Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…
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48 results for “unified theories”
Paper studies flows of spinor fields with flux for unified theories.
problem Existence of covariantly constant spinors in unified theories.
method Introduces parabolic flows of spinor fields to find stationary points.
result Establishes short-time existence and smoothing estimates for spinor flows.
Survey of geometric flows from unified string theories.
problem None explicitly stated, but related to understanding geometric flows in string theories.
method Survey of geometric flows in various geometries (complex, almost-complex, symplectic) motivated by string theories.
result Intermediate flows between Ricci and Kähler-Ricci flows, often coupled to additional fields.
Historical economic growth in Latin America is analysed using the data of Maddison. Unified Growth Theory is found to be contradicted by these data in the same way as it is contradicted by the economic growth in Africa, Asia, former USSR, Western Europe, Eastern Europe and by the world economic growth. Paradoxically, U…
Symmetry unifies AI learning dynamics, complexity, and representation.
problem Fragmented theories of AI learning mechanisms.
method Synthesis of parameter symmetry in AI models.
result Parameter symmetry breaking and restoration unify AI learning hierarchies.
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, e…
Proper Orbifold Cohomologymath.AT
Unified theory of orbifolds and cohomology.
problem Formulating a general theory of orbifolds unifying differential and equivariant cohomology.
method Abstract axiomatization in higher topos theory and concrete models for various orbifolds.
result Fully faithful embedding of orbifolds into a cohesive infinity-topos with proper equivariant cohomology.
Unified approach to totally ramified values in various surface theories.
problem Totally ramified values in value distribution theory, normal family theory, and Gauss maps of surfaces.
method Bloch--Ros principle applied to various surface theories.
result Unified approach to phenomena concerning totally ramified values.
Data describing historical economic growth are analysed. They demonstrate convincingly that the takeoffs from stagnation to growth, claimed in the Unified Growth Theory, never happened. This theory is again contradicted by data, which were used, but never properly analysed, during its formulation. The absence of the cl…
Unified treatment of gauge theories and Yang-Mills theory duality.
problem Unified treatment of gauge theories and Yang-Mills theory duality.
method Cohomological localization techniques and Atiyah-Singer index theorem.
result Unified framework and simplified derivations of localization formulas.
The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions. Some of these myths are discussed. The examination of data shows that the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) did not exist and that Industrial Revo…
Unified framework for Morita invariant cohomology of Lie groupoids.
problem Proving Morita invariance of cohomology theories for Lie groupoids.
method Viewing cohomology as sheaves of modules on the nerve of the groupoid and establishing criteria for Morita invariance.
result Established criteria for Morita invariant cohomology theories.
Historical economic growth in Asia (excluding Japan) is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used (but not analysed) during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malthusian…
One of the fundamental postulates of the Unified Growth Theory is the claimed existence of three distinctly different regimes of economic growth governed by three distinctly different mechanisms of growth. However, Galor also proposed that the timing of these regimes is different for developed countries and for less-de…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based approach and aim to provide a tutorial to the computations.
Unified proof of Nielsen-Thurston classification via Teichmüller's theorem.
problem Classifying mapping class groups and rational maps.
method Unified proof following Bers' approach.
result Unified proof of Nielsen-Thurston classification.
The so-called great divergence in the income per capita is described in the Unified Growth Theory as the mind-boggling and unresolved mystery about the growth process. This mystery has now been solved: the great divergence never happened. It was created by the manipulation of data. Economic growth in various regions is…
Unified framework for feature-based explanations using ANOVA and game theory.
problem Differences between feature-based explanations methods limit their applicability.
method Introduces a unified framework combining fANOVA and cooperative game theory.
result Uncovered similarities and differences between various explanation techniques.
We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured spars…
Unified theory for learning, optimization, and modelling.
problem Understanding the interplay between problem setup, method choice, and solution in learning.
method Defining solvable problems and parametrized methods, sketching a universal convergence theorem.
result Unified convergence theorem for learning, reducing study to few ideas.
We show that generalised geometry gives a unified description of bosonic eleven-dimensional supergravity restricted to a -dimensional manifold for all . The theory is based on an extended tangent space which admits a natural action. The bosonic degrees of freedom are unified as…
Unified framework for explaining models by removing features.
problem Unclear relationships and preferences among existing model explanation methods.
method Removal-based explanations characterized by three dimensions.
result Unified framework unifies 26 existing methods.
Geometrically classifies maps from R^0|2 to any manifold, unifying theories.
problem Classifying maps from R^0|2 to any manifold without auxiliary structures.
method Relates maps to pullback of decomposable bivector bundle over S via algebraic constraints.
result Reduced manifold has fiber dimension dim(S) + 1, unifying topological and algebraic views.
We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff's ergodic theorem for the class of immersions of solenoids with a trapping region.
Unified theory explains market impact using a simplified supply-demand parameter.
problem Understanding the market impact of metaorders and excess volatility.
method Coarse-grained approach with a single parameter ρ to model supply-demand equilibrium and market impact.
result Establishes a connection between excess volatility and order-driven markets through the square-root law.
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation theory of -surfaces.
