The multivariate Alexander module of a link L has several subsets that admit quandle operations defined using the module operations. One of them, the fundamental multivariate Alexander quandle, determines the link module sequence of L.
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A commuting -tuple of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module over in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h…
Let be a set of commuting bounded linear operators on a Hilbert space . Then the -tuple turns into a module over in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \raro \clh, \quad \quad …
This paper generalize [7](math.GT/0601291): We construct new links invariants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module. Using this, we get a multivariable link invariant associated to any one …
New Alexander quandles reveal more about link substructures.
problem Understanding sublinks through Alexander quandles.
method Analysis of sublink quandles within multivariate Alexander modules.
result Multivariate Alexander quandles uniquely identify sublink structures.
MTHetGNN models complex relations in multivariate time series forecasting.
problem Complex relations among variables in multivariate time series forecasting.
method Designs a relation embedding module and a temporal embedding module, using graph neural networks and CNNs.
result Achieves state-of-the-art results in multivariate time series forecasting.
Proposes a GNN for multivariate time-series prediction with filtering.
problem Low signal-to-noise ratio in complex systems data.
method Integrates a spatial-temporal GNN with a matrix filtering module to generate filtered graphs.
result Proposed model outperforms baseline approaches in multivariate time-series prediction.
We study various specializations of the colored HOMFLY-PT polynomial. These specializations are used to show that the multivariable link invariants arising from a complex family of sl(m|n) super-modules previously defined by the authors contains both the multivariable Alexander polynomial and Kashaev's invariants. We c…
Constructs the medial quandle from link's peripheral structure.
problem Building the medial quandle of links.
method From reduced Alexander module's peripheral structure.
result Medial quandle constructed successfully.
Study Type skein modules using webs and construct transparent elements.
problem Understanding Type skein modules and constructing transparent elements.
method Diagrammatic approach using multivariable Chebyshev polynomials and explicit braiding formulas.
result Construction of transparent elements in the skein module at roots of unity.
In this paper, a generalized multivariate Student-t mixture model is developed for classification and clustering of Low Probability of Intercept radar waveforms. A Low Probability of Intercept radar signal is characterized by a pulse compression waveform which is either frequency-modulated or phase-modulated. The propo…
ScoreGrad predicts multivariate time series with energy-based models, achieving state-of-the-art results.
problem Predicting multivariate time series with generative models while considering noise and distribution.
method ScoreGrad uses continuous energy-based generative models with a feature extraction and score matching module.
result ScoreGrad achieves state-of-the-art results on six real-world datasets.
STanHop predicts multivariate time series with memory-enhanced capabilities.
problem Predicting multivariate time series with memory-enhanced capabilities.
method Sparse Tandem Hopfield Network (STanHop) with two external memory modules.
result STanHop outperforms dense Hopfield models in memory retrieval error.
Proposes a GNN framework for multivariate time series forecasting.
problem Lack of exploiting latent spatial dependencies in multivariate time series forecasting.
method Automatically extracts graph structures from multivariate time series data, integrates external knowledge, and uses mix-hop and dilated inception layers for capturing dependencies.
result Outperforms state-of-the-art methods on 3 out of 4 benchmark datasets.
OLinear forecasts time series more efficiently by transforming data orthogonally.
problem Efficiently forecasting time series with entangled dependencies.
method OLinear uses OrthoTrans to transform data orthogonally, then applies NormLin for linear layer.
result OLinear achieves state-of-the-art performance with high efficiency.
ABF-T-GLCP forecasts and calibrates uncertainty for multivariate nonstationary time series.
problem Forecasting and uncertainty quantification in nonstationary multivariate time series.
method Adaptive multi-scale forecasting and Gate-Localized Conformal Prediction.
result Consistent gains in point forecasting accuracy and narrower prediction intervals with close empirical coverage.
CATS enhances MTSF by generating ATS from OTS to improve forecasting accuracy.
problem Recent deep learning models often outperform multivariate ones in MTSF.
method CATS constructs ATS from OTS using a 2D temporal-contextual attention mechanism.
result CATS achieves state-of-the-art performance with reduced complexity.
DUET enhances multivariate time series forecasting by clustering time and channels.
problem Heterogeneous temporal patterns and complex channel correlations in multivariate time series.
method DUET uses dual clustering on temporal and channel dimensions to handle these challenges.
result DUET achieves state-of-the-art performance on 25 real-world datasets.
Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of d…
The paper extends Alexander invariant and medial quandle equivalence to links.
problem Understanding stronger invariants for links than Alexander modules.
method Extending Joyce's observation to multiple medial quandles and reduced Alexander modules.
result Medial quandles provide stronger invariants than reduced Alexander modules for links.
Study links using quandles and groups, proving key properties.
problem Understanding links through algebraic structures.
method Analyzing modules and quandles, focusing on metabelian quotients and medial quandles.
result Fundamental multivariate Alexander quandle is isomorphic to the metabelian quotient of the link group.
Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.
problem Analyzing complex multivariate distributions and quantum mechanics.
method Generalizes kernel mean embedding to von Neumann-algebra-valued measures in reproducing kernel Hilbert modules.
result Injectivity and universality of the generalized KME are confirmed.
CATS adapts multivariate time series models by addressing correlation shift.
problem Correlation differences across domains in multivariate time series data.
method CATS introduces correlation shift to measure domain differences, and uses a graph attention module and temporal convolution to align target correlations with source correlations.
result CATS increases over 10% average accuracy compared to vanilla Transformer-based models with minimal additional parameters.
