Parabolic mapping class acts on curve graphs of infinite type surfaces.
problem Understanding parabolic isometries on curve graphs of infinite type surfaces.
method Fine curve graph tools to prove existence of parabolic isometries.
result Existence of parabolic isometries on graphs of curves of infinite type surfaces.
Study the Gromov boundary of fine curve graph for surface homeomorphisms.
problem Understanding the boundary of fine curve graph for surface homeomorphisms.
method Examined the Gromov boundary and local topology near specific foliations and laminations.
result Found elements with positive stable commutator length and proved a Tits alternative.
New findings on hyperbolicity of fine curve graphs and their subgraphs.
problem Investigating hyperbolicity of fine curve graphs and their subgraphs.
method Analyzing large subgraphs of fine curve graphs and computing distances in specific cases.
result Large subgraphs of fine curve graphs contain flats of every finite dimension, indicating they are not hyperbolic.
Automorphisms of fine 1-curve graph linked to surface homeomorphisms.
problem Understanding automorphisms of fine 1-curve graphs.
method Isomorphic mapping to surface homeomorphisms.
result Automorphism group is isomorphic to homeomorphism group of a surface.
Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.
problem Understanding automorphisms of fine curve graphs on surfaces.
method Analyzing vertices and edges of fine curve graphs to match with surface homeomorphisms.
result Automorphism group of fine curve graphs is naturally isomorphic to the homeomorphism group of boundaryless planar surfaces with at least 7 punctures.
The fine curve graph is hyperbolic and contains all countable graphs as induced subgraphs.
problem Characterizing the structure and properties of fine curve graphs.
method Analyzing the hyperbolicity and induced subgraph properties of fine curve graphs and their direct limits.
result The finitary curve graph has diameter 2, contains every countable graph as an induced subgraph, and has the homeomorphism group of the surface as its automorphism group.
Automorphisms of fine curve graph match surface homeomorphisms.
problem Understanding automorphisms of curve graphs for surfaces.
method Building on previous work, proving isomorphism to surface homeomorphisms.
result The group of automorphisms of the fine curve graph is isomorphic to the extended mapping class group of the surface.
Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.
problem Identifying automorphisms of nonorientable surface curve graphs.
method Using Bowden, Hensel, and Webb's fine curve graph and Long, Margalit, Pham, Verberne, and Yao's proof as a foundation.
result Automorphism group of nonorientable surface curve graph is isomorphic to the surface's homeomorphism group.
Study automorphisms of smooth curve graphs on surfaces.
problem Understanding automorphisms of fine curve graphs.
method Examined automorphisms of continuously differentiable curves on surfaces.
result Automorphisms on surfaces of genus ≥ 2 are induced by homeomorphisms.
The paper studies the connectedness of a graph's boundary for surfaces.
problem Understanding the topology of the Gromov boundary of fine curve graphs for surfaces.
method Proved a bounded geodesic image theorem, used to show linear connectivity of the Gromov boundary.
result The Gromov boundary of fine curve graphs for surfaces is linearly connected.
Stable cylinders found in hyperbolic groups and curve graphs.
problem Torsionfree hyperbolic groups and curve graphs of surfaces have globally stable cylinders.
method Generalised Sageev's construction to improve fine properties of hyperbolic spaces.
result Proved curve graphs of surfaces admit equivariant quasi-isometric embeddings in finite products of quasitrees.
The study proves conditions for hyperbolic isometries on fine curve graphs of higher genus surfaces.
problem Conditions for hyperbolic isometries on fine curve graphs of higher genus surfaces.
method Proves equivalence of conditions involving isotopic maps, pseudo-Anosov maps, and ergodic rotation sets.
result Ergodic homological rotation sets have nonempty interior for certain isotopic maps.
Classification of torus homeomorphisms on fine curve graph completed.
problem Classifying actions of torus homeomorphisms on fine curve graph.
method Proof involving slow rotation sets for torus homeomorphisms.
result Actions of torus homeomorphisms on fine curve graph classified.
Abstract: Proves generic torus diffeomorphisms act parabolically and non-properly on fine curve graph and have generalized rotation sets.
problem Generic torus diffeomorphisms on fine curve graph.
method Proves generic torus diffeomorphisms act parabolically and non-properly on fine curve graph.
result Generic torus diffeomorphisms have generalized rotation sets of any point-symmetric compact convex homothety type.
