We show that, under some technical conditions, the Strong Slope Conjecture proposed by Kalfagianni and Tran is closed under connect sums and cabling. As an application, we establish the Strong Slope Conjecture for graph knots.
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48 results for “strong connectivity”
On a compact complex manifold we study the behaviour of strong Kähler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the analogous result of Miyaoka extension theorem. Studying the blow-up of a strong KT…
We derive sufficient conditions for the vanishing of plurigenera, , on compact (l|k)-strong, , Kaehler manifolds with torsion. In particular, we show that the plurigenera of compact (l|k)-strong manifolds, k<n-1, for which the holonomy of the unique Hermitian connectio…
Strong Frankel theorem for shrinkers in all dimensions.
problem Intersection of shrinkers in large balls.
method Proof using strong Bernstein theorem for stable Gaussian surfaces.
result Shrinkers are connected in all large balls.
The study connects hypergraphs to strong homotopy Lie algebras.
problem Characterizing hypergraphs with a system of distinct representatives.
method Describing a procedure to attach nilpotent strong homotopy Lie algebras to hypergraphs.
result Isomorphic hypergraphs correspond to isomorphic strong homotopy Lie algebras.
Spaces of circle embeddings in curved surfaces indexed by trees.
problem Classifying spaces of braided automorphism groups of trees.
method Indexed connected components with finite rooted trees, constructed strong deformation retract.
result Connected components are classifying spaces of braided automorphism groups.
Study on compact strong HKT manifolds and their properties.
problem Characterizing the structure of compact strong HKT manifolds.
method Geometric analysis, rigidity theorems, classification, and properties of Ricci foliations.
result Compact strong HKT manifolds are Hopf fibrations over compact 4-dimensional orbifolds.
We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that every strong L-space is the branched double cover of an alternating link in the t…
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
problem Understanding strong coupling SYM amplitudes.
method Integrable systems, pseudo-hyperkähler geometry, twistor theory.
result Remainder function is a pseudo-Kähler scalar in hyperkähler geometry.
Quaternionic CR Geometrymath.DG
Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of the Tanaka-Webster con…
Novel 'strong neuron' improves deep learning efficiency and robustness.
problem Improving deep learning efficiency and robustness against adversarial attacks.
method Introducing a novel 'strong neuron' model and a constructive training algorithm.
result Achieved 10x-100x reduction in operations count and hardware requirements.
The paper classifies algebraic curves in 4-balls and their boundaries.
problem Understanding algebraic curves in 4-dimensional balls and their boundaries.
method Analyzing algebraic curves in complex 2-space and their intersections with 4-balls.
result Classification of algebraic curves with up to 5 crossings.
Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noisemath.OC
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.
problem Understanding geometric structures related to geodesic foliations and dynamics.
method Introducing symmetric Poisson structures, proving correspondences with geodesic foliations and Jordan algebras.
result Symmetric Poisson structures correspond to totally geodesic foliations and Jacobi-Jordan algebras.
Study finds abnormal paths on specific Lie groups using algebraic structures.
problem Identifying abnormal extremals on Lie groups with quasimetrics.
method Analyzing Lie algebras and seminorms to determine abnormal extremals.
result Established criterion for strong abnormality of extremals.
The study shows strong formality in certain complex manifolds.
problem Investigating strong formality in complex manifolds.
method Adapting -strong formality from Fernandez and Muñoz to the pluripotential setting.
result Compact Kähler manifolds and generalized complete intersections are strongly formal.
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical systems, construct their cross-products, and introduce representation theory of …
Penrose's conjecture links black holes and gravitational singularities.
problem Deterministic nature of General Relativity and black holes.
method Modern techniques in partial differential equations applied to gravitational collapse.
result Recent advances in understanding Strong Cosmic Censorship.
We generalize the "hamiltonian topology" on hamiltonian isotopies to an intrinsic "symplectic topology" on the space of symplectic isotopies. We use it to define the group of strong symplectic homeomorphisms, which generalizes the group of hamiltonian homeomorphisms introduced by Oh and Mull…
The paper defines strong emergence in field theories and proves it exists between certain theories.
problem Defining and proving the existence of strong emergence phenomena between field theories.
method Formal definition and sufficient conditions for emergence, proving existence in Euclidean background.
result Strong emergence exists between certain parameterized Lagrangian field theories.
Coarse homotopy theory connects Euclidean cones to shape theory of compact spaces.
problem Establishing connections between coarse homotopy theory and shape theory.
method Using pointed shape invariants and inverse mapping telescopes.
result Proving two compact spaces are strong shape equivalent if their Euclidean cones are coarsely homotopy equivalent.
We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than t…
New method connects curvature and Persistent Homology for networks.
problem Efficient computation of Persistent Homology for complex networks.
method Discrete Morse Theory, Bloch's extension, Forman-Ricci curvature.
result Efficient Persistent Homology scheme using curvature-based approach.
