We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed orientable irreducible 3-manifold M with nonzero second homol-ogy carries a hyperti…
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48 results for “contact interactions”
Physics-informed GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
Study of contact whirl curves in Sasakian Lorentzian 3-manifolds.
problem Understanding the geometric properties of curves in Lorentzian contact manifolds.
method Introducing and analyzing contact whirl curves, deriving differential equations, and proving rigidity phenomena.
result Every non-geodesic Legendre Frenet curve is a contact whirl curve with constant torsion τ=1.
Characterizes Anosov flows via contact geometry.
problem Understanding Anosov 3-flows through contact geometry.
method Investigates interactions with Reeb dynamics and proves a technical theorem.
result Space of adapted geometries homotopy equivalent to Anosov flows.
Monopole invariant studies contact structures on 3-manifolds.
problem Topology of contact structures on 3-manifolds.
method Generalized Kronheimer--Mrowka--Ozsváth--Szabó contact invariant for families of contact structures.
result Obstructs the existence of sections and detects exotic loops of contact structures.
Study of submanifolds in symplectic and contact manifolds using Hausdorff metrics.
problem Understanding the subtle interactions between submanifolds and metrics in symplectic and contact geometry.
method Applying Hausdorff metric to study sequences of submanifolds and proving metric versions of conjectures.
result Proves metric versions of the nearby Lagrangian conjecture and Viterbo conjecture on spectral norm.
Introduces GFC for learning complex dynamical systems with geometric constraints.
problem Challenges in accurately modeling and predicting complex dynamical systems with geometric constraints.
method Geometric Contact Flows (GFC) using Riemannian and Contact geometry as inductive biases.
result Ensemble of contactomorphisms adapt the latent contact Hamiltonian model to target dynamics while preserving desirable properties.
Silent abandonment reduces contact center efficiency by 5%-15%.
problem Measuring customer abandonment and patience in text-based contact centers is challenging due to uncertainty.
method Developed methodologies to identify silent-abandonment customers and estimate customer patience using text analysis and queueing models.
result Silent abandonment accounts for 30%-67% of customer abandonments and reduces system efficiency by 5%-15%.
We find necessary and sufficient conditions for the bi-Legendrian connection associated to a bi-Legendrian structure on a contact metric manifold being a metric connection and then we give conditions ensuring that coincides with the (generalized) Tanaka-Webster connecti…
Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.
problem Characterizing Einstein metrics in weak β-Kenmotsu manifolds.
method Adapted -Ricci tensor to weak almost contact manifolds and studied its interaction with weak β-Kenmotsu structures.
result New characteristics of Einstein metrics obtained.
Forman--Ricci Curvature on Contact-Sequence Temporal Networks via Spatiotemporal Prism Complexesmath.DG
Study develops curvature for contact-sequence networks, revealing temporal dynamics.
problem Lack of geometric analysis for temporal network sequences.
method Develops Forman--Ricci curvature on spatiotemporal prism complexes.
result Two curvature variants disagree on 56-67% of temporal edges.
Geometric flow on curves in S^3 generates YO equations solutions.
problem Modeling short wave-long wave interaction.
method Simple geometric flow on curves in .
result Constructs transverse curves for YO equations periodic solutions.
A Novel Mathematical Model of Protein Interactions from the Perspective of Electron Delocalizationq-bio.BM
A new model explains protein interactions via electron delocalization.
problem Understanding how protein interactions affect each other.
method Quantized discrete differential geometry of n-simplices.
result Allosteric regulation follows from the model of interactions.
We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with constant negative curvature. This study uses an interaction between Kähler geometr…
Study aims to develop a humanoid robot dialogue system.
problem Current dialogue systems lack attention to non-verbal cues.
method Participated in a competition to develop a system with facial expressions and gaze control.
result Developed a humanoid robot dialogue system.
DIGIT is a low-cost tactile sensor for in-hand manipulation.
problem Difficulty in sensing contact forces limits robotic manipulation.
method DIGIT miniaturizes and improves a vision-based tactile sensor.
result DIGIT enables better control of interactions with the environment.
Improved sample efficiency in reinforcement learning with deep Gaussian processes.
problem Efficiently learn to control actions with limited interaction data.
method Deep Gaussian processes that simulate dynamics with depth and prior knowledge.
result Significantly improved early sample efficiency across various tasks, including half-cheetah control.
We propose an extended public goods interaction model to study the evolution of cooperation in heterogeneous population. The investors are arranged on the well known scale-free type network, the Barabási-Albert model. Each investor is supposed to preferentially distribute capital to pools in its portfolio based on the …
Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because the structure of these interactions matters for spreading processes, the pairwise …
Study on contact Hamiltonian functions for singular contact structures.
problem Understanding infinitesimal contact transformations on singular contact structures.
method Showed injectivity and provided an explicit local formula for the inverse map.
result Explicit local formula for the inverse map when contact structure has singularities of the first type.
The purpose of this article is to study co-dimension iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold iso-contact embeds in a contact manifold provided contact embeds in with a trivial normal bundle and the contact s…
Contact surgery numbersmath.GT
The paper defines and studies contact surgery numbers for contact 3-manifolds.
problem Understanding the minimal number of components of a surgery link describing a contact 3-manifold.
method Defined and studied various versions of contact surgery numbers, relating them to other invariants and computing specific cases.
result There exist infinitely many non-isotopic contact structures on certain manifolds that cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere.
Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifoldsmath.DG
Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.
problem Generalize K-contact and Sasakian manifolds criteria using weak quasi contact metric manifolds.
method Study weak quasi contact metric manifolds and generalize theorems for K-contact and Sasakian manifolds.
result Provide new criterions for K-contact and Sasakian manifolds in terms of curvature tensor and geometric objects.
