Proposes a constraint for deep clustering to handle both simple and complex topologies.
problem Limited prior knowledge for deep clustering methods to perform well on complex topologies.
method Introduces a constraint using symmetric InfoNCE to enhance deep clustering performance.
result The constraint improves deep clustering methods' performance on both simple and complex topologies.
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.
Defines constraint tensor for null hypersurfaces, providing explicit geometry.
problem Defining constraint tensor for null hypersurfaces with any topology.
method Explicit definition in extrinsic geometry, covariant for any topology.
result Simple form of constraint tensor on transverse submanifolds.
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.
Study on constraints for topological and smooth realizations of line arrangements and configurations.
problem Investigating constraints on topological and smooth realizations of combinatorial line arrangements and (nk)-configurations. method Exploring constraints via locally-flatly or smoothly embedded 2-spheres, using Furuta's 10/8-Theorem, and G-signature theorem.
result Established a new lower bound for (nk)-configurations, showing n≥k2−5 for topological realizations. Method optimizes knotting pathways in constrained polymers.
problem Understanding how geometric constraints affect knot formation in polymers.
method Topological steering using knotoid spectrum and mean unravelling number.
result Geometric constraints increase the frequency of twist knots in polymers.
Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.
problem Preserving Hermitian-symplectic structures under pluriclosed flow.
method Consideration of an extra evolution equation determined by the Bismut-Ricci form.
result Obtained topological obstruction to long-time existence in arbitrary dimensions.
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…
Study shows only two topological configurations for Spin(7)-manifold fibrations, ruling out smooth Cayley fibrations.
problem Understanding smooth fibrations of compact Spin(7)-manifolds by Cayley submanifolds.
method Geometric and topological constraints from Spin(7)-structure, spinnability criterion, gauge-theoretic input.
result Rules out smooth Cayley fibrations on all known compact torsion-free Spin(7)-manifolds.
New unknots with geometric constraints exist, proving a long-standing conjecture.
problem Existence of distinct isotopy classes of physical unknots with geometric constraints.
method Parametrised thickness and geometric thresholds to fragment isotopy classes.
result Existence of gordian unknots with prescribed geometric constraints.
Study on packing links with geometric constraints.
problem Maximizing link density in space with geometric restrictions.
method Investigates packing essential links within Euclidean space.
result Upper bounds on maximal density are found, but are large.
Bayesian method infers transition matrices from incomplete graph data with topological constraints.
problem Inference of transition matrices from incomplete graph data with topological constraints.
method Bayesian approach using repeated interactions and a topological prior.
result Higher accuracy in inferring transition probabilities, improving downstream tasks.
We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal representations before a linear classifier. Specifically, we impose a topological …
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
HLTF generates chemically valid 3D molecules with improved topology control.
problem Generating chemically valid 3D molecules is challenging due to bond topology errors.
method HLTF uses a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures.
result HLTF achieves high validity and uniqueness on QM9 and GEOM-DRUGS datasets.
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
Study rigidifies torus bundles under first Betti number constraints.
problem Understanding the structure of torus fibrations under first Betti number restrictions.
method Established rigidity results and necessary/sufficient conditions for topological splitting.
result Classification of torus bundles under specific Betti number constraints.
The paper studies constraint maps with singularities and free boundaries, proving continuity near singularities and optimality.
problem Analyzing the structure of constraint maps with singularities and free boundaries.
method Establish continuity near singularities using a new quantitative unique continuation principle, and investigate the presence of branch points leading to new singularities.
result Topological singularities can only lie in the interior of the contact set in the uniformly convex setting, and the optimality of this result is proven.
Study topological constraints for minimal hyperbolic surface laminations.
problem Understanding which topological surfaces can be leaves in minimal hyperbolic surface laminations.
method Analyzes topological obstructions and embeddings of Cantor tree-like surfaces.
result All possible topological types of leaves can be simultaneously embedded in a lamination.
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold to an asymptotically Euclidean solution of the constraints on R^n. Fo…
When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and continuous with a continuous inverse. Using topological arguments, we show that wh…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with s>23. The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped st…
New algorithm optimizes DAGs by swapping node pairs to avoid cycles.
problem Optimizing DAGs with non-convex constraints to avoid cycles.
method Bi-level algorithm with iterative node swaps and off-the-shelf solvers.
result Guaranteed to find local minima or KKT points with lower scores.
