A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
Two proofs of Kalman Theorem using flows of vector fields.
Ricci flow controls curvature on manifolds with bounds.
The control of complex systems is of critical importance in many branches of science, engineering, and industry. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automo…
Optimal market making strategy for electronic markets with persistent order flows.
EnCF improves data assimilation for implicit, non-smooth observations.
We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with ti…
We prove that for the mean curvature flow of two-convex hypersurfaces the intrinsic diameter stays uniformly controlled as one approaches the first singular time. We also derive sharp -estimates for the regularity scale of the level set flow with two-convex initial data. Our proof relies on a detailed analysis…
Ricci flow smooths locally collapsing manifolds with controlled curvature.
Study Transformer layers under cross-entropy training using mean field control.
Derivative estimates for pluriclosed flow control curvature and torsion.
GeneraLight improves traffic signal control models' generalization ability.
FlowSelect uses normalizing flows to control FDR in feature selection.
Model analyzes OTC market making with reputation feedback.
Model analyzes how reputation feedback affects OTC market making.
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…
Curve shortening flow's regularity depends on initial conditions after a certain time.
A new framework for generative modeling using controlled vector fields.
In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer--fields as a flexi…
Sharp chord-arc estimates for curve shortening flow on spheres.
We are concerned with bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularity. The analysis is involved with CW complex bifurcations of flow-invariant Clifford hypertori, where we refer to these toral manifolds by toral CW complexes. We observe from primary to tertiary fl…
This work discusses a closed-loop control strategy for complex systems utilizing scarce and streaming data. A discrete embedding space is first built using hash functions applied to the sensor measurements from which a Markov process model is derived, approximating the complex system's dynamics. A control strategy is t…
Stable neural flows ensure robustness and efficiency in deep learning.
In this paper we consider the Ricci flow on manifolds with boundary with appropriate control on its mean curvature and conformal class. We obtain higher order estimates for the curvature and second fundamental form near the boundary, similar to Shi's local derivative estimates. As an application, we prove a version of …
New framework for Bayesian inference using neural Schrödinger-Föllmer flows.
Modern information technology services largely depend on cloud infrastructures to provide their services. These cloud infrastructures are built on top of datacenter networks (DCNs) constructed with high-speed links, fast switching gear, and redundancy to offer better flexibility and resiliency. In this environment, net…
CPFM integrates dimensionality reduction and reconstruction with flow networks.
We show that the distance function under the Ricci flow is uniformly continuous in the time direction, assuming only the scalar curvature is bounded.
We consider the general Kähler-Ricci flows which exist for all time. The zeroth order control on the flow metric potential for various infinite time singularities is the focus. The possible semi-amplness for numerically effective classes serves as the main motivation.
New method for high-dimensional submanifolds using surgery and curvature control.
Improved neural ODEs learn adaptable flows.
Exact universal interpolation property for landmark configurations in Euclidean space.
In this paper, we study the moduli spaces of noncollapsed Ricci flow solutions with bounded energy and scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study isoperimetric constant control, Kähler Ricci flow and moduli space of gradient shrinking solitons.
Adjoint Matching improves flow and diffusion models with reward fine-tuning.
In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. Each private actor aims to maximize its expected terminal logarithmic utility. The…
This paper uses normalizing flows to approximate transport maps between densities.
An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is contr…
We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We …
Smooth flows with surgery approximate weak mean curvature flows with spherical and neck-pinch singularities.
We prove an optimal control on the time-dependent measure of a measurable set under a reparametrized Lagrangian mean curvature flow of almost calibrated submanifolds in a Calabi-Yau manifold. Moreover we give a classification of those Lagrangian translating solitons in that evolve by this reparametrized …
We consider Ricci flow invariant cones C in the space of curvature operators lying between nonnegative Ricci curvature and nonnegative curvature operator. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to Ricci flow has its curvature operator which satsisfies R+εI \in C…
The geometry of a ball within a Riemannian manifold is coarsely controlled if it has a lower bound on its Ricci curvature and a positive lower bound on its volume. We prove that such coarse local geometric control must persist for a definite amount of time under three-dimensional Ricci flow, and leads to local C/t deca…
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along the lines of the flow interpretation of the Lie bracket. This geometric interpre…
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…
New proof of generalized Chow-Rashevskii theorem for non-linear systems.
In this short paper, we show that Kähler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems. Section 1 underlines some science domains where appear multitime optimal control prob…
Optimal control of reserve assets for stablecoins to maintain peg stability.