We show that all non-trivial continuous endomorphisms of the circle group are topologically mixing. We also show that there exists a large infinite class of continuous endomorphisms of any n-dimensional torus group which are topologically mixing. Lastly, we prove that any continuous endomorphism on an abelian polish se…
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48 results for “Mixed topology”
Characterizes continuity of monotone functionals in mixed topology.
problem Continuity of monotone functionals in mixed topology.
method Characterization through lower semicontinuity and dual representations.
result Continuity in mixed topology is equivalent to dual representation in terms of countably additive measures.
Geodesic flow mixing on convex projective manifolds proven.
problem Understanding mixing properties of geodesic flow on convex projective manifolds.
method Introduced biproximal unit tangent bundle and proved mixing properties.
result Geodesic flow is topologically mixing on biproximal unit tangent bundle.
New method detects essential tori in mixed singularity links.
problem Detecting essential tori in mixed singularity link complements.
method Analyzing properties of defining mixed polynomials.
result Explicit criteria for essential tori existence.
Maximizes mixing efficiency in surface braids.
problem Finding the maximum mixing efficiency in surface braids.
method Introduced an efficient algorithm to compute topological entropy and TEPO for surface braids.
result Conjectured a novel candidate braid to have maximal mixing efficiency.
Study on singularities of specific polynomial functions.
problem Characterizing the topology of singularities of mixed functions.
method Introduced inner non-degenerate mixed functions and used Newton boundary to characterize links.
result Links of singularities can be completely characterized under certain conditions.
If X is a proper CAT(-1)-space and a non-elementary discrete group of isometries acting properly discontinuously on X, it is shown that the geodesic flow on the quotient space Y=X/ is topologically mixing, provided that the generalized Busemann function has zeros on the boundary and the non-wanderin…
Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-spacemath.DG
We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.
Mixing of the Mineyev flow, orbital counting and Poincaré series for strongly hyperbolic metricsmath.DS
Study on counting orbits and Poincaré series for specific hyperbolic metrics.
problem Counting orbits and analyzing Poincaré series for strongly hyperbolic metrics.
method Combining ergodic theory techniques with topological flows and symbolic dynamics.
result Obtained orbital counting results and described the domain of analyticity for Poincaré series.
Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4-manifoldsmath.DG
The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fun…
In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low dimensional topological map for each of them. When it is trained as an autoencoder, th…
Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Boundmath.DG
Study quantifies geometric complexity of connections on product surfaces.
problem Understanding geometric complexity of connections on product manifolds.
method Establishes a topological lower bound on the holonomy of cohomologically calibrated connections.
result Proves a bound on the dimension of the holonomy that is a topological invariant.
We provide a measure based topology for certain unions of C2 rectifiable submanifolds of mixed dimensions in Rn. In this topology lower dimensional sets remain in the limit as measures when higher dimensional sets collapse down to them. For example a decreasing sequence of spheres may have a limit consisting of just a …
A new framework uses an Incremental Transformer to design geopolymer mixtures efficiently.
problem Designing geopolymer mixtures with limited data and physical constraints.
method Topology-aware surrogate framework guided by Incremental Transformer.
result The design space is redundant, with fewer effective mixture regimes.
We consider curvature flows in hyperbolic space with a monotone, symmetric, homogeneous of degree 1 curvature function F. Furthermore we assume F to be either concave and inverse concave or convex. For compact initial hypersurfaces, which are strictly convex by horospheres, we show the long time existence of mixed volu…
An asset network systemic risk (ANWSER) model is presented to investigate the impact of how shadow banks are intermingled in a financial system on the severity of financial contagion. Particularly, the focus of this study is the impact of the following three representative topologies of an interbank loan network betwee…
Proves hyperbolic 3-manifolds have angle structures under certain conditions.
problem Proving angle structures for non-compact hyperbolic 3-manifolds.
method Subdividing ideal polyhedral decompositions and applying topological conditions.
result Proves existence of ideal triangulations with angle structures.
Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed l…
Enhances topology optimization with multiclass microstructures using latent variable Gaussian process.
problem Lack of an inherent ordering or distance measure between different classes of microstructures.
method Extended latent-variable Gaussian process (LVGP) models to multi-response LVGP (MR-LVGP) models for metamaterials.
result Improved performance through consistent load-transfer paths for micro- and macro-structures.
Improves decentralized learning by optimizing graph mixing for data heterogeneity.
problem Data heterogeneity impacts convergence in decentralized learning, but existing methods ignore this.
method Characterized and quantified the relationship between graph mixing and data heterogeneity. Proposed an optimization approach to improve convergence.
result Our approach leads to improved test performance across various tasks.
Study bi-Lipschitz equivalence of mixed polynomials under specific conditions.
problem Classify bi-Lipschitz equivalence of mixed polynomials with inner non-degeneracy.
method Defined metric links and introduced new data to determine bi-Lipschitz equivalence.
result Neither Newton boundary nor C-face diagram is an invariant for bi-Lipschitz equivalence.
We construct triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space, with the same topology as the triply periodic minimal surfaces in the Euclidean 3-space, called Schwarz rPD surfaces.
Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.
problem Analyzing geodesic flows on compact manifolds without conjugate points and with visibility universal covering.
method Using topological mixing, local product structure, and properties of geodesic flows, the authors prove the existence of an expansive factor and uniqueness of measure of maximal entropy.
result The geodesic flow on compact manifolds without conjugate points has a unique measure of maximal entropy.
The paper finds pseudo-Anosov-like maps on an infinite ladder surface.
problem Exploring dynamics on infinite surfaces.
method Lifts Penner-type pseudo-Anosov maps from a closed surface to an infinite ladder surface.
result Existence and properties of pseudo-Anosov-like maps on the infinite ladder surface.