A new method for predicting uncertainties in stream networks.
problem Uncertainty quantification in spatiotemporal graphs with directional flow constraints.
method Spatio-Temporal Adaptive Conformal Inference (STACI) integrating network topology and temporal dynamics.
result STACI effectively balances prediction efficiency and coverage, outperforming existing methods.
We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.
We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.
We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …
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.
The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.
problem Estimating Laplacian matrices with structural constraints and sparsity.
method Linear reparametrization and closed-form expressions for Cramer-Rao bounds tailored to Laplacian matrix estimation.
result The derived CRBs provide performance limits for Laplacian matrix estimation and are validated in various applications.
Consider an effective Hamiltonian torus action T×M→M on a topologically twisted,generalized complex manifold M of dimension 2n. We prove that the rank(T)≤n−2 and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying $rank(T) =…
We derive the Space-Time Positive Mass theorem in arbitrary dimensions, without topological constraints. The main new tools are skin structures and surgeries on minimal and marginally outer trapped hypersurfaces.
Paper proves a new criterion for time-like geodesics in flat spacetimes.
problem Existence and nature of time-like geodesics in asymptotically flat spacetimes.
method Generalized topological criterion using the Jordan-Brouwer Separation Theorem and differential geometry.
result Conclusively affirms the presence of time-like geodesics intersecting transversally.
Study confirms Chern's conjecture on compact Hessian manifolds and classifies their topologies.
problem Global topological constraints and structural properties of compact Hessian manifolds.
method Novel fibration and splitting theorems, Chern's conjecture, Hitchin systems, Cheng-Yau solution.
result Topological classification of complete Hessian surfaces and closed orientable Hessian 3-manifolds.
Study on surfaces minimizing elastic energy with boundary constraints.
problem Finding stable configurations of surfaces with elastic boundaries and surface energy.
method Investigation of critical surfaces with mean curvature and spontaneous curvature, coupled to boundary elastic energy.
result Characterization and minimization of surface energy for specific topological shapes.
A new algorithm infers causal networks from data using topological thresholds.
problem Inferring causal networks from data.
method Two methods for determining topological thresholds: one to leave no disconnected nodes, the other to find a causal large connected component.
result The novel algorithm is faster and more accurate than the PC algorithm.
DMT enhances deep neural networks to better preserve data structures.
problem Preserving geometric, topological, and distributional structures of data in NLDR.
method Deep manifold transformation (DMT) using cross-layer LGP constraints.
result DMT networks outperform existing NLDR methods in preserving data structures.
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…
The study examines Eschenburg orbifolds with positive sectional curvature and their geometric/topological properties.
problem Understanding the geometric and topological constraints of positively curved Eschenburg orbifolds.
method Proved restrictions on singular sets and computed orbifold cohomology rings.
result Distinctive behavior in cohomology groups of positively curved Eschenburg orbifolds.
Decussation improves robustness of 3D neural networks.
problem Understanding the functional advantage of decussation in neural wiring.
method Examined constraints of topology on 3D wiring.
result Decussated arrangements are more robust against wiring errors than same-sided schemes.
Study on spherical CR manifolds with non-trivial Chern classes.
problem Understanding Chern classes in spherical CR manifolds.
method Construction and proof of constraints on Chern classes.
result Topological obstruction to spherical CR structures on contact manifolds.
The paper establishes a connection between force-free fields and conformally geodesic fields.
problem Understanding the relationship between force-free fields and conformally geodesic fields.
method Developed an equivalence between force-free fields and conformally geodesic fields, generalized to arbitrary dimensions.
result Established that stationary points of hierarchies of L2 and L1-optimization problems are related by a conformal change of metric. 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.
Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and are identical to that of a suitable Kerr slice (or identical to a member of som…
We obtain constraints on the topology of families of smooth 4-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation of Donaldson's diagonalisation theorem and Furuta's 10/8 theorem. As an appli…
This paper characterizes stable polynomial mappings in a specific set.
problem Characterizing stable polynomial mappings in a given set.
method Analyzing polynomial mappings with specific degrees and determining topological equivalence.
result Effective determination of mappings with generic topology.
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum margin Markov networks. The main difficulty is that the parameters in a Bayesian ne…
The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
problem Proving finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.
method The approach removes constraints of sectional curvature or conjugate radius and extends to previous related studies.
result Theorems are proven for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume, without the need for triangle comparison of Toponogov type.