Not finitely presented group from CAT(0) cube complexes.
problem Identifying finitely presented groups.
method Developing techniques for proving non-simple connectedness of subcomplexes of CAT(0) cube complexes.
result Basilica Thompson group is not finitely presented.
Study on frequencies of non-simple curves in surfaces of large genus.
problem Frequency of non-simple curves in surfaces of large genus.
method Expression for frequency, large genus asymptotics, comparison with previous work.
result Identify most common types of non-simple curves with K intersections.
The length of shortest non-simple geodesics grows logarithmically with surface genus.
problem Understanding the behavior of shortest non-simple closed geodesics on hyperbolic surfaces.
method Investigation of asymptotic behavior on random hyperbolic surfaces using the Weil-Petersson measure.
result The non-simple systole behaves like log(g) as g goes to infinity.
Simple lifts of non-simple curves on surfaces.
problem Finding simple lifts of non-simple closed curves on surfaces.
method Constructing finite covers and curves on surfaces.
result Explicit non-simple closed curves with simple lifts on degree n covers.
By proving a connected sum formula for the Legendrian invariant λ+ in knot Floer homology we exhibit infinitely many transversely non simple knots.
Shortest non-simple closed geodesics on hyperbolic surfaces found.
problem Finding the shortest non-simple closed geodesics on hyperbolic surfaces.
method Analyzing closed geodesics with at least k self-intersections on hyperbolic surfaces.
result The shortest non-simple closed geodesics lie on an ideal pair of pants and have length $2\arccosh(2k+1)$.
The paper studies stability of Einstein metrics on non-simple Lie group homogeneous spaces.
problem Classifying compact homogeneous spaces with standard Einstein metrics.
method Analysis of scalar curvature functional and coindex.
result Most standard Einstein metrics on non-simple Lie group homogeneous spaces are unstable.
Study shows infinitely many non-simple Legendrian knots in two-bridge knots.
problem Characterizing non-simple Legendrian knots in two-bridge knots.
method Using knot Floer homology and continued fraction expansions.
result Infinitely many Legendrian and transversely non-simple knot types among two-bridge knots.
New examples of non-simple knots in Lens spaces show rich botany.
problem Understanding the variety of Legendrian and transversal knots in Lens spaces.
method Presented new families of non-simple knots in tight Lens spaces.
result More non-isotopic Legendrians topologically isotopic to the n-twist knot in Lens spaces than in S3. New knots are found to be non-simple in Legendrian contact geometry.
problem Identifying non-simple Legendrian knots in contact geometry.
method Utilized knot Floer homology and the distinguished surgery triangle.
result Whitehead doubles of the trefoil are Legendrian non-simple.
Stabilization operation for high-dimensional contact manifolds, proving many links are non-simple.
problem Understanding the structure and properties of high-dimensional contact manifolds.
method Definition and proof of stabilization operation for codimension 2 contact submanifolds in dim≥5 contact manifolds. result Many transverse links are non-simple.
Study shows how oil and forex markets are connected, with monetary policy affecting forex volatility.
problem Understanding connectedness between oil and forex markets.
method High-frequency intra-day data, variance decompositions, realized semivariances.
result Adding oil to a forex portfolio decreases total connectedness, but asymmetries and frequency connectedness are relatively small.
Study ping-pong dynamics in hyperbolic-like groups with non-simple points.
problem Investigate the ping-pong dynamics of hyperbolic-like groups.
method Explicitly provide a proper ping-pong partition for any pair of non-cyclic point stabilizers.
result Existence of a proper ping-pong partition for any pair of non-cyclic point stabilizers.
Easy condition for local k-connectedness in inverse limits of polyhedra.
problem Local k-connectedness of inverse limits of polyhedra.
method Easy condition for local k-connectedness.
result Provided an easily verifiable condition.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.
We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot …
New infinite series of hyperbolic polytopes with special growth rates found.
problem Finding new infinite series of non-compact hyperbolic polytopes.
method Constructing infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes.
result Growth rates of the constructed polytopes are Perron numbers.
