A study ranks critical Lean Six Sigma tools for implementation in Portuguese companies.
problem Identifying the most important tools for successful Lean Six Sigma implementation in Portugal.
method An online survey with Portuguese consultants evaluated 37 tools based on frequency of use, difficulty, importance, and impact. A ranking was developed using a procedure to assess consultants' know-how.
result Honshin Kanri, VOC, VSM were identified as the most important tools for Lean Six Sigma implementation.
iPromoter-BnCNN identifies and classifies six types of sigma promoters.
problem Accurate classification of sigma promoters remains challenging.
method Convolutional Neural Network (CNN) combining local features.
result Supremacy on 5-fold cross-validation and independent test datasets.
Lean Copilot uses LLMs to assist theorem proving in Lean, improving efficiency and automation.
problem Challenges in using existing neural theorem provers to prove novel theorems autonomously.
method Introduces Lean Copilot, a framework for integrating LLMs into Lean's theorem proving process.
result Lean Copilot automates 74.2% of proof steps on average, significantly improving over existing methods.
Report on formalizing differential geometry in Lean.
problem Formalizing differential geometry in a proof assistant.
method Lean's type theory approach to formalization.
result Surprising differences between formal and informal proofs.
Formalizes synthetic differential geometry in Lean.
problem Formalizing synthetic differential geometry in a proof assistant.
method Formalization of synthetic differential geometry with Lean and mathlib.
result Proves a Taylor theorem for functions of several variables.
Lean 4 formalizes Stokes' theorem for smooth singular cubes.
problem Formalizing Stokes' theorem for singular cubes in arbitrary dimensions.
method Using true differential-form pullback via Frechet derivative, bridging to mathlib4's extDeriv.
result d^2=0 for singular cubical chains, chain-level Stokes extended.
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.
Scores political leanings in Web3 betting markets.
problem Understanding political motivations in decentralized prediction markets.
method Constructing PBLS from Polymarket data, analyzing 15k addresses, 4k events, 8k markets.
result Validated PBLS through internal and external comparisons, revealing political and profit motives.
LeanML reduces machine learning project waste by estimating best performance without training models.
problem Avoidable wastes in machine learning projects.
method Lean design pattern based on mutual information and performance metrics.
result Estimating best performance without training models is faster and cheaper.
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbif…
This paper formalizes Q-learning and linear TD convergence using Lean 4.
problem Formalizing convergence properties of Q-learning and linear TD learning. method Formal verification using Lean 4 theorem prover and Mathlib library.
result Formalized almost sure convergence of Q-learning and linear TD learning. Formalizes integral curves on Banach manifolds in Lean.
problem Existence and uniqueness of integral curves on Banach manifolds.
method Formalized differential equations on Banach spaces, then generalized to Banach manifolds.
result Established theorems for integral curves on Banach manifolds.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
problem Formal verification of complex financial mathematics.
method Lean 4 proof assistant, Mathlib, BrownianMotion package, formal verification of over 200 theorems.
result Formal verification yields certified unification of known financial results.
We show that for any given n, there exists a sequence of words a_k in the generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the identity element of B_n, such that the number of braid relations of the form sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass from a_k to the…
Transformed geometry into algebra to prove Pick's theorem efficiently.
problem Translating geometric Pick's theorem into formal algebraic proof.
method Formalized geometric Pick's theorem into algebraic proof using Lean.
result Efficient formal proof of Pick's theorem.
Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the multiplicative homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma…
Sigma-Pi-Sigma neural networks (SPSNNs) as a kind of high-order neural networks can provide more powerful mapping capability than the traditional feedforward neural networks (Sigma-Sigma neural networks). In the existing literature, in order to reduce the number of the Pi nodes in the Pi layer, a special multinomial P_…
Generalizes Hamiltonian structures to Dirac structures for new mechanics models.
problem Extending Hamiltonian structures to non-symplectic manifolds.
method Introduces Hamiltonian Lie algebroids and momentum sections over Dirac structures.
result Constructs new sigma models based on these structures.
Compressed Monte Carlo improves efficiency in Bayesian inference.
problem Efficiently approximating posterior distributions in Bayesian models.
method Introduces Compressed Monte Carlo (C-MC) to compress statistical information.
result C-MC schemes outperform traditional methods in particle filtering and adaptive IS algorithms.
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, …
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.
problem Formalizing and proving the von Neumann-Morgenstern utility theorem.
method Implement classical axioms in Lean 4, formalizing preference relations over lotteries.
result Machine-verified proofs of existence and uniqueness of utility representations.
The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory a…
In this paper, we characterize the sigma-adequacy of a link diagram in two ways: in terms of a certain edge subset of its Tait graph and in terms of a certain product of Tutte polynomials. Furthermore, we show that the symmetrized Tutte polynomial of the Tait graph of a link diagram can be written as a sum of these pro…
SIGMA issues a special birthday tribute to Fuchs.
problem N/A
method N/A
result N/A
Summarizes geometric connections between sigma models and Gross-Neveu models.
problem Understanding geometric connections between sigma models and Gross-Neveu models.
method Geometric facts and connections to nilpotent orbits, Springer resolutions, and quiver varieties.
result Sheds light on the general setup of the correspondence.