Automorphisms of fine graphs for surfaces and tori are studied.
problem Understanding automorphisms of fine graphs for surfaces and tori.
method Extending previous results to tori and discussing smooth versions.
result Automorphism groups of fine graphs for surfaces and tori are naturally isomorphic to homeomorphism groups.
Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.
problem Understanding dynamics of homeomorphisms on fine curve graphs of surfaces.
method Analyzing the action of homeomorphisms on the fine curve graph and relating to classical curve graphs.
result Homeomorphisms induce parabolic isometries, and all positive reals are realized as asymptotic translation lengths.
Study on stable translation lengths of surface homeomorphisms and their approximations.
problem Understanding stable translation lengths of homeomorphisms and their finite approximations.
method Comparing stable translation lengths of homeomorphisms and their finite approximations on curve graphs.
result Stable translation length of homeomorphisms with dense periodic points equals the supremum of their approximations.
Homotopy types of curve and arc complexes are studied.
problem Understanding the homotopy types of curve and arc complexes.
method Proving homotopy equivalence and contractibility of complexes.
result Fine curve complex is homotopy equivalent to curve complex, fine arc complex is contractible.
Study shows surfaces without certain curves have infinite orbit graph.
problem Characterizing surfaces with specific curve properties.
method Utilized tools from mapping class group geometry.
result Infinite-invariance index 1 surfaces lack good curve graphs.
We investigate the geometry of the graphs of nonseparating curves for surfaces of finite positive genus with potentially infinitely many punctures. This graph has infinite diameter and is known to be Gromov hyperbolic by work of the author. We study finite covers between such surfaces and show that lifts of nonseparati…
Researchers reconstruct algebraic maps onto curves based on prescribed Reeb graphs.
problem Reconstructing smooth real algebraic maps onto curves with specific Reeb graphs.
method Developed a method to reconstruct functions from general finite graphs, focusing on curves.
result Reconstructed functions from prescribed Reeb graphs, providing a new approach in real algebraic geometry.
Characterizes geometric actions on graphs with flexible stabilizers.
problem Understanding geometric actions on flexible stabilizers.
method Defining generalized fine actions and proving relative quasi-convexity criteria.
result Characterizes Bowditch boundary points in relatively geometric actions.
This paper restricts efficient geodesics to non-separating curves.
problem Finding efficient geodesics in the complex of curves.
method Analysis of the dot graph and surgeries.
result Efficient geodesics can be restricted to the non-separating curve complex.
Study measures complexity of surfaces using a new graph to prove group properties.
problem Understanding the complexity and structure of mapping class groups.
method Introduces a non-peripheral curve graph and uses it to analyze the structure of mapping class groups.
result Proves properties of the mapping class group based on the complexity measure.
The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.
problem Problems with previous descriptions of realizable Gauss diagrams.
method Experimental checking and formulation of new descriptions of realizable circle graphs.
result New descriptions of realizable circle graphs and an algorithm for checking realizability.
Paper fine-tunes LLaMA-3-8B for financial NER using instruction and LoRA.
problem LLMs struggle with financial NER, especially differentiating entities and amounts.
method Instruction fine-tuning combined with LoRA for parameter-efficient learning.
result Micro-F1 score of 0.894 on financial NER tasks, outperforming other models.
Study efficient geodesics in curve complex using dot graphs.
problem Characterize efficient geodesics in curve complexes.
method Introduced dot graphs to record intersection patterns and used them to prove existence and properties of efficient geodesics.
result The shape of dot graphs for efficient geodesics is contained within a spindle shape region, controlling curve coordinates.
Let C(Sg,p) denote the curve complex of the closed orientable surface of genus g with p punctures. Masur-Minksy and subsequently Bowditch showed that C(Sg,p) is δ-hyperbolic for some δ=δ(g,p). In this paper, we show that there exists some δ>0 independent of g,p such that the cu…
Daydream predicts DNN optimization efficacy efficiently.
problem Inefficiency and error in evaluating DNN optimizations.
method Models DNN execution with a dependency graph, predicts runtime based on simulation.
result Accurately predicts performance improvements from DNN optimizations.
Improved graph neural network bounds using graph diffusion matrix.
problem Empirical performance of graph neural networks on real-world graphs.
method Unified model of graph neural networks, focusing on feature diffusion matrix stability.
result Generalization bounds scale with largest singular value of feature diffusion matrix, smaller than prior bounds.
