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...pt of information projection can be extended to arbitrary [[f-divergence|''f''-divergence]]s and other [[Divergence (statistics)|divergence]]s.<ref>{{Ci ...

...cific divergences and classes of divergences, notably [[f-divergence|''f''-divergences]] and [[Bregman divergence]]s (see {{slink||Examples}}). ...vatives are required. In practice, commonly used statistical manifolds and divergences are infinitely differentiable ("smooth").}} <math>M</math> of dimension <ma ...

...ions over a set <math>\mathcal X</math>, defined by a class <math>\mathcal{F}</math> of real-valued functions on <math>\mathcal{X}</math> as ...- \mathbb E_{Y \sim Q} f(Y) \big| = \sup_{f \in \mathcal F} \big| P f - Q f \big|;</math> ...

{(F^{\mu\nu})^2 \over 4} for <math> F^{\mu\nu}= \partial^\mu A^\nu - \partial^\nu A^\mu </math> and the boson mas ...

...n be modelled as a [[function (mathematics)|mathematical function]] <math> f : A \cup\{\perp\} \rightarrow B \cup\{\perp\}</math> where ⊥ ([[bottom elem ...noted <math>\mathbf{div}</math>. One semantic model of CSP is the failures-divergences models, which refines the stable failures model by distinguishes processes ...

...ient of a scalar function is a [[vector field]] ''v''&nbsp;=&nbsp;&nabla;''f''&nbsp;:&nbsp;'''R'''^''n''&nbsp;→&nbsp;'''R'''^''n''. ...]] and [[Lp space|''L''²-norm]] for suitable scalar functions ''f'': ...

...anography: Past, Present, and Future |book-title=Proceedings Of COMMISSION F SYMPOSIUM on Frontiers of Remote Sensing of the Oceans and Troposphere from ...ay="block">\frac{Du}{Dt} = -\frac{1}{\rho} \frac{\partial p}{\partial x} + f v + \frac{1}{\rho} \frac{\partial \tau_x}{\partial z}</math> ...

:<math> \mathcal L = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \bar{\psi}(i \partial\!\!\!/ - m )\psi + e \bar{\psi} \gamma^\m :<math> \mathcal L = -\frac{1}{4} Z_3 F_{\mu \nu,r} F^{\mu \nu}_r + Z_2 \bar{\psi}_r(i \partial\!\!\!/ - m_r )\psi_r - \bar{\psi} ...

...er's inequality uses the [[partition inequality]] for [[f-divergence|''f''-divergences]]. ...

...] in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by [[Steven Weinberg]] to find a theory of [[ ...imensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in [[S-Matrix|scattering amplitudes]]. The requirement of a UV fixed ...

Or as an expected value of simpler Kullback–Leibler divergences: Let <math>(\Omega, \mathcal F, \mathfrak P)</math> be a [[probability space]], and let the random variabl ...

...of centroid E and the points B and C are in the blue cluster of centroid F, as the intra-cluster distance in not minimal]] |chapter = Total Jensen divergences: Definition, properties and clustering ...

...|last2=Cseke |first2=Botond |last3=Tomioka |first3=Ryota |date=2016 |title=f-GAN: Training Generative Neural Samplers using Variational Divergence Minim ...K\sup_{\|f\|_L \leq K} \mathbb{E}_{x\sim \mu}[f(x)] -\mathbb E_{y\sim \nu}[f(y)]</math> ...

...be a real valued function of the vector '''v'''. Then the derivative of ''f''('''v''') with respect to '''v''' (or at '''v''') is the '''vector''' defi ...{v}}\cdot\mathbf{u} = Df(\mathbf{v})[\mathbf{u}] = \left[\frac{d}{d\alpha}~f(\mathbf{v} + \alpha~\mathbf{u})\right]_{\alpha=0}</math> ...

\int D \rho \; \delta \left[ \rho - \hat{\rho} \right] F \left[ \rho \right] = F \left[ \hat{\rho} \right], \qquad (4) ...

...]], and [[signal processing]]. Some aspects can be traced as far back as [[F. L. Hitchcock]] in 1928,<ref name=":0">{{Cite journal|last=Hitchcock|first= ...\Sigma_m V^T_m </math>, and store the left singular vectors <math>U_m \in F^{I_m \times R_m}</math>; ...

...e cluster properties<ref name="Antonuccio:1997tw">{{ cite journal |author1=F. Antonuccio |author2=S. J. Brodsky |author3=S. Dalley | ...duality<ref name="BloomGilman1">{{ cite journal |author1=E. Bloom |author2=F. Gilman | ...

...">{{ cite journal | author1= S. J. Brodsky|author2= F. -G. Cao|author3= G. F. de Teramond | title= AdS/QCD and Applications of Light-Front Holography | ...}</ref><ref name="RenGp1b">{{ cite journal | author1=M. Gell-Mann|author2= F. E. Low | title=Quantum electrodynamics at small distances | journal=[[Phys ...

...t{- \det (g)} (g^{\mu \alpha} g^{\nu \beta} \mathcal{F}_{\mu \nu} \mathcal{F}_{\alpha \beta})</math> <math>\mathcal{F}^{\mu \nu} = \nabla^\mu \mathcal{A}^\nu - \nabla^\nu \mathcal{A}^\mu</math> ...

...STS aims to explain long-range dynamical phenomena such as [[Pink noise|1/f]], [[Flicker noise|flicker]], and [[crackling noise|crackling]] noises and ...necessitates the long-range response, which may account for [[pink noise|1/f noise]]. The [[Edge of Chaos]] is interpreted as noise-induced chaos -- a d ...