Study Whitehead torsions in inertial h-cobordisms.
problem Understanding Whitehead torsions in specific geometric contexts.
method Analyzing inertial h-cobordisms to identify subsets of the Whitehead group.
result Identified various types of Whitehead torsions representing nested subsets of the Whitehead group.
Study compares h-cobordism categories to standard spaces.
problem Comparing h-cobordism categories to standard spaces. method Topological category of h-cobordisms between manifolds. result Homotopy type comparison of h-cobordism categories. Study h-cobordisms of complexity 2 in 5D, finding obstructions and examples.
problem Understanding h-cobordisms of complexity 2 in 5D. method Compute monopole Floer homology and action of twisting involution.
result Obtained obstructions and constructed examples of high complexity.
Study shows mapping class groups differ for h-cobordant manifolds.
problem Mapping class groups are invariant under h-cobordism. method Introduced moduli spaces of h-block bundles to distinguish manifolds. result Mapping class groups of h-cobordant manifolds can differ. The study explores conditions for h-cobordisms between smooth 4-manifolds.
problem Determining when smoothly h-cobordant 4-manifolds are also s-cobordant. method Providing new conditions for positive answers to the s-cobordism theorem. result Conditions under which standard methods to construct h-cobordisms fail. Constructs a functor for equivariant smooth h-cobordisms.
problem Defines a functor for equivariant smooth h-cobordisms.
method Constructs an (∞,1)-functor mapping smooth G-manifolds to spaces of equivariant h-cobordisms. result The functor structure is subtle and relies on new ideas.
Research shows how complexity of h-cobordisms affects double points in 4-manifolds.
problem Understanding the complexity of h-cobordisms and its impact on double points in 4-manifolds.
method Analyzing the number of double points of smoothly immersed 2-spheres in 4-manifolds.
result The number of double points increases with the complexity of h-cobordisms.
We study the homeomorphism types of manifolds h-cobordant to a fixed one. Our investigation is partly motivated by the notion of special manifolds introduced by Milnor in his study of lens spaces. In particular we revisit and clarify some of the claims concerning h-cobordisms of these manifolds.
We consider ribbon R4's, that is, smooth open 4-manifolds, homeomorphic to R4 and associated to h-cobordisms between closed 4-manifolds. We show that any generalized ribbon R4 associated to a sequence of h-cobordisms between non-diffeomorphic 4-manifolds is exotic. Notion of a positive ribbon R4 is defi…
In this note we classify the diffeomorphism classes rel. boundary of smooth h-cobordisms between two fixed 1-connected 4-manifolds in terms of isometries between the intersection forms.
New method uses reverse thinking to correct machine learning errors.
problem Machine learning methods form inertial thinking schemes that can lead to errors when testing data are vastly different.
method Proposes a new method that uses reverse thinking to correct illusion inertial thinking in machine learning.
result Increases the generalization ability of machine learning methods.
We prove that any two smooth h-cobordant simply-connected 4-manifolds can be obtained by taking two manifolds with boundary, one of which is contractible, and gluing them along the boundary via two different attaching maps.
Computes invariant for smooth h-cobordisms families, proving duality and vanishing theorems.
problem Computing invariants for smooth h-cobordisms families.
method Using Dwyer, Weiss, and Williams work, fiberwise generalized Morse function, fiberwise Poincaré--Hopf theory.
result Duality theorem for smooth structure class, vanishing theorem for Rigidity Conjecture.
We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
This is primarily an exposition, combining work of several authors (Curtis, Hsiang, Freedman, Stong, Matveyev, and Bizaca), of the proof that a smooth 5-dimensional h-cobordism between simply connected 4-manifolds is a product off of a contractible piece which itself is diffeomorphic to the 5-ball.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
Alexander trick applied to homology spheres for manifold homeomorphisms.
problem Group of homeomorphisms of contractible manifolds.
method Strong uniqueness statement for one-sided h-cobordisms.
result Group of homeomorphisms is contractible for d≥6. RIO uses rotation-equivariance to train robust inertial odometry models.
problem Training robust inertial odometry models with limited labeled data.
method Rotation-equivariance as self-supervisor, adaptive Test-Time Training (TTT).
result RIO-trained models achieve on-par performance with full-labeled data models.
