New group shows knots can't always be simplified.
problem Understanding concordance in long virtual knots.
method Introduced long virtual knot concordance group and proved a band-pass invariant not a concordance invariant.
result For every concordance class, there exists a knot not band-pass equivalent to the original or other specific knots.
Classical and welded knot moves are classified and their interrelationships discussed.
problem Classical and welded knot moves and their interrelationships.
method Algebraic classification and topological interpretations of local moves.
result All local moves are unknotting operations for welded knots.
We study generalizations of finite-type knot invariants obtained by replacing the crossing change in the Vassiliev skein relation by some other local move, analyzing in detail the band-pass and doubled-delta moves. Using braid-theoretic techniques, we show that, for a large class of local moves, generalized Goussarov's…
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given. Determinations of the four-ball genus of positive virtual knots are given using the results of a companion paper by the author an…
Complete classification of links up to specific moves.
problem Classifying links using specific local moves.
method Clasper theory.
result Complete classification of links up to clasp-pass moves.
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
problem Learning long-range graph relations and extracting meaningful features from graphs.
method Proposes a learnable geometric scattering (LEGS) module in graph neural networks (GNNs), incorporating wavelet filters.
result LEGS-based GNNs outperform existing methods in graph classification and feature extraction tasks.
The paper addresses instability in CNNs' first layer by proving max pooling's shift invariance.
problem Instability in CNNs' first layer, leading to sensitivity to small input shifts.
method Establishing conditions for max pooling's shift invariance and deriving a measure of stability.
result Max pooling approximates a nearly shift-invariant complex modulus under certain conditions.
The paper analyzes MACD using operator theory.
problem Understanding the mathematical foundation of MACD.
method Developed a functional-analytic framework interpreting MACD as a phase-corrected, smoothed derivative operator.
result MACD is structurally equivalent to a band-pass filter and can be expressed as a finite difference of delayed and doubly averaged signals.
Scattering GCN improves graph neural networks by filtering oversmoothing.
problem Oversmoothing in GCNs limits their ability to distinguish graph nodes.
method Augmenting GCNs with geometric scattering transforms and residual convolutions.
result Scattering GCN outperforms GAT in semi-supervised node classification.
We introduce a new GP kernel based on the sinc function for band-limited signals.
problem Designing covariance kernels for band-limited signals.
method Proposes a Gaussian process kernel with a power spectral density modeled by a rectangular function.
result The sinc kernel facilitates efficient signal processing applications like stereo modulation and band-pass filtering.
Proposes a new method to improve CNNs' shift invariance and accuracy.
problem Improving CNNs' shift invariance and prediction accuracy.
method Replaces RMax with CMod, a Gabor-like structure, to increase shift invariance and accuracy.
result Achieves superior accuracy on ImageNet and CIFAR-10 classification tasks.
Improved multi-modal emotion recognition using deep learning.
problem Combining acoustic and text modalities for emotion recognition.
method Proposes a deep learning-based approach to fuse text and acoustic data using SincNet for acoustic features and parallel DCNN and Bi-RNN branches for text processing with cross attention.
result Achieves 3.5% improvement in weighted accuracy compared to existing methods.
Novel CNN integrates learnable FIR filters for heart sound detection.
problem Automatic detection of heart sound abnormalities for early diagnosis.
method Proposes a CNN with tConv layers to learn FIR filter-bank parameters.
result Proposed models outperform state-of-the-art systems in heart sound detection.
A new hybrid GNN framework tackles oversmoothing in graph data.
problem Oversmoothing in graph convolutional networks limits their expressive power and generalization.
method Combines traditional GCN filters with band-pass filters defined via geometric scattering and introduces an attention framework.
result Improves expressive power and generalization of graph convolutional networks.
Paper uses VAEs and GANs to estimate cryo-EM image orientation and camera parameters.
problem Estimating orientation and camera parameters from noisy cryo-EM images.
method Combines VAEs and GANs to learn latent representation, then designs estimation method.
result Geometric approach for fast cryo-EM biomolecule reconstruction.
End-to-end DRNs outperform ConvNets in EEG decoding.
problem Improving performance of Deep Riemannian Networks (DRNs) in EEG decoding.
method Wide, end-to-end DRN architecture designed and tested on five public EEG datasets.
result EE(G)-SPDNet outperforms state-of-the-art ConvNets in EEG decoding.