New measure proves Poncelet-type theorems.
problem Proving Poncelet-type theorems.
method Introducing a new invariant measure on the circle.
result Simple proof of Emch closing theorem.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
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48 results for “Zigzag theorem”
We construct an action of the free group on the homotopy category of projective modules over a finite dimensional zigzag algebra. The main theorem in the paper is that this action is faithful. We describe the relationship between homotopy classes of paths in the punctured disc and complexes of projective zigzag m…
The paper characterizes Conway-Coxeter friezes using rational links.
problem Characterizing Conway-Coxeter friezes of zigzag type.
method Characterization via rational links and application to Jones polynomial.
result Jones polynomial can be defined for Conway-Coxeter friezes of zigzag type.
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…
Lagrangian Zigzag Cobordismsmath.SG
Study Lagrangian zigzag cobordisms for Legendrian knots, comparing to smooth concordance.
problem Understanding Legendrian knots through Lagrangian cobordisms.
method Defined an equivalence relation on Legendrian knots using interpolating zigzag Lagrangian cobordisms, studied metric monoid, and compared to other concordance types.
result Proved structural results on torsion and satellite operators in the Lagrangian zigzag concordance classes.
Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.
problem Sampling from strongly log-concave distributions efficiently and with low computational complexity.
method Zigzag sampling algorithm with warm start assumption, focusing on gradient evaluations.
result Achieves ε error in chi-square divergence with computational cost of O(κ²d^(1/2)(log(1/ε))^(3/2)) gradient evaluations.
The study explores cohomological invariants and decomposes them into irreducible parts, focusing on zigzags.
problem Finding cohomological invariants and their decomposition into irreducible parts.
method Investigates various cohomological invariants on double complexes, focusing on the multiplicities of zigzags.
result The multiplicities of zigzags in double complexes are not sufficient to distinguish non-isomorphic double complexes.
Z-GCNETs uses topological data to improve time series forecasting.
problem Improving time series forecasting accuracy.
method Integrates topological data into graph convolutional networks (GCNs) using zigzag persistence.
result Z-GCNETs outperforms 13 state-of-the-art methods in traffic forecasting and Ethereum price prediction.
Study cohomology of Bigolin complex on complex manifolds.
problem Characterize cohomology of Bigolin complex on compact complex manifolds.
method Analyze the decomposition of the double complex into squares and zigzags, focusing on the zigzags contributing to cohomology.
result In complex dimension 3, multiplicities of zigzags are characterized by Betti, Hodge, Aeppli numbers plus Bigolin numbers.
New algebra connects braid group actions to disc curves.
problem Understanding braid group actions on disc curves.
method Constructed a type B zigzag algebra and showed its categorical action on projective modules.
result Type B braid group action on homotopy category of projective modules.
Every triangulation of a surface can be shredded into a z-knotted map.
problem Understanding the structure of triangulations of surfaces.
method Introducing and analyzing z-knotted maps within triangulations.
result Every triangulation of a surface admits a z-knotted shredding.
We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry groups of the spheres that showed up. In Section 4 we introduce a new Goldberg-…
In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on . In particular, given the local data for a gerbe with structure 2-group given by a crossed module of matrix-groups, there is an element in our curved zigzag Hochschil…
New categorical actions link topological and algebraic structures.
problem Understanding relationships between topological and algebraic structures.
method Categorical actions of type B braid group on homotopy categories.
result Proves Rouquier's conjecture on faithfulness of Type B 2-braid group.
Paper connects Conway-Coxeter friezes and rational tangles.
problem Understanding the relationship between Conway-Coxeter friezes and rational tangles.
method Using Kauffman bracket polynomials to compute and connect friezes and rational tangles.
result Provides a complete invariant for Conway-Coxeter friezes of zigzag-type.
TabPFN's internal geometry topology correlates with dataset reliability.
problem Understanding TabPFN's behavior on structurally difficult tabular geometries.
method Using zigzag persistent homology, studying TabPFN's internal representations on synthetic tabular tasks with known topology.
result Topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability.
The paper calculates critical configurations and Morse indices for polygons on circles or ellipses.
problem Finding critical configurations and their properties for polygons on circles or ellipses.
method Computing Morse indices and gradient vector fields for isolated critical points, relating to eigenvalue questions.
result Computed Morse indices and relationships to eigenvalue questions for polygons on circles or ellipses.
Complete classification of rod complements in 3-torus using topology.
problem Classifying rod complements in the 3-torus.
method Topological arguments.
result Complete classification of all rod complements in the 3-torus.
An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hed…
The paper explores the structure of double complexes and their applications.
problem Understanding the structure and properties of double complexes.
method Investigates the folklore statement about double complexes and their decomposition into squares and zigzags, and computes the Grothendieck ring of double complexes.
result Obtained a Poincaré duality for higher pages of the Frölicher spectral sequence and constructed a functorial three-space decomposition of the middle cohomology.
Traditional models of macroeconomic dynamics are fundamentally incorrect. The reason lies in a misunderstanding of peculiarities of the analysis of infinitesimal quantities. However, even those types of solutions that are envisaged by the above-mentioned models are nonrepresentative in the sense of the reflection of re…
Develops a first-order interior-point method for solving constrained variational inequalities.
problem Solving constrained variational inequalities with nontrivial constraints.
method ADMM-based interior-point method for constrained VIs (ACVI).
result First-order interior-point method with global convergence guarantees for general cVI problems.
