Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
Constructs covariant derivatives for Ehresmann connections.
problem Developing a method for covariant derivatives in fibre bundles.
method Introducing a vertical endomorphism to construct covariant derivatives on vertical and horizontal distributions.
result Covariant derivatives can be constructed separately on vertical and horizontal distributions and then glued together.
Unique vertical isomorphisms between Fedosov dg manifolds are proven for Lie pairs.
problem Vertical isomorphisms of Fedosov dg manifolds associated with Lie pairs.
method Construction of Fedosov dg manifolds via splitting and connection, proving unique isomorphisms using iteration formula.
result Existence and uniqueness of vertical isomorphisms between Fedosov dg manifolds.
We uncover some connections between the topology of a complete Riemannian surface M and the minimum number of vertices, i.e., critical points of geodesic curvature, of closed curves in M. In particular we show that the space forms with finite fundamental group are the only surfaces in which every simple closed curve ha…
In this paper we study some problems related to a vertical Liouville distribution (called vertical Liouville-Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vrănceanu type on Cartan spaces related to some foliated structures. Also, we identify a cer…
On the slit tangent manifold TM0 of a Finsler space (M,F) there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle…
Constructs Lepage equivalents for arbitrary-order Lagrangians.
problem Creating Lepage equivalents for complex Lagrangians.
method Uses variational bicomplex and symmetric linear connections to construct Lepage equivalents satisfying the closure property.
result Shows how to extend global Lepage equivalents to ones satisfying the closure property.
New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.
problem Ensuring graph rigidity and global rigidity in the Euclidean plane.
method Improving algebraic connectivity bounds for graph rigidity and global rigidity.
result Every 6-connected graph is rigid and globally rigid if its algebraic connectivity exceeds specific thresholds.
We study the existence and uniqueness problem of compact minimal vertical graphs in Hn×R, n≥2, over bounded domains in the slice Hn×{0}, with non-connected boundary having a finite number of C0 hypersufaces homeomorphic to the sphere Sn−1, with prescri…
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.
Rectangular diagrams of links are link diagrams in the plane R2 such that they are composed of vertical line segments and horizontal line segments and vertical segments go over horizontal segments at all crossings. P. R. Cromwell and I. A. Dynnikov showed that rectangular diagrams of links are useful for d…
We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces.
We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.
Study of Poincaré-Reeb graphs for algebraic domains.
problem Characterizing geometric shapes of algebraic domains.
method Collapsing vertical segments to form Poincaré-Reeb graphs and analyzing their properties.
result Any transversal graph with specific properties can be realized as a Poincaré-Reeb graph.
Connected graph for twice-punctured torus curves.
problem Structure of tri-pants graph on twice-punctured torus.
method Examined relationship with Farey complex to prove connectivity and infinite diameter.
result Tri-pants graph is connected and has infinite diameter.
An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a h…
An embedding of a graph into R3 is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding f of a graph G into R3 is free, if π1(R3−f(G)) is a free group. It was known that for any complete graph its linear embedding is always free.…
Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are impose…
Establishes equivalent formulations of connections in tangent categories.
problem Generalizing connections in tangent categories.
method Defined and generalized the notion of connection on differential bundles in tangent categories, provided equivalent formulations, and showed equivalences with specific morphisms and diagrams.
result Equivalent formulations of connections in tangent categories reduce the amount of specified structure and axioms required.
Paper classifies surface-links using charts with specific properties.
problem Classifying surface-links with specific charts.
method Using quandle colorings to differentiate charts representing different surface-links.
result Charts in the second class represent different surface-links.
The paper splits local rigidity into vertical and horizontal types.
problem Local rigidity of Clifford-Klein forms in homogeneous spaces.
method Introducing a splitting of local rigidity into vertical and horizontal rigidity.
result Refined results and a new approach to Baklouti's conjecture.
New proof shows extendable shellability for simple complexes.
problem Proving extendable shellability for specific simplicial complexes.
method Considering chordal graph structure and linear quotients.
result All d-dimensional complexes with d+3 vertices are extendably shellable. The paper solves the Integration Problem for principal connections.
problem Describing discrete connections associated with a principal connection.
method Using the Lie or derivative functor to induce connections on the principal bundle.
result For flat principal connections, the Integration Problem has a unique solution among flat discrete connections.
A new asynchronous method for vertical federated learning improves privacy and efficiency.
problem Solving vertical federated learning in an asynchronous manner with privacy and efficiency.
method A simple FL method that allows clients to run stochastic gradient algorithms asynchronously with a new perturbed local embedding technique.
result The method improves privacy and communication efficiency compared to centralized and synchronous FL methods.