Simplified construction of contact triad connection for analysis.
problem Analyzing contact instanton equation on contact triads.
method Characterization via almost contact structure and construction using almost contact moving frame.
result Simpler and more canonical construction of contact triad connection.
The paper examines conditions for contact surgeries on rational homology 3-spheres.
problem Conditions for contact surgeries on rational homology 3-spheres.
method Analyzes sufficient conditions for contact surgeries using Legendrian knots and links.
result Provides sufficient conditions for surgeries to have vanishing contact invariants or to be overtwisted.
We study the contact equivalence problem for toric contact structures on -bundles over . That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To f…
Develops scalable differentiable physics for complex object interactions.
problem Limited scalability of existing differentiable physics solvers.
method Adopting meshes for arbitrary geometry, localized collision handling, and accelerated implicit differentiation.
result Significantly reduces memory and computation requirements compared to particle-based methods.
Abstract: Survey on contact submanifolds.
problem Understanding contact submanifolds.
method None specified, survey of existing knowledge.
result Discussion of various contact submanifolds.
New contact structures on folded sums of contact mapping tori are tight under certain conditions.
problem Understanding tight contact structures on folded sums of contact mapping tori.
method Alternative bundle-theoretical construction and gluing process near the fold.
result Folded contact structures on folded sums of contact mapping tori are tight under specific conditions.
Study explores weak generalized K-contact structures in contact metric spaces.
problem Exploring weak generalized K-contact structures in contact metric spaces.
method Introducing a weak condition and proving existence of K-contact and -structures.
result Existence of K-contact and -structures under certain conditions on the Boeckx invariant.
New contact structures detected by contact homology.
problem Detecting pseudo-Anosov flows in contact structures.
method Introducing pseudo-Anosov contact structures and using contact homology.
result Contact homology detects pseudo-Anosov flows and contact structures properties.
Local flatness theorem for paraquaternionic contact structures.
problem Local flatness of paraquaternionic contact manifolds.
method Defined paraquaternionic contact conformal curvature tensor and showed local flatness condition.
result Paraquaternionic contact conformal curvature vanishing implies local flatness.
Aggregation and structural phase transitions of semiflexible polymer bundles: a braided circuit topology approachcond-mat.soft
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
New examples show contact invariants can be non-zero even with half Giroux torsion.
problem Understanding contact invariants and their obstructions in 3-manifolds.
method Use bordered contact invariants and innermost contact structures.
result Found closed contact 3-manifolds with non-vanishing contact invariants.
Survey of contact homology for contact manifolds.
problem Understanding contact manifolds through homology.
method Holomorphic curves invariants.
result Useful for students and young mathematicians.
We consider certain type of fiber bundles with odd dimensional compact contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorphisms of the fiber. We call such fibrations "contact symplectic fibrations". By a result of Hajduk-Walczak, some of these admit contact struc…
Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact structure on any closed orientable 3-manifold is constructed from the standard con…
The paper connects complex contact structures to specific types of almost contact 3-structures.
problem Understanding the relationship between complex contact structures and almost contact 3-structures.
method Proving that every complex contact structure gives rise to a distinguished almost contact metric 3-structure.
result The paper provides new examples of manifolds with specific contact and almost contact structures.
We use multiple measures of graph complexity to evaluate the realism of synthetically-generated networks of human activity, in comparison with several stylized network models as well as a collection of empirical networks from the literature. The synthetic networks are generated by integrating data about human populatio…
The paper constructs contact-hyperbolic manifolds with large automorphism groups.
problem Finding contact-hyperbolic manifolds with large automorphism groups.
method Holomorphic contact structures, pseudometrics, and symplectic quotients.
result Explicit examples of contact-hyperbolic contact manifolds are constructed.
Contact Dual Pairsmath.DG
We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of …
Study contact structures on specific manifolds, proving infinite non-isotopic structures and tight/overtwisted classifications.
problem Classifying contact structures with specific contact surgery numbers on Brieskorn spheres and lens spaces.
method Algorithm for computing Euler class from rational contact surgery, Legendrian knot classification, and analysis of contact structures.
result Infinitely many non-isotopic contact structures on Brieskorn spheres and lens spaces cannot be obtained by a single rational contact surgery.
Develops k-contact geometry theory for field theories.
problem Analyse field theories using k-contact geometry.
method Distributions maximally non-integrable with k commuting Lie symmetries.
result Established k-contact distributions and their relationships.
Contact round surgeries on help in constructing and understanding contact 3-manifolds.
problem Constructing contact 3-manifolds using Legendrian surgeries.
method Introducing contact round surgeries of indices 1 and 2, and associating them with surgery diagrams.
result Every closed connected contact 3-manifold can be obtained by a sequence of contact round surgeries on Legendrian knots in .
The existing automatic fingerprint verification methods are designed to work under the assumption that the same sensor is installed for enrollment and authentication (regular matching). There is a remarkable decrease in efficiency when one type of contact-based sensor is employed for enrolment and another type of conta…
Contact surgeries yield algebraically overtwisted manifolds.
problem Understanding algebraically overtwisted contact manifolds through surgeries.
method Contact -surgeries on Legendrian spheres in flexibly fillable contact manifolds.
result Yielding algebraically overtwisted manifolds when the Legendrian's homology class is not annihilated.
We consider contact elements in the sutured Floer homology of solid tori with longitudinal sutures, as part of the (1+1)-dimensional topological quantum field theory defined by Honda--Kazez--Matić in \cite{HKM08}. The of these solid tori forms a "categorification of Pascal's triangle", and contact structur…
A contact projective structure is a contact path geometry the paths of which are among the geodesics of some affine connection. In the manner of T.Y. Thomas there is associated to each contact projective structure an ambient affine connection on a symplectic manifold with one-dimensional fibers over the contact manifol…