We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.
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48 results for “train track criterion”
Polynomial-time algorithm detects fully irreducible automorphisms in Out(F_N).
problem Deciding whether an element is fully irreducible in Out(F_N).
method Refined algorithm eliminating inefficient features and parallel processes.
result Produces polynomial-time algorithm for deciding fully irreducible automorphisms.
This paper optimizes portfolio selection by penalizing tracking error, improving Sharpe ratio.
problem Optimizing portfolio allocation with a penalty for deviation from a reference portfolio.
method Formulated as a McKean-Vlasov control problem, provides explicit solutions and asymptotic expansions.
result The penalized portfolio strategy outperforms standard mean-variance and reference portfolios in most cases.
V-SysId identifies keypoints and 3D system from unlabeled videos.
problem Identifying keypoints and 3D system from unlabeled videos.
method Alternates between parameter estimation and extrinsic camera calibration, using motion equations as weak supervision.
result Utility of the approach demonstrated across various settings.
Proposes a new active learning criterion to maximize classifier instability.
problem Efficiently train classifiers with minimal labeled data.
method Maximizes variance of output changes for unlabeled data.
result Achieves state-of-the-art performance in experiments.
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.
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.
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…
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 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.
The paper defines and proves the existence of train track maps on graphs of groups.
problem Understanding homotopy equivalences in graphs of groups.
method Developed the theory of train track maps on graphs of groups, defining maps and homotopy equivalences.
result Any homotopy equivalence of a graph of groups may be represented by a relative train track map under certain conditions.
The study characterizes train tracks and measured laminations on infinite surfaces.
problem Characterizing geodesic laminations on infinite surfaces.
method Defining train tracks and parametrizing measured laminations by edge weight systems.
result A homeomorphism exists between bounded measured laminations and edge weight systems.
Study Agol cycles in pseudo-Anosov 3-braids.
problem Understanding conjugacy invariants of pseudo-Anosov maps.
method Investigate train tracks associated with Farey intervals and describe Agol cycles.
result Complete description of Agol cycles in pseudo-Anosov 3-braids.
Study of endperiodic maps on infinite graphs, proving homotopy and eigenvalue properties.
problem Understanding endperiodic maps on infinite graphs with finitely many ends.
method Adapting relative train track maps and combinatorial techniques to infinite type setting.
result Any generalized endperiodic map is homotopic to a relative train track map.
Using Lipschitz distance on Outer space we give another proof of the train track theorem.
Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by Hsieh et al., probably best known under the name of the "liblinear" implementation,…
The study of pseudo-Anosov maps with minimum expansion factor using train tracks.
problem Finding pseudo-Anosov maps with minimum expansion factor.
method Analysis of standardly embedded train tracks and Thurston symplectic form.
result The expansion factor of pseudo-Anosov maps is bounded by a specific inequality involving the golden ratio.
A new algorithm removes stale observations in dynamic Bayesian optimization.
problem Optimizing functions that change over time, keeping track of the optimum.
method Wasserstein distance-based criterion to quantify relevancy, removing stale observations.
result W-DBO maintains good predictive performance and high sampling frequency.
In this paper we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of -trees with possibly non-trivial vertex stabilisers. The strategies are the same…
We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound depending only on P, so that there exists a presentation of the fundament…
Let denote the genus orientable surface with punctures. We show that nested train track sequences constitute -quasiconvex subsets of the curve graph, effectivizing a theorem of Masur and Minsky. As a consequence, the genus disk set is -quasiconvex. We also show that splitti…
The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.
problem Representing automorphisms of hyperbolic groups using train track maps.
method Using graphs of groups and Bestvina-Handel's irreducible train track maps, the thesis constructs relative train track maps.
result Outer automorphisms of finitely-generated word hyperbolic groups satisfy a dynamical trichotomy.
Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphism of the fundamental group gives rise to an expa…
Masked LARk prevents cross-site tracking while training models.
problem Cross-site tracking of user data through third-party cookies.
method Secure multi-party compute (MPC) protocol with masking.
result Prevents cross-site tracking and maintains model training flexibility.
Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Imagesmath.DG
A new snake model improves segmentation of SEM images.
problem Efficiently segmenting overlapping electronic structures in SEM images.
method Geodesic tracking on projective line bundle with a geometric criterion for switching between fast spatial snakes and minimizing geodesics.
result Improved robust and automatic segmentation of overlapping electronic structures in SEM images.
New architecture tracks objects in cluttered scenes without supervision.
problem Learning to track objects in large scenes with many objects.
method Spatially invariant computations and representations.
result Outperforms competing methods in tracking objects in cluttered scenes.
BootsTAP uses real-world data to improve TAP tracking performance.
problem Lack of large-scale groundtruth training data for TAP.
method Bootstrapped training with a self-supervised student-teacher setup.
result State-of-the-art performance on TAP-Vid benchmarks.
