A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. A splitting is full if it does not have the disjoint curve proper…
Approximates cycles in planar and bounded-genus graphs.
problem Finding many disjoint cycles in planar and bounded-genus graphs.
method Constant-factor approximation algorithms for vertex-disjoint and edge-disjoint cycles.
result First algorithms for vertex-disjoint paths in fully planar and bounded-genus instances.
Paper constructs graphs with girth four and distinct properties.
problem Characterize Ricci-flat graphs with specific girth.
method Constructs and characterizes graphs with girth four, focusing on edge-disjoint and vertex-disjoint 4-cycles.
result Characterizes all Ricci-flat graphs of girth four with vertex-disjoint 4-cycles.
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
The paper explores isotopic triples of triangles in 3D space.
problem Determining if triples of triangles are combinatorially isotopic.
method Continuous motion of triangles with disjoint outlines, algorithmic checks, and elementary proofs.
result Different types of triples of disjoint triangles are not isotopic.
We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X which precisely characterizes when X times R has the Disjoint Disks Property. As a consequence, X times R is a manifold if and only if X is resolvable and it possesses this Disjoint Path Concordances Property.
Simple proof shows uncountable Möbius bands are impossible in space.
problem Proving the impossibility of uncountably many disjoint Möbius bands in 3D space.
method Algebraic proof
result Proves uncountable Möbius bands are impossible in R3 and higher dimensions. A new classification method using disjoint centroids and normalized distance.
problem Improving classification accuracy and feature selection.
method Nearest disjoint centroid classifier with normalized distance.
result Our method outperforms other classifiers in terms of misclassification rates and feature usage.
New method shows disjoint set-theoretic subsolutions remain so for longer.
problem Ensuring disjointness of set-theoretic subsolutions under mean curvature flow.
method Set-theoretic approach to mean curvature flow on Riemannian manifolds.
result Disjoint subsolutions remain disjoint for longer periods if one is compact.
Uniform bounds found for Sierpinski carpet hyperbolic components.
problem Bounding hyperbolic components of Sierpinski carpet type.
method Establishing uniform a priori bounds and analyzing quadratic-like restrictions.
result Sierpinski carpet hyperbolic components of disjoint type are bounded.
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear involutions without flips. They are analogs of classical interval exchanges, and are…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number of circles meeting in a given cyclic order given 6 disjoint smooth closed curves…
The paper introduces MU for NMF with β-divergences and disjoint constraints.
problem Nonnegative matrix factorization with constraints.
method Design multiplicative updates for NMF based on β-divergences with disjoint constraints. result Multiplicative updates satisfy constraints and decrease the objective function.
We prove that the number s(n) of disjoint minimal graphs supported on domains in R^n is bounded by e(n+1)^2. In the two-dimensional case we show that s(2) is at most three (the conjectured number is two).
Survey of non-uniqueness in anisotropic Calderón problem with disjoint boundary data.
problem Non-uniqueness in anisotropic Calderón problem with disjoint boundary measurements.
method Analysis of conformal metrics and nonlinear elliptic PDEs.
result Existence of infinite conformal metrics with identical boundary measurements on disjoint sets.
We show that many algebraic actions of higher-rank abelian groups on zero-dimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov--Rokhlin formula for half-space entropies.
New theorem on embedding Moebius bands in 3D space.
problem Proving the impossibility of placing uncountably many disjoint Moebius bands in 3D space.
method Generalization of Grushin and Palamodov's result to tame subsets in R^N and arbitrary topological embeddings in R^3.
result The impossibility of embedding uncountably many pairwise disjoint Moebius bands in 3D space, even for arbitrary topological embeddings.
The study bounds the excess of disjoint nonorientable surfaces in a 4-manifold.
problem Bounding the excess of disjoint nonorientable surfaces in a 4-manifold.
method Combining tubing construction with signature and Euler-characteristic formulas for 2-fold branched covers.
result The normal-Euler excess is bounded by a constant depending only on the ambient 4-manifold.
