Typilus predicts types for Python programs using neural networks.
problem Type inference in dynamically typed languages is challenging.
method Graph neural network model that predicts types by probabilistically reasoning over program structure, names, and patterns.
result Typilus can predict types for 70% of all annotatable symbols and type checks 95% of the predicted types.
LambdaNet infers TypeScript types using graph neural networks.
problem Automatic inference of TypeScript type annotations.
method Graph Neural Network for type dependency graph analysis.
result LambdaNet outperforms existing methods by 14%.
Study shows partially-typed NER datasets can match fully-typed ones in model performance.
problem Leveraging multiple partially-typed NER datasets for training models without fully-typed annotations.
method Systematic analysis and controlled experiments comparing partially-typed and fully-typed datasets.
result Models trained with partially-typed annotations can achieve similar performance to those trained with fully-typed annotations.
New model predicts fine-grained types for high-multiplicity entities.
problem Fine-grained entity typing with high type multiplicity.
method Set-prediction approach to high-multiplicity fine-grained typing.
result Model outperforms baselines on Wikipedia-based corpus.
The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…
Paper introduces a new adversarial attack type that cheats classifiers with significant changes.
problem Cheating well-trained classifiers with small permutations.
method Supervised variation autoencoder and gradient-based updates to latent variables.
result The proposed attack significantly cheats classifiers with significant changes, reducing Type I error.
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …
Constructs odd Khovanov homotopy types for links, linking them to even types.
problem Understanding and constructing odd Khovanov homotopy types for links.
method Constructs stable homotopy types X^j_o(L) for links L, with cohomology matching odd Khovanov homology.
result Odd Khovanov homotopy types carry a Z/2 action whose fixed points are related to even Khovanov homotopy types.
Study shows infinite real homotopy types for complex nilmanifolds.
problem Understanding real homotopy types of complex nilmanifolds.
method Analyzing 2n-dimensional nilmanifolds with generalized complex structures. result Infinitely many real homotopy types exist for 2n-dimensional nilmanifolds. ptype infers data types robustly in real-world data.
problem Type inference fails with missing data and anomalies.
method Probabilistic robust type inference method.
result Outperforms existing methods.
Category theory generalizes finite type invariants using diagrams systems.
problem Generalizing finite type invariants using category theory.
method Relating generating sets for generalized finite type theories with diagrams systems.
result Demonstrates the correspondence between finite type theories and diagrams systems.
New spherical curve deformations solve a conjecture.
problem Solving the Östlund Conjecture for spherical curves.
method Introducing a new type of deformation (β) and proving equivalence under specific deformations.
result Equivalence of spherical curves under specific deformations.
Finite-type surfaces have a topological Hopf property.
problem Characterizing surfaces with a topological Hopf property.
method Using topological analogs of the Hopf property.
result Infinite-type surfaces do not have the Hopf property.
Study shows transfer of adversarial robustness between different perturbation types is limited.
problem Understanding adversarial robustness across various perturbation types.
method Evaluated 32 attacks of 5 different types on models trained on a subset of ImageNet.
result Adversarial robustness transfer between perturbation types is limited and depends on the specific type of perturbation.
Kähler-Ricci flow singularity type is independent of initial metric.
problem Independence of singularity type for Kähler-Ricci flows.
method Analyzing solutions to the Kähler-Ricci flow on numerically effective manifolds.
result The singularity type of solutions is independent of the initial metric.
The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.
problem Classifying knot projections based on weak homotopy equivalence.
method Defining weak (1, 2, 3) homotopy and using it to find an invariant.
result There are an infinite number of weak (1, 2, 3) homotopy equivalence classes of knot projections.
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type D structure by adding a "vertical" type D structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type D structure is that it is homotopy equivalent to a type $…
In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every δ(3)-ideal nul…
Extends techniques to show existence of all cusp types in convex projective manifolds.
problem Existence of all cusp types in convex projective manifolds.
method Extension of techniques by Ballas-Marquis.
result Existence of all cusp types in all dimensions except diagonalizable.
Study BF invariants using simple type concepts.
problem Understanding Bauer--Furuta invariants for 4-manifolds.
method Extend simple type concept to BF blowup and BF homogeneous types, prove gluing formulae and adjunction inequality.
result Determine Bauer--Furuta invariant of a specific 4-manifold and give constraints on gluing decompositions.
It is known that all left-invariant pseudo-Riemannian metrics on H3 are algebraic Ricci solitons. We consider generalizations of Riemannian H-type, namely pseudoH-type and pH-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transver…
Classifies special Lie algebras with semisimple types.
problem Classifying Lie algebras of semisimple type.
method Introduced conformal pseudo-subriemannian fundamental graded Lie algebras and provided their classification.
result Classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their prolongations.
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
problem Understanding relationships between triangulations of infinite type surfaces via flips.
method Associate triangulations to flip graphs and study sequences of simultaneous flips.
result Flip graphs for infinite type surfaces have uncountably many connected components.
