New conditions found for hyperbolic bicycle tracks.
problem Conditions for hyperbolic bicycle tracks.
method Hyperbolic development interpretation of bicycling monodromy.
result New necessary and sufficient conditions for hyperbolic bicycle tracks.
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48 results for “bicycle tracks”
Bicycle paths form geodesics in 3D subspaces, related to Kirchhoff rods.
problem Optimizing bicycle paths between two points.
method Variational equations and geometric analysis of bicycle paths.
result Bicycle geodesics are contained in 3D subspaces and relate to Kirchhoff rods.
We study a simple model of bicycle motion: a segment of fixed length in multi-dimensional Euclidean space, moving so that the velocity of the rear end is always aligned with the segment. If the front track is prescribed, the trajectory of the rear wheel is uniquely determined via a certain first order differential equa…
We study closed smooth convex plane curves enjoying the following property: a pair of points can traverse so that the distances between and along the curve and in the ambient plane do not change; such curves are called {\it bicycle curves}. Motivation for this study comes from the problem how to d…
The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its…
Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.
Sub-Riemannian geometry connects bike paths to mathematical curves.
problem Understanding bike paths and their mathematical properties.
method Relating sub-Riemannian geometry to bicycle motion and curve shapes.
result Geodesics in sub-Riemannian geometry correspond to specific bike paths.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
A spiral unibike track emerges from a mathematical construction.
problem Finding a unibike curve with a spiral shape.
method Starting with a polar square root curve, iteratively applying a differential equation to create a spiral unibike track.
result A spiral unibike curve is found with a precision error less than 10^-7.
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
The paper concerns a simple model of bicycle kinematics: a bicycle is represented by an oriented segment of constant length in n-dimensional space that can move in such a way that the velocity of its rear end is aligned with the segment (the rear wheel is fixed on the bicycle frame). Starting with a closed trajectory o…
Dataset of 4500 bicycle designs aids in design analysis and synthesis.
problem Identify gaps in bicycle market and design space, classify bicycles, synthesize new designs.
method Processed dataset, unsupervised dimensionality reduction, supervised classification, machine learning synthesis.
result Identified design parameters and factors influencing bicycle classification.
New model for visual cortex border completion using bicycle wheel motions.
problem Understanding border completion in the visual cortex V1.
method Sub-Riemannian Hamiltonian formalism and bicycle wheel analogy.
result Analogies between visual cortex border completion and bicycle wheel motions.
Paper presents LSTMMDN for hourly bike flow estimation in Copenhagen.
problem Sparse or unavailable hourly bike flow data for safety analysis.
method Hybrid LSTM MDN model for hourly bike flow estimation.
result 66-77% more accurate bike flow estimates compared to calibration factors.
We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic wave fronts (i.e. piecewise smooth curves which may have cusps). We then discuss "bicycle curves" using the generalized isoperimetric inequalities. The euclidean model of a bicycle is a unit segment AB that can move so that it re…
We generalize the notion of planar bicycle tracks -- a.k.a. one-trailer systems -- to so-called tractor/tractrix systems in general Riemannian manifolds and prove explicit expressions for the length of the ensuing tractrices and for the area of the domains that are swept out by any given tractor/tractrix system. These …
New method linearizes Darboux transformations of discrete curves.
problem Linearizing Darboux transformations of discrete curves.
method Expressing Darboux transformations as parallel sections of discrete connections in quaternionic formalism.
result Closed-form discrete parametrisations of all Darboux transforms and bicycle correspondences.
The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…
Model predicts multi-agent trajectories using a differentiable simulator.
problem Predicting future positions of multiple interacting agents.
method Conditional recurrent variational neural networks (CVRNNs) with a kinematic bicycle model.
result Achieves state-of-the-art results on INTERACTION dataset.
We prove that if is a rational number between zero and one, then there is no integer such that This has interpretations both in the theory of bicycle curves and that of mathematical billiards.
MCD automates counterfactual design searches for multi-modal tasks.
problem Designing for multi-objective goals and complex constraints.
method Model-agnostic counterfactual search method for multi-modal design modifications.
result MCD streamlines and automates counterfactual search, recommending effective design modifications.
We introduce a two-player contest for evaluating the safety and robustness of machine learning systems, with a large prize pool. Unlike most prior work in ML robustness, which studies norm-constrained adversaries, we shift our focus to unconstrained adversaries. Defenders submit machine learning models, and try to achi…
RL approach for target tracking with unknown dynamics and sensor control.
problem Tracking an unknown target with sensor control.
method Track-MDP formulation for RL, compared with POMDP.
result Optimal RL policy tracks all target paths with certainty.
This work uses SVM to identify track component failures in AC Track Circuits.
problem Detecting and identifying specific track component failures in AC Track Circuits.
method Applied SVM classifier to STDS track circuit data.
result Successfully classified 15 different track component failures.
New train tracks for complex homeomorphisms found.
problem Existence of irreducible train tracks for pseudo-Anosov homeomorphisms.
method Starting from a veering triangulation, identify and modify branches to bypass obstructions.
result Construction of invariant train tracks with irreducible transition matrix.
Beyond 4D Tracking: Using Cluster Shapes for Track Seedingphysics.ins-det
New method uses cluster shapes to improve track finding in particle collisions.
problem Combining timing and additional detector information for efficient track finding.
method Neural networks to analyze cluster shapes for track seeding.
result Cluster shapes reduce fake combinatorial backgrounds while maintaining high track efficiency.
