CMRFs extend PGMs for topological data, capturing both conditional and marginal dependencies.
problem Limited expressiveness of PGMs for topological data.
method Introducing Colored Markov Random Fields (CMRFs) that model Gaussian edge variables on topological spaces.
result CMRFs improve distributed estimation over physical networks compared to baselines.
In this paper we show that topological subgroupoids of Lie groupoids, under special circumstances are Lie subgroupoids. Giving an example, we indicate that having the same topological dimension is a necessary condition for topological subgroupoids to be Lie subgroupoids. Also, we provide some conditions for double subg…
Paper tackles dynamic behavior of variable topology mechanisms, presenting new transition conditions.
problem Dynamic behavior of mechanisms with changing kinematic topology.
method Presented new transition conditions for variable topology mechanisms using projected motion equations and Voronets equations.
result Results show the dynamic behavior of joint locking in 3R and 6DOF mechanisms.
The study finds conditions for nonmaximal topological complexity of manifolds with abelian fundamental groups.
problem Conditions for nonmaximal topological complexity of manifolds with abelian fundamental groups.
method Analyzes conditions and examples to generalize results on topological complexity and Lusternik-Schnirelmann category.
result Generalizes results on topological complexity and Lusternik-Schnirelmann category for manifolds with abelian fundamental groups.
The paper explores conditions for topological rigidity in quotients of the Davis complex.
problem Understanding when quotients of the Davis complex are topologically rigid.
method Analyzing quotients of the Davis complex of right-angled Coxeter groups and conditions on defining graphs.
result Introduction of infinitely many infinite topologically rigid subclasses.
New Milnor's invariant condition for topologically slice links.
problem Conditions for topologically slice links involving Milnor's invariant.
method Different Milnor's invariant condition to handle cases not covered by previous theorem.
result New sufficient conditions for topologically slice links.
This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations…
In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are…
Generalizes sigma model with Lie algebroid structure and geometric conditions.
problem Consistency of constraints and gauge symmetry in topological sigma models.
method Analysis of geometric conditions and constraints in Hamiltonian and Lagrangian formalisms.
result Identifies universal compatibility condition between Lie algebroid and multi-symplectic structure.
We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergro…
Sharp pinching conditions restrict the geometry and topology of submanifolds.
problem Understanding submanifolds under pinching conditions in arbitrary Riemannian manifolds.
method Analyzing submanifolds with pinching conditions involving second fundamental form and mean curvature.
result The pinching condition imposes strong geometric and topological restrictions on submanifolds.
Enhanced neural network framework improves constraint satisfaction with topological conditioning.
problem Maintaining semantic coherence while satisfying physical and logical constraints in neuro-symbolic reasoning.
method Integrates topological conditioning with gradient stabilization mechanisms using Forman-Ricci curvature, Deep Delta Learning, and Covariance Matrix Adaptation Evolution Strategy.
result Achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate.
Proposes a new metric space example showing non-constant topological dimension.
problem Non-constant topological dimension in metric measure spaces.
method Refines Ketterer and Rajala's example to satisfy CD(0,∞) condition.
result Shows non-constancy of topological dimension for CD spaces.
Topological anomaly scores predict return curves in S&P 500 stocks
problem Detecting anomalies in financial time series
method BallMapper, decoder-conditional VAE, Function-on-Function regression
result Anomaly history carries predictive content for return curves
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the (ε,λ)--topology and the locally L0-- convex topolo…
We give necessary and sufficient topological conditions for the existence of an irreducible SO(3)-structure on a 5-manifold. Using these conditions we provide some new examples of 5-manifolds with an irreducible SO(3)-structure.
Authors classify 3D locally standard T-pseudomanifolds under weaker conditions.
problem Classifying equivariant homeomorphism types of 3D locally standard T-pseudomanifolds.
method Introduced and classified by characteristic data under homotopy equivalence condition.
result Condition for classification can be removed when dimension is at most three.
Detect anomalies in complex networks using topological subspace detectors.
problem Detect anomalies in complex networks defined by simplicial complexes.
method Formulate a hypothesis testing framework using Neyman-Pearson matched topological subspace detectors.
result Effective detection of anomalies in foreign currency exchange networks and other real-world data.
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.
Paper classifies structures on 5D manifolds with specific rank and conditions.
problem Classifying tangent distributions on 5D manifolds.
method Established necessary and sufficient topological condition for existence.
result Classification of structures up to homotopy as formal Cartan distributions.
Minimal volume entropy vanishes or is positive under certain fiber growth conditions.
problem Conditions for minimal volume entropy to be zero or positive.
method Analyzes topological conditions related to fiber growth of maps.
result Examples of finite simplicial complexes with zero simplicial volume and large minimal volume entropy.
We show that many Lorentzian manifolds of dimension >2 do not admit a spacelike codimension-one foliation, and that almost every manifold of dimension >2 which admits a Lorentzian metric at all admits one which satisfies the dominant energy condition and the timelike convergence condition. These two seemingly unrelated…
Sharp conditions link separators to R-trees for space transformations.
problem Conditions for separators to form R-trees under group actions.
method Sharp conditions linking separators to R-trees for space transformations.
result Sharp conditions linking separators to R-trees for space transformations.
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.
