A new CNN approach for time series forecasting outperforms traditional RNNs.
problem Time series forecasting using conventional RNNs.
method Temporally folded convolutional neural networks (TFC's) for sequence forecasting.
result TFC's outperform conventional RNNs on sequential MNIST and JSB chorals datasets.
Study examines how different time series cross-validation methods affect anomaly detection in multivariate time series.
problem Evaluating anomaly detection in multivariate time series requires preserving temporal dependencies, especially for subsequence anomalies.
method Systematically investigates walk-forward and sliding window methods across various validation configurations and classifier types.
result Sliding window method consistently yields higher precision-recall scores and reduced fold-to-fold performance variance, particularly for deep learning models.
TG-GAN models dynamic graph evolution for continuous-time temporal graphs.
problem Challenges in modeling dynamic temporal graphs, especially in continuous time.
method Temporal Graph Generative Adversarial Network (TG-GAN) that models truncated edge sequences, time budgets, and node attributes.
result TG-GAN significantly outperforms existing methods in efficiency and effectiveness.
PSTN improves traffic condition forecasting with deep neural networks.
problem Challenges in accurately forecasting traffic conditions due to complex spatiotemporal correlations.
method Proposes PSTN with three modules: graph convolutional network, temporal convolutional network, and gated recurrent unit framework.
result Significantly outperforms state-of-the-art benchmarks in short-term traffic conditions forecasting.
DASA speeds up SA with delayed agents, achieving N-fold speedup.
problem Speeding up Stochastic Approximation with asynchronous delays.
method DASA: Delay-Adaptive Multi-Agent Stochastic Approximation algorithm.
result First algorithm with convergence rate dependent on mixing time and average delay.
We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning (RL) algorithms can be cast as SAs driven by a `controlled Markov' process. In t…
We prove the existence of asymptotically cylindrical (ACyl) Calabi-Yau 3-folds starting with (almost) any deformation family of smooth weak Fano 3-folds. This allow us to exhibit hundreds of thousands of new ACyl Calabi-Yau 3-folds; previously only a few hundred ACyl Calabi-Yau 3-folds were known. We pay particular att…
Study on folded ribbon knots and their minimum length.
problem Finding the minimum length of folded ribbon knots.
method Using Kauffman's model of folded ribbon knots and analyzing their properties.
result Proved bounds on the minimum folded ribbonlength for various types of knots.
Hybrid QNN-LSTM predicts financial stock market trends using quantum computing.
problem Complex temporal dependencies and market fluctuations in financial time-series forecasting.
method Custom QNN regressor with hybrid optimization strategies.
result Hybrid models integrate quantum computing into financial forecasting workflows.
This is a survey paper of author's results on cobordism groups and semigroups of fold maps and simple fold maps. The results include: establishing a relation between fold maps and immersions through geometrical invariants of cobordism classes of fold maps and simple fold maps in terms of immersions with prescribed norm…
This paper confirms a bound for folded ribbonlength of 2-bridge knots.
problem Bounding the folded ribbonlength of 2-bridge knots.
method Investigated the folded ribbonlength of 2-bridge knots and proved a linear upper bound.
result The folded ribbonlength of a 2-bridge knot K is bounded above by 2c(K)+2. We derive formulas for the mean curvature of associative 3-folds, coassociative 4-folds, and Cayley 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those G2-structures (resp., Spin(7)-structures) for which every associative 3-fold (resp. coassociative…
The paper proves the existence of a folded annulus with multiple creases.
problem Existence of a folded annulus with multiple creases.
method Analyze developable surfaces, use normal curvature and relative torsion, compute geometric descriptors, prove propagation of folds.
result Proves the existence of a folded annulus with multiple creases.
First steps towards a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of Hilb^2(K3). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of Type A or Type B. A 4-fold of Type A is a double cover of a (singular) sextic hype…
Upper bounds on ribbonlength of various knots, showing linear and sub-linear behavior.
problem Estimating the ribbonlength of different types of knots.
method Using Kauffman's model of folded ribbon knots, we derive upper bounds on ribbonlength for specific knot types.
result Upper bounds on ribbonlength are linear in crossing number for some knots and sub-linear for others.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Origami can create complex knots, with minimum creases defining a new knot invariant.
problem Creating complex knots using origami folds.
method Developed a new knot invariant called the fold number, defined as the minimum number of creases required to obtain an equivalent knot.
result No proper foldings can produce nontrivial knots, but improper foldings can.
