifi-fantasy  signum 
february 2017 by nhaliday
infinitely divisible matrices
the use of Hilbert spaces for establishing matrices are Gram matrices (and hence PSD) is interesting
tidbits  math  algebra  pdf  yoga  linear-algebra  inner-product  positivity  signum 
august 2016 by nhaliday
PHYS771 Lecture 9: Quantum
There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex.

The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want. This second approach is the one I'll be following here.
exposition  teaching  physics  quantum  tcs  rhetoric  aaronson  tcstariat  lecture-notes  positivity  nibble  thinking  hi-order-bits  big-picture  quantum-info  signum 
may 2016 by nhaliday

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