We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most L grows exponentially in L. We get exponentially tighter bounds given…
Given a one-dimensional homology class in a lens space, a question related to the Berge conjecture on lens space surgeries is to determine all knots realizing the minimal rational genus of all knots in this homology class. It is known that simple knots are rational genus minimizers. In this paper, we construct many non…
Retrospective and prospective analysis of Diebold-Yilmaz connectedness research.
problem Assessing the Diebold-Yilmaz approach to dynamic network connectedness.
method Retrospective and prospective analysis of Diebold-Yilmaz (2014) and personal recollections.
result Personal insights and retrospective analysis of Diebold-Yilmaz connectedness research.
We propose a new framework for measuring connectedness among financial variables that arises due to heterogeneous frequency responses to shocks. To estimate connectedness in short-, medium-, and long-term financial cycles, we introduce a framework based on the spectral representation of variance decompositions. In an e…
Study examines grain futures connectedness during Russia-Ukraine conflict.
problem Quantile return connectedness of grain futures markets during geopolitical instability.
method Dynamic quantile VAR combined with frequency-domain decomposition.
result Heterogeneous spillovers across quantiles, with strong transmitters and persistent receivers.
We find the shape of the Donaldson invariants of a 4-manifold with b_1=0 and b^+>1, which may be not of simple type. The invariants appear as the q^0 coefficient of a expression given in terms of modular forms (as was predicted by Moore and Witten). We re-express the formula using complete elliptic integrals to prove a…
Study shortest non-simple geodesics on 2-orbifolds, finding unique shortest curve.
problem Finding shortest non-simple closed geodesics disjoint from orbifold points.
method Fundamental domains and hyperbolic trigonometry.
result Identified and classified all figure eight geodesics on triangle group orbifolds.
Study on geodesics on high genus expander surfaces, proving filling and non-simple properties.
problem Properties of geodesics on expander surfaces of high genus.
method Adapting Margulis' counting strategy to low length scales.
result Almost every geodesic of certain lengths is filling or non-simple.
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and some non-simple m…
The paper connects curvature positivity to rational connectedness in complex geometry.
problem Establishing a geometric criterion for rational connectedness.
method Uhlenbeck-Yau's continuity method applied to mean curvature positivity.
result Holomorphic tangent bundle mean curvature positivity is equivalent to rational connectedness of compact Kähler manifolds.
Study shows connectedness of Bowditch boundary persists in long Dehn fillings.
problem Persistence of Bowditch boundary connectedness in Dehn fillings.
method Analysis of relatively hyperbolic group pairs and peripheral subgroups.
result Connectedness of Bowditch boundary persists in sufficiently long Dehn fillings without needing restrictions.
This paper develops a new portfolio optimization framework that considers network spillovers.
problem Modern financial markets' complex interconnections are not fully captured by variance alone.
method Formulates a three-objective optimization problem with a quadratic measure of network spillovers.
result Establishes a three-dimensional efficient surface and a risk-risk frontier.
The paper studies complexes of hypersurfaces in homology classes and proves their connectedness and simple connectedness.
problem Investigating complexes of hypersurfaces in homology classes and proving their topological properties.
method Defining and analyzing simplicial complexes S†(M,φ) and T†(M,φ) for properly embedded hypersurfaces in n-manifolds, proving connectedness and simple connectedness. result Proves connectedness and simple connectedness of the complexes S†(M,φ) and T†(M,φ). Connectedness proved for Zd actions on 1D manifolds by C2 diffeomorphisms.
problem Connectedness of Zd actions by C2 diffeomorphisms on 1D manifolds. method Proved connectedness through continuous paths of C1+ac diffeomorphisms. result Connectedness of Zd actions by C2 diffeomorphisms on 1D manifolds. We prove that transversal non-simplicity is preserved under taking connect sum, generalizing Vertesi's result.