New algorithms reduce online learning regret using empirical Rademacher complexity.
problem Adaptive online learning with bounded regret against any sequence.
method Developed a novel family of algorithms based on empirical Rademacher complexity and decoupling inequalities.
result Achieved adaptive regret bounds for various hypothesis classes.
AI generates theorems and proofs for training theorem provers.
problem Limited human-written theorems and proofs for supervised learning.
method Proposes a neural generator to automatically synthesize theorems and proofs.
result Synthetic data improves automated theorem proving in Metamath.
Global inverse function theorem proved easily using Riemannian geometry.
problem Global inverse function theorem in Riemannian geometry.
method Hopf--Rinow theorem in Riemannian geometry.
result Hadamard's global inverse function theorem is proven easily.
A new comparison theorem for geometric spaces.
problem Geometric space comparison theorems.
method Relative form of Toponogov comparison theorem.
result New geometric space comparison theorem established.
The paper proves a new theorem in Riemannian geometry and offers a new proof for Toponogov's theorem in Alexandrov geometry.
problem Proving new theorems in Riemannian and Alexandrov geometries.
method Inspired by the proof of the Schur-Toponogov theorem, a new proof of Toponogov's theorem is provided.
result A new theorem in Riemannian geometry and a new proof of Toponogov's theorem in Alexandrov geometry.
Revises a theorem by Thurston, finding a counter-example and a weaker version.
problem The bounded image theorem in Haken manifolds.
method Providing a counter-example and a weaker version of the second statement of Thurston's theorem.
result A counter-example and a weaker version of the second statement of Thurston's theorem are presented.
The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.
problem Establishing theorems for subharmonic and holomorphic functions on specific geometric structures.
method Using subharmonic and holomorphic functions on Riemannian manifolds and gradient shrinking Ricci solitons.
result Proves Liouville type theorems as applications of the established theorems.
Paper develops formulas and theorems in Hermitian geometry.
problem None explicitly stated in the abstract.
method Develops second variational formulas and index forms in Hermitian geometry.
result Establishes results analogous to classical theorems in Riemannian geometry.
Proves Markov theorem for trivalent braids using L-move approach.
problem Proving Markov theorem for trivalent braids.
method Follows L-move approach to prove Markov theorem.
result Proves one-move Markov-type theorem and algebraic Markov-type theorem for trivalent braids.
Proofs for Moon's theorem and its generalization.
problem Proving Moon's theorem and its generalization.
method Proofs based on key lemmas.
result Generalization of the four-vertex theorem.
New theorem for doodles on sphere, similar to Markov's.
problem Understanding doodles on a sphere.
method Description of twins with equivalent closures.
result Analogous to Markov's theorem for doodles.
Investigates proving geometric theorems over complex and real numbers using tilings.
problem Proving incidence theorems over C and R using the master theorem.
method Formalizes tiling proofs and introduces a hierarchy of theorems based on topological spaces.
result Identifies which theorems can or cannot be proved over C and R.
Analyzes Saito vanishing theorem using methods.
problem Proving the Saito vanishing theorem.
method Uses -methods to prove the theorem.
result Analytic proof of the Saito vanishing theorem.
Extends calculus theorem to higher dimensions.
problem Calculus theorem limitations in higher dimensions.
method Type Stokes' theorem for type -chains.
result Extends fundamental theorem of calculus.
Extends symplectic reduction and theorem to Lie algebroids.
problem Symplectic reduction and theorem for Lie algebroids.
method Extends Marsden-Weinstein reduction and Darboux-Moser-Weinstein theorems.
result Obtained coisotropic embedding theorem for symplectic Lie algebroids.
Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
problem Complex Brunn-Minkowski theory and extension theorems.
method Hilbert bundle approach to complex Brunn-Minkowski theory.
result Generalizes Guan's sharp strong openness theorem and sharp Ohsawa-Takegoshi extension theorem.
Proves Thurston's bounded image theorem for Haken manifolds.
problem Proving Thurston's bounded image theorem for Haken manifolds.
method Using recent developments in Kleinian group theory.
result A proof of Thurston's original bounded image theorem.
Method upgrades limit theorems to mixing limit theorems for dynamical systems.
problem Improving limit theorems for dynamical systems.
method General method for upgrading limit theorems to mixing limit theorems.
result Mixing limit theorems for specific subbundles of the Kontsevich-Zorich cocycle.
Formulates Index III lemma and Rauch III theorem with applications.
problem Develops new mathematical theorems based on existing ones.
method Formulation of Index III lemma and Rauch III theorem based on Index I, II lemmas and Rauch I, II theorems.
result Presented Rauch's type theorem and volume comparison result as applications.
In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
INT benchmark tests theorem proving agents' ability to generalize to unseen theorems.
problem Evaluating theorem proving agents' ability to generalize to unseen theorems.
method INT benchmark based on a theorem generation and proof procedure with adjustable knobs for measuring 6 types of generalization.
result MCTS can help agents prove new theorems.
Proves two theorems on odd-dimensional manifolds with boundary.
problem Proving theorems on manifolds with boundaries.
method Proof of theorems using mathematical techniques.
result Proved the general Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki type theorems.
Sharp convergence theorem for sphere submanifolds proved.
problem Sphere submanifolds in spheres.
method Proved a sharp convergence theorem.
result New differentiable sphere theorem for submanifolds in spheres.
Abstracts a theorem for non-smooth maps in infinite dimensions.
problem Generalizing inverse mapping theorem for non-smooth maps.
method Introduces property A and applies it to non-smooth maps.
result Generalized inverse mapping theorems for non-smooth maps.
A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.