We show that if K is any knot whose Ozsvath-Szabo concordance invariant tau(K) is positive, the all-positive Whitehead double of any iterated Bing double of K is topologically but not smoothly slice. We also show that the all-positive Whitehead double of any iterated Bing double of the Hopf link (e.g., the all-positive…
Study on moduli spaces of Higgs bundles over Abelian varieties, focusing on their topology and polynomials.
problem Determine the topology and polynomials of moduli spaces of Higgs bundles over Abelian varieties.
method Analyzing the Poincaré polynomials and mixed Hodge polynomials of moduli spaces for various groups G and dimensions d.
result Explicit formulas for Poincaré polynomials and mixed Hodge polynomials in specific cases, including rank 2 and 3 Higgs bundles.
Study local topological constraints on Berry curvature in spin-orbit coupled Bose-Einstein condensates.
problem Understanding local topological obstructions to flattening Berry curvature in spin-orbit-coupled Bose-Einstein condensates.
method Adapting Pigazzini-Toda lower bound to Kaluza-Klein setting, analyzing harmonic part of torsion 3-form, and using exact pointwise curvature analysis.
result Obstruction kernel vanishes, preventing complete gauging-away of Berry phases even at zero net topological charge.
We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of constraints compared to popular MIP models based on cycle elimination constraint…
Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen-Margulis' measure finiteness assumption used in recent work of Ricks is removed. We also construct examples of CAT(0) spaces which do not admit finite Bowen-Margulis measure.
Unified framework for stability and generalization of Push-Sum in decentralized learning over directed graphs.
problem Understanding stability and generalization of Push-Sum in decentralized learning over directed networks.
method Developed a unified uniform-stability framework for SGP algorithm, incorporating imbalance-aware consistency bounds.
result Established finite-iteration stability and optimization guarantees for convex and non-convex objectives.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
Wealth Dynamics on Complex Networkscond-mat.dis-nn
We study a model of wealth dynamics [Bouchaud and Mézard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a ful…
In neuroimaging data analysis, Gaussian graphical models are often used to model statistical dependencies across spatially remote brain regions known as functional connectivity. Typically, data is collected across a cohort of subjects and the scientific objectives consist of estimating population and subject-specific g…
Study uses graph techniques to understand meromorphic quadratic differential strata.
problem Understanding the topology of meromorphic quadratic differential strata.
method Exchange graph techniques to study fundamental groups; generalizes relations for mixed-angulations.
result Explicit presentations of fundamental groups in genus-zero case with four singularities.
Sharp rates found for learning with dependent data, avoiding sample size deflation.
problem Learning with dependent data and square loss.
method Combining weak sub-Gaussian class and mixed tail generic chaining.
result Achieves a rate that only depends on class complexity and second order statistics.
In this paper we show that, after completing in the -adic topology, the Turaev cobracket on the vector space freely generated by the closed geodesics on a smooth, complex algebraic curve with an algebraic framing is a morphism of mixed Hodge structure. We combine this with results of a previous paper (arXiv:1710…
Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of layers, each of which applies a graph convolution, followed by a pointwise nonlinea…
In this paper, we give an equivariant compactification of the space PFlat(S) of homothety classes of half-translation structures on a compact, connected, orientable surface S. We introduce the space PMix(S) of homothety classes of mixed structures on S, that are CAT(0) tree-graded spaces in the sense of Drutu and Sapir…
New algorithm disentangles latent features without strict assumptions.
problem Disentangling complex data-generating mechanisms into causally interpretable latent features.
method Linear CRL algorithm with topological ordering, pruning, and disentanglement.
result Recovering latent causal features up to an equivalence class under weaker assumptions.
We prove that the (-weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant introduced by Manolescu and the first author in [CM19] is generically independent of the parameter and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked in [CM19]. Our arguments inv…
The Index of Some Mixed Order Dirac-Type Operators and Generalised Dirichlet-Neumann Tensor Fieldsmath.FA
Computes indices of mixed order Dirac-type operators and related tensor fields.
problem Computing indices of mixed order Dirac-type operators and tensor fields.
method Using Hilbert complexes and differential operators of mixed order, computing indices with cohomology groups of tensor fields.
result Computation of indices for elasticity and biharmonic complexes.
The paper studies the convergence of SAA for systemic risk measures.
problem Theoretical convergence of SAA for set-valued systemic risk measures.
method General theory and specific case study with mixed-integer programming formulations.
result Theoretical convergence results for SAA under Wijsman and Hausdorff topologies.
New K-theory approach classifies anyonic topological phases in 2D semimetals.
problem Classifying interacting topological phases remains open.
method TED K-theory of configuration spaces of points in the Brillouin torus.
result Classifies su(2)-anyonic topological order in 2D semimetals.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
Framework for joint inference of network topology and interaction types in heterogeneous systems.
problem Joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems.
method Three-stage approach: shared structure recovery, discrete interaction type identification, and matrix factorization.
result The method yields accurate reconstruction of underlying dynamics and is robust to noise.
In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …
Study non-semisimple TQFT for Burau representation density and unitarity.
problem Density and unitarity of the Burau representation from a non-semisimple TQFT perspective.
method TQFT construction of Squier's Hermitian form on the Burau representation.
result Density of the image of braid group in unitary representations.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
problem Capturing topological inductive biases in machine learning models.
method Proposes Gaussian processes on cellular complexes, introducing novel kernels.
result Derives two novel kernels for modeling interactions between cells.