Formalizes the Fundamental Theorem of Asset Pricing in Lean 4.
problem Formalizing the Fundamental Theorem of Asset Pricing in a proof assistant.
method Formalization in Lean 4 over Mathlib, covering three market settings.
result Constructs the equivalent martingale measure explicitly and proves its properties.
Grassmannian sigma models extend Gross-Neveu model formulations.
problem Understanding sigma models on Grassmannian targets.
method Chiral Gross-Neveu model formulations for orthogonal and symplectic Grassmannians.
result One-loop β-functions proportional to dual Coxeter numbers. In this paper, given a knot K, for any integer m we construct a new surface Sigma_K(m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the `rim surgery' which was introduced by Fintushel and Stern, by doing additional twist spi…
New sigma models compute graviton scattering amplitudes from quaternionic geometry.
problem Computing graviton scattering amplitudes from quaternionic geometry.
method Introducing new twistor sigma models that encode finite non-linear perturbations of flat structures.
result Provides a first-principles derivation of Hodges' formula for MHV graviton amplitudes.
One has believed that low energy effective theories of the Higgs branch of gauged linear sigma models correspond to supersymmetric nonlinear sigma models, which have been already investigated by many works. In this paper we discuss a explicit derivation of supersymmetric nonlinear sigma models from gauged linear sigma …
BiHermitian geometry, discovered long ago by Gates, Hull and Roceck, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we work out the type A and B topological sigma models for a general biHermtian target spac…
We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional surfaces immersed in the su(N) algebra. In the special case of the CP^1 sigma model we …
For the existence of a branched covering Sigma~ --> Sigma between closed surfaces there are easy necessary conditions in terms of chi(Sigma~), chi(Sigma), orientability, the total degree, and the local degrees at the branching points. A classical problem dating back to Hurwitz asks whether these conditions are also suf…
Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.
problem Classical aspects of N=(2,2) supersymmetric sigma models with Hermitian symmetric target spaces. method Reformulation using Gross-Neveu formalism, proposing two types of equivalent Lagrangians.
result Proposed two types of equivalent Lagrangians for maximal isotropic Grassmannians, making either supersymmetry or geometry manifest.
Solves sigma model on U(3)/U(1)^3, describing geodesics and spectrum.
problem Classical and quantum problems for 1D sigma model with specific target space.
method Mapping to Gaudin model, solving polynomial equations.
result Explicit description of geodesics and spectrum found.
We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Sigma_g, and let sigma…
Generalizes sigma model with Lie algebroid structure and geometric conditions.
problem Consistency of constraints and gauge symmetry in topological sigma models.
method Analysis of geometric conditions and constraints in Hamiltonian and Lagrangian formalisms.
result Identifies universal compatibility condition between Lie algebroid and multi-symplectic structure.
LeanDojo removes barriers to theorem proving with open-source tools and data.
problem Difficulty in reproducing and building on existing theorem proving methods.
method Introduces LeanDojo, an open-source Lean playground with toolkits, data, models, and benchmarks.
result ReProver, an LLM-based prover augmented with retrieval, outperforms non-retrieval baselines and GPT-4.
Study of quantum aspects of generalized Gross-Neveu models, focusing on sigma models.
problem Quantum aspects and anomalies in generalized Gross-Neveu models.
method Admissible gauge Aμ=0, study of chiral anomalies, integration over moduli spaces of connections on a Riemann surface. result Integration over moduli spaces of connections on a Riemann surface.
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
problem Formalizing Herbert Simon's bounded rationality concept in economic decision-making.
method Developed FFSD framework using Lean 4 theorem prover, proving equivalence to expected utility theory.
result Equivalence theorem linking FFSD to expected utility maximization for approximate indicator functions.
We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic manifold by considering gauged sigma models on a highe…
BiKaehler geometry is characterized by a Riemannian metric g_{ab} and two covariantly constant generally non commuting complex structures K_+^a_b, K_-^a_b, with respect to which g_{ab} is Hermitian. It is a particular case of the biHermitian geometry of Gates, Hull and Roceck, the most general sigma model target space …
Introduces a new phase space for 2D supersymmetric sigma models.
problem Developing a new Hamiltonian formulation for 2D supersymmetric sigma models.
method Introduces a phase space with spinorial momenta and derives a covariant Hamiltonian formulation.
result Shows the existence of additional supersymmetries in the new formulation.
We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo Riemannian 3-s…
Let Sigma be a smooth complex curve, and let S be the product ruled surface Sigma \times CP^1. We prove a correspondence conjectured by Donaldson between finite energy U(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2 holomorphic bundles over S whose restrictions to the divisors at infinity are st…
Introduces a new spectral geometry framework with dissipative data.
problem Deforming spectral triples with dissipative Lindblad operators.
method Lindblad-deformed spectral geometry framework with heat-kernel asymptotics.
result First nontrivial dissipative effect appears at order gamma^4.