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.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
Study on Heisenberg group's Lorentzian problems using Pontryagin's principle.
TRAKNN detects rare atmospheric trajectories efficiently.
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike norma…
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.
Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.
We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface in a -dimensional Finsler space with possibly irreversible Finsler metric. An example of such a system is a billiard in a sufficiently weak magnetic field. The -periodic Fin…
ELM combines machine learning and feature engineering for anomalous diffusion detection.
Deep neural networks improve ensemble weather forecasts.
Cube edges curves minimize systole length.
Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.
Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single trajectory information? How can we further generalize the mobility inference to ac…
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that…
Deep learning models can infer individual trajectories from sparse data.
We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. We demonstrate the computations in the CAS Maple package DifferentialGeometry.
This work reviews left-invariant optimal control problems on Lie groups.
New method learns cell trajectories and network interactions from single-cell data.
Study shows similarities and differences in crypto and equity dynamics during pandemic.
Study uses vehicle trajectory data to predict traffic incidents on highways.
Generalizes pseudo-product structures with abnormal extremals.
Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.
Mode connectivity is a recently introduced frame- work that empirically establishes the connected- ness of minima by finding a high accuracy curve between two independently trained models. To investigate the limits of this setup, we examine the efficacy of this technique in extreme cases where the input models are trai…
Paper examines adversarial attacks on weather forecasting models, focusing on TC trajectory prediction.
Study shows reinforcement learning is possible with once-per-episode feedback.
Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this…
In this paper, we design a navigation policy for multiple unmanned aerial vehicles (UAVs) where mobile base stations (BSs) are deployed to improve the data freshness and connectivity to the Internet of Things (IoT) devices. First, we formulate an energy-efficient trajectory optimization problem in which the objective i…
We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of sym…
Study of ants' movement rules on a 6D space, revealing distribution structures and singular trajectories.
Model uses smartphone data to assess MS trajectories.
A new framework uses stochastic optimal control to estimate rare events more accurately.
The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic nonholonomic systems in four-dimensional space with two-dimensional control, for instance to a system which describes motion of mobile robot with a trailer. The global optimality of extre…
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
New method learns dynamics from sparse data using geometric constraints.
CDLF predicts product life-cycles in cold-start phases with high accuracy.
Reduces necessary conditions for collision avoidance on curved spaces.
Paper tackles hard shape constraints in kernel machines.
Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional Hénon map at the classical parameters. The task is to determine whether a trajec…
This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant subma…
Diffusion models simulate molecular dynamics with adjustable accuracy.
RDLI integrates domain logic and context grounding to detect crypto anomalies under scarce labels.
Lagrangian data assimilation is a complex problem in oceanic and atmospheric modeling. Tracking drifters in large-scale geophysical flows can involve uncertainty in drifter location, complex inertial effects, and other factors which make comparing them to simulated Lagrangian trajectories from numerical models extremel…
Deep reinforcement learning techniques have demonstrated superior performance in a wide variety of environments. As improvements in training algorithms continue at a brisk pace, theoretical or empirical studies on understanding what these networks seem to learn, are far behind. In this paper we propose an interpretable…
A new method uses deep learning to predict rare events in complex systems.
Paper proposes RRD to learn proxy rewards for sparse delayed rewards in episodic reinforcement learning.
New measure EC assesses node contributions in nonlinear, time-varying systems.
This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features such as trajectories and length. We also define several differential operators on q…
Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conv…
We study the problem of discriminative sub-trajectory mining. Given two groups of trajectories, the goal of this problem is to extract moving patterns in the form of sub-trajectories which are more similar to sub-trajectories of one group and less similar to those of the other. We propose a new method called Statistica…