arXiv research

Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.

The paper studies the combinatorial p-th Calabi flow for finite and infinite circle patterns.

Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lag…

The paper solves curvature problems on graphs using a special flow.

Compact curve solution emerges from non-compact curve.

Paper shows no finite time singularities for smooth conformal heat flow of harmonic maps.

I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…

New bounds derived for KG algorithm's performance in finite time.

Let $p$ be an odd prime. We construct a non-abelian extension $Γ$ of $S^1$ by $Z/p \times Z/p$, and prove that any finite subgroup of $Γ$ acts freely and smoothly on $S^{2p-1} \times S^{2p-1}$. In particular, for each odd prime $p$ we obtain free smooth actions of infinitely many non-metacyclic rank two $p$-groups on $…

New model clusters discrete time series data.

The OLS estimator optimally identifies stable linear systems with a finite number of samples.

Study inverse mean curvature flow on entire graphs, proving finite time existence for certain asymptotic cases.

We investigate the scalar curvature behavior along the normalized conical Kähler-Ricci flow $ω_t$, which is the conic version of the normalized Kähler-Ricci flow, with finite maximal existence time $T<\infty$. We prove that the scalar curvature of $ω_t$ is bounded from above by $C/(T-t)^2$ under the existence of a con…

Anisotropic curvature flow of networks shows unique solutions and behavior under finite time.

We construct a non-abelian extension $Γ$ of $S^1$ by $\cy 3 \times \cy 3$, and prove that $Γ$ acts freely and smoothly on $S^{5} \times S^{5}$. This gives new actions on $S^{5} \times S^{5}$ for an infinite family $\cP$ of finite 3-groups. We also show that any finite odd order subgroup of the exceptional Lie group $G_…

We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional …

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with larg…

We consider a short time existence problem motivated by a conjecture of Joyce. Specifically we prove that given any compact Lagrangian $L\subset \mathbb{C}^n$ with a finite number of singularities, each asymptotic to a pair of non-area-minimising, transversally intersecting Lagrangian planes, there is a smooth Lagrangi…

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated an…

We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

We show some results for the $L^2$ curvature flow linked by the theme of addressing collapsing phenomena. First we show long time existence and convergence of the flow for $SO(3)$-invariant initial data on $S^3$, as well as a long time existence and convergence statement for three-manifolds with initial $L^2$ norm of c…

Developed LQ MFG theory with common noise, proving existence and uniqueness.

New discrete-time model shows insider trading dynamics.

Let H_g denote the closed 3-manifold obtained as the connected sum of g copies of S^2 times S^1, with free fundamental group of rank g. We prove that, for a finite group G acting on H_g which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but that…

New heat flow for harmonic maps avoids singularities but not bubbles.

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …

New study confirms some mean curvature flow solutions have bounded mean curvature.

Suppose that $Γ_0\subset\mathbb R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{n+1}\setminus Γ_0$ consists of more than one connected component. Assume that the $n$-dimensional Hausdorff measure of $Γ_0$ is finite or grows at most exponentially near infinity. Under these assumptions, we…

The study finds billiard trajectories with infinitely many reflections in certain cones.

This work achieves finite-time stabilization of uncertain LQ systems using random feedbacks.

The paper studies a gradient flow of $G_2$ structures and proves existence and convergence results.

New algorithms for risk-averse bandits minimize regret in finite time.

We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region.

Study on new flow equation on Riemann surfaces, with existence and singularity results.

Study on BSDEs with random time horizon, focusing on existence and properties.

The abstract proves the existence and regularity of Brakke flows starting from a given set.

A new method samples CGMY processes efficiently by decomposing their time changes.

New algorithm speeds up path computation for optimal models.

New method estimates treatment effects over time for survival data, improving accuracy and smoothness.

First-order method solves stochastic bilevel optimization with linear constraints.

In this paper we consider the steepest descent $H^{-1}$-gradient flow of the length functional for immersed plane curves, known as the curve diffusion flow. It is known that under this flow there exist both initially immersed curves which develop at least one singularity in finite time and initially embedded curves whi…

Researchers prove long-time existence for two landmark Brownian motion.

Paper analyzes convergence rates for multi-agent learning in games.

In this work one shows that given a connected $C^\infty$-manifold $M$ of dimension $\geq 2$ and a finite subgroup $G\subset \Diff(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\times \mathbb{R}$ where the factor $\mathbb{R}$ comes from the flow of $X$.

Study of combinatorial Yamabe flows in 3D spaces.

In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to stu…

Existence and uniqueness theorem for Ricci flow on weighted graphs proved.

Study long-term asset liquidation behavior with external flows.