Extends knot invariant to filtered grid complexes.
problem Knot invariants and grid complexes.
method Combining Ozsváth-Szabó-Stipsicz crossing-change maps with Alishahi-Eftekhary l(K) invariant.
result Combinatorial formulation of knot invariant.
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48 results for “crossed complexes”
New structures allow for self-crossing singularities, leading to new families of stable generalized complex manifolds.
problem Stable generalized complex structures in higher dimensions with self-crossing singularities.
method Extending stable generalized complex structures to include anticanonical sections with normal self-crossings.
result Construction of large families of stable generalized complex manifolds in four dimensions.
New estimate of semimeander complexity for knots with more than 10 crossings.
problem Estimating the complexity of semimeander diagrams of knots.
method Proved a new upper bound on the number of crossings for semimeander diagrams of knots with more than 10 crossings.
result For knots with more than 10 crossings, semimeander diagrams have no more than crossings.
Verifies knot conjecture for 24-crossing knots.
problem Jones Unknot Conjecture for knots up to 24 crossings.
method Described method of verification with complexity analysis.
result Jones Unknot Conjecture verified for 24 crossings.
This paper computes Kakimizu complexes for all 11 crossing prime alternating knots.
problem Computing Kakimizu complexes for prime, alternating knots with 11 crossings.
method Used known algorithms and Murasugi sums with sutured manifold theory.
result Explicitly described Kakimizu complexes for all 11 crossing prime alternating knots.
Cross-regularization adapts model complexity during training.
problem Manual tuning of model complexity for overfitting prevention.
method Directly adapts regularization parameters through validation gradients during training.
result Organic emergence of architecture-specific regularization during training.
Classifies Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
problem Identifying Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
method Comprehensive classification of commensurability classes of cusped, arithmetic, and non-arithmetic complex hyperbolic 2-manifolds.
result Some Nil 3-manifolds are cross-sections in every commensurability class, while others are cross-sections in only one.
On the Homotopy Type and the Fundamental Crossed Complex of the Skeletal Filtration of a CW-Complexmath.GT
We prove that if is a CW-complex, then the homotopy type of the skeletal filtration of does not depend on the cell decomposition of up to wedge products with -disks , when the later are given their natural CW-decomposition with unique cells of order 0, and ; a result resembling J.H.C. Whi…
We use Korányi--Reimann complex cross--ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of complex hyperbolic space and the first Heisenberg group.
We introduce a -valued cross ratio on Roller boundaries of cube complexes. We motivate its relevance by showing that every cross-ratio preserving bijection of Roller boundaries uniquely extends to a cubical isomorphism. Our results are strikingly general and even apply to infinite dimensional…
Investigates ropelength of complex knots and links.
problem Establishing ropelength for knots and links beyond tested crossing numbers.
method Investigated torus knots up to 1023 crossings, satellite knots up to 42 crossings, and used a model of repeated Hopf links.
result Found power-law scaling in T(p,p+1) and derived formulae for predicting crossing-ropelength relationships.
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift movesmath.GT
Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in . Later Horiuchi and Ohyama defined Gordian complex of virtual knots using -move and forbidden moves. In this paper we discuss Gordian complex of knots by region crossing cha…
Clusters cryptocurrency market states via cross correlation analysis.
problem Analyse cryptocurrency market dynamics.
method Cross correlation structure analysis over 5 years.
result Cryptocurrency market clusters into 4 states.
Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a circle pattern on the closed surface. In particular, there is an ass…
Study shows crossing numbers for algebraic knots can differ by arbitrarily large amounts.
problem Comparing two crossing number definitions for algebraic knots.
method Analyzed Hopf fibration and complex singularities to compare crossing numbers.
result Difference between crossing numbers can be arbitrarily large.
We show that the genus problem for alternating knots with crossings has linear time complexity and is in Logspace. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show that the genus problem for these knots belongs to circuit complexity c…
XTNet estimates complex cross-treatment effects in multi-category, multi-valued settings.
problem Challenges in estimating causal effects for multi-category, multi-valued treatments.
method Dynamic Neural Masking for capturing treatment interactions without restrictive assumptions.
result XTNet consistently outperforms state-of-the-art baselines in multi-category, multi-valued treatment effect estimation.
A fast bootstrap method estimates cross-validation standard error.
problem Uncertainty quantification in cross-validation estimates.
method Random-effects model to estimate variance component.
result Valid confidence intervals for model performance.
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the pow…
Cross-entropy loss linked to metric learning, outperforming complex pairwise losses.
problem Improving metric learning performance without complex optimization schemes.
method Theoretical analysis linking cross-entropy to pairwise losses, showing cross-entropy as an upper bound and equivalent to mutual information maximization.
result Minimizing cross-entropy is equivalent to maximizing mutual information, leading to state-of-the-art performance.