The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. We study these curves first in a general setting and then in an asymptotic one. In particular, we consider sufficiently small levels of a real bivariate polynomial in a small enough neighbou…
The paper conjectures and proves fixed points for certain group actions on nonpositively curved spaces.
problem Actions by automorphisms of finitely generated groups on nonpositively curved complexes without fixed points.
method Use of Helly graphs and geodesic clique paths to prove ellipticity results.
result Finitely generated torsion groups cannot act without fixed points on nonpositively curved spaces.
Fine-tunes GNNs by preserving generative patterns to improve transferability.
problem Vanilla fine-tuning fails due to structural divergence between pre-training and downstream graphs.
method G-Tuning, which reconstructs the generative patterns of the downstream graph using graphon bases.
result G-Tuning achieves an average improvement of 0.5% and 2.6% on in-domain and out-of-domain transfer learning experiments.
New framework learns labels at both bag and graph levels.
problem Learning multi-label classifiers from multi-graph bags.
method Designing scoring functions and rank-loss objective for graph and bag levels; developing sub-gradient descent algorithm.
result Superior performance over state-of-the-art algorithms.
Polynomial bound on tightening curves on surfaces without increasing crossings.
problem Proving a polynomial bound on the number of monotonic homotopy moves for curves on surfaces.
method Combining tools from hyperbolic geometry and graph drawing algorithms.
result First polynomial bound on the number of monotonic homotopy moves, improving from exponential.
We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago--Ivanov--Polterovich. …
In this work, we study the cellular decomposition of S induced by a filling pair of curves v and w, Decv,w(S)=S−(v∪w), and its connection to the distance function d(v,w) in the curve graph of a closed orientable surface S of genus g. Efficient geodesics were introduced by the first author in j…
Learning image representations to capture fine-grained semantics has been a challenging and important task enabling many applications such as image search and clustering. In this paper, we present Graph-Regularized Image Semantic Embedding (Graph-RISE), a large-scale neural graph learning framework that allows us to tr…
New model generates larger molecules more effectively.
problem Previous graph generation techniques struggle with larger molecules.
method Hierarchical graph encoder-decoder using structural motifs.
result Model significantly outperforms previous baselines on molecule generation tasks.
Here we develop some basic analytic tools to study compactness properties of J-curves (i.e. pseudo-holomorphic curves) when regarded as submanifolds. Incorporating techniques from the theory of minimal surfaces, we derive an inhomogeneous mean curvature equation for such curves, we establish an extrinsic monotonicity…
A new neural network model for molecular graphs that learns efficiently and accurately.
problem Learning on molecular graphs with cycles and complex structures.
method Hierarchical inter-message passing using raw graph and junction tree representations.
result The model outperforms classical GNNs in detecting cycles and is efficient to train.
Study on homeomorphisms preserving C1 curves on surfaces.
problem Characterizing homeomorphisms that preserve C1 curves. method Local conditions on induced map on projective tangent bundle.
result Characterization of Homeo1(S) for most closed surfaces. FinDKG uses LLMs to detect financial trends from news articles.
problem Detecting global financial trends from unstructured text data.
method Fine-tuned LLMs for generating DKGs, KGTransformer for analysis.
result KGTransformer outperforms existing thematic ETFs in financial thematic investing.
New method enhances model fine-tuning with minimal data.
problem Improving model performance on new tasks with limited data.
method Introducing α-LoRA, a reparameterization method for fine-tuning. result Enhanced generalization ability of fine-tuned models.
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
problem Challenges in estimating epistemic uncertainty in LoRA-based Bayesian inference.
method Introduces LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with free and anchored configurations.
result Empirically shows that connecting independent LoRA optima through continuous low-loss valleys improves mutual information of the predictive distribution.
We develop computationally efficient Riemannian manifolds for graph embeddings.
problem Challenging to maintain computational tractability in non-Euclidean graph embeddings.
method Explore computationally efficient matrix manifolds for graph embeddings.
result Consistent improvements over Euclidean geometry and outperforming hyperbolic and elliptical embeddings.
We study the boundary L_t of the Milnor fiber for the non-isolated singularities in C^3 with equation z^m - g(x,y) = 0 where g(x,y) is a non-reduced plane curve germ. We give a complete proof that L_t is a Waldhausen graph manifold and we provide the tools to construct its plumbing graph. As an example, we give the plu…
The study shows that certain curve graphs are hierarchically hyperbolic but not Gromov hyperbolic.
problem Characterizing the hyperbolicity of curve graphs and their boundaries.
method Using hierarchical hyperbolicity and framed curves, the study examines the properties of curve graphs and their boundaries.
result The curve graphs and their boundaries are hierarchically hyperbolic but not Gromov hyperbolic.