New contact structures on folded sums of contact mapping tori are tight under certain conditions.
problem Understanding tight contact structures on folded sums of contact mapping tori.
method Alternative bundle-theoretical construction and gluing process near the fold.
result Folded contact structures on folded sums of contact mapping tori are tight under specific conditions.
Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We define folded holomorphic maps, i.e. pseudo-holomorphic maps that are discontinuou…
A smooth map having only fold singularities is called a fold-map. We will give effective conditions for a continuous map to be homotopic to a fold-map from the viewpoint of the homotopy principle.
This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.
problem Understanding the kinematics and nonlinear phenomena of Spidron units.
method Analysis of single unit cell kinematics and recursive construction of multiple cells.
result Non-periodic folding restricts isotropic folding as the number of unit cells increases.
A generic smooth map of a closed 2k-manifold into (3k−1)-space has a finite number of cusps (Σ1,1-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of only fold singularities (Σ1,0-singularities). Two fold maps are fold bordant if the…
The study examines K-polystability on Fano 4-folds with specific Lefschetz defects.
problem Investigating K-polystability on Fano 4-folds with Lefschetz defect at least 2.
method Examining 19 families of Fano 4-folds with Lefschetz defect 3 and 175 families with Lefschetz defect 2, proving K-polystability and instability.
result Exactly 5 out of 19 families of Fano 4-folds with Lefschetz defect 3 are K-polystable, and 5 out of 175 Casagrande-Druel Fano 4-folds with Lefschetz defect 2 are K-polystable.
Study on the ribbonlength of knots and links, improving upper bounds.
problem Finding the infimal folded ribbonlength of knots and links.
method Creating new folded ribbon knots and applying them to improve upper bounds.
result Improved upper bounds for (2,q)-torus links, twist knots, and pretzel links. Paper explores folding patterns of curved creases preserving their geometric properties.
problem Investigating rigid-ruling folding motions of curved crease-rule patterns.
method Deriving conditions for rigid-ruling foldability and analyzing combinations of creases.
result Constant fold-angle creases are only compatible with other constant fold-angle creases.
SOAK assesses data subset similarity for better model training.
problem Estimating similarity between data subsets for accurate predictions.
method Same/Other/All K-fold cross-validation method.
result SOAK estimates similarity of learnable/predictable patterns in data subsets.
This paper is a follow-up to an earlier paper math.DG/0410260 on desingularizations of Calabi-Yau 3-folds with a conical singularity. In math.DG/0410260 we study Calabi-Yau 3-folds M_0 with a conical singularity at x modelled on some Calabi-Yau cone V, and construct a desingularization of M_0 by gluing in an Asymptotic…
Paper constructs fold maps with useful singular value sets.
problem Creating fold maps with specific singular value sets.
method Surgery operations to construct fold maps with crossings.
result Fold maps with singular value sets containing crossings.
Study submersions with definite folds on manifolds with boundary into Euclidean spaces.
problem Understanding differential-topological properties of manifolds with boundary under submersions with definite folds.
method Analyzing submersions with definite folds on manifolds with boundary into Euclidean spaces, focusing on restrictions to the boundary and using results for m-functions.
result Obtained restrictions on the diffeomorphism types of the source manifolds and studied the diffeomorphism types and Euler characteristics of manifolds admitting such maps.
New linking numbers link complex cycles to Calabi-Yau 3-folds.
problem Understanding complex analytic cycles and their Massey products.
method Relating ABC Massey products to holomorphic linking numbers.
result Constructed a family of Calabi-Yau 3-folds with non-vanishing Massey products.
