Paper surveys Yang-Baxter homology journey and introduces new insights.
problem Yang-Baxter homology and knot theory.
method Historical survey and novel insights.
result New insights into Yang-Baxter homology.
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48 results for “Loops'13”
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.
We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic -space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient. These generators have the most natural fo…
Minimal grid diagrams found for 13-crossing prime knots.
problem Finding the simplest grid diagrams for prime knots with 13 crossings.
method Converted prime alternating knots to grid diagrams, focusing on minimal configurations.
result 4878 prime alternating knots with 13 crossings have been represented by grid diagrams with 15 vertical segments.
The paper classifies certain 13-dimensional manifolds up to various equivalences.
problem Classifying certain 13-dimensional manifolds up to diffeomorphism, homeomorphism, and homotopy equivalence.
method Analyzing cohomology rings and proving existence of metrics of non-negative sectional curvature.
result Certain 13-dimensional manifolds are classified up to various equivalences.
Minimal grid diagrams found for 13-crossing prime knots with 13 arc index.
problem Finding minimal grid diagrams for prime knots with specific crossing and arc indices.
method Used Knotscape to generate spanning trees and obtain minimal arc presentations in grid diagrams.
result 9,988 prime knots with 13 crossings and 13 arc index were identified.
DQN outperforms static policies in a dynamic fee environment for automated market makers.
problem How automated market makers (AMMs) perform under dynamic fees is unknown.
method Constructed a closed-loop simulator with dynamic fees, noise flow, and arbitrage.
result A small DQN policy outperforms static policies in a dynamic fee environment.
New insights into a complex hyperbolic braid group quotient.
problem Understanding a complex hyperbolic braid group quotient.
method Analyzing the moduli space of 12-tuples in CP1 and identifying loops.
result Identifying loops in the 9-ball quotient corresponding to standard braid generators.
We show that some embedded standard -spheres in Shimada's exotic -spheres have quotient spaces, s, that are fake real -dimensional projective spaces, i.e., they are homotopy equivalent, but not diffeomorphic to the standard . As observed by F. Wilhelm and th…
This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. ([7] = arXiv:1809.00593, [13] = arXiv:15…
A new framework reduces inconsistencies in chaotic surrogate modeling.
problem Consistency issues between probabilistic objectives and dynamical system dynamics.
method KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter.
result KAFFEE mitigates the dynamic-probabilistic consistency gap, improving reconstruction and predictive scores.
In this article we show that if a knot diagram admits a non-trivial coloring modulo 13 then there is an equivalent diagram which can be colored with 5 colors. Leaning on known results, this implies that the minimum number of colors modulo 13 is 5.
An infinite family of pairwise nonhomeomorphic 13-dimensional positively curved manifolds is constructed
Totally geodesically embeddings of infinitely many closed 7-manifolds into 13-dimensional positively curved closed Riemannian manifolds are constructed. The problems of computing pinching constants and existence of other totally geodesical embeddings are discussed.
Firstly, we wish to motivate that Conley pairs, realized via Salamon's definition [17], are rather useful building blocks in geometry: Initially we met Conley pairs in an attempt to construct Morse filtrations of free loop spaces [21]. From this fell off quite naturally, firstly, an alternative proof [20] of the cell a…
Classifies certain high-dimensional manifolds with specific cohomology properties.
problem Classifying smooth manifolds with a specific cohomology structure.
method Analyzes cohomology rings and uses topological equivalences.
result Classifies manifolds up to diffeomorphism, homeomorphism, and homotopy equivalence.
We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following movements at time scale…
Minimal grid diagrams for 15,735 knots with 14 crossings and arc index 14.
problem Representing prime knots with 14 crossings and specific arc indices using grid diagrams.
method Enumerated all prime knots with 14 crossings, categorized by arc index, and found minimal grid diagrams for those with arc index 14.
result 8,027 knots with arc index 13 and 15,735 knots with arc index 14 were represented by minimal grid diagrams.