This paper optimizes object tracking on edge devices with small matrices.
problem Efficiently tracking objects in video sequences on edge devices with small matrices.
method Parallelized a Simple Online and Real-time Tracking (SORT) application on shared-memory multicores.
result Throughput-based parallelization technique outperforms multi-threading for small matrices.
A DRL-based strategy improves vehicle tracking accuracy while saving energy.
problem Enhancing vehicle tracking accuracy in WSNs without increasing energy consumption.
method Decentralized strategy with dynamic reinforcement learning to adjust sensing areas.
result Simulation results demonstrate superior performance of DRL-aided design.
This master thesis focuses on practical application of Convolutional Neural Network models on the task of road labeling with bike attractivity score. We start with an abstraction of real world locations into nodes and scored edges in partially annotated dataset. We enhance information available about each edge with pho…
Paper introduces TAP-Vid, a benchmark for tracking any point in videos.
problem Tackles the problem of tracking arbitrary physical points on surfaces over longer video clips.
method Formalizes the problem as TAP, introduces TAP-Vid benchmark, uses crowdsourced pipeline with optical flow estimates, proposes TAP-Net model.
result TAP-Net outperforms all prior methods on TAP-Vid benchmark when trained on synthetic data.
The efficiency of a modern economy depends on what we call the Value-Tracking Hypothesis: that market prices of key assets broadly track some underlying value. This can be expected if a sufficient weight of market participants are valuation-based traders, buying and selling an asset when its price is, respectively, bel…
We show that the subsurface projection of a train track splitting sequence is an unparameterized quasi-geodesic in the curve complex of the subsurface. For the proof we introduce induced tracks, efficient position, and wide curves. This result is an important step in the proof that the disk complex is Gromov hyperbolic…
Train track automata for fully irreducible elements in Out(F_r).
problem Understanding fully irreducible elements in Out(F_r).
method Describing train track automata and geodesics in Outer Space.
result Geodesics in Culler-Vogtmann Outer Space for fully irreducible elements.
Dynamic tracking error framework shows similar performance but varying volatility across different constraints.
problem Differences in governance parameters between Total Portfolio Approach and Strategic Asset Allocation.
method Portfolio simulations using U.S. equity and bond data from 2000 to 2026, spanning 2004 to 2026.
result Realized tracking error volatility varies 12-fold across different constraints, with costs highest during crises.
Paper improves Lasso for S&P500 index tracking with post-selection inference.
problem Index tracking for S&P500 with many applications.
method Used Lasso for dimension reduction and post-selection inference.
result Lasso method for S&P500 index tracking shows high performance.
Bayesian approach for constructing and rebalancing sparse index-tracking portfolios.
problem Sparse tracking of a reference index with uncertainty quantification.
method Sparse linear regression with Laplace prior, empirical-Bayes calibration, Langevin-type MCMC, threshold-based rules.
result Posterior uncertainty on tracking error, portfolio composition, and rebalancing moves.
Automatic selection of eye tracking variables in visual categorization in adults and infantsq-bio.QM
Automated method selects eye tracking variables for categorization tasks.
problem Limited duration of infant cooperation and biases in handpicked eye tracking variables.
method Automated selection of eye tracking variables using statistical techniques.
result Same eye tracking variables classify category learners from non-learners in adults and infants with high accuracy.
We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, …
We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. We present an algorithm based on a specialist approach; we develop the machinery of cluster specialists which probabilistically exploits the cluster structure in the graph. Our algorithm has two va…
Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.
problem Understanding pseudo-Anosov mapping classes on surfaces.
method Using Goncharov--Shen's potential function, the paper translates train track concepts into cluster algebra language.
result Proves sign stability of general pseudo-Anosov mapping classes.
This paper reviews and analyzes various modeling approaches for financial index tracking.
problem Efficient replication of market index performance in financial markets.
method Categorization into three frameworks: optimization, statistical, and machine learning; empirical study on S&P 500 dataset.
result Optimization-based models deliver the most precise index tracking, statistical-based models achieve the strongest return-risk balance, and data-driven models provide competitive performance.
New data-driven Cartan connection tracks complex vascular structures.
problem Tracking complex vascular structures in multi-orientation images.
method Formulated a data-driven Cartan connection on for geodesic tracking.
result Improved geodesic tracking of vascular trees with globally optimal curves.
A new method tracks retinal vessels more accurately than existing methods.
problem Tracking retinal vessels accurately in spherical images.
method Computing cusp-free, crossing-preserving geodesics on spherical positions and orientations.
result Crossing-preserving tracking shows clear advantages over non-crossing-preserving tracking.
RL policy tracks dynamic targets in partially known environments robustly.
problem Active target tracking in partially known environments.
method Deep reinforcement learning (RL) approach for in-sight tracking, navigation, and exploration.
result Unified RL policy shows robust behavior for agile and anomalous targets.
Online Multi-Object Tracking (MOT) from videos is a challenging computer vision task which has been extensively studied for decades. Most of the existing MOT algorithms are based on the Tracking-by-Detection (TBD) paradigm combined with popular machine learning approaches which largely reduce the human effort to tune a…
We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VI…
Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows…
Online learners track optimal solutions with constant step-size.
problem Tracking optimal solutions in online learning settings.
method Established a link between steady-state performance and tracking performance using analogies with adaptive filters.
result Inferred tracking performance from steady-state expressions directly.