Paper analyzes complexity of proximal inertial gradient descent.
problem Computational complexity of proximal inertial gradient descent.
method Analyzed convergence rates and proved various rates under different conditions.
result Proved non-ergodic O(1/k) rate for coercive objective functions.
Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.
Framework transfers inertial motion across domains without labeled data.
problem Inertial measurements are sensitive to sensor placement and motion dynamics.
method Extracts domain-invariant features and transfers them to new domains.
result Framework converts raw IMU sequences into accurate inertial trajectories.
Method infers depth from sparse points and camera motion.
problem Depth inference from limited sparse data.
method Constructs a planar scaffolding and uses predictive cross-modal criterion.
result State-of-the-art performance on depth completion benchmark.
This paper proposes IMU preintegrated features for efficient deep inertial odometry.
problem Efficient odometry from IMU data is challenging due to sensor imperfections and noise.
method Proposes IMU preintegrated features exploiting IMU motion model's manifold structure.
result Improves odometry performance and reduces computational burdens.
New map constructed from equivariant spectra for manifold study.
problem Understanding equivariant parametrized h-cobordism in non-manifold settings.
method Constructed a map from suspension G-spectrum to equivariant A-theory spectrum, compatible with tom Dieck splitting formulas.
result Fiber of constructed map is wedge of stable h-cobordism spectra.
In this paper, we develop a geometric procedure for producing a reverse to Quillen's plus construction, a construction called a 1-sided h-cobordism or semi-h-cobordism. We then use this reverse to the plus construction to produce uncountably many distinct ends of manifolds called pseudo-collars, which are stackings of …
The abstract explains counterexamples in 4-manifold topology.
problem Understanding the equivalence relations on 4-manifolds.
method Explains and provides counterexamples for various equivalence relations.
result Illustrates the failure of potential implications between equivalence relations.
Inertial methods solve non-convex non-smooth optimization problems efficiently.
problem Non-convex non-smooth optimization problems.
method Inertial block proximal methods for solving these problems.
result The methods converge globally under certain conditions and perform well in applications like NMF.
Neural networks outperform conventional filters in inertial sensor-based attitude estimation.
problem Limited accuracy in inertial sensor-based attitude estimation due to dynamic and static motion.
method Investigated neural networks versus conventional filters for improving accuracy.
result Neural networks outperform conventional filters only with domain-specific optimizations.
The paper constructs infinitely many G-smoothings of a G-manifold.
problem Constructing G-smoothings of a G-manifold. method Using controlled h-cobordisms. result Infinitely many G-smoothings of a G-manifold are constructed and are isotopic after taking a product with R. Improved UAV navigation and landing using deep learning.
problem Autonomous navigation and landing of UAVs with high accuracy.
method Multimodal fusion of visual and inertial sensor data using deep neural networks.
result 25% improvement in pose estimation accuracy compared to traditional methods.
This work uses scientific constraints to validate neural network predictions in fusion physics.
problem Verifying the scientific plausibility of neural network predictions in fusion physics.
method Using known scientific constraints as a validation tool.
result Validated neural network predictions in fusion physics using scientific constraints.
New deep fusion methods improve human action recognition using depth and inertial sensor data.
problem Existing multimodal HAR frameworks lack mid-level feature fusion.
method Proposes three deep multilevel multimodal fusion frameworks, transforming depth and inertial sensor data into images and using convolution with Prewitt filter to create modality within modality.
result Supremacy of proposed fusion frameworks over existing methods on three publicly available datasets.
WiFi helps align and calibrate foot-mounted IMU trajectories.
problem Inertial drift and unknown initial states in FMIP.
method Graph-based SLAM with RSS measurements for WiFi APs.
result Aligns and calibrates trajectories accurately.