This is the second in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The first paper was math.DG/0008021, which studied special Lagrangian m-folds with large symmetry groups. The third is math.DG/0010036, which uses ideas from this paper to construct families of special Lag…
Study predicts coastal water quality using machine learning, identifying salinity as key factor.
problem Predicting and managing coastal water quality for public health and tourism.
method Machine learning models (Catboost, Xgboost, Random Forests, Support Vector Regression, Artificial Neural Networks) trained on environmental data.
result Catboost algorithm performed best, with R² values of 0.71 and 0.68 for E. Coli and enterococci predictions.
The paper details folding of branched covers of the 3-sphere over knots.
problem Understanding folding of branched covers of the 3-sphere over knots.
method Presenting detailed foldings of dihedral covers of the 3-sphere branched over torus knots.
result Detailed foldings of dihedral covers of the 3-sphere branched over torus knots are presented.
Sharp lower bound on fold singularities self-intersections.
problem Finding a lower bound on the number of self-intersections of fold singularities.
method Established a sharp lower bound on the number of self-intersections of the boundary of an immersed surface, then applied this to fold singularities.
result Sharp lower bound on the number of self-intersections of fold singularities.
Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular …
We give complete geometric invariants of cobordisms of framed fold maps. These invariants consist of two types. We take the immersion of the fold singular set into the target manifold together with information about non-triviality of the normal bundle of the singular set in the source manifold. These invariants were in…
Study symmetry of cross-cap surfaces with folding maps.
problem Reflectional symmetry of cross-cap surfaces.
method Characterization of singularities in folding maps.
result Characterized generic singularities on cross-cap.
Study on manifolds that map to lower dimensions with specific critical points.
problem Characterizing manifolds that map to Rn−1 with round fold maps. method Analyzing smooth n-dimensional closed manifolds with n≥4 and classifying round fold maps up to C∞ A--equivalence. result Determine which manifolds admit round fold maps into Rn−1 and classify these maps. Given a complex 4-fold X with an (Calabi-Yau 3-fold) anti-canonical divisor Y, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of Y. We also discuss gluing formulas which relate relative invariants and DT4 invariants for Calabi-Yau 4-folds.
Generalized quandle polynomial used for stuquandles, stuck links, and RNA folding.
problem Defining polynomial invariants for stuquandles, stuck links, and RNA foldings.
method Introduced a generalized quandle polynomial and proved its invariance for stuquandles. Used this invariant to define polynomials for stuck links and RNA foldings.
result Polynomial invariants for stuquandles, stuck links, and RNA foldings.
Techniques for constructing codimension 2 embeddings and immersions of the 2 and 3-fold branched covers of the 3 and 4-dimensional spheres are presented. These covers are in braided form, and it is in this sense that they are folded. More precisely the composition of the embedding (or immersion) and the canonical proje…
Paper studies surface knotting and its fold curves.
problem Understanding the knotting of surfaces and their fold curves.
method Examines the relationship between surface knotting and fold curves, defines a new invariant.
result Every surface can be isotoped so that its fold curves form an unlink.
This paper introduces ∞- and n-fold vector bundles as special functors from the ∞- and n-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of n-fold vector bundles and we prove that any n-fold vector bundle admits a non-canonical isomorphism to a decomposed …
3D manifolds can map to a plane with specific curve patterns.
problem Characterizing 3D manifolds that can map to the plane with certain curve patterns.
method Analyzing fold maps and their critical value sets.
result Closed orientable 3-manifolds admit round fold maps into the plane if and only if they are graph manifolds.
This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. It is aimed at graduate students i…
Study maxfaces and minfaces converging to surfaces with folded singularities.
problem Analyzing surfaces with folded singularities and their convergence properties.
method Constructing families of maxfaces and minfaces with increasing cuspidal crosscaps.
result Maxfaces and minfaces converge to surfaces with folded singularities.
We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that this cobordism group of simple fold maps is isomorphic to the direct sum of the (n-1)th stable …
In this paper we introduce the area of 2-ruled 4-folds in R^n (n=7 or 8), that is, submanifolds M of R^n that admit a fibration over some 2-fold Sigma such that each fibre is an affine 2-plane in R^n. This is motivated by the paper math.DG/0012060 by Joyce on ruled special Lagrangian 3-folds in C^3 and the work of the …