Every negative amphichiral knot is rationally slice.
problem Proving every negative amphichiral knot is rationally slice.
method Systematic analysis of the action induced by the negative amphichiral map on the JSJ decomposition of the link exterior.
result Every negative amphichiral link is rationally slice.
Study proves obstructions to equivariantly slice strongly negative amphichiral knots.
problem Proving obstructions for equivariantly slice strongly negative amphichiral knots.
method Using determinant, Spinc-structures, Donaldson's theorem, and Heegaard Floer correction terms.
result 8 out of 16 strongly negative amphichiral knots with 12 or fewer crossings are not equivariantly slice.
New proof for some knots being topologically slice.
problem Understanding which knots are topologically slice.
method Equivariant topological slice disks for strongly negative amphichiral knots.
result Strongly negative amphichiral knots with trivial Alexander polynomial are equivariantly topologically slice.
We give a simple obstruction for a knot to be amphichiral, in terms of the homology of the 2-fold branched cover. We work with unoriented knots, and so obstruct both positive and negative amphichirality.
New knots found that are 4-genus minimal.
problem Finding knots with minimal 4-genus.
method Constructing infinitely many amphichiral knots with specific properties.
result Knots with 4-genus minimal for each g>0. New 4-manifold accounts for rationally slice knots.
problem Characterize rationally slice knots.
method Show independence of construction of rational homology ball VK. result Single 4-manifold accounts for all known rationally slice knots.
Paper defines half-Conway polynomial and computes it for knots up to 12 crossings.
problem Computing and characterizing half-Conway polynomials of knots.
method Normalized Conway polynomial, equivariant skein relation, diagrammatic interpretation.
result First examples of non-slice strongly negative amphichiral knots with determinant one.
Study on equivariant Q-sliceness for strongly invertible knots.
problem Understanding Q-sliceness for strongly invertible knots.
method Constructive and obstructive approaches using Fox-Milnor condition and equivariant concordance.
result Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball.
Tanaka shows amphichiral symmetric unions of the unknot are trivial.
problem Understanding amphichiral symmetric unions and their Jones polynomials.
method Analyzing the Jones polynomial of amphichiral symmetric unions of the unknot and generalizing to other knots.
result Amphichiral symmetric unions of any knot with one twist region are trivial.
The paper explores symmetric representations of links and conditions for amphichirality.
problem Investigating symmetric representations of links and conditions for amphichirality.
method Using antipodally self-dual and antipodally symmetric maps, the authors provide sufficient combinatorial conditions for amphichirality.
result A link is amphichiral if its self-dual pairing is not one of 6 specific ones.
Research classifies knots based on sliceness and amphichirality.
problem Classifying odd-stranded Turk's head knots based on sliceness and amphichirality.
method Constructing commuting pairs of ambient involutions and analyzing the equivariant Fox-Milnor square condition.
result Established a sharp parity dichotomy for equivariant rational sliceness and Klein amphichirality of odd-stranded Turk's head knots.
Survey on embedding 3-manifolds in definite 4-manifolds, focusing on Donaldson's theorem.
problem Understanding embeddings of 3-manifolds in definite 4-manifolds.
method Utilizes Donaldson's diagonalization theorem and combinatorics of integral lattices.
result New result on embedding amphichiral lens spaces in negative-definite manifolds.
In 1997 Cochran-Orr-Teichner introduced a natural filtration, called the n-solvable filtration, of the smooth knot concordance group, C. Its terms {F_n} are indexed by half integers. We show that each associated graded abelian group G_n=F_n/F_{n.5}, n>1, contains infinite linearly independent sets of elements of order …
Survey of Turk's head knots and links properties.
problem Characterize Turk's head knots and links.
method Discussion of various results in the mathematical literature.
result Turk's head links are alternating, fibered, hyperbolic, invertible, non-split, periodic, and prime.
The paper classifies involutions on S^4, proving linearities under certain conditions.
problem Classifying involutions on S^4 with specific fixed-point sets.
method Combining surgery theory, Schoenflies theorem, and equivariant topology.
result Linear involutions on S^4 with 1-dimensional fixed-point sets are proven.
Using computational techniques we tabulate prime knots up to five crossings in the solid torus and the infinite family of lens spaces L(p,q). For these knots we calculate the second and third skein module and establish which prime knots in the solid torus are amphichiral. Most knots are distinguished by the skein mod…
We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gaussian parity, to which it reduces on virtual knots. We show that the 2-c…
Classifies symmetries of knots using group actions and orthogonal representation theory.
problem Classifying symmetries of knots in 3-sphere.
method Using geometrization and orthogonal representation theory, constructing examples, and distinguishing symmetries.
result Cyclic and dihedral families of symmetries of prime knots and composite knots.
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary depth of the derived series of the fundamental group, and can detect torsion wh…
It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant of an amphichiral integral homology 3-sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M, we construct a manifold pair (Y,Q) of dimensions 6 and 3 equipped with so…
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
nUDEs use neural networks to model biology without negative values.
problem Unrealistic negative values in hybrid models of biology.
method Developed non-negative UDEs (nUDEs) with regularization techniques.
result nUDEs provide realistic solutions for biological models.
Construct Kähler metrics with negative holomorphic bisectional curvature on compact relative Kähler fibrations.
problem Constructing Kähler metrics with negative holomorphic bisectional curvature on compact relative Kähler fibrations.
method Constructing Kähler metrics with negative holomorphic bisectional curvature on compact relative Kähler fibrations using specific curvature conditions.
result Explicit construction of Kähler metrics with negative holomorphic bisectional curvature on compact relative Kähler fibrations.