Unified theory for adaptive image convolutions using metric perspectives.
problem Fixed kernels in convolutions limit adaptability in image processing.
method Metric perspective on images as 2D manifolds with local distances, proposing metric convolutions.
result Metric convolutions provide better generalisation and competitive performance.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
problem Unifying Higgs bundle vacua from different string compactifications.
method Developed formalism for M-theory on local Spin(7) spaces and constructed explicit solutions.
result Unified 3D effective field theory from 4D M- and F-theory vacua.
Unified model optimizes experiment performance and reduces duration.
problem Balancing reward maximization and experiment termination.
method Unified model that considers both within-experiment and post-experiment outcomes.
result Familiar algorithms can optimize a broad class of objectives with proper parameter adjustment.
Precise Dynamics of Diagonal Linear Networks: A Unifying Analysis by Dynamical Mean-Field Theorystat.ML
Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.
problem Understanding the overall dynamics of diagonal linear networks (DLNs) in neural network training.
method Dynamical Mean-Field Theory (DMFT) applied to DLNs.
result Derives low-dimensional effective process capturing high-dimensional gradient flow dynamics.
Unified theory of -expectations derived from chaotic dynamics.
problem Non-convex stochastic control problems outside G-expectations.
method Spectral theory of transfer operators for uniformly hyperbolic flows, viscosity solutions to HJB equations.
result Affine Hessian, non-convex gradient structure of -expectation.
Unified theory of deep learning from approximation to emergence.
problem Understanding the mechanisms behind deep learning.
method Unified, proof-oriented approach tracing from classical foundations to contemporary mechanisms.
result Unified theory explaining deep learning from approximation to emergence.
Unified framework recovers and improves classical Brouwer homeomorphism results.
problem Classical Brouwer homeomorphism theory and its dynamics.
method Unified foliated framework combining Le Calvez's and Handel's methods.
result Recovery and improvement of classical results in Brouwer homeomorphism theory.
Unified framework for 3D and 4D manifold and knot theory.
problem Unified understanding of manifold and knot theory.
method Unified correspondence between different subfields of low-dimensional topology.
result Unified algebraic manifestations of 3D and 4D manifold and knot theory.
Atoms meet symbolsmath.AG
Unified approach to invariants in equivariant geometry.
problem Constructing invariants in -equivariant birational geometry.
method Combining atom theory and modular symbols.
result Developed new geometric invariants for orbifolds and surfaces.
A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regressionstat.ML
Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
Unified framework for active learning problems using information theory.
problem Combining level set estimation and Bayesian optimization.
method Information-theoretic criterion and acquisition function.
result Unified framework achieves state-of-the-art performance.
Unified method proves integrality of LMOV invariants for framed unknot.
problem Proving the integrality of LMOV invariants for framed unknots.
method Unified method to prove integrality of explicit formulae for LMOV invariants.
result Proves integrality of certain LMOV invariants for framed unknots in higher genera.
Develops a unified theory of Yang-Mills and GR using generalized principal bundles.
problem Combining Yang-Mills theories and General Relativity into a single framework.
method Using generalized principal bundle theory, the authors develop a new approach to field theories.
result Recover General Relativity within the framework of generalized principal connections.
New invariant unifies two theories of 3-manifolds, recovering quantum invariants.
problem Quantum invariants of 3-manifolds at roots of unity.
method Introduces a unified invariant for negative definite plumbed 3-manifolds.
result 2-variable refinement of the -invariant.
Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.
problem Index theory and analytic torsion of nonlinear PDEs.
method Microlocal sheaf theory, factorization algebras, Spencer hypercohomology.
result Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.
Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
Unified review of Conformal Prediction theory and applications.
problem Distribution-free, non-parametric forecasting method for valid prediction sets.
method Minimal assumptions, straightforward predictions sets valid in finite sample cases.
result Unified review of Conformal Prediction theory and applications.
Unified framework for DRO using OT with constraints.
problem Handling ambiguity in likelihood ratios and outcomes.
method Unified framework leveraging optimal transport with conditional moment constraints.
result Unified approach enables adversarial perturbation of likelihood ratios and outcomes.
Unified theory for representation learning using learnable functions.
problem Insufficient theoretical understanding of unsupervised and self-supervised learning.
method Discriminative theoretical framework for analyzing sample complexity.
result Learnable regularization functions can reduce the amount of labeled data needed.
Unified theory of measure-preserving diffusions on manifolds.
problem Deriving a complete recipe for measure-preserving diffusions on manifolds.
method Developed a geometric theory that unifies and generalizes previous constructions, relying on intrinsic geometry of the target measure.
result The completeness result is a direct consequence of manifold topology and target measure geometry.
Unified proof of knot unknotting bounds using Ma-Qiu index.
problem Finding bounds on the number of moves to unknot knots.
method Using the Ma-Qiu index to bound presentation distances and Gordian distances.
result Unified proof of various unknotting number bounds.
Unified learning bound for covariate and concept shifts.
problem Generalization under distribution shift in machine learning.
method Support-agnostic definitions of covariate and concept shifts using entropic optimal transport, leading to a unified error bound applicable to various loss functions and label spaces.
result Development of estimators for shifts with concentration guarantees and the DataShifts algorithm for quantifying and estimating the error bound.