Combings of oriented compact 3-manifolds are homotopy classes of nowhere zero vector fields in these manifolds. A first known invariant of a combing is its Euler class, that is the Euler class of the normal bundle to a combing representative in the tangent bundle of the 3-manifold . It only depends on the Spin-s…
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “combing”
Financial Frequency Combsnlin.PS
Financial frequency combs emerge from macroeconomic long-range memory.
problem Financial economy's long-run cyclic structure
method Incommensurate fractional-order financial model
result Frequency comb structure in steady-state spectrum
Polynomial braid combingmath.GT
Braid combing is a procedure defined by Emil Artin to solve the word problem in braid groups for the first time. It is well-known to have exponential complexity. In this paper, we use the theory of straight line programs to give a polynomial algorithm which performs braid combing. This procedure can be applied to braid…
New invariant counts graph configurations in 3D manifolds.
problem Counting graph configurations in 3D manifolds.
method Using combings instead of parallelizations for a more flexible definition.
result Universal finite type invariant of three-manifolds.
A closed formula is obtained for the integral of tautological classes over the locus of hyperelliptic Weierstraß points in the moduli space of curves. As a corollary, a relation between Hodge integrals is obtained. The calculation utilizes the homeomorphism between the moduli…
New invariant calculates 4-manifolds using trisection diagrams and combings.
problem Calculating non-semisimple 4-manifold invariants.
method Using trisection diagrams and combings of the trisection surface.
result Invariant calculated for Stein nuclei, generalizing earlier semisimple version.
The Theta invariant is the simplest 3-manifold invariant defined with configuration space integrals. It is actually an invariant of rational homology spheres equipped with a combing over the complement of a point. It can be computed as the algebraic intersection of three propagators associated to a given combing X in t…
This research connects combinatorial Teichmüller space geometry to Weil-Petersson geometry.
problem Understanding the geometry of combinatorial Teichmüller space.
method Developed a parallel between combinatorial Teichmüller space and Weil-Petersson geometry, using measured foliations and Fenchel-Nielsen coordinates.
result Established a geometric recursion and topological recursion for mapping class group invariants.
The invariant is an invariant of rational homology 3-spheres equipped with a combing over the complement of a point. It is related to the Casson-Walker invariant by the formula , where is an invariant of combings that is simply related to a Gompf invariant. In [arXiv:1209.32…
Study measures volume of foliations on surfaces, finding integrability range.
problem Volume of combinatorial unit ball of measured foliations on bordered surfaces.
method Analyzes combinatorial moduli spaces and Kontsevich measure.
result Determines range of integrability for .
Market simulation with hierarchical information fluxcond-mat.stat-mech
We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.
New model captures insurance risk dependencies efficiently.
problem Dependence modeling in sparse time series of insurance claims.
method Comb-Bernoulli model bridging Lévy copulas and zero-mixed models.
result Model enables tractable simulation, likelihood evaluation, and parameter estimation.
A partial formula is provided to calculate the smallest number of vertices possible in a quadrangulation on the closed orientable 2-manifold of given genus. This extends the previously known partial formula due to N. Hartsfield and G. Ringel [J. Comb. Theory, Ser. B, 1989, 46, 84-95].
In high frequency financial data not only returns but also waiting times between trades are random variables. In this work, we analyze the spectra of the waiting-time processes for tick-by-tick trades. The numerical problem, strictly related with the real inversion of Laplace transforms, is analyzed by using Tikhonov's…
We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that these invariants apply in particular to (the exterior of) Legendrian links in c…
New Roman pipeline detects astronomical transients.
problem Automated detection of transients from Roman Space Telescope data.
method Machine learning model RuBR for distinguishing real from fake detections.
result Effective real-bogus classification in Roman era.
The paper computes the Kauffman bracket skein module of -torus knots using braids.
problem Computing the Kauffman bracket skein module of -torus knots.
method Using geometric mixed braids and parting/combing techniques, the paper establishes a relation between the module and the genus 2 handlebody, and computes the module using a basis of the handlebody's module.
result A basis for the Kauffman bracket skein module of -torus knots is found.
Let denote the classical braid group on strands and let the {\em mixed braid group} be the subgroup of comprising braids for which the first strands form the identity braid. Let . We will describe explicit algebraic moves on such that equivale…
Simplified combinatorial descriptions of branched spines for 3-manifolds using primary MP move and sliding moves.
problem Combinatorial descriptions of branched spines for 3-manifolds and their equivalence relations.
method Demonstrated that 16 MP moves on branched spines are derived from a primary MP move, pure sliding moves, and their inverses.
result Simpler combinatorial descriptions for closed 3-manifolds and combed 3-manifolds.
The first part of this paper is a survey on Teichmueller curves and Veech groups, with emphasis on the special case of origamis where much stronger tools for the investigation are available than in the general case. In the second part we study a particular configuration of origami curves in genus 3: A "base" curve is i…
This work studies the entity-wise topical behavior from massive network logs. Both the temporal and the spatial relationships of the behavior are explored with the learning architectures combing the recurrent neural network (RNN) and the convolutional neural network (CNN). To make the behavioral data appropriate for th…
We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of \emph{expert prediction problem} in finite horizon setting with experts. The \emph{expert prediction problem} is formulated as a zero sum game between a player and an adversary. By showing that the solution is $\mathcal{C…
Spaces containing compact subsets with polyhedral complements are studied.
problem Characterizing and understanding spaces with specific topological properties.
method Introduced coronated polyhedra and used them to derive new cohomology and homotopy sequences.
result Spaces with the specified property have well-defined cohomology and homotopy sequences.