This paper classifies 13D manifolds based on Bazaikin spaces.
problem Classifying 13-dimensional manifolds based on Bazaikin spaces.
method Topological classification modelled on Aloff-Wallach spaces and Eschenburg spaces.
result Complete topological classification for 13D manifolds based on Bazaikin spaces.
Projective loops generate rational loop groups without needing nilpotent loops.
problem Generating rational loop groups with noncompact reality conditions.
method Used projective loops to prove rational loop groups can be generated.
result Projective loops alone are sufficient to generate rational loop groups.
Two elements generate all mappings of a nonorientable surface.
problem Generating the mapping class group of a nonorientable surface.
method Proving two elements generate the mapping class group for .
result The mapping class group of a nonorientable surface of genus can be generated by exactly two elements.
Study loop ensembles on graphs, linking group theory and topology.
problem Understanding loop homotopy classes and homologies on graphs.
method Determined distributions of loop homotopy classes and homologies using the lower central series of the fundamental group.
result Distributions of loop homotopy classes and homologies defined by the lower central series of the fundamental group.
Study smooth loops and loop bundles, relating to -structures.
problem Properties of smooth loops and their applications.
method Analyze smooth loops, introduce loop bundles, define torsion and curvature.
result Showed how loop bundles relate to -structures.
The evolving of Data Science and the Saudi Arabia case. How much have we changed in 13 years?stat.AP
This study analyzes data science vocabulary changes over 13 years.
problem Understanding evolution of data science terms over time.
method Exploratory Data Analysis, Latent Semantic Analysis, Latent Dirichlet Analysis, N-grams Analysis.
result Identified new vocabulary and its incorporation into scientific literature.
GPA improves LLM training speed by 8.71% for Llama-160M models.
problem Training Large Language Models (LLMs) with high memory overhead and slow convergence.
method Generalized Primal Averaging (GPA) extends Nesterov's method to eliminate memory-intensive two-loop structure.
result GPA achieves up to 10.13% speedup over AdamW in training Llama-1B model.
Skew loops in flat torimath.DG
We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop in the unit sphere as tangent ind…
The paper proves T-duality and Hori formulae for winding loop spaces.
problem Realizing T-duality and Hori formulae for loop spaces.
method Proving T-duality and Hori formulae for winding q-loop spaces.
result T-duality and Hori formulae for winding q-loop spaces are proven.
Paper establishes loop space T-duality formulae and refines earlier work.
problem Establishing T-duality on loop spaces with background flux.
method Developed loop Hori map and twisted Bismut-Chern character.
result Loop Hori map induces quasi-isomorphism on loop spaces.
The 2-loop polynomial is a polynomial presenting the 2-loop part of the Kontsevich invariant of knots. We show a cabling formula for the 2-loop polynomial of knots. In particular, we calculate the 2-loop polynomial for torus knots.
The study constructs metrics with positive 2nd Ricci curvature on various manifolds.
problem Constructing metrics with positive 2nd Ricci curvature on closed manifolds.
method Generalization of the concept of fatness to ensure the existence of metrics with positive 2nd Ricci curvature on certain homogeneous bundles.
result Infinitely many examples of manifolds with positive 2nd Ricci curvature, including non-simply connected spaces.
Kähler manifold loop space inherits Kähler structure and is complete.
problem Characterizing the geometric properties of loop spaces of Kähler manifolds.
method Proving the Kähler structure and completeness of the loop space.
result The loop space of a Kähler manifold is complete and inherits a Kähler structure.
New structure found in loops on quasi-surfaces.
problem Understanding operations on loops in quasi-surfaces.
method Defined a quasi-Lie bialgebra structure.
result Natural operations on loops form a quasi-Lie bialgebra.