Paper defines topology automaton for Barański carpets and proves Hölder equivalence conditions.
problem Tackles Hölder equivalence of Barański carpets.
method Defines topology automaton and applies method from previous studies.
result Obtains sufficient condition for Hölder equivalence of Barański carpets.
Paper introduces TVaRD, a new topological risk measure for financial portfolios.
problem Traditional risk measures like VaR and CVaR are insufficient for complex market conditions.
method Topological data analysis (TDA) using cohomology groups on financial time series data.
result TVaRD reveals significant changes in financial time series during stress conditions.
The paper formalizes robot environments using topological concepts.
problem Determining indistinguishable environments for robots.
method Formalizing robot systems as topological dynamical systems, using covering maps and bisimulation.
result Covering maps can witness indistinguishability of environments under general conditions.
Proves simple type conjecture for mod 2 Seiberg-Witten invariants.
problem Proving simple type conjecture for mod 2 Seiberg-Witten invariants.
method Analyzes cohomology ring conditions to prove simple type for all smooth structures.
result Shows existence of topological 4-manifolds with mod 2 simple type.
We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups. We show that the profinite topology of the above group is strongly connected wit…
This study examines the topology of singularities in optimal semicouplings between unequal spaces.
problem Topology of singularities in optimal semicouplings between unequal spaces.
method Continuous strong deformation retracts and Uniform Halfspace condition.
result Homotopy-reductions from a source space onto singularities of c-optimal semicouplings. We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective ho…
Paper finds conditions for two geodesics on complex manifolds.
problem Existence of two distinct closed geodesics on manifolds with infinite fundamental group.
method Topological and metric conditions for existence of geodesics in Riemannian and Finsler metrics.
result Generic Finsler metrics have two distinct closed geodesics.
Bayesian networks are typically faithful, with implications for causal inference.
problem Determining the typicality of faithfulness in Bayesian networks.
method Analysis of Bayesian networks over a given DAG, parametrized by conditional exponential families, and nonparametric conditional densities.
result The faithful Bayesian networks are dense and open with respect to the total variation metric, extending existing results for specific classes of Bayesian networks.
Study shows conditions for continuity of foliated homeomorphisms action on space of leaves.
problem Conditions for continuity of foliated homeomorphisms action on space of leaves.
method Investigated sufficient conditions for continuity of the homomorphism ψ: H(X, Δ) → H(Y) induced by the action of foliated homeomorphisms on the space of leaves.
result Similar results hold for a more general class of partitions of locally compact Hausdorff spaces.
Study shows curvature constraints force submanifolds to have specific topology or geometry.
problem Curvature constraints on submanifolds in nonnegative curvature spaces.
method Investigates submanifolds with lower bounds on sectional curvature and mean curvature.
result Curvature constraints force submanifolds to have specific topology or geometry.
We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally alternating. We also give a topological characterization of almost-alternating knots whi…
This paper clarifies a global structure of Stokes-Dirac structures used for describing interconnected port-Hamiltonian systems defined on manifolds with non-trivial topology under consistent boundary condition.
Simple condition proves when 2-bridge knots are quasipositive.
problem Characterizing quasipositive two-bridge knots.
method Continued fraction expansion of p/q to prove a necessary and sufficient condition.
result Simple condition proves when 2-bridge knots are quasipositive.
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise c…
The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.
problem Extending Penrose's singularity theorem and Hawking's topology theorem to weighted spacetimes.
method Using weighted null energy condition and synthetic dimension to generalize the theorems.
result Generalized versions of the Penrose and Hawking theorems hold under a weighted null energy condition.
For Riem(M) the space of Riemannian metrics over a compact 3-manifold without boundary M, we study topological properties of the dense open subspace Riem'(M) of metrics which possess no Killing vectors. Given the stratification of Riem(M), we work under the condition that, in a sense defined in the text, the connecte…
By means of color chord diagrams we establish a necessary and sufficient condition for O-topological equivalence of functions with one essentially critical point on oriented surfaces with edge. We also calculate the number of O-topologically non-equivalent functions with one essentially critical point on oriented s…
We present sufficient conditions for topological stability of continuous functions f:R→R having finitely many local extrema with respect to averagings by discrete measures with finite supports.
The abstract applies waist inequality to dynamical systems and entropy.
problem Understanding the relationship between waist inequality and dynamical systems.
method Applying waist inequality to entropy and mean dimension of dynamical systems.
result Maps between dynamical systems have positive conditional metric mean dimension under certain conditions.
Mathematical approach defines stability conditions for ML models.
problem Ensuring stability of machine learning models.
method Adopted topological and metric spaces theory to define stability.
result Stability of ML models depends on topological properties of classification sets.
Revisit Fenn's table theorem from a differential-topological perspective.
problem Prove zero-existence theorem on a cylinder and horizontal square-table theorem under Fenn's boundary conditions.
method Differential-topological approach.
result Prove horizontal square-table theorem under more general boundary conditions.
The study connects curvature operators' positivity to manifold topology.
problem Positivity of curvature operators and their geometric implications.
method Analysis of Garding cones and positivity properties of curvature operators.
result Shifted cone conditions on curvature operators constrain manifold topology.
Study on topological rigidity of ALE vector bundles with specific conditions.
problem Classifying ALE vector bundles with asymptotically conical total spaces.
method Topological classification and geometric analysis of ALE vector bundles.
result Only 2-sphere, projective plane, and open contractible manifolds admit ALE tangent bundles.