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.
SANS uses graph structure to find meaningful negatives for entity and relation embeddings.
problem Finding hard negatives for entity and relation embeddings in knowledge graphs.
method Structure Aware Negative Sampling (SANS) that selects negatives from a node's k-hop neighborhood.
result SANS finds semantically meaningful negatives and is competitive with state-of-the-art approaches.
Uniform negative immersions prove coherence of one-relator groups.
problem Proving coherence of one-relator groups.
method Using uniform negative immersions and linear-programming techniques.
result One-relator groups with uniform negative immersions are coherent.
Algorithm transforms weakly negative plumbing trees to negative definite ones.
problem Transforming weakly negative plumbing trees to negative definite ones.
method Combining plumbing calculus with diagonalization algorithm to systematically eliminate positive eigenvalues.
result Explicit algorithm reduces weakly negative definite plumbing trees to negative definite ones.
New manifolds with negative curvature limit to one with negative curvature.
problem Preserving nonnegative scalar curvature under intrinsic flat convergence.
method Constructing sequences of manifolds with positive scalar curvature.
result Intrinsic flat limit of manifolds with negative scalar curvature.
Study finds negatively curved spheres in elliptic surfaces and their modifications.
problem Finding negatively curved spheres in elliptic surfaces.
method Using elliptic fibrations with specific singular fibers.
result Identifies spheres with very negative self-intersections in elliptic surfaces and their modifications.
New compact K-E manifolds with negative curvature found.
problem Constructing compact Kähler-Einstein manifolds with negative curvature.
method Created compact Kähler-Einstein manifolds of dimension n with negative sectional curvature.
result Found compact Kähler-Einstein manifolds of negative curvature not covered by the ball.
New metrics found without topological restrictions.
problem Finding metrics with constant negative scalar-Weyl curvature.
method Extended Aubin's construction to prove existence.
result Every manifold admits a metric with constant negative scalar-Weyl curvature.
DeepMP improves non-negative sparse recovery performance.
problem Recovering non-negative sparse signals with high coherence.
method Reformulated non-negative matching pursuit as a deep neural network.
result DeepMP yields significant improvement in exact recovery performance.
Novel neural likelihood ratio estimation for negative data in particle physics.
problem Estimating likelihood ratios with negative probability densities and weights.
method Introducing a novel loss function and a new model architecture based on signed mixture models.
result Demonstrated improved estimation on a real-world example from particle physics.
New unsupervised method selects hard negative samples for contrastive learning.
problem How to select good negative examples for contrastive learning without using true similarity information.
method Developed a new family of unsupervised sampling methods for hard negative selection.
result Improves downstream performance across multiple modalities.
We analyze properties of links which have diagrams with a small number of negative crossings. We show that if a nontrivial link has a diagram with all crossings positive except possibly one, then the signature of the link is negative. If a link diagram has two negative crossings, we show that the signature of the link …
We show the existence of complete negative Kähler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature. We prove that any Kähler metrics on such manifolds can be deformed to the complete negative Kähler-Einstein metric using the normalized Kähler-Ricci flow.
Negative step sizes improve second-order methods for neural networks.
problem Second-order methods discard negative curvature, limiting their effectiveness.
method Introduce negative step sizes in second-order methods combined with Wolfe line search.
result Negative step sizes lead to global convergence and improved performance.
Classifies contact structures on negative-definite Seifert fibred spaces.
problem Classifying fillable contact structures on negative-definite Seifert fibred spaces.
method Using Alexander filtration in lattice cohomology and Stein structures.
result Unique negative maximal twisting number and explicit computation.
New solutions found with negative mass in general relativity.
problem Finding metrics with negative mass in general relativity.
method Constructing families of metrics with specific properties.
result Obtained new classes of solutions with negative mass.
Study on negative Sasakian structures on specific 5-manifolds.
problem Existence of negative Sasakian structures on simply-connected 5-manifolds.
method Analysis of rational homology spheres and Smale-Barden manifolds.
result Proves existence of negative Sasakian structures on specific 5-manifolds.
Sharp inequality in spaces with non-negative Ricci curvature.
problem Proving a sharp isoperimetric inequality in metric measure spaces.
method Using volume entropy in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
result Proved a sharp dimension-free isoperimetric inequality.
The paper extends a theorem about Kähler manifolds with quasi-negative curvature to almost quasi-negative curvature.
problem Understanding the ampleness of canonical line bundles for Kähler manifolds with specific curvature properties.
method Introducing a new notion of almost quasi-negative holomorphic sectional curvature and extending the theorem to this setting.
result The theorem is extended to compact Kähler manifolds with almost quasi-negative holomorphic sectional curvature, and a gap-type theorem is derived.
We study the Teichmüller space of negatively curved metrics on a high dimensional manifold, with applications to bundles with negatively curved fibers.
Constructs metrics with negative constant scalar curvature.
problem Negative constant scalar curvature metrics.
method One-parameter family of complete metrics.
result Verifies positive energy conjecture for these metrics.
It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if the…
Study negative definite spin fillings of knot covers.
problem Existence of negative definite spin fillings in branched double covers.
method Derive obstructions and characterize special knots.
result Characterization of special alternating knots.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
Study negative band numbers in braids and links.
problem Characterizing braids with negative band numbers.
method Using Birman, Ko, and Lee's left-canonical form.
result Characterize strongly and almost strongly quasipositive braids.