Crooked planes in 3D Minkowski space can be foliated.
problem Understanding foliations between crooked planes in 3D Minkowski space.
method Showed that any two disjoint crooked planes are leaves of a crooked foliation.
result Answered a question about foliations between crooked planes in 3D Minkowski space.
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.
New embeddings show answer to Baker-Laidacker question can be yes or no.
problem Answer to Baker-Laidacker question about disjoint compacta in R^N.
method Use of specific wild Cantor sets and Antoine's methods.
result Answer to Baker-Laidacker question can be twofold.
Satellite knots can be trivialized by a single band move.
problem Satellite knots and their trivialization.
method Infinite family of satellite knots and a single band move.
result No disjoint band unknotting exists for satellite knots.
Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product F×I, or they lie on opposite ends of a kind of "twisted" product $F \widetilde{\boldsymbol{…
The following problem was proposed in 2010 by S. Lando. Let M and N be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-space such that their intersection is transversal and is a union of disjoint circles that is situated as M in one sphere and as N in the ot…
Simple curves enclose two small disks if they're wide and bend moderately.
problem Bounding the diameter of a curve to enclose two disjoint unit disks.
method Analyzing curvature and diameter constraints of a simple closed curve.
result A curve with curvature ≤1 and diameter ≥4 encloses two disjoint open unit disks.
MTL method uses unlabeled data with pseudo labels to improve classification with disjoint datasets.
problem Improving classification performance with disjoint labeled datasets using unlabeled data.
method Proposes MTL-SA method to select and augment unlabeled data with confident pseudo labels and close distribution to labeled data.
result Extensive experiments show the effectiveness of MTL-SA method in improving classification performance.
Neural Bayes simplifies computing complex stats for unsupervised learning.
problem Computing mutual information and optimal labeling of disjoint manifolds in unsupervised learning.
method Parameterization using neural networks to express statistical quantities in closed form.
result Neural Bayes enables efficient computation of mutual information and optimal labeling of disjoint manifolds.
A biclustering algorithm finds dense disjoint subgraphs in weighted bipartite graphs.
problem Finding dense disjoint bicliques in a weighted bipartite graph.
method Semidefinite programming-based branch-and-cut algorithm with upper and lower bounds.
result The algorithm can solve much larger instances than general-purpose solvers.
We study the structure of finite quandles in terms of subquandles. Every finite quandle Q decomposes in a natural way as a union of disjoint Q-complemented subquandles; this decomposition coincides with the usual orbit decomposition of Q. Conversely, the structure of a finite quandle with a given orbit decomposit…
Paper proposes a clustering algorithm for nonnegative data.
problem Clustering nonnegative data in disjoint subspaces.
method Simple algorithm to cluster nonnegative data.
result Matrix completion algorithm outperforms standard methods.
Let Y be a compact, oriented 3-manifold with a contact form a. For any Dirac operator D, we study the asymptotic behavior of the spectral flow between D and D+cl(-ira) as r very large. If a is the Thurston-Winkelnkemper contact form whose monodromy is the product of Dehn twists along disjoint circles, we prove that the…
Improved defense against data poisoning attacks by aggregating smaller subsets.
problem Mitigating the impact of poisoned data on model robustness.
method Finite Aggregation method that combines duplicates of smaller disjoint subsets for training.
result Consistent improvement in certified robustness bounds, up to 4.77% on GTSRB.
Researchers find multiple supporting minimal Lefschetz pencils for a complex fibration.
problem Finding multiple supporting minimal Lefschetz pencils for a specific Lefschetz fibration.
method Analyzing maximal disjoint (−1)-sections of the Matsumoto-Cadavid-Korkmaz Lefschetz fibration. result The Matsumoto-Cadavid-Korkmaz Lefschetz fibration has more than one supporting minimal Lefschetz pencils.
