arXiv research

No-collision maps improve manifold learning for image data.

New strategy achieves optimal regret without communication or collisions in multi-player bandit.

A new algorithm reduces regret in multi-player bandits without collision info.

Two non-communicating players minimize regret in a multi-armed bandit game.

We study multiplayer stochastic multi-armed bandit problems in which the players cannot communicate and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider two feedback models: a model in which the players can observe whether a collision has occurred an…

We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in the process of motion. The ultimate goal is to construct an algorithm which will…

A new algorithm RESYNC for defenders against malicious attackers in multi-player bandits.

No communication allows optimal instance-dependent regret guarantees in multi-player bandits.

The article explores the mapping class group using unicellular maps and provides filtrations.

Constructs a moment map flow for isotropic maps on surfaces.

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

The paper constructs biharmonic maps between spheres using polynomial maps.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

Research explores real algebraic realization of round fold maps of codimension -1.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Paper defines and studies Clairaut warped product Riemannian maps.

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

This paper constructs real algebraic maps that are topologically special generic maps.

A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse functions, their higher dimensional versions including fold maps and general stable…

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Characterizes a general range decreasing group homomorphism.

The paper examines $HM$-tensional and $HS$-tensional maps between Riemannian manifolds.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Dirac-harmonic maps are uncoupled under certain conditions.

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.

The article explores constructing biharmonic and conformal biharmonic maps to spheres.

Harmonic map flow preserves almost-holomorphic maps without singularities.

Method computes harmonic and conformal maps from point clouds.

New theorem proves convergence of various discrete conformal structures to conformal maps.

This paper classifies semi-equivelar maps on a special surface.

Constructs harmonic maps between special geometric shapes.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

Study isotropic Riemannian maps and helices along them.

Study on harmonic maps on weighted Riemannian foliations.

Maps and measures on surfaces link best Lipschitz and least gradient functions.

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …

Paper proves existence and gives construction of Symphonic map between ellipsoids.

Study heat flow for half-harmonic maps and harmonic maps with free boundary.

Paper proves symphonic map result similar to Eells-Sampson.

A vertex-transitive map $X$ is a map on a closed surface on which the automorphism group ${\rm Aut}(X)$ acts transitively on the set of vertices. If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse…

Embeddings of mapping tori for end-periodic graph maps are proven.

The study restricts manifolds with certain explicit SGL maps and constructs them.

Biharmonic maps are generalizations of harmonic maps. A well-known result of Eells and Wood on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere (whatever the metrics chosen) in the homotopy class of maps of Brower degree $\pm 1$. It would be interesting to know if there …