3 ms·

Combinatorics are fun. People who like reading this article would absolutely like Knuth's 4A volume of The Art of Computer Programming. Which discusses Permut

• westurner 3y ago
  /? Knuth's 4A volume of The Art of Computer Programming site:github.com : https://www.google.com/search?q=Knuth%27s+4A+volume+of+The+Art+of+Computer+Programming+site%3Agithub.com https://www.google.com/search?q=Knuth%27s+4A+volume+of+The+A... : > Generate {n-tuples, permutations, combinations, partitions, set partitions, trees,} with combinatorial patterns Combinatorics: https://en.wikipedia.org/wiki/Combinatorics https://en.wikipedia.org/wiki/Combinatorics - Exercise: Permutations [& Combinations]: https://rosettacode.org/wiki/Permutations#Python https://rosettacode.org/wiki/Permutations#Python https://rosettacode.org/wiki/Combinations_and_permutations#Python https://rosettacode.org/wiki/Combinations_and_permutations#P... - Exercise: Rewrite itertools.product as a generator that yields in a different order than itertools.product; write a different graph traversal that also covers without repetition - Exercise: The Birthday problem and actual probability of cryptographic hash collision given hash length n: https://en.wikipedia.org/wiki/Birthday_problem https://en.wikipedia.org/wiki/Birthday_problem - Exercise: The Gambler's Fallacy: Given a sequence of random values that satisfy many of the tests in e.g. Google/paranoid_crypto.lib.randomness_tests, where would Gambler's Fallacy have caused loss? https://en.wikipedia.org/wiki/Gambler%27s_fallacy https://en.wikipedia.org/wiki/Gambler%27s_fallacy https://github.com/google/paranoid_crypto/tree/main/paranoid_crypto/lib/randomness_tests https://github.com/google/paranoid_crypto/tree/main/paranoid... Combinatorics and physics: https://en.wikipedia.org/wiki/Combinatorics_and_physics https://en.wikipedia.org/wiki/Combinatorics_and_physics /?hnlog Ctrl-f Hilbert : "Matrices and Graph" https://news.ycombinator.com/item?id=36739579 https://news.ycombinator.com/item?id=36739579 : > [ Multigraph, networkx.MultiDiGraph , RDF Linked Data ] > Tensor product of graphs: https://en.wikipedia.org/wiki/Tensor_product_of_graphs https://en.wikipedia.org/wiki/Tensor_product_of_graphs > Hilbert space: https://en.wikipedia.org/wiki/Hilbert_space https://en.wikipedia.org/wiki/Hilbert_space : >> In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space. >> [...] The inner product between two state vectors is a complex number known as a probability amplitude. Wave interference > Quantum interference: https://en.wikipedia.org/wiki/Wave_interference#Quantum_interference https://en.wikipedia.org/wiki/Wave_interference#Quantum_inte... EM waves have amplitude in the interval [-1,1] or [-inf, +inf]. With EM waves we typically model constructive interference and destructive interference. There is also a particle-like phononic quantum wave interpretation of EM waves. Quantum waves are in the interval [0,1]. Quantum embedding is the process and study of encoding data as wave functions with e.g. phase. https://news.ycombinator.com/item?id=38255569 https://news.ycombinator.com/item?id=38255569 : > How many ways are there to roll a {2, 8, or 6}-sided die with qubits and quantum embedding? Quantum superposition and combinatorics; why can't the quantum simulator run this code like an actual QC? "Where does energy go during destructive interference?" (2018) https://news.ycombinator.com/item?id=32421509 https://news.ycombinator.com/item?id=32421509 : > From Conservation_of_energy#Quantum_theory https://en.wikipedia.org/wiki/Conservation_of_energy#Quantum_theory https://en.wikipedia.org/wiki/Conservation_of_energy#Quantum... : >> In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the Hilbert space (or a space of wave functions) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent [If the Hamiltonian is a time-independent operator] {Employee, Conference, Computational resource} Scheduling with priority: https://news.ycombinator.com/item?id=22589911 https://news.ycombinator.com/item?id=22589911 : > https://en.wikipedia.org/wiki/Hilbert_curve_scheduling https://en.wikipedia.org/wiki/Hilbert_curve_scheduling : >> [...] the Hilbert curve scheduling method turns a multidimensional task allocation problem into a one-dimensional space filling problem using Hilbert curves, assigning related tasks to locations with higher levels of proximity.[1] Other space filling curves may also be used in various computing applications for similar purposes. [2] And then fluids. Computational Fluid Dynamics is still one of the harder problems in classical high performance computing and quantum computing because it is a combinatorically hard problem to model every possible fluid outcome in order to predict the most likely outcome(s). /?hnlog Navier [e Euler, Stokes,] : - "Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations" https://news.ycombinator.com/item?id=31049608 https://news.ycombinator.com/item?id=31049608 : > [awesome-fluid dynamics, jax-cfd,] And then Evolutionary Algorithms, - Infinite Monkey Theorem: https://en.wikipedia.org/wiki/Infinite_monkey_theorem https://en.wikipedia.org/wiki/Infinite_monkey_theorem - https://news.ycombinator.com/item?id=39110110#39139198 https://news.ycombinator.com/item?id=39110110#39139198 : > Holman's "elegant normal form", Evolutionary Algorithms > Convergence: https://en.wikipedia.org/wiki/Evolutionary_algorithm#Convergence https://en.wikipedia.org/wiki/Evolutionary_algorithm#Converg... : > For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof: [...]
  • westurner 3y ago
    The discrete convolution is combinatorial. Convolution > Discrete convolution: https://en.wikipedia.org/wiki/Convolution#Discrete_convolution https://en.wikipedia.org/wiki/Convolution#Discrete_convoluti... Category:Combinatorics: https://en.wikipedia.org/wiki/Category:Combinatorics https://en.wikipedia.org/wiki/Category:Combinatorics