Crowdsourced labeling recovers task types with minimal queries.
problem Labeling tasks accurately with minimal queries.
method Worker clustering, skill estimation, weighted majority voting.
result Achieves any targeted recovery accuracy with minimum queries.
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…
New extremal Poincaré type metrics found via blow-up theorem.
problem Finding new extremal Poincaré type metrics.
method Proved Arezzo-Pacard-Singer blow-up theorem for Poincaré type metrics and applied to new examples.
result Found new examples of extremal Poincaré type metrics with an additional obstruction.
Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.
problem Creating metrics with negative scalar curvature.
method Constructed two types of Eguchi-Hanson metrics.
result Found metrics with negative scalar curvature.
In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore,…
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
problem Tackles the B-type skein relation and introduces new coefficient polynomials.
method Introduces coefficient polynomials associated with the B-type skein relation and proves their invariance under Reidemeister moves.
result Shows that the generating series of these coefficient polynomials recovers the Kauffman polynomial.
Study of Lagrangian mean curvature flow with equivariant symmetry.
problem Understanding singularities in Lagrangian mean curvature flow.
method Structural theorems about blowups of finite-time singularities.
result Classification of singularities in equivariant case.
New representations for discrete surfaces derived from dual transforms.
problem Constructing discrete surfaces in differential geometry.
method Using Ω-dual transform and lightlike Gauss maps in Laguerre geometry. result All discrete linear Weingarten surfaces arise via Weierstrass-type representations.
Geodesic convexity types differ in Riemannian manifolds.
problem Characterizing geodesic convexity types in Riemannian manifolds.
method Reverse engineering to characterize manifolds with coinciding convexity types.
result Characterized complete manifolds with coinciding geodesic convexity types.
Paper shows certain algebra types are not differentially smooth.
problem Characterizing smoothness in double extension regular algebras.
method Analyzing algebra type (14641) for differential smoothness.
result Double extension regular algebras of type (14641) are not differentially smooth.
Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the cha…
Characterizes monodromies of projective structures on finite-type surfaces.
problem Understanding monodromies of projective structures on finite-type surfaces.
method Geometrical/topological study of local conical projective structures.
result Any representation can be represented as the holonomy of a branched projective structure.
Study covers of surfaces, showing types and properties.
problem Characterize homeomorphism types of surface covers.
method Analyzing homeomorphism types of covers of surfaces, identifying universal covers and homology covers.
result Identify four possible homeomorphism types for certain covers of surfaces.
New cylindrical solutions found for Grushin-type problem.
problem Critical Grushin-type problem on CR sphere.
method Local Pohozaev identities for non-degeneracy, Lyapunov-Schmidt reduction for solutions.
result New type of multi-bubbling cylindrical solutions constructed.
The study identifies helicoids and spheres as the only finite III-type ruled and quadric surfaces.
problem Characterizing finite III-type ruled and quadric surfaces.
method Analyzing surfaces in 3D Euclidean space with respect to the third fundamental form.
result Helicoids and spheres are the only finite III-type ruled and quadric surfaces.
Identifies all type D^k spacetimes in arbitrary dimensions.
problem Characterizing and distinguishing type D^k spacetimes.
method Analyzing curvature tensors and their invariants for degenerate Kundt metrics.
result Locally boost isotropic spacetimes are type D^k spacetimes.
The paper provides gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
problem Proving gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
method Using Hamilton type and Li-Yau type estimates, the paper proves gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure spaces with compact boundary.
result Gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
In this paper, we study the Lorentzian minimal surfaces in the Minkowski space-time with finite type Gauss map. First, we obtain the classification of this type of surfaces with pointwise 1-type Gauss map. Then, we proved that there are no Lorentzian minimal surface in the Minkowski space-time with null 2-type Gauss ma…
We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister Omega_2-moves. We also show that our proof is compatible with known results for the other move types, in the sense that every knot type admits a pair of diagrams that cannot be made identical without using al…
The paper estimates curvature for a specific type of equations.
problem Estimating curvature for Hessian type equations.
method Establishing curvature estimates for a class of Hessian type equations.
result Curvature estimates for Hessian type equations have been successfully established.
We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kaehler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projectve spin threefolds of general type. Finally, on a fixed spin 6-manifold, …
Artin groups of types F4 and H4 are not commensurable with D4.
problem Determining commensurability between Artin groups of spherical type.
method Realized the abstract commensurator of D4 as the extended mapping class group of a torus with three punctures; found the automorphism group and described torsion elements. result Artin groups of types F4 and H4 are not commensurable with D4. Computes knot types using HOMFLY-PT polynomial.
problem Determining chiral knot and link types with small crossing numbers.
method Uses the HOMFLY-PT polynomial to compute knot types from 3D coordinates.
result Efficacy of HOMFLY-PT for knot types up to crossing number 16.
New method detects events with keywords, adapting to new types.
problem Adapting event detection to new types with predefined sets.
method Feature-based attention mechanism for CNNs.
result Benefits for new type extension and attention mechanism.