Unified gravity and electromagnetism using algebroid structures.
problem Unified theory of gravity and electromagnetism.
method Algebroid bundle associated with affine metrics.
result Geometrization of matter.
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48 results for “geometric unification”
Geometric approach unifies GR and QM without additional objects.
problem Unified theory of GR and QM without extra objects.
method Geometric properties of pseudo-Riemannian manifold (M, g) to define physical phenomena.
result Equations of GR and QM derived from geometric constraints.
Geometric cohomology model uses co-oriented maps to define a product structure.
problem Constructing a geometric model for cohomology of smooth manifolds.
method Develops a cochain complex model based on co-oriented smooth maps, focusing on their pull-back product structure.
result Geometric cochains with a partially defined product structure induce the cup product in cohomology.
New mathematical structure adds multiple fibers to spacetime models.
problem Need for spacetime models with more than five dimensions.
method Introduces a generalized fiber bundle structure .
result Possible definition of objects depending on one component of the global fiber.
Paper proposes Unification Networks to learn invariants from examples.
problem Learning to recognize common underlying principles across examples.
method End-to-end differentiable neural network approach with soft unification.
result Learning invariants improves performance on various datasets.
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
We investigate unification of two systems of identical elements having different dimensions which may be of interest for both physics and economics. Characteristic parameters as well as explicit formulae for the temperature (in economics - capital turnover) and dimension of the united system are obtained as functions o…
In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This paper is a continuation of [4] such that the complex variant of that theory yields …
Unified Kähler-Ricci and Anomaly flows with new formulation.
problem Unified Kähler-Ricci and Anomaly flows.
method New formulation of Anomaly flow with vanishing slope parameter, unifying with Kähler-Ricci flow.
result Unified Kähler-Ricci and Anomaly flows with new formulation.
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in thi…
Survey of knot polynomials and their categorification, including quiver-knot correspondence.
problem Understanding the relationship between knot polynomials and quivers.
method Overview of classical knot polynomials, physical and geometric insights, and 3d theory analysis.
result Exploration of the LMOV invariants and their connection to BPS states.
Unified study of Riemannian and sub-Riemannian geometries with synthetic Ricci curvature bounds.
problem Unified framework for Riemannian and sub-Riemannian geometries.
method Study of gauge metric measure spaces.
result Unified synthetic Ricci curvature lower bounds for both Riemannian and sub-Riemannian structures.
The paper proposes a method to improve data analysis by considering multiple subsets of attributes (views) to enhance geometric information.
problem Distortion of distance metrics in high-dimensional data analysis.
method Partitioning attributes into multiple subsets (views) and using consensus between views to extract geometric information.
result Enhanced geometric information from multiple views improves data analysis.
Stock mechanics: unification with economyphysics.comp-ph
Associating stock mechanics to real economy, in terms of volume, number of transactions, and cost, i.e. money flow for shares, we obtained the fundamental laws of stock mechanics.
Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogrou…
Unified geometric principles unify neural network architectures.
problem High-dimensional learning tasks with underlying low-dimensionality and structure.
method Unified geometric principles applied to neural network architectures.
result Unified mathematical framework for neural network architectures.
We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an orientation with respect to the corresponding normed algebra A. For example, special Riema…
Study shows EU countries have worsening debts and deficits.
problem Worsening public debts and deficits in EU countries.
method Statistical analysis of public debts and deficits between EU and non-EU countries.
result EU countries have worse public debts and deficits than non-EU countries, especially after Euro introduction.
This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small Data and Big Data, especially mixed data (discrete, continuous).
Unified field theory from higher-order Riemannian geometry.
problem Field-theoretical unification of fundamental forces.
method Exploiting higher-order Riemannian geometry and Einstein-Hilbert action, deriving gauge theories and predicting physical constants.
result Theoretical predictions for Weinberg angle and Coulomb's constant match experimental values.
The paper glosses different forms of an introducing of higher order tangent-like functors, especially functors derived from higher order nonholonomic tangent functors. A special attention is devoted to higher order osculating bundles: their identification with higher order tangent bundles is demonstrated as the main re…
The paper improves on existing algorithms for minimizing different types of regret in online learning.
problem Minimizing external, internal, and swap regret in online learning with multiple experts.
method Develops a single algorithm using φ-regret minimization and Haar-wavelet-inspired matrix features to achieve optimal bounds in various scenarios.
result Achieves optimal bounds for external, internal, and swap regrets in different expert scenarios.
New method estimates covariance matrices without restrictive assumptions.
problem Estimating high-dimensional covariance matrices under restrictive assumptions.
method Distributionally robust covariance estimation problems with mild conditions.
result Robust estimators are efficient, consistent, and perform well.
