A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends folding techniques to study subgroups of CAT(0) cube complexes.
Paper proposes a new method for population-wise matching of sulcal graphs.
A novel method compresses point cloud attributes by folding them onto a 2D grid.
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…
Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is generally not well documented in the literature. It is the goal of this paper to in…
Study on the parity of fold map singular points, showing non-invariance for odd-dimensional manifolds.
The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.
In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topolo…
We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyani…
K-fold CV improves machine learning model selection but faces challenges with small datasets.
The principal theory of this paper comprises a technique for constructing associative, coassociative and Cayley submanifolds of Euclidean space with symmetries, using first-order ordinary differential equations. Explicit examples of U(1)-invariant associative cones in R^7 and SU(2)-invariant Cayley 4-folds in R^8 are t…
Proves bounds on ribbonlength for various knot types.
Classifies knots in the Poincaré sphere, using fixed points and folding automata.
Solvents can induce helical knots in simulated biopolymer tubes.
Isothermic nets created from special maps for smooth surfaces.
Our paper introduces an efficient combination of established techniques to improve classifier performance, in terms of accuracy and training time. We achieve two-fold to ten-fold speedup in nearing state of the art accuracy, over different model architectures, by dynamically tuning the learning rate. We find it especia…
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…
Paper proves ribbonlength grows linearly with knot complexity.
Study on folded ribbon knots and their minimum length.
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…
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on exceptional holonomy, in two parts. Part I introduces the exceptional holonomy groups, and explains constructions for compact 7- and 8-manifolds …
This paper confirms a bound for folded ribbonlength of 2-bridge knots.
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.
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.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
Origami can create complex knots, with minimum creases defining a new knot invariant.
New contact structures on folded sums of contact mapping tori are tight under certain 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.
Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain noncompact folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to parametrise solutions of the Yang-Mills equation over the manifolds obtain…
A generic smooth map of a closed -manifold into -space has a finite number of cusps (-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 (-singularities). Two fold maps are fold bordant if the…
The study examines K-polystability on Fano 4-folds with specific Lefschetz defects.
Study on the ribbonlength of knots and links, improving upper bounds.
Paper explores folding patterns of curved creases preserving their geometric properties.
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…
The paper uses singularity theory to find normal forms for sub-Riemannian exponential maps.
Paper constructs fold maps with useful singular value sets.
Study submersions with definite folds on manifolds with boundary into Euclidean spaces.
New linking numbers link complex cycles to Calabi-Yau 3-folds.
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…
We develop a robust convex algorithm to select the regularization parameter in model selection. In practice this would be automated in order to save practitioners time from having to tune it manually. In particular, we implement and test the convex method for -fold cross validation on ridge regression, although the …
In machine learning, statistics, econometrics and statistical physics, cross-validation (CV) is used asa standard approach in quantifying the generalisation performance of a statistical model. A directapplication of CV in time-series leads to the loss of serial correlations, a requirement of preserving anynon-stationar…
The paper details folding of branched covers of the 3-sphere over knots.
Sharp lower bound on fold singularities self-intersections.
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 …