Direct method finds Yang-Mills connections for SO(3) bundles.
problem Finding Yang-Mills connections for SO(3) bundles over closed 4-manifolds.
method Direct minimizing method with test connections and assumptions.
result Minimizing sequence converges to a minimizer or anti-selfdual/selfdual connection.
The aim of this paper is to study compact 5--manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel--Whitney class have to satisfy strong restrictions. We then show that for simply connected 5--manifolds these restrictions are neces…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this connection allows us to obtain strong multiplicative performance bounds on several meth…
Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.
problem The original Strong Cosmic Censorship conjecture.
method Weakens the conjecture to allow manifolds with bounded curvature and Lipschitz continuity of metrics.
result Proves the conjecture with bounded curvature for sufficiently large p (p>4 with uniform bounds, p>2 without uniform bounds).
In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise t…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a one-to-one correspondence, between the module structure of the 1-forms and the …
Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: is constant for . We characterize the manifolds satisfying strong stability: is constant for $k\gg…
Study counts sub-chord diagrams to classify spherical curves.
problem Classifying spherical curves using chord diagrams.
method Counting sub-chord diagrams under specific moves.
result New invariant classifies prime reduced spherical curves.
We investigate certain natural connections between subriemannian geometry and hyperbolic dynamical systems. In particular, we study dynamically defined horizontal distributions which split into two integrable ones and ask: how is the energy of a subriemannian geodesic shared between its projections onto the integrable …
The study examines vector fields with integer singularities in 3D balls.
problem Characterizing the strong -closure of vector fields with finitely many integer singularities.
method Characterization and decomposition of vector fields with finitely many integer singularities.
result Decomposition theorem for elements in , revealing information about mass-minimizing currents.
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hyp…
Study integrability of generalized almost complex structures on S^6.
problem Integrability of generalized almost complex structures on the 6-dimensional sphere.
method Local coordinate criteria for integrability with respect to brackets and Courant integrability for strong structures.
result No nontrivial spherical combinations of the canonical structures are integrable with respect to the Levi-Civita connection.
The study shows how to measure translation surfaces with short saddle connections.
problem Measuring the probability of surfaces with short saddle connections.
method Using the multi-scale compactification of strata and algebraicity results.
result Proves strong regularity for invariant measures on translation surfaces.
Implicit discourse relation classification is of great challenge due to the lack of connectives as strong linguistic cues, which motivates the use of annotated implicit connectives to improve the recognition. We propose a feature imitation framework in which an implicit relation network is driven to learn from another …
Study on G2 structures with torsion and existence of solutions.
problem Existence and properties of strong G2-structures with torsion.
method Investigation of the twisted G2 equation and analysis of invariant structures.
result Non-existence of non-trivial solutions on compact solvmanifolds.
In this paper we give a complete description of the set of discrete faithful representations SH(M) uniformizing a compact, orientable, hyperbolizable 3-manifold M with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part …
A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form is -closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a -dimensional SKT Lie algebra $\mathfr…
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…
Develops equivariant connections for Yang-Mills equations, simplifying interactions modeling.
problem Simplifying interactions modeling in Yang-Mills equations for different bundles.
method Introduces -equivariance to reduce Yang-Mills equations.
result Models electroweak interaction and interactions with differential and wave equations.
The paper proves that most metrics satisfy a strong version of Arnold's conjecture for Laplace eigenvalues.
problem Understanding metrics that satisfy a strong version of Arnold's conjecture for Laplace eigenvalues.
method Using geometric characterizations and perturbation theory, the paper proves the conjecture for most metrics.
result The Strong Arnold Hypothesis is satisfied for all metrics except for a set of infinite codimension.
The moduli space of Hermitian-Einstein connections on certain manifolds has a strong Kähler with torsion structure.
problem Characterizing the moduli space of Hermitian-Einstein connections on manifolds with a dilaton field.
method Demonstrates the existence of a strong Kähler with torsion structure on the moduli space under specific conditions on the Lee form and dilaton field.
result The moduli space admits an induced holomorphic and Killing vector field when the manifold has a holomorphic and Killing vector field invariant under the dilaton.
On astheno-Kaehler metricsmath.DG
A Hermitian metric on a complex manifold of complex dimension is called {\em astheno-Kähler} if its fundamental -form satisfies the condition . If , then the metric is {\em strong KT}, i.e. is -closed. By using blow-ups and the …
We present an introduction to the geometry of higher order vector and co-vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with ass…
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We sugge…
This work refines claims about neural network connectivity, showing that simultaneous linear connectivity is possible under certain conditions.
problem Neural networks' loss landscapes are non-convex due to permutation symmetries, leading to high loss barriers between permuted networks.
method The authors introduce and analyze three claims of increasing strength regarding the connectivity of neural networks, focusing on permutations that align networks.
result The authors provide evidence that strong linear connectivity may be possible under certain conditions, specifically when interpolating among three networks of increasing width.