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite di…
As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neura…
Echo State Networks (ESNs) are known for their fast and precise one-shot learning of time series. But they often need good hyper-parameter tuning for best performance. For this good validation is key, but usually, a single validation split is used. In this rather practical contribution we suggest several schemes for cr…
The present paper is devoted to some results concerning with the complete lifts of an almost complex structure and a connection in a manifold to its (0,q)-tensor bundle along the corresponding cross-section.
A scalable PyTorch framework for non-crossing quantile regression.
problem Non-crossing quantile regression to avoid impossible negative probability densities.
method CJQR-ALM combining Augmented Lagrangian Method, differentiable pinball loss, and L-BFGS optimization.
result Achieves near-zero crossing rates on large datasets within minutes.
The properties of q-dependent cross-correlation matrices of stock market have been analyzed by using the random matrix theory and complex network. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those a…
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering problems. In our MFPC, the given samples are projected into multiple subspaces t…
The paper connects fibrations to generalized complex structures in semi-toric geometry.
problem Understanding the relationship between fibrations and generalized complex structures.
method Using moment maps in semi-toric geometry and Gompf--Thurston methods for Lie algebroids.
result Constructs self-crossing stable generalized complex four-manifolds and proves compatibility with connected sums.
FluxLayer solves cross-chain liquidity fragmentation for better MEV capture.
problem Cross-chain fragmented liquidity and MEV optimization.
method Three-layer framework integrating settlement, intent, and leverage mechanisms.
result FluxLayer enhances cross-chain MEV by capturing more arbitrage opportunities.
DNN2LR bridges DNN power and LR interpretability.
problem Combining DNN power and LR interpretability for real-world tabular data.
method Automatic feature crossing method based on DNN interpretation inconsistencies.
result DNN2LR outperforms complex DNN models and feature crossing methods.
We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an efficient method for computing the gradient of a cross-validation criterion. To the b…
Measures neural network complexity via effective degrees of freedom.
problem Challenges in quantifying neural network complexity.
method Adapts generalized degrees of freedom (GDF) for binary outcomes and compares with cross-validation and null degrees of freedom.
result GDF provides a robust measure of model complexity for neural networks.
Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross correlations based on wavelet analysis, termed multifractal cross wavelet analysis…
We show that the maximal number of singular moves required to pass between any two regularly homotopic planar or spherical curves with at most n crossings, grows quadratically with respect to n. Furthermore, this can be done with all curves along the way having at most n+2 crossings.
The paper describes topological properties of arcs and crossings in knot theory.
problem Understanding the topological nature of arcs and crossings in knot theory.
method Topological description of arcs and crossings as isotopy classes of probes, homotopy classes of diagram elements.
result Sets of arcs and crossings are fundamental for algebraic objects like quandles, partial ternary quasigroups, biquandloids, and crossoids.
We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. The problem boils down to the construction of a set of special…
Estimates cross-impact on derivatives markets using E-Mini futures and options.
problem Empirical estimation of cross-impact on complex financial instruments like derivatives.
method Modeling derivatives prices as a function of stochastic factors and trades on both factors and derivatives.
result Simple framework successfully captures cross-impact on derivatives markets.
We show that group actions on irreducible cube complexes with no free faces are uniquely determined by their length function. Actions are allowed to be non-proper and non-cocompact, as long as they are minimal and have no finite orbit in the visual boundary. This is, to our knowledge, the first …
We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G there is a complex projective surface S with simple normal crossing singularities only, so that the fundamental group of S is isomorphic to G. …
Study uses detrended cross-correlation to analyze cryptocurrency market, revealing robust collective modes and distinguishing interdependencies.
problem Nonstationarity, long-range memory, and heavy-tailed fluctuations obscure traditional correlations in complex systems.
method Constructs detrended correlation matrices using multifractal detrended cross-correlation coefficient to emphasize different fluctuations.
result Detrending and fluctuation analysis reveal distinct spectral properties from random case, identifying market and sectoral components.
In this paper, we introduce a new concept of stability for cross-validation, called the -stability, and use it as a new perspective to build the general theory for cross-validation. The -stability mathematically connects the generalization ability and the stability of…
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it is motivated by works of Harer, Mosher and Penner. Using properties of the flip graph, we show that the midcubes in the polygonalisation com…
Many classical objects on a surface S can be interpreted as cross-ratio functions on the circle at infinity of the universal covering. This includes closed curves considered up to homotopy, metrics of negative curvature considered up to isotopy and, in the case of interest here, tangent vectors to the Teichmüller space…
Nowadays, users open multiple accounts on social media platforms and e-commerce sites, expressing their personal preferences on different domains. However, users' behaviors change across domains, depending on the content that users interact with, such as movies, music, clothing and retail products. In this paper, we pr…
Cross-GCN models cross features in GCN for better performance.
problem GCN's lack of cross feature modeling limits its effectiveness.
method Introduces Cross-feature Graph Convolution (Cross-GCN) to model cross features explicitly.
result Explicit cross feature modeling improves GCN's performance on tasks requiring cross features.
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…