Foam cobordism groups linked to interval exchange automorphisms.
problem Understanding cobordism groups of foams.
method Using the Sah-Arnoux-Fathi invariant and K-theory.
result Identified cobordism groups with homology and K-groups.
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48 results for “invariant interval”
We consider the problem of undirected graphical model inference. In many applications, instead of perfectly recovering the unknown graph structure, a more realistic goal is to infer some graph invariants (e.g., the maximum degree, the number of connected subgraphs, the number of isolated nodes). In this paper, we propo…
Data augmented bootstrap: Unifying confidence interval construction by approximate invariancestat.ME
Data augmented bootstrap unifies various confidence interval construction methods.
problem Constructing confidence intervals from data transformations.
method Data augmented bootstrap (DAB) framework.
result Establishes theoretical coverage results for DAB methods.
Extends knotoid theory to include multiple poles and intervals.
problem No new problem introduced.
method Definition of generalized knotoids and graphs, exploration of invariants.
result Theory subsumes various topological objects and introduces new cases.
Efficient algorithm computes knot invariants quickly.
problem Computing finite type invariants efficiently for knots.
method Create look-up tables for subdiagrams indexed by dyadic intervals, then compute invariants in time.
result Finite type invariants can be computed on an -crossing knot in time, significantly faster than previous methods.
New derivation shows spacetime interval is quadratic without light.
problem Deriving spacetime geometry from fundamental principles.
method Formalizing axioms of smoothness, homogeneity, isotropy, and determinism.
result Invariant spacetime interval is quadratic, independent of light.
Study Agol cycles in pseudo-Anosov 3-braids.
problem Understanding conjugacy invariants of pseudo-Anosov maps.
method Investigate train tracks associated with Farey intervals and describe Agol cycles.
result Complete description of Agol cycles in pseudo-Anosov 3-braids.
An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope …
Using the theory of involutive Heegaard Floer knot theory developed by Hendricks-Manolescu, we define two involutive analogs of the Upsilon knot concordance invariant of Ozsvath-Stipsicz-Szabo. These involutive invariants are piecewise linear functions defined on the interval [0,2]. Each is a concordance invariant and …
Khovanov homology extended to 3-manifolds, linking tangles.
problem Extending Khovanov homology to 3-manifolds.
method Cutting 3-manifolds into intervals, constructing type D and A structures, gluing back.
result Recovering Khovanov homology of links in 3-manifolds.
New tree structure for pseudo-Anosovs from interval maps.
problem Understanding pseudo-Anosovs from interval maps.
method Tree structure on pseudo-Anosovs using rational numbers.
result Deepened dictionary between invariants.
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
Lee metrics on groupsmath.GR
The study examines Lee metrics on groups and their properties.
problem Characterizing groups that admit Lee metrics.
method Analyzing conditions for groups to have or not have Lee metrics, studying specific families of groups, and providing tables for groups of order ≤ 31.
result Conditions for groups to have Lee metrics, including specific families and non-cyclic groups.
Paper develops new conformal prediction methods for sum or average of unknown labels.
problem Uncertainty quantification in joint distributions of random variables.
method Introduces novel conformal prediction methods for sum or average of unknown labels.
result Validates the proposed method for sum or average of unknown labels under permutation invariant assumptions.
The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary invariants, each of which assigns to a knot a piecewise linear function on [0,2].…
The knot concordance invariant Upsilon, recently defined by Ozsvath, Stipsicz, and Szabo, takes values in the group of piecewise linear functions on the closed interval [0,2]. This paper presents a description of one approach to defining Upsilon and of proving its basic properties related to the knot 3-genus, 4-genus, …
We study and classify topologically invariant -ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cub…
We prove Fu's power series conjecture which relates the algebra of isometry invariant valuations on complex space forms to a formal power series from combinatorics which was introduced by Tutte. The -th coefficient of this series is the number of triangulations of a triangle with internal edges; or the number o…
Study topological invariants of complexes for Riemannian manifolds.
problem Understanding topological properties of Riemannian manifolds.
method Analyzing Betti numbers and Euler characteristic of Vietoris-Rips and Čech complexes.
result Betti curve converges to manifold's Betti number within a scale parameter interval.
Relativity Without Light: Homogeneity, Isotropy, and Determinism Force Quadratic Spacetime Metricsmath-ph
Develops a foundational argument for Lorentzian or Euclidean spacetime geometry without light or electromagnetic phenomena.
problem Relativity without light
method Formalizing physical principles as axioms about an invariant interval function
result Invariant interval functions are powers of nondegenerate quadratic forms
For every smooth del Pezzo surface , smooth curve and , we compute the -invariant of Tian and prove the existence of Kähler--Einstein metrics on with edge singularities along of angle for in certain interval. In particular we give lower bounds for the inva…
New knots share same Upsilon invariant despite different Alexander polynomials.
problem Identifying concordant knots via Upsilon invariant.
method Examined hyperbolic L-space knots and their Upsilon invariants.
result Infinitely many pairs of hyperbolic L-space knots with distinct Alexander polynomials share the same Upsilon invariant.