This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus .
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.
Estimates hyperbolic volume via rearranged train tracks.
problem Estimating hyperbolic volume of mapping tori.
method Rearranging and untwisting train track sequences to estimate distances in pants graphs.
result Hyperbolic volume estimates via rearranged train tracks.
Study Agol cycles on 2-punctured torus and 5-punctured sphere, finding new dilatation formula.
problem Understanding Agol cycles on specific surfaces.
method Computed measured train tracks and Agol cycles for pseudo-Anosov maps.
result Found a new formula for the dilatation of pseudo-Anosov maps.
Carbontracker tracks and predicts training DL models' carbon footprint.
problem Exponential growth in energy consumption for training deep learning models.
method Carbontracker tool for tracking and predicting energy and carbon footprint.
result Promotes responsible computing and encourages energy-efficient deep learning.
Privacy Preserving Gaze Estimation using Synthetic Images via a Randomized Encoding Based Frameworkcs.CV
Privacy-preserving eye tracking framework using synthetic images.
problem Preserving sensitive personal information in eye tracking technology.
method Randomized encoding for privacy, Support Vector Regression model training on synthetic eye images.
result Framework achieves real-time gaze estimation with same accuracy as non-private version.
Deep learning tracks body parts without markers, improving efficiency in neuroscience.
problem Efficiently tracking specific behaviors in animals without intrusive markers.
method Transfer learning with deep neural networks for markerless tracking.
result Deep learning achieves excellent tracking performance with minimal labeled data.
nuScenes dataset includes multimodal sensor data for autonomous vehicle training.
problem Training robust detection and tracking methods for autonomous vehicles.
method Presented the first multimodal dataset with 6 cameras, 5 radars, and 1 lidar, 360-degree field of view.
result 7x more annotations and 100x more images than KITTI dataset.
Improved tracking and prediction of moving objects in visual data streams.
problem Tracking and predicting multiple moving objects in visual data streams.
method Disentangled latent state-space model with amortized variational Bayesian inference.
result Significantly improved long-term prediction and object decomposition in the presence of occlusions.
A novel tracking method for dense honeybee colonies using pixel personality.
problem Tracking large numbers of densely-arranged, interacting objects in a 2D environment.
method Segmentation-based object detection followed by adaptive object recognition through visual appearance.
result Reconstructed ~46% of trajectories in 5 minutes and 71% of tracks for at least 2 minutes.
Tribuo integrates ML models with provenance in Java.
problem Tracking and ensuring ML models behave appropriately as they grow in number and complexity.
method Integrates model training, inference, type-safety, runtime checking, and automatic provenance recording into a single Java library.
result Automatic recording of full processing pipeline and training details inside the model object.
DeepDA uses LSTM to track multiple targets in clutter.
problem NP-hard combinatorial optimization in multi-target tracking with clutter.
method LSTM-based deep learning for data association.
result Significant performance on association ratio, target ID switching, and time-consuming tracking.
Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes al…
ACI uses Bayesian data assimilation to trace causes from effects in complex systems.
problem Capturing instantaneous, time-evolving causal relationships in complex, high-dimensional systems.
method Assimilative causal inference (ACI) leverages Bayesian data assimilation to trace causes backward from observed effects.
result ACI provides online tracking of causal roles that may reverse intermittently and reveals how far effects propagate.
A new method for tracking objects using diverse templates.
problem Improving visual tracking performance and robustness.
method Proposes a framework that uses additional object templates and a new diversity measure in siamese feature space.
result Achieves strong empirical results on tracking benchmarks, improving performance and robustness.
The study examines the stretch factors of outer automorphisms and their latent symmetry.
problem Understanding stretch factors of outer automorphisms in free groups.
method Analyzes the latent symmetry of graphs and uses it to bound stretch factors.
result A precise notion of latent symmetry provides a lower bound on the number of folds required.
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
New RL method improves financial index tracking accuracy.
problem Optimizing financial index tracking with dynamic market information.
method Discrete-time dynamic model, Banach fixed point iteration, deep reinforcement learning.
result Proposed RL method outperforms benchmarks in tracking accuracy.
Proposes a contextual bandit method for demand side management.
problem Managing demand response through price incentives.
method Contextual bandit approach with quadratic loss measurement.
result Upper bounds on regret with fast rates under stronger assumptions.
Enhances particle filters with neural augmentation for multi-sub-state tracking.
problem Particle filters struggle with complex or approximated models and low latency requirements.
method Learning Flock (LF) uses a neural network to correct particle weights based on sub-particle relationships.
result LF improves performance, robustness, and latency in radar multi-target tracking.
Paper proposes GAN models for generating multi-track music.
problem Generating music with multiple tracks and temporal dynamics.
method Generative adversarial networks (GANs) for multi-track music generation.
result Models can generate coherent music of four bars right from scratch.