We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module over the Laurent polynomial ring . If is a diagram of a link with components, then the colorings of with values in form a -module…
ForecastGAN: A Decomposition-Based Adversarial Framework for Multi-Horizon Time Series Forecastingcs.LG
ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.
problem Limited performance of existing approaches in short-term and long-term forecasting.
method Decomposition, model selection, adversarial training.
result ForecastGAN consistently outperforms state-of-the-art transformer models for short-term forecasting.
Air quality forecasting has been regarded as the key problem of air pollution early warning and control management. In this paper, we propose a novel deep learning model for air quality (mainly PM2.5) forecasting, which learns the spatial-temporal correlation features and interdependence of multivariate air quality rel…
Unified normative modeling for neuroimaging phenotypes using denoising diffusion models.
problem Discarding multivariate dependence in neuroimaging pipelines.
method Denoising diffusion probabilistic models (DDPMs) with FiLM and SAINT backbones.
result Unified multivariate normative modeling with better calibration and dependence preservation.
New knot polynomials derived from Nichols algebras and braided Hopf algebras.
problem Developing new knot invariants from algebraic structures.
method Constructing knot invariants from solutions to the Yang--Baxter equation over generalized Yetter--Drinfel'd modules.
result Reproduces known knot polynomials and discovers new multivariable invariants.
CoIFNet unifies imputation and forecasting for robust multivariate time series prediction with missing values.
problem Pervasive missing values degrade multivariate time series forecasting accuracy.
method CoIFNet integrates imputation and forecasting through Cross-Timestep Fusion and Cross-Variate Fusion modules.
result CoIFNet achieves 24.40% improvement over state-of-the-art methods at 0.6 point (block) missing rate.
We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this case we show that these invariants are equal and extend to what we call a relativ…
MPPN network improves long-term time series forecasting accuracy.
problem Inaccurate long-term time series forecasting due to noise and lack of interpretability.
method MPPN network constructs context-aware multi-resolution semantic units and employs multi-periodic pattern mining and channel adaptive module.
result MPPN significantly outperforms state-of-the-art methods on nine real-world benchmarks.
Proposes a model for predicting events from event streams.
problem Predicting events like part replacement and failure in manufacturing and teleservice systems.
method Non-parametric prognostic framework using MGCP modulated Poisson processes.
result MGCP prior facilitates sharing of information and analysis of flexible event patterns.
MRC-LSTM predicts Bitcoin prices using CNN and LSTM.
problem Predicting Bitcoin price with high volatility and complex factors.
method Combines MRC and LSTM, focusing on multi-scale features and long-term dependencies.
result MRC-LSTM significantly outperforms other models in Bitcoin price prediction.
Unified framework connects deformation theory and derived categories for multiparameter persistence.
problem Algebraic complexity of multiparameter persistence modules hinders classification, stability, and interpretability.
method Combines deformation theory and derived categories to study multiparameter persistence geometrically.
result Unified conjecture relating interleaving distance to derived convolution metrics established.
BrainCast predicts whole-brain fMRI time series from short scans.
problem Short scans reduce fMRI data quality and statistical power.
method Spatio-temporal forecasting framework for fMRI time series.
result BrainCast improves fMRI time series quality and prediction.
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take …
We define and prove properties of link lattice complexes for plumbed links.
problem Understanding the homology and formality of plumbed L-space links.
method Define and analyze link lattice complexes, proving homotopy equivalence and formality properties.
result Link lattice complexes are homotopy equivalent to link Floer complexes for plumbed links.
FiLM improves deep learning for long-term time series forecasting.
problem Preserving historical information without overfitting noise.
method Applies Legendre Polynomials and Fourier projections, adds low-rank approximation.
result Significantly improves multivariate and univariate forecasting accuracy.
New framework predicts time series with missing values without imputation.
problem Predicting time series with missing values, especially when there's no ground truth for missing data.
method CRIB framework, combining attention mechanism and consistency regularization.
result CRIB framework predicts accurately even under high missing rates.
CARRNN tackles deep learning for sporadic data, improving prediction errors in healthcare.
problem Challenges in learning temporal patterns from sporadic multivariate longitudinal data.
method Developed a novel deep learning architecture combining RNN and CAR models, using a generalized discrete-time autoregressive model.
result CARRNN achieves the lowest prediction errors in multivariate time-series regression tasks.
Classifies modules of surface-knots in terms of their properties.
problem Characterizing modules of surface-knots in terms of their properties.
method Using homology and covering spaces, the reduced first module is characterized.
result The reduced first module for every genus g is characterized in terms of properties of a finitely generated module.
ProbRes calibrates probabilistic forecasts by learning volatility dynamics.
problem Quantifying risk and uncertainty in time series forecasting.
method ProbRes learns conditional mean and volatility separately, generating well-calibrated prediction intervals.
result ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.
New method learns both module structure and sequencing in neural networks.
problem Learning only the parameters and order of execution of neural modules.
method Expands the approach to learn the internal structure of modules, including the ordering and combination of arithmetic operators.
result Performance comparable to hand-designed modules achieved without extra supervisory signals.
Merlin improves robustness of MTSF models to missing data.
problem Suboptimal forecasting performance due to unfixed missing rates in MTSF models.
method Offline knowledge distillation and multi-view contrastive learning.
result Merlin enhances robustness of MTSF models while preserving accuracy.
Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent attention models over possibly large external memory modules constitute the core m…
Curvature defined for Hilbert modules and Kasparov modules.
problem Defining and studying curvature in Hilbert modules and Kasparov modules.
method Introduced curvature for densely defined universal connections on Hilbert -modules relative to spectral triples.
result Curvature only depends on the represented form of the universal connection modulo junk forms.
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.