Paper introduces a new invariant for planar knotoids.
problem Defining an invariant for planar knotoids.
method Using Gauss diagrams and transcendental functions.
result The invariant is a Vassiliev invariant of order one.
Rationality of conformally invariant local correlation functions on compactified Minkowski spacehep-th
Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…
We present an efficient technique, which allows to train classification networks which are verifiably robust against norm-bounded adversarial attacks. This framework is built upon the work of Gowal et al., who applies the interval arithmetic to bound the activations at each layer and keeps the prediction invariant to t…
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs …
New hyperbolic knots with convex Upsilon invariants constructed.
problem Constructing knots with convex Upsilon invariants.
method Combinatorial method for -knots and connected sum operation.
result Infinitely many mutually non-concordant hyperbolic knots with convex Upsilon invariants.
New signs and gradings enable detailed comparison in Heegaard Floer theory.
problem Comparing decategorified Heegaard Floer theory with modern TQFTs.
method Added signs and gradings to interval gluing theorem over Z.
result Detailed comparison possible with modern TQFTs.
Floer homology applied to inscribing rectangles into curves.
problem Determining if a Jordan curve can inscribe a square.
method Constructing Floer homology from inscribed rectangles and using spectral invariants.
result A Jordan curve inscribes a square if its enclosed area exceeds half a circle's area.
Kapustin and Witten associate a Hecke modification of a holomorphic bundle over a Riemann surface to a singular monopole on a Riemannian surface times an interval satisfying prescribed boundary conditions. We prove existence and uniqueness of singular monopoles satisfying prescribed boundary conditions for any given He…
We consider families of Dirac operators on the unit interval which depend on parameters via boundary conditions. We study the associated eta forms and Maslov cocyles. With this simple example we show how previous results of Lesch/Woiciechowski and the first author on the eta invariant of cylinders generalize to the fam…
Incompressible fluid dynamics on special manifolds.
problem Fluid dynamics on specific geometric manifolds.
method Analyzes -invariant vector fields on compact manifolds.
result Shows existence of smooth solutions to Euler equations.
CF-GNN provides reliable uncertainty estimates for graph data.
problem Lack of rigorous uncertainty estimates in GNNs.
method Conformal prediction extended to graph-based models (CF-GNN).
result CF-GNN produces prediction sets with provable coverage probability.
We consider expanding vacuum spacetimes with a CMC foliation by compact spacelike hypersurfaces. Under scale invariant a priori geometric bounds (type-III), we show that there are arbitrarily large future time intervals that are modelled by a flat spacetime or a Kasner spacetime. We give related results for a class of …
Let be a connected non-compact -dimensional manifold possibly with boundary and be a foliation on such that each leaf is homeomorphic to and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. H…
The paper tackles distribution-free prediction intervals for multi-source data.
problem Challenges in achieving valid inferences due to distribution shifts and privacy concerns.
method Derives efficient influence functions, incorporates machine learning, and proposes data-adaptive strategies.
result Achieves parametric rates of convergence to nominal coverage probabilities for prediction intervals.
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We cons…
Proposes a method for forecasting large-scale interval-valued time series.
problem Modeling and forecasting large-scale interval-valued time series.
method Feature extraction procedure involving auto-segmentation, clustering, and precision matrix estimation.
result The method enhances forecasting performance for large-scale interval-valued time series.
Let G be compact Lie group. It is shown that the cotangent bundle of the complexification of G admits a hyperkahler structure which is invariant under left and right translations by elements of G. The proof is to realize the cotangent bundle of the complex group as a moduli space of solutions to Nahm's equations on the…
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distributi…
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We name such intervals predictive intervals. This work presents a new method to fi…
New quantum invariants for 3-manifolds with boundary defined via virtual links.
problem Quantum invariants for 3-manifolds with non-vacuous boundaries.
method Surgery on manifolds of the form and virtual link diagrams.
result First meaningful, nontrivial, calculable quantum invariants of 3-manifolds with non-vacuous boundary.
We present a class of knots associated with labelled generic immersions of intervals into the plane and compute their Gordian numbers and 4-dimensional invariants. At least 10% of the knots in Rolfsen's table belong to this class of knots. We call them track knots. They are contained in the class of quasipositive knots…
Defines a new Upsilon torsion function for knot Floer homology.
problem Obtaining constraints on knot cobordisms.
method Defines a one-parameter family of Heegaard Floer torsion invariants.
result Provides new obstructions related to the Gordian distance between knots.
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques f…
New methods for ordinal classification of interval-valued data and functional data.
problem Ordinal classification of interval-valued data and functional data.
method Six ordinal classifiers are proposed, including parametric, binary decomposition, logistic regression, distance-based, k-nearest-neighbor, kernel PCA, and random forest methods.
result Considering ordering and interval-valued information improves the accuracy of ordinal classification.
Develops active intervals for geodesics in Teichmüller space.
problem Understanding geodesics in Teichmüller space with no backtracking.
method Defines active intervals for subsurfaces along geodesics in Thurston metric.
result Active intervals represent reparametrized quasi-geodesics in curve graphs with bounded movement outside.