惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

Martin Fowler
Martin Fowler
博客园 - 【当耐特】
GbyAI
GbyAI
M
MIT News - Artificial intelligence
Microsoft Azure Blog
Microsoft Azure Blog
A
About on SuperTechFans
罗磊的独立博客
Apple Machine Learning Research
Apple Machine Learning Research
腾讯CDC
F
Fortinet All Blogs
IT之家
IT之家
WordPress大学
WordPress大学
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
Last Week in AI
Last Week in AI
Google DeepMind News
Google DeepMind News
Jina AI
Jina AI
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
D
DataBreaches.Net
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
H
Help Net Security
V
Visual Studio Blog
小众软件
小众软件
Y
Y Combinator Blog

math.PR updates on arXiv.org

Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
The Mathematics of Evolution: The Price Equation, Natural...
Tom LaGatta · 2022-02-21 · via math.PR updates on arXiv.org

George Price introduced his famous equation to study selective and environmental effects in discrete populations. We extend Price's framework to the measurable and quantum cases, decomposing all evolutionary processes into selective and environmental components. We also extend Fisher's fundamental theorem, showing that selective change of relative fitness equals variance of relative fitness. We introduce novel selective and environmental entropy functionals. Selective entropy is non-positive, representing biological negentropy, and environmental entropy is non-negative, representing physical entropy. Environmental entropy further decomposes into dispersion and mixing entropies. We prove four novel Laws of Natural Selection, showing that selection consistently acts to increase selection, but can be disrupted by environmental change. We apply convex analysis to variance and entropy functionals and their selective changes, and equilibrium processes arise to optimize these inequalities. These laws are inspired by but distinct from the classical Thermodynamic Laws. Our Zeroth Law is a refinement of Fisher's theorem, showing that variance of relative fitness is bounded below by a quantity depending on the child-bearing population. Our First Law shows that selective acceleration of relative fitness is also bounded below, depending on the variance. This is a non-conservative, selective version of the Thermodynamic First Law. Our Second Law shows that the selective change of selective entropy and its selective acceleration are similarly bounded by non-positive constants. This is a formal, rigorous version of the Thermodynamic Second Law. Our Third Law shows that for a class of equilibrium processes, selective change of environmental entropy vanishes, and otherwise may vary in an open window around zero. This is a selective version of the Third Law of Thermodynamics.