New method learns routines from inertial data without privacy concerns.
problem Recognizing human activities with limited sets of specific activities.
method Metric learning problem defined for time series, SS2S architecture.
result Clustering recovers daily routines from learned distance.
New complexity measure for shake-slice knots established.
problem Defining and measuring complexity for shake-slice knots.
method Using dualizable patterns and studying knot signatures.
result Existence of n-shake-slice knots with specified complexity. Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by unveiling the intrinsic mathematical structure of time in Lagrangian mechanics. Moreover…
Study classifies surface types for autonomous indoor robots using inertial data.
problem Classifying surface types for wheeled robots in indoor environments.
method Prepared a time series dataset of inertial measurements, used deep learning and ensemble machine learning models.
result Baseline model achieved over 68% accuracy on a nine-category surface type dataset.
New method improves matrix factorization speed and accuracy.
problem Matrix factorization optimization problems suffer from biased solutions and lack of convergence guarantees.
method Proposes a novel Bregman distance for matrix factorization, enabling non-alternating schemes with convergence proof.
result Convergence to a stationary point proved for matrix factorization problems.
SympFormer accelerates attention blocks using inertial dynamics on density spaces.
problem Improving the efficiency of self-attention blocks in Transformers.
method Introduced accelerated attention blocks derived from inertial Nesterov dynamics on density spaces.
result Accelerated attention blocks converge faster than classical blocks while preserving oracle calls.
Accelerates coordinate descent methods for machine learning problems.
problem Slowness of coordinate descent methods in machine learning.
method Extrapolation-based accelerated coordinate descent.
result Significant speed-up in practice compared to existing methods.
Paper proposes a deep learning method for better IMU gyroscope data.
problem Improving accuracy of IMU gyroscope data for robot orientation estimation.
method Dilated convolution neural network, proper loss function, key points identification.
result Algorithm outperforms state-of-the-art on unseen test sequences.
CNNs classify human activities from IMU data.
problem Automatic identification of physical activities using motion sensors.
method Used Convolutional Neural Networks (CNNs) with raw IMU data.
result CNNs perform well in classifying 16 lower-limb activities.
Improved neural network surrogates for ICF using manifold and cycle consistency.
problem Modeling and predicting complex physical processes in inertial confinement fusion.
method Training neural network surrogates that are consistent with the physical manifold and cyclically consistent.
result Surrogates are superior in predictive performance, more resilient to sampling artifacts, and more data efficient.
TransFall uses transfer learning to improve activity recognition from mobile sensors.
problem Performance degradation due to platform and user movement differences.
method Two-tier data transformation, label estimation, and model generation layers.
result TransFall enhances activity recognition accuracy for new scenarios.
New findings show infinitely many non-homeomorphic manifolds with same proper homotopy type.
problem Characterizing nonrigidity of open contractible manifolds.
method Construction of infinitely many pairwise nonhomeomorphic smooth open contractible manifolds.
result Existence of infinitely many pairwise nonhomeomorphic smooth open contractible manifolds with same proper homotopy type.
Novel AI-IMU method accurately estimates vehicle position and orientation.
problem Accurate dead-reckoning for wheeled vehicles using only IMU.
method Kalman filter and deep neural networks for noise adaptation.
result Average 1.10% translational error, competitive with LiDAR or stereo vision methods.
Jointly estimates flow fields and particle properties from Lagrangian data.
problem Estimating flow fields and particle properties from sparse, noisy Lagrangian data.
method Data assimilation framework coupling Eulerian and Lagrangian models.
result Joint estimation of flow fields and particle properties in various flow regimes.
Seq2seq models predict complex multi-physics systems' time evolution.
problem Predicting the time-evolution of complex multi-physics systems.
method Sequence-to-sequence models applied to multi-physics simulations.
result Seq2seq models accurately emulate complex systems and predict their evolution.