In this paper we present several counterexamples to Rasmussen's conjecture that the concordance invariant coming from Khovanov homology is equal to twice the invariant coming from Ozsv{á}th-Szab{ó} Floer homology. The counterexamples are twisted Whitehead doubles of the (2,2n+1) torus knots.
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.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Ozsváth-Szabó correction terms”
In this paper we study the knot Floer homology invariants of the twisted and untwisted Whitehead doubles of an arbitrary knot K. We present a formula for the filtered chain homotopy type of HFK(D(+,K,t)) in terms of the invariants for K, where D(+,K,t) denotes the t-twisted positive-clasped Whitehead double of K. In pa…
We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the …
New deformations of lattice cohomology help calculate knot invariants.
problem Calculating knot invariants using lattice cohomology.
method Using holomorphic triangles counting and lattice cohomology.
result Combinatorial formulae for the upsilon invariant are derived.
New knot concordance invariants derived from regions in the plane.
problem Knot concordance and distinguishing knots from thin or algebraic ones.
method Associate invariants to regions in the plane, compute for specific knots, and use to obstruct concordances.
result Compute and use new invariants to obstruct concordances to specific types of knots.
We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind-Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsvath and Szabo. A consequence of our result is that the Casso…
The paper constructs homology spheres with large correction terms.
problem Finding homology spheres with large correction terms.
method Constructing families of homology spheres that bound 4-manifolds with intersection forms isomorphic to -E8.
result Homology spheres have arbitrarily large correction terms.
Study shows vanishing correction terms for doubly slice knots.
problem Understanding doubly slice knots and their properties.
method Analyzing connected sums of knots with coprime Alexander polynomials and using Ozsváth-Szabó correction terms.
result Correction terms vanish for doubly slice knots, providing new insights.
Study proposes a new method to estimate bias-correction term for ATE estimation.
problem Estimating the bias-correction term for ATE estimation.
method Directly estimating the bias-correction term by minimizing Bregman divergence.
result Automatic covariate balancing property achieved through specific model choices.
Lattices embeddability determined by correction terms.
problem Embeddability of nonunimodular definite lattices.
method Using Elkies' theorem and lattice correction terms.
result Embeddability of lattices is determined by correction terms.
We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin structures, generalising the correction terms (or --invariants) defined by Ozsváth and Szabó for integer homology 3-spheres and, more generally, for 3-manifolds with stan…
Design experiments to correct misspecified dynamical models efficiently.
problem Efficiently correct misspecified dynamical models with limited data.
method Model the correction term as a Gaussian Process and use submodular optimization for optimal experimental design.
result Approximately optimal designs can be efficiently derived for Gaussian Process models.
A new correction term improves sample efficiency in deep reinforcement learning.
problem Momentum accumulation in TD learning leads to doubly stale gradients.
method Proposed a correction term to address the issue of doubly stale gradients.
result Improves sample efficiency in policy evaluation.
In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as . Furthermore, numerical simulations show that it reduc…
We make use of the action of in Heegaard Floer homology to generalize the Ozsváth-Szabó correction terms for -manifolds with standard . We establish the basic properties of these invariants: conjugation invariance, behavior under orientation reversal, additivity, and spin ratio…
Manolescu correction terms are numerical invariants of homology three-spheres arising from -equivariant Seiberg-Witten theory that contain information about homology cobordism. We discuss several constraints on these invariants for homology spheres obtained by Dehn surgery on a knot in the three-sphere…
The Heegaard Floer correction term (-invariant) is an invariant of rational homology 3-spheres equipped with a Spin structure. In particular, the correction term of 1-surgeries along knots in is a (-valued) knot concordance invariant . In this paper, we estimate for the -cabl…
Closed formulas for η-corrections in the once-punctured torus identified.
problem Identifying η-corrections in the Kauffman bracket skein algebra of the once-punctured torus.
method Explicit closed formulas for Chebyshev-threaded families and η-corrections.
result Explicit Chebyshev expansions and coefficients for η-corrections.
Corrects earlier work on surface orbifold pure braid groups.
problem Proving a four-term exact sequence for surface orbifold pure braid groups.
method Analyzes surface orbifold pure braid groups for all genus ≥ 1, 2D orientable orbifolds with cone points.
result Proves a four-term exact sequence for surface orbifold pure braid groups.
Análisis de cointegración con una aplicación al mercado de deuda en Estados Unidos, Canadá y Méxicoq-fin.GN
Study analyzes cointegration in US, Canadian, and Mexican bond markets.
problem Identify long-term common factors driving government bond interest rates.
method Used vector autoregression (VAR) and error correction models to analyze cointegration.
result Found long-term common factors influencing US, Canadian, and Mexican bond markets.
The signature of a splicemath.GT
We study the behavior of the signature of colored links [Flo05, CF08] under the splice operation. We extend the construction to colored links in integral homology spheres and show that the signature is almost additive, with a correction term independent of the links. We interpret this correction term as the signature o…
Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionalsecon.EM
New method for estimating treatment effects without complex propensity models.
problem Estimating treatment effects in dynamic treatment regimes.
method Recursive Riesz representer estimation for de-biasing corrections.