New conditions ensure geodesic connectedness of affine manifolds.
problem Ensuring geodesic connectedness in affine manifolds.
method New sufficient conditions for geodesic connectedness, weaker than previous work.
result Elementary proof of geodesic connectedness.
Connectedness constraint for sparse graph learning.
problem Learning sparse graphs often results in disconnected components.
method Formulated connectedness as a convex constraint.
result Connected sparse graphs can be learned from data.
In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.
This study analyzes dynamic connectedness in global supply chain infrastructure portfolios, identifying key risk factors and extreme events.
problem Understanding dynamic connectedness in global supply chain infrastructure portfolios under various risk factors and extreme events.
method Time-varying parameter vector autoregression (TVP-VAR) model to study spillover and interconnectedness of risk factors.
result Risk shocks influence dynamic connectedness between portfolios and risk factors, and extreme events affect investment outcomes.
Clusters on simple manifolds have connected boundaries.
problem Understanding the connectedness of boundaries of isoperimetric clusters.
method Analyzing isoperimetric clusters on simply connected homogeneous Riemannian manifolds.
result Clusters on such manifolds have connected boundaries.
We study the connectedness of the planar self-affine sets T(A,D) generated by an integer expanding matrix A with ∣det(A)∣=3 and a non-collinear digit set D={0,v,kAv} where k∈Z∖{0} and v∈Z2 such that {v,Av} is linearly independent. By chec…
A game on diagrams switches crossing directions to achieve connectedness.
problem Achieving connectedness in diagrams through crossing switches.
method Players switch crossing directions on regions of a diagram to achieve connectedness.
result Connectedness can be achieved through strategic crossing switches.
Work consists of introduction, two chapters, conclusion and four applications. In this work is examined the condition, with which the wave space metrics of Riemann- Cartan is the solution of Einstein equation in the void. Geometric structures were for this purpose studied on the differentiated variety: connectedness, c…
Connectedness of small clusters in Riemannian and Finsler manifolds proven.
problem Understanding connectedness of small clusters in Riemannian and Finsler manifolds.
method Proved connectedness and small diameter properties for clusters of small volume in both manifolds.
result Clusters in Riemannian manifolds are connected and have small diameter; in Finsler manifolds, they are at most m connected components of small diameter.
Develops a new framework to measure network connectedness across and within markets.
problem Lack of flexible methods to measure network connectedness and its evolution.
method Allows network nodes to be connected in clusters, with shocks orthogonal across clusters and correlated within clusters.
result Demonstrates the effectiveness of the new framework in a detailed empirical analysis of equity markets.
Graph conditions ensure matching arc complexes are connected and hyperbolic.
problem Conditions for connectedness and hyperbolicity of matching arc complexes.
method Conditions on finite simplicial graphs guaranteeing connectedness and hyperbolicity of matching arc complexes.
result Conditions on finite simplicial graphs ensure connectedness and hyperbolicity of matching arc complexes.
A motif-based framework identifies local spillover structures in financial markets.
problem Aggregate risk spillovers obscure local interaction patterns in systemic risk.
method Develops a motif-based framework using multiscale backbones and colored motifs.
result Motif-based portfolios outperform traditional benchmarks on risk-adjusted returns.
Paper measures asymmetric fear network connectedness for risk prediction.
problem Predicting macroeconomic conditions and economic uncertainty.
method Forward-looking measures from bank option prices.
result Asymmetric network structure predicts economic conditions.
New proof shows path-connectedness of actions on intervals and circles.
problem Path-connectedness of C1+ac actions of Zd. method New proof using C1 diffeomorphisms with absolutely continuous derivative. result Path-connectedness of the space of actions.
It is investigated Hurwitz numbers, that correspond to covering of disk with single non-simple boundary critical value. It is found differential equations, that describe a generating function for these numbers.
Study shows regional banking uncertainty spillovers over 10 years.
problem Understanding uncertainty spillovers between regional banking systems.
method Improved Diebold-Yilmaz method using daily returns and ridge regularization.
result Regional uncertainty is significantly causally related, with North America influencing EU and ASEAN.