The paper examines vertical curves and fibers in the Heisenberg group, proving properties and constructing counterexamples.
problem Characterizing and measuring vertical curves and fibers in the Heisenberg group.
method Metric analysis of vertical curves and fibers of maps from the Heisenberg group to the plane.
result Vertical curves in the Heisenberg group can have Hausdorff dimensions strictly larger or smaller than 2, unlike intrinsic Lipschitz graphs.
New graphs show hierarchical hyperbolic properties, extending previous work.
problem Characterizing hierarchically hyperbolic properties of multiarc and curve graphs.
method Analyzing the geometric intersection number and using PMod(S) action.
result Multiarc and curve graphs are hierarchically hyperbolic.
Various curve complexes with vertices representing multicurves on a surface S have been defined, for example [3], [4] and [8]. The homology curve complex HC(S,α) defined in [7] is one such complex, with vertices corresponding to multicurves in a nontrivial integral homology class α. Given two multicurve…
We prove that any non-simply connected planar domain can be properly and minimally embedded in H^2 x R. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.
New algorithm finds corrupted vertices in graphs with few queries.
problem Adversarial tampering of graph edges and vertices.
method Active learning algorithm with polynomial query complexity.
result Efficiently recovers corrupted vertices with small query complexity.
A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In…
New bounds on triangulations of manifolds with non-free fundamental groups.
problem Finding lower bounds on the number of vertices in PL-triangulations of manifolds.
method Using fundamental group structure and Lusternik-Schnirelmann category theory.
result Every PL-triangulation of a d-dimensional manifold with non-free fundamental group has at least 3d+1 vertices. Efficiently searches ancestral graphs using multivariate information.
problem Discovering causal relationships in graphs with latent variables.
method Greedy search-and-score algorithm with two-step approach.
result Outperforms existing methods on benchmark datasets.
We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold is a Calabi-Eckmann manifold. Moreover we show that a complete, simply connected, normal metric contact pair manifold such that the foliation induced by the vertical subbundle is regular and reflections in the integ…
Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.
problem Finding the optimal coupling among random vectors with known statistics and correlation structure.
method Formulating the problem as a minimum spanning tree over measure-valued vertices and solving it in two steps.
result Optimal coupling found using the minimum spanning tree approach.
Moves connect multibranched surfaces with same neighborhoods.
problem Connecting multibranched surfaces with identical neighborhoods.
method Introduces moves to connect multibranched surfaces.
result Any two multibranched surfaces can be connected in finitely many steps.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
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.
We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particular…
Estimates graph connected components from sampled subgraphs.
problem Estimating the number of connected components in large graphs from subgraph samples.
method Subgraph sampling model, focusing on chordal graphs.
result Optimal sample complexity and linear-time estimators for chordal graphs.
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex ar…
The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. I…
The study constructs minimal hypersurfaces in MimesR with helicoid and catenoid properties.
problem Constructing minimal hypersurfaces with helicoid and catenoid properties in MimesR. method Conditions on height functions and horizontal sections to define vertical helicoids and catenoids; local characterization of hypersurfaces with constant angle function.
result Vertical helicoids and catenoids exist in MimesR under certain conditions on M. This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.
problem Recovering clusters in a stochastic Ising model on a SBM graph.
method Proposes a Stochastic Ising Block Model (SIBM) and establishes a sharp threshold for exact recovery.
result Sharp threshold m∗ for exact recovery of clusters in SIBM, with O(n) time complexity for m≥m∗. Spheres in curve graphs are connected, proving Gromov boundary linearity.
problem Understanding connectivity in curve graphs and their boundaries.
method Defining spheres and analyzing their connectivity for different complexities.
result Spheres in high complexity curve graphs are always connected, with weaker results for low complexity.
Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.
problem Sub-Riemannian problem on solvable, non-nilpotent Lie groups.
method Qualitative phase-space analysis of Hamiltonian system, focusing on vertical component.
result Explicit upper bound for cut time in terms of pendulum period.
The paper defines vector 1-forms on Finsler manifolds and constructs connections.
problem Characterizing conservative connections on Finsler manifolds.
method Defining conservative semibasic vector 1-forms and constructing connections.
result A correspondence between torsion-free semibasic vector 1-forms and vertical vector fields.
For an arrangement of n pseudolines in the real projective plane let us denote by ti the number of vertices incident to i lines. We obtain a linear on ti inequality similar to the Hirzebruch one, but with an elementary proof. We present an algorithm for producing lower bounds of the number of regions basing o…
A new discrete formula connects vertex and edge distributions on graphs.
problem Optimal transport on graphs with mixed vertex and edge distributions.
method Discrete transport equation and Benamou-Brenier formulation.
result Classification of all Wasserstein-1 geodesics on graphs.