Sandbox 7

Welcome to a free encyclopedia on complexity sciences and information physics anyone can edit! Contact me at: moc.liamg|8ngnsx#moc.liamg|8ngnsx! IJBOL THEORY WIKI 複雑科学研究所 "Research is about friendship and having fun." (edit the sidebar) • (edit this header) • (edit top row)] $$\sigma_\mu(A) = -\log\; \mu(A)$$ Recently Added Articles: (edit this page) Week of 7/31/2023 to 8/06/2023 Week of Mon, 7/31/2023 - Sun, 8/06/2023: Wed 8/2/2023: (7 new pages): Vector field • Topological social choice • Eilenberg-MacLane space • Sheaf neural network • Morse Theory • Coupled map Thu 8/3/2023: (7 new pages): Configuration space • Transversality • Machine learning • Supervised learning • Unsupervised learning • Quenched Disorder • Morse Homology Fri 8/4/2023: (9 new pages): Hopf decomposition • Centrality • Hopfield Model • Boltzmann Machine • Graph Laplacian • Tangent Space • Tangent Bundle • Cotangent Space • Cotangent Bundle Sat 8/5/2023: (8 new pages): Ising model • Symplectic geometry • Symplectic manifold • Rényi entropy • Spectral sheaf theory • Stratified space • Flag Complex • Vietoris-Rips complex Sun 8/6/2023: (2 new pages): Nerve • Transient chaos Week of 8/07/2023 to 8/13/2023 Week of Mon, 8/7/2023 - Sun, 8/13/2023: Break. No additions. Week of 8/14/2023 to 8/20/2023 Week of Mon, 8/14/2023 - Sun, 8/20/2023: Thu 8/17/2023: (1 new page): Energy-Based Model, and added to page(s): Tangent Bundle Fri 8/18/2023: Landing page remodeled. Sat 8/19/2023: (4 new pages): Boltzmann Distribution • log-likelihood • Cell complex • Regular Cell Complex Sun 8/20/2023: (1 new page): Weighted Cellular Sheaf Week of 8/21/2023 to 8/27/2023 Week of Mon, 8/21/2023 - Sun, 8/27/2023: Mon 8/21/2023: Hilbert Space Tue 8/22/2023: Mercer's Theorem, we added User Pages, and began working on Wiki Syntax, Wiki Style Guide and Frequently Asked Questions pages all of which are present in the top bar menu. Thu 8/24/2023: Cognitive Effort • Argot Sat 8/26/2023: Entropy-Complexity Curve • Topological Complexity Sun 8/27/2023: Reproducing Kernel Hilbert Space • Lusternik–Schnirelmann category In the works: Cognitive Effort • Order parameter • Topological Data Analysis • Statistical mechanics • Equilibrium Statistical mechanics • Non-Equilibrium Statistical mechanics • Spin glass • Kuramoto Model • Neural Mean-Field Theory • Phase Space • Discourse sheaf • Čech cohomology • Čech complex • Topological Entropy • Metric Measure Space • Gromov–Hausdorff Distance (Gromov–Wasserstein Distance) • Holonomy • Kalman Filter • Algorithmic Probability • Cognitive Effort • Salience Network • Autoencoder • Taken's theorem • Manifold Learning • Kullback-Leibler divergence • Maximum Likelihood Estimation • Mean-Field Theory (Curie-Weiss Theorem, Bethe-Peierls Approximation) Rewrite: Hopf Decomposition Did you know that… (edit this page) Boltzmann machine, a predecessor of modern machine learning models, is based on a spin-glass model of Sherrington-Kirkpatrick's stochastic Ising Model. Nerves, a construct of Čech cohomology theory, can be used to track down attractors in spike train activity in computational neuroscience? The loss function landscape pertaining to can be thought of thermodynamically as an energy function over thermal degrees of freedom? Stochastic gradient descent then acts as a dissipative process introducing self-generated disorder. Any real function on a cotangent bundle can be interpreted to be a Hamiltonian, so real-valued cotangent bundle is a phase space. A more general form of Arrow's impossibility theorem can be shown to be true as a consequence of homotopy. A recent model called rapid freeze neuroplasticity, a phenomenon similar to frozen random patterns in coupled map lattices pertaining to self-organized quenched disorder, was proposed as an explanation for neurodynamics of conspiracy theories? Philip J. Anderson's treated emergence centrally through generalized rigidity, to be understood as a consequence of broken symmetry and the order parameter. A pair of homologous cycles in a cellular sheaf has effective resistance as defined via the minimal-norm bounding chain. Effective resistance acts as a probability on graph cycles, thus allowing for random sampling to compress a sheaf with control of the eigenspectrum of the sheaf Laplacian. Cellular sheaves thus have natural variational approximations.