arXiv research

New Ricci flow method for directed graphs with balancing factor.

Proposes a new model for traffic flow on directed graphs.

CDFD analyzes circularity and directionality in weighted directed networks.

The study characterizes heat flow and concentration on directed graphs with a lower Ricci curvature bound.

Predicts short-term futures contract direction using neural networks and order flow data.

The set of directions from a quadratic differential that diverge on average under Teichmuller geodesic flow has Hausdorff dimension exactly equal to one-half.

DIGRAC clusters directed graphs using flow imbalance, outperforming existing methods.

Geodesic flows with specific integrals are linked to special 4-webs.

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…

Survey on Chern-Ricci flow for complex manifolds.

Paper confirms Thom's conjecture for nonlinear evolutions on manifolds.

Study on rigidity of translating hypersurfaces not in graphical direction.

Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacel…

Filters on order flow improve short-term market directionality.

We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold $S$ changes its signature (degenerates) along a curve $S_0$, which locally separates $S$ into a Riemannian ($R$) an…

We analyse a multiplex of networks between OECD countries during the decade 2002-2010, which consists of five financial layers, given by foreign direct investment, equity securities, short-term, long-term and total debt securities, and five environmental layers, given by emissions of N O x, P M 10 SO 2, CO 2 equivalent…

SurVAE Flows combine VAEs and flows using surjective transformations.

Autoregressive flow models can perform causal discovery and inference tasks.

We provide a direct proof of time-slice weak compactness along the Kähler Ricci flow on Fano manifolds.

Causal autoregressive flows enable accurate causal inference and prediction.

We give a short, direct proof that the full holonomy group of a solution to the Ricci flow is invariant up to isomorphism using the invariance of the reduced holonomy under the flow.

Paper develops models to forecast private equity fund cash flows.

In this paper we study the Teichmüller harmonic map flow as introduced by Rupflin and Topping [15]. It evolves pairs of maps and metrics $(u,g)$ into branched minimal immersions, or equivalently into weakly conformal harmonic maps, where $u$ maps from a fixed closed surface $M$ with metric $g$ to a general target manif…

Constructs explicit solutions to Spin(7)-structures gradient flow.

We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost e…

We show that the distance function under the Ricci flow is uniformly continuous in the time direction, assuming only the scalar curvature is bounded.

In this paper, we first develope the concept of Lyapunov graph to weighted Lyapunov graph (abbreviated as WLG) for nonsingular Morse-Smale flows (abbreviated as NMS flows) on $S^3$. WLG is quite sensitive to NMS flows on $S^3$. For instance, WLG detect the indexed links of NMS flows. Then we use WLG and some other tool…

We study the motion of an $n$-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power $p$ of the mean curvature. We prove that for any $p\in (0,1]$, the flow exists for all time when the Ricci tensor of the ambient s…

In the present paper, an aerodynamic investigation of a high-speed train is performed. In the first section of this article, a generic high-speed train against a turbulent flow is simulated, numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations combined with the turbulence model are applied to solve incompr…

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.

Study shows directional convergence for neural networks under spherical symmetry.

The paper studies neural networks' convergence near origin and saddle points.

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.

Study of straight-line flows on a unique infinite surface.

We introduce a framework for Newton's flows in probability space with information metrics, named information Newton's flows. Here two information metrics are considered, including both the Fisher-Rao metric and the Wasserstein-2 metric. A known fact is that overdamped Langevin dynamics correspond to Wasserstein gradien…

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.

We explain a characterization of Einstein-Fano manifolds in terms of the lower bound of the density of the volume of the Kähler-Ricci Flow. This is a direct consequence of Perelman's uniform estimate for the Kähler-Ricci Flow and a $C^0$ estimate of Tian and Zhu.

We study the behavior of the second order Renormalization Group flow on locally homogeneous metrics on closed three-manifolds. In the cases $\mathbb R^3$ and $\text{SO}(3)\times \R$, the flow is qualitatively the same as the Ricci flow. In the cases $\text{H}(3)$ and $\text{H}(2)\times \R$, if the curvature is small, t…

Enhances multi-modular models by directing information flow between components.

Unified framework maps financial market dynamics using TE and KM, revealing directional information flow.

New flow generates surfaces with constant curvature.

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

MAGIC-Flow generates and classifies medical images with interpretability.

Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most information. According to the minimum spanning tree, the GSPC is located at…

This work improves policy-based training by proposing an evaluation balance objective for GFlowNets.

Paper studies heat flow for maps on manifolds, avoiding singularities.

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for…