arXiv research

Solves NP-hard MAP inference by avoiding fractional vertices.

Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and as…

This paper explores how rational numbers on the Stern-Brocot diagram map to lines when terms are extended.

A new method calculates fractional moments using the moment-generating function.

New conjectures link SU(r) Vafa-Witten invariants to Ramanujan's continued fractions.

Paper analyzes misclassification in binary stochastic block model with correlated degrees.

Graphs grow with preferential attachment, incorporating communities.

Algorithm recovers communities in preferential attachment graphs.

Statistical framework for inexact graph matching with errorfully observed graphs.

Estimates smooth graph signals from partial measurements.

New algorithm detects communities even with corrupted data, reaching Kesten-Stigum threshold.

This paper resolves the all-or-nothing phase transition in graph matching.

Study sharpens threshold for matching correlated graphs without labels.

This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.

Estimates graph connected components from sampled subgraphs.

Adversarial inference on tree models is possible with limited corruption, improving on Kesten-Stigum threshold.

Geometrical spines are defined for 3-manifolds with natural metrics, in particular, for lens manifolds. We show that any spine of L(p,q) close enough to its geometrical spine (i.e., to the cut locus with respect to the standard metric) contains at least E(p,q)-3 vertices, which is exactly the conjectured value for Matv…

Algorithm matches vertices of correlated Erdős-Rényi graphs efficiently.

Paper tackles graph matching with partially correct seeds, improving performance guarantees.

Combines classifiers from different types to improve ensemble accuracy.

Spectral algorithm recovers community structure in sparse hypergraphs.

Local algorithms can achieve optimal performance in block models with side information.

Legendrian surgery describes canonical contact structures and calculates Gompf's θ-invariant.

The paper generalizes Farey tessellation to 3D hyperbolic space.

Efficient algorithm for graph matching in correlated stochastic block models.

A geodesic net with 4 boundary vertices and 25 balanced vertices is constructed.

In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generaliz…

Classifies intrinsically linked tournaments by their score sequences.

Introduces fractional k-dimensional measure bridging fractional length and area.

The theory of derivative of noninteger order goes back to Leibniz, Liouville and Riemann. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics. In this paper we define the fractional tangent bundle on a manifold, using a method of Radu Miron. The fractional Lei…

Let $S_g$ be a closed orientable surface of genus $g \geq 2$ and $C$ a simple closed nonseparating curve in $F$. Let $t_C$ denote a left handed Dehn twist about $C$. A \textit{fractional power} of $t_C$ of \textit{exponent} $\fraction{\ell}{n}$ is an $h \in \Mod(S_g)$ such that $h^n = t_C^{\ell}$. Unlike a root of a $t…

Study on fractional curvature flow on unit sphere, extending previous work.

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution …

Using Caputo fractional derivative of order $α$ we build the fractional jet bundle of order $α$ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are studied.

Volatility roughness studied using fractional noise-driven models.

Develops hedging formula in fractional model with costs.

Develops Poisson structures on weak Sobolev loop spaces for integrable systems.

Using the reviewed Riemann-Liouville fractional derivative we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures.

String vertices proven in hyperbolic geometry, unique up to transformations.

The study proves fractional-order differences and equations are key to modeling long and short memory in economics.

Introduces fractional length and nonlocal curvature for smooth curves.

The paper corrects the Black-Scholes formula for fractional stochastic volatility.

Develops fractional de Rham theory for Maxwell equations.

Modeling financial markets with memory using fractional calculus and Brownian motion.

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …

The paper extends fractional Laplacian theory using symmetric spaces and extension problems.

Study smooth solutions to fractional mean curvature flow, proving uniqueness and finite extinction time.

Extends fractional $L^p$ uncertainty principles with extremizers and stability results.