Study LMOV invariants for a framed unknot in toric Calabi-Yau 3-folds.
problem Computing LMOV invariants for a specific topological string setup.
method Explicit computation and reformulation of LMOV invariants for genus 0 and higher.
result Proved integrality of LMOV invariants and reformulated higher genus invariants.
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…
Defines new rho invariant for topological groups.
problem No specific problem stated; focuses on new invariant.
method Adapts Weinberger's work using differential geometry.
result Defines additive higher rho invariant for structure groups.
The subject of this paper is Beurling's celebrated extension of the Riemann mapping theorem \cite{Beu53}. Our point of departure is the observation that the only known proof of the Beurling-Riemann mapping theorem contains a number of gaps which seem inherent in Beurling's geometric and approximative approach. We provi…
Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, u i u_i u i , can be detected and quantified by studying the correlations in the magnitude series ∣ u i ∣ |u_i| ∣ u i ∣ , i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact …
This paper presents algebraic structures of Lie-Butcher series.
problem No specific problem is mentioned; it's about the algebraic structures of Lie-Butcher series.
method The paper reviews algebraic operations on Lie-Butcher series and reformulates them as recursive formulae.
result The algebraic theory of Lie-Butcher series has matured.
Research tackles unequal length time series for classification.
problem Unequal length time series in real-world data.
method Identified and evaluated two classes of unequal length mechanisms.
result Practical recommendations for handling unequal length time series.
GRATIS generates diverse time series for benchmarking.
problem Lack of diverse time series data for evaluation.
method Uses mixture autoregressive (MAR) models to generate time series.
result Generates diverse and controllable time series efficiently.
Study series invariants of plumbed 3-manifolds using root lattices.
problem Understanding invariants of plumbed 3-manifolds twisted by root lattices.
method Use formal series to study invariants, decompose Z ^ ( q ) \widehat{Z}(q) Z ( q ) , and compute in specific cases. result Show that Z ^ ( q ) \widehat{Z}(q) Z ( q ) is unique and decomposes into related series invariant under five Neumann moves. Machine learning models outperform traditional time series models in financial series prediction.
problem Precise financial series prediction due to instability and noise.
method Comparison between traditional time series models (ARIMA, GARCH) and machine learning models (deep learning) using real stock index data.
result Machine learning models significantly outperform traditional models in financial series prediction accuracy.
New formula and properties of inverted Habiro series derived from GM series.
problem Understanding and manipulating knot invariants using series expansions.
method Developed a new formula for the inverted Habiro series (IHS) in terms of GM series and theta functions. Proved a multiplication formula for IHS.
result Established a natural ring structure for IHS and studied its residues, applying them to Dehn surgery formulas.
Paper introduces novel distances for clustering ordinal time series.
problem Clustering ordinal time series with discrete response.
method Introduces two novel distances and fuzzy clustering algorithms.
result Fuzzy clustering algorithms accurately group series from similar stochastic processes.
MDF represents time series motifs as images for improved classification.
problem Classifying time series data with high-order patterns.
method Motif Difference Field (MDF) using Fully Convolutional Networks (FCN).
result MDF outperforms other methods on UCR time series datasets.
Catch22 reduces time series feature space to 22 canonical characteristics for efficient analysis.
problem Efficiently capturing and comparing time series properties for diverse applications.
method Inference of minimal sets of time-series features from a comprehensive library.
result Catch22 (22 canonical characteristics) reduces computation time and complexity.
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.
New infinite series of hyperbolic polytopes with special growth rates found.
problem Finding new infinite series of non-compact hyperbolic polytopes.
method Constructing infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes.
result Growth rates of the constructed polytopes are Perron numbers.
Archive of 20 time series datasets for forecasting evaluation.
problem Lack of comprehensive time series forecasting datasets.
method Compilation and characterisation of 20 datasets from various domains.
result Characterisation and performance evaluation of datasets.
Automatically extracts features from time series data for improved forecasting.
problem Manual feature selection for time series forecasting is inefficient and prone to errors.
method Extracts features from time series using recurrence plots and computer vision algorithms.
result Automatically extracted features lead to highly comparable and sometimes superior forecasting performance.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
Analyzes sequence-to-sequence models for time series forecasting.
problem Choosing between sequence-to-sequence models and classical time series models.
method Theoretical analysis of sequence-to-sequence models for time series forecasting.
result Provides a quantitative guide for practitioners.
Paper proposes a robust time series classification method using ResNet and Recurrence Plots.
problem Classifying time series data is challenging and underexplored.
method Transfer learning in Deep Neural Networks, 2D Recurrence Plots, ResNet architecture, simplified preprocessing.
result First time multi-time series classification using a single network.
Two new data synthesizers generate multidimensional time series for analysis.
problem Evaluate distance functions on high-dimensional time series.
method Proposed two new data synthesizers: CBF and RAM.
result Evaluation of 1-nearest neighbor classifier using DTW on generated datasets.
Improved prediction of hierarchical time series using structured regularization.
problem Making coherent forecasts for hierarchical time series.
method Structured regularization method for bottom-level time series predictions.
result Superior prediction accuracy and computational efficiency compared to previous methods.
New kernel handles irregularly-spaced multivariate time series.
problem No kernel exists for irregularly-spaced multivariate time series.
method Built a series kernel from vector kernels, ensuring it's PSD.
result Validated the series kernel on multiple datasets and time series classification.
New method uses Transformers for flu forecasting.
problem Forecasting influenza-like illness trends.
method Transformer-based machine learning models with self-attention.
result Forecasting results are competitive with state-of-the-art methods.