Classifies pairs of hyperplanes in Einstein universe, contributing to crooked surfaces classification.
problem Classifying pairs of hyperplanes in the Einstein universe.
method Algebraic invariant and symplectic splittings model Einstein hyperplanes.
result Contributes to a complete disjointness criterion for crooked surfaces.
Study on planar graph braid groups' second homology.
problem Characterize the second homology of planar graph braid groups.
method Analyzing configuration spaces of planar graphs under specific operations.
result The second homology is generated by three specific graphs.
In this paper we study how to distinguish two embeddings of a finite collection of disjoint circles into the plane up to planar isotopy. We adopt the spirit of the approach by V. Turaev, Operator Invariants of Tangles, Math. USSR-Izv. 35 (1990), 411--444, by considering a category of planar tangles and representing it …
Direct proof of implication between geometric convex hull statements.
problem Deriving one geometric convex hull statement from another.
method Direct proof of implication between statements.
result Direct derivation of one geometric convex hull statement from another.
Short proofs for complex Tverberg theorems using prime powers.
problem Proving Tverberg-type theorems for cell complexes.
method Short proofs using prime powers and continuous maps.
result Pairwise disjoint faces of a complex intersect under continuous maps.
In this paper we consider compact, Riemannian manifolds M1,M2 each equipped with a one-parameter family of metrics g1(t),g2(t) satisfying the Ricci flow equation. Motivated by a characterization of the super Ricci flow developed by McCann-Topping, we introduce the notion of a super Ricci flow for a family of …
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that such subgraphs can be recovered from the solution of a particular semidefinite re…
Let M be a compact connected orientable 3-manifold, with non-empty boundary that contains no 2-spheres. We investigate the existence of two properly embedded disjoint surfaces S_1 and S_2 such that M - (S_1 \cup S_2) is connected. We show that there exist two such surfaces if and only if M is neither a Z_2 homology sol…
The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.
problem Proving the Discrete Schwarz-Pick Lemma for circle packings with various inversive distances.
method Using a variational principle for circle packings with inversive distances, the paper extends the lemma to a broader range of packings.
result The Discrete Schwarz-Pick Lemma holds for circle packings with inversive distances in (−1,1], provided an additional condition on triangle weights. Avoids noncompact hypersurfaces from touching in evolving flows.
problem Preventing noncompact hypersurfaces from touching in evolving flows.
method Analyzes mean curvature flow and weak set flows in Euclidean and Riemannian spaces.
result Proves that noncompact hypersurfaces remain disjoint in evolving flows.
Improved TTS style transfer across disjoint datasets with adversarial cycle consistency.
problem Suboptimal TTS style transfer on disjoint datasets with underrepresented styles.
method Adversarial cycle consistency training with paired and unpaired triplets.
result 78% improvement in style transfer with minimal reduction in fidelity and naturalness.
We link disjoint longitudinal data for rare disease patients using latent representations and mixed-effects regression.
problem Analyzing treatment switches in rare diseases with limited data and changing measurement instruments.
method We embed item values into a shared latent space using variational autoencoders and apply mixed-effects regression to quantify treatment effects.
result Our approach allows for statistical inference and quantifies the impact of treatment switches in spinal muscular atrophy.
We show that every canonical Seifert surface is (up to isotopy) given by a knot diagram in which the (open) Seifert disks are pairwise disjoint.
The paper explores winding numbers of almost embeddings of a 4-vertex graph in the plane.
problem Understanding the winding numbers of almost embeddings of a 4-vertex graph in the plane.
method Constructing examples to show the only relation between the winding numbers of cycles in the graph.
result The sum of winding numbers is odd, and this is the only relation between them.
2D complexes can be almost-embedded in 4D space without self-intersections.
problem Understanding the embedding properties of 2-dimensional complexes in 4-dimensional space.
method Analyzing specific 2-complexes constructed by Freedman-Krushkal-Teichner and showing they can be PL immersed in R4 without self-intersections. result Many 2-complexes can be PL almost-embedded in R4 with singularities only as self-intersections of some 2-cells.