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 framework simplifies DPO algorithms for LLM alignment.
problem Vast number of DPO variants complicates model alignment.
method Mutual information inspired unifying framework with flexible priors.
result Many DPO variants can be derived from the new framework.
Unified framework for spectral methods, kernel learning, and manifold unfolding.
problem Tackles the unification and optimization of spectral dimensionality reduction methods.
method Unified spectral methods as kernel PCA, kernel learning by SDP, and detailed explanation of MVU variants.
result Unified understanding and optimization of manifold learning techniques.
Unified algorithms for structured sparsity problems with optimal convergence rates.
problem Solving minimization problems with structured sparsity assumptions.
method Unified continuum of preconditioned forward-backward operator splitting algorithms and accelerated algorithms.
result The continuum of algorithms attains the theoretically optimal rate of convergence.
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.
Associated to oriented surfaces immersed in R^3 here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k_1, k_2 of the immersion, is positive. The leaves of the foliations are the lines of M- m…
Principled Fine-tuning of LLMs from User-Edits: A Medley of Preference, Supervision, and Rewardcs.LG
Paper fine-tunes LLMs using user edits, unifying preference, supervision, and reward feedback.
problem Adapting LLMs to user preferences and feedback types.
method Derives bounds for learning algorithms from user edits, proposes an ensembling procedure.
result Ensembling procedure outperforms individual feedback methods and robustly adapts to different user-edit distributions.
A novel class of integrable surfaces is recorded. This class of O surfaces is shown to include and generalize classical surfaces such as isothermic, constant mean curvature, minimal, `linear' Weingarten, Guichard and Petot surfaces and surfaces of constant Gaussian curvature. It is demonstrated that the construction of…
We use a new approach that we call unification to prove that standard weighted double bubbles in -dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight…
Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we present a unification for associative algebras, Jordan algebras and Lie algebras…
A Power Transformcs.LG
Novel power transform unifies various mathematical functions.
problem Normalizing and standardizing datasets.
method Presented a novel power transform.
result Unified various mathematical functions.
Paper connects two portfolio methods, HRP and Minimum Variance, revealing their underlying similarity.
problem Inability to universally adopt optimization-based portfolio construction methods.
method Unifies Hierarchical Risk Parity and Minimum Variance approaches.
result Schur complementary allocation reveals the connection between HRP and Minimum Variance.
We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants form a class of knot and link invariants that includes biquandle cocycle invariants and skein invariants such as the HOMFLY…
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Buehler and Christian Blanchet we extended his construction to a larger class of 3-manifolds. The unified invariants provide a stron…
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
problem Formal verification of complex financial mathematics.
method Lean 4 proof assistant, Mathlib, and BrownianMotion package.
result Formal verification yields certified unification of known results.
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space and anti-de Sitter 3-space is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula wh…
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
Paper proves Liouville theorems for harmonic functions under specific curvature bounds.
problem Analyzing harmonic functions on manifolds with lower bounds of -weighted Ricci curvature.
method Uses Moser's iteration procedure to prove Liouville theorems.
result Establishes Liouville theorems for harmonic functions with sublinear growth and under weaker bounds of -weighted Ricci curvature.
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and gene…
Paper constructs new extremal Kähler metrics on holomorphic submersions.
problem Finding unique constant scalar curvature Kähler metrics on holomorphic submersions.
method Introduces optimal symplectic connection equation to solve geometric partial differential equation.
result Shows existence of extremal metrics on total space of holomorphic submersions.
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
DL models can outperform regionalized models in hydrology by pooling diverse data.
problem Traditional wisdom in hydrology suggests regionalization improves model performance, but DL models can unify data for better performance.
method Used DL models on pooled data from different regions, showing improved performance compared to regionalized models.
result DL models can improve performance by pooling diverse data, highlighting the 'data synergy' effect.
In this paper, we give a framework for the study of the extremal length geometry of Teichmüller space after S. Kerckhoff, F. Gardiner and H. Masur. There is a natural compactification using extremal length geometry introduced by Gardiner and Masur. The compactification is realized in a certain projective space. We deve…
The Plug-in Approach for Average-Reward and Discounted MDPs: Optimal Sample Complexity Analysiscs.LG
Optimal sample complexity analysis for plug-in approach in average-reward MDPs.
problem Learning optimal policies in average-reward MDPs with a generative model.
method Plug-in approach that constructs a model estimate and computes an optimal policy.
result Optimal sample complexities for the plug-in approach without prior knowledge of problem parameters.
Unified cosmological and Einstein polytope theories.
problem Unified understanding of cosmological and Einstein polytope theories.
method Unified combinatorial perspective of cosmological and Einstein polytope theories.
result Unified construction of cosmological and Einstein polytope theories.