Modeling regime shifts in co-evolving time series with interactions and time-dependency.
problem Discovering and modeling regime shifts in multiple time series with relationships and time-dependent behaviors.
method Modeling interactions and time-dependency in co-evolving time series using a mapping grid and dynamic network representation for regime identification and time-dependent Cox regression for regime transition probabilities.
result A principled approach for modeling interactions and time-dependency in co-evolving time series.
Introduces a new benchmark for time series extrinsic regression.
problem Predicting a single continuous value from univariate or multivariate time series, not necessarily related to the predictor.
method Developed a new benchmarking archive for time series extrinsic regression.
result Initial benchmarking of existing models on the new TSER datasets.
Proximity Forest classifies time series in milliseconds from large datasets.
problem Classifying time series from large datasets with high accuracy and speed.
method Ensemble of randomized Proximity Trees, leveraging proximity measures instead of attribute values.
result Proximity Forest achieves high accuracy on large datasets and is significantly faster than state-of-the-art models.
Few-shot learning improves time-series forecasting with limited data.
problem Limited data in target tasks degrade forecasting performance.
method A few-shot learning method using recurrent neural networks with attention.
result The model forecasts future values effectively with minimal data.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Transformers improve time series modeling by capturing long-range dependencies.
problem Capturing long-range dependencies in time series data.
method Summarized and reviewed adaptations of Transformers for time series analysis.
result Transformers enhance time series forecasting, anomaly detection, and classification.
Global models outperform univariate benchmarks in complex time series forecasting.
problem Comparing global forecasting models to univariate benchmarks in various challenging scenarios.
method Simulated datasets with controlled characteristics, including homogeneity, complexity, and series lengths. Global forecasting models (RNN, LGBM) compared to univariate techniques.
result Global models like RNN and LGBM are competitive in complex scenarios with short series lengths and heterogeneous data.
Adversarial regularization helps learn interpretable shapelets for time series classification.
problem Difficult to interpret learned shapelets in time series classification.
method Use of adversarial regularization to constrain model to learn more interpretable shapelets.
result Adversarially regularized method learns interpretable shapelets.
Proposes copulas for heteroskedastic time series with improved volatility measures.
problem Capturing serial dependence in stationary time series with varying volatility.
method Developed parametric copulas for Markov and multivariate series, derived volatility proxy copulas, and proposed new volatility dependence measures.
result Proposed copulas outperform GARCH models in capturing volatility and producing accurate risk forecasts.
We provide the proof that the space of time series data is a Kolmogorov space with T 0 T_{0} T 0 -separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…
A novel time series clustering method that considers segment typologies.
problem Lack of consideration for the similarity of different subsequences in time series clustering.
method Two-stage clustering: polynomial segmentation followed by hierarchical clustering of segments, then final clustering of time series.
result The method outperforms state-of-the-art techniques on UCR Time Series Classification Archive datasets.
theft package simplifies feature extraction for time series analysis in R.
problem Lack of a unified access point and methodological pipelines for feature-based time series analysis.
method theft package provides a unified framework for computing features from six open-source time series feature sets.
result theft enables comprehensive quantification and interpretation of time series structure.
Model uses RNNs to forecast similar time series groups.
problem Forecasting similar time series databases with traditional methods.
method Time series clustering and LSTM networks.
result Outperforms baseline LSTM model and other methods in forecasting competitions.
SOEM clusters time series data with improved accuracy.
problem Clustering non-aligned time series data.
method Generalizes SOFM to matrix input using approximate joint diagonalisation of covariance structures.
result SOEM produces valid topological clustering of time series data.
Dilated CNN improves multivariate time series classification.
problem Multivariate time series classification.
method Transformed multivariate time series into image-like style, applied dilated and strided convolutions.
result Automatic features extracted by dilated CNN are as effective as hand-crafted features.
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.
Study q-series for 3-manifolds with line defects, proving homomorphism and conjecturing holomorphic modularity.
problem Understanding BPS q q q -series for 3-manifolds with line defects. method Proving homomorphism from skein module to space of q q q -series, conjecturing holomorphic modularity. result Holomorphic quantum modularity of q q q -series suggests new approach to Langlands duality. Quantum modularity proven for specific theta series.
problem Proving quantum modularity for partial theta series with periodic coefficients.
method Explicit proof using Kontsevich-Zagier series and colored Jones polynomials.
result Kontsevich-Zagier series is a weight 3/2 quantum modular form.
A hybrid loss framework improves time series forecasting by balancing global and component errors.
problem Current time series methods may prioritize less significant sub-series, leading to forecasting bias.
method Proposes a hybrid loss framework combining global and component losses, dynamically adjusting weights.
result Improves time series forecasting performance by 0.5-2% on average.
New deep probabilistic model handles missing data in time series forecasting.
problem Handling missing data in time series forecasting.
method Combination of deep learning and probabilistic methods.
result Advantage in forecasting and novelty detection with missing data.
A new framework for generating predictive features in noisy multivariate time series.
problem Predicting noisy multivariate time series with limited user effort.
method Develops a feature programming framework based on spin-gas dynamical Ising models.
result Validated the method on synthetic and real-world datasets.
Bayesian QFSTS model tackles feature selection in quantile time series analysis.
problem Quantile feature selection in correlated multivariate time series data.
method Bayesian dimension reduction methodology using QFSTS model with multivariate asymmetric Laplace distribution, spike-and-slab prior, Metropolis-Hastings algorithm, and Bayesian model averaging.
result QFSTS model outperforms in feature selection, parameter estimation, and forecasting.
Method summarizes and predicts time series data for COVID-19 cases and deaths.
problem Summarizing and predicting time series data for multiple related time series.
method Hierarchical algorithm generating shapelets for centroids, nearest neighbor search for labeling, dynamic time warping for non-uniform lengths.
result Predictive model for individual time series based on aggregated statistics.