Discovery of a 13-Sharpe OOS Factor: Drift Regimes Unlock Hidden Cross-Sectional Predictabilityq-fin.TR
High-performing equity factor with Sharpe ratio above 13 out-of-sample.
problem Hidden cross-sectional predictability in stock returns.
method Regime-conditional signal activation combining value and short-term reversal signals.
result Annualized returns of 158.6% with 12.0% volatility, strong performance out-of-sample.
Using the relations between the theory of differentiable Bol loops and the theory of affine symmetric spaces we classify all connected differentiable Bol loops having an at most -dimensional semi-simple Lie group as the group topologically generated by their left translations. We show that all these Bol loops are is…
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Introduces string structures linking to loop spaces.
problem Understanding geometric string structures.
method Explains connections to loop spaces.
result String structures linked to loop spaces.
Study shows looping a 6-manifold over a 4-manifold results in a product of loops on spheres.
problem Understanding the homotopy properties of 6-manifolds over 4-manifolds.
method Analyzes the homotopy equivalence and rational homotopy of the total space of a sphere bundle over a 4-manifold.
result Looping a 6-manifold over a 4-manifold is homotopy equivalent to a product of loops on spheres.
Integral invariants for framed 3-manifolds associated to trivalent graphs possibly with self-loopsmath.GT
New theory defines invariants for framed 3-manifolds using trivalent graphs with self-loops.
problem Defining invariants for framed 3-manifolds with semi-simple Lie groups.
method Constructing graph complexes and cocycles, including self-loops, to define invariants.
result Higher-loop invariants can be defined by graph cocycles with or without self-loops.
Method calculates loop intersections on surfaces.
problem Computing intersections of loops on surfaces.
method Nielsen fixed point theory and Gröbner-Shirshov basis.
result Simple method to compute intersection numbers.
Geodesic loops on tetrahedra are studied in spherical and hyperbolic spaces.
problem Characterize geodesic loops on tetrahedra in different types of spaces.
method Analytical proofs for spherical and hyperbolic spaces.
result Existence and properties of geodesic loops on tetrahedra in various spaces.
New definition of twisted 1-loop invariant using Ptolemy coordinates.
problem Defining and proving properties of twisted 1-loop invariants.
method Alternative definition via Jacobian of Ptolemy coordinates.
result Twisted 1-loop invariant equals adjoint twisted Alexander polynomial for hyperbolic once-punctured torus bundles.
Training-free looped transformers improve model performance without additional training.
problem Improving model performance without additional training or fine-tuning.
method A lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning.
result Our method improves model performance across various model families.
Study path spaces and their homology, extending loop products and coproducts.
problem Understanding the homology of path spaces in closed manifolds.
method Morse-Bott theory and homology operations.
result Complete computation of extended loop product and coproduct on spheres.
Study the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds.
problem Global topology of loops of contactomorphisms and Legendrians in non-orderable manifolds.
method Filtering loops by positivity and analyzing subspaces of the filtration.
result Homotopy groups of the space of loops are subgroups of the positive loops subspace.
This paper reformulates the -adic Littlewood Conjecture using infinite loops.
problem The -adic Littlewood Conjecture in number theory.
method Introducing infinite loops mod and linking them to the conjecture.
result A real number is a counterexample to the -adic Littlewood Conjecture if and only if is an infinite loop mod for all .
This contribution to the CPT'13 meeting briefly introduces Lorentz and CPT violation and outlines two recent developments in the field.
Complex surfaces show non-simply connected diffeomorphism groups with non-homotopic loops.
problem Complex surfaces with non-simply connected diffeomorphism groups and non-homotopic loops.
method Exhibited examples of complex surfaces.
result Diffeomorphism groups of complex surfaces are not simply-connected and contain non-homotopic loops.
New basis and Schur-Weyl duality for loop Hecke algebra defined.
problem Define a new basis for the loop Hecke algebra.
method Use higher linear rewriting theory and combinatorics of Dyck paths.
result Yields a conjecture of Damiani-Martin-Rowell and provides a representation theoretic interpretation.