arXiv research

New formulas for colored Jones polynomials of double twist knots and related series.

Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new families of $q$-hypergeometric series generalizing the Kontsevich-Zagier series. Comparing with the cyc…

Recent advances in Quantum Topology assign $q$-series to knots in at least three different ways. The $q$-series are given by generalized Nahm sums (i.e., special $q$-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those $q$-series that come from planar gra…

Proves formula for 3D index change with Dehn filling.

We give a formula for the radial asymptotics to all orders of the special $q$-hypergeometric series known as Nahm sums at complex roots of unity. This result is used in~\cite{CGZ} to prove one direction of Nahm's conjecture relating the modularity of Nahm sums to the vanishing of a certain invariant in $K$-theory. The …

Paper constructs new identities linking quantum invariants and modular forms.

Quantum modularity proved for a knot manifold.

Given an element of the Bloch group of a number field~$F$ and a natural number~$n$, we construct an explicit unit in the field $F_n=F(e^{2 πi/n})$, well-defined up to $\nn$-th powers of nonzero elements of~$F_n$. The construction uses the cyclic quantum dilogarithm, and under the identification of the Bloch group of~$F…

We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}. We show that the A-polynomial of the torus knot can be derived from this difference equation. Also constructed is a q-hyp…

Quantum K-theory of quintic 3-fold conjectured with non-polynomial coefficients.

Introduces modular $q$-holonomic modules to solve $q$-difference equations.

The tetrahedral index connects to a q-Bessel function, revealing new mathematical techniques.

Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.

Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact …

Research tackles unequal length time series for classification.

GRATIS generates diverse time series for benchmarking.

Lie-Butcher (LB) series are formal power series expressed in terms of trees and forests. On the geometric side LB-series generalizes classical B-series from Euclidean spaces to Lie groups and homogeneous manifolds. On the algebraic side, B-series are based on pre-Lie algebras and the Butcher-Connes-Kreimer Hopf algebra…

Study series invariants of plumbed 3-manifolds using root lattices.

New formula and properties of inverted Habiro series derived from GM series.

Paper introduces novel distances for clustering ordinal time series.

MDF represents time series motifs as images for improved classification.

Catch22 reduces time series feature space to 22 canonical characteristics for efficient analysis.

MPPN network improves long-term time series forecasting accuracy.

Overview of high-dimensional time series regression methods.

Archive of 20 time series datasets for forecasting evaluation.

Automatically extracts features from time series data for improved forecasting.

Paper proposes a robust time series classification method using ResNet and Recurrence Plots.

New method uses Transformers for flu forecasting.

Improved prediction of hierarchical time series using structured regularization.

New kernel handles irregularly-spaced multivariate time series.

Modeling regime shifts in co-evolving time series with interactions and time-dependency.

Introduces a new benchmark for time series extrinsic regression.

Few-shot learning improves time-series forecasting with limited data.

Meta-learning for Koopman spectral analysis with short time-series data.

Transformers improve time series modeling by capturing long-range dependencies.

We provide the proof that the space of time series data is a Kolmogorov space with $T_{0}$-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…

Adversarial regularization helps learn interpretable shapelets for time series classification.

Global models outperform univariate benchmarks in complex time series forecasting.

theft package simplifies feature extraction for time series analysis in R.

SOEM clusters time series data with improved accuracy.

Dilated CNN improves multivariate time series classification.

CATS enhances MTSF by generating ATS from OTS to improve forecasting accuracy.

Study q-series for 3-manifolds with line defects, proving homomorphism and conjecturing holomorphic modularity.

Quantum modularity proven for specific theta series.

A hybrid loss framework improves time series forecasting by balancing global and component errors.

Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task is to search for similar time series. Dynamic Time Warping (DTW) is a common di…

New deep probabilistic model handles missing data in time series forecasting.

Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series classification. The largest dataset in the UCR archive holds 10 thousand time series only; w…