This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) of combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness is the condition under which our construction of the corona works. Under the as…
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions, one can restrict to simplicial spheres of particular shapes, called "round" and "u…
In this note it is shown that Berwald spaces admitting the same norm-preserving torsion-free affine connection have the same (weighted) Ricci curvatures. Combing this with Szabó's Berwald metrization theorem one can apply the Cheeger-Gromoll splitting theorem in order to get a full structure theorem for Berwald spaces …
The paper finds minimum Steklov eigenvalues on combinatorial graphs.
problem Finding the minimum Steklov eigenvalues on combinatorial graphs.
method Extending Friedman's nodal domain theory for Laplacian eigenfunctions to Steklov eigenfunctions.
result The minimum of the Steklov eigenvalue on a connected combinatorial graph is essentially attained by a star or a regular comb with minimal brooms.
In this paper we describe braid equivalence for knots and links in a 3-manifold obtained by rational surgery along a framed link in . We first prove a sharpened version of the Reidemeister theorem for links in . We then give geometric formulations of the braid equivalence via mixed braids in using the…
Compact Einstein manifolds with specific curvature operators are constant curvature spaces.
problem Characterizing compact Einstein manifolds with certain curvature operators.
method Bochner technique and Li's result [10]
result Compact Einstein manifolds with specific curvature operators are constant curvature spaces.
New gauge invariants from framed 3-manifolds match Hopf algebra indicators.
problem Computing indicators for Hopf algebras.
method Using Kuperberg invariants from framed 3-manifolds.
result Kuperberg invariants match higher Frobenius-Schur indicators of Hopf algebras.
New geometric properties discovered in a specific Frobenius manifold.
problem Exploring hidden geometric aspects of a specific Frobenius manifold.
method Proved the manifold is pseudo-elliptic, sub-manifold of a Lorentzian projective manifold, and unraveled Maurer-Cartan structures.
result Found causality conditions bridging Lorentzian and probabilistic concepts.
New strategies avoid forced exploration for unimodal bandits.
problem Optimal exploration of unimodal bandit problems.
method Adapting IMED strategy to unimodal structure without forced exploration.
result Proven optimal strategies for unimodal bandits.
We inspect Vietoris-Rips complexes of certain metric spaces using a new generalization of Bestvina-Brady discrete Morse theory. Our main result is a pair of metric criteria on , called the Morse Criterion and Link Criterion, that allow us to deduce information about the homotopy types of certain $VR_t(…
CAI automates extraction and validation of corporate GHG emission metrics.
problem Manual extraction of corporate GHG emission metrics is labor-intensive and error-prone.
method CAI uses LLMs to automate extraction and validation of metrics from corporate disclosures.
result CAI improves data collection efficiency and accuracy by automating the process.
New quantum invariant for framed 3-manifolds using ideal triangulations.
problem Quantum invariants of framed 3-manifolds with vanishing first Betti number.
method Based on ideal triangulations and Hopf algebras, using the pentagon equation and graphical representations.
result Construction of a new quantum invariant for closed framed 3-manifolds.
Machine learning models, especially neural network (NN) classifiers, are widely used in many applications including natural language processing, computer vision and cybersecurity. They provide high accuracy under the assumption of attack-free scenarios. However, this assumption has been defied by the introduction of ad…
Study improves sugarcane plot prediction using data interpolation.
problem Predicting adventive plants in sugarcane plots with limited data.
method Interpolation techniques (Gaussian processes, kriging) for geo-referenced data augmentation.
result GP-COMB outperforms other methods with less additional data.
Dualizable tensor categoriesmath.QA
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-di…
Meta-learning predicts optimal ensemble size and methods for time series forecasting.
problem Finding the best ensemble of time series forecasting methods.
method Two-step approach using meta-learning to predict ensemble size and methods.
result Meta-learning outperformed benchmarks in forecasting errors for all data types and horizons.
Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this multiplexity will lead to misleading results. On the other hand, there exists redunda…
We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to t…
We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with pro…
New method extracts brain age from MRI sequences over time.
problem Lack of ground-truth labels in longitudinal neuroimaging data.
method Combines factor disentanglement with self-supervised learning.
result Extracts brain age information from MRI sequences.
BPVAE enhances VAE robustness to OOD inputs.
problem VAEs struggle with OOD detection, assigning higher likelihoods to some OOD samples.
method Combines VAE with two independent priors: training dataset and simple dataset.
result BPVAE outperforms standard VAEs in OOD detection and generalization.
New method uses offline data to improve online bandit learning, even when distributions differ.
problem Improving online bandit learning with different offline and online distributions.
method MIN-UCB policy that adapts to offline data when informative, achieving tight regret bounds.
result MIN-UCB policy outperforms UCB policy with offline data and provides tight regret bounds.
We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a permanent price impact. The volatility, the volume of different types of orders, the b…
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
S2OSC improves OSC by filtering and re-training models with out-of-class instances.
problem Difficulty in classifying out-of-class instances during inference.
method S2OSC combines semi-supervised learning, out-of-class instance filtering, and model re-training.
result S2OSC achieves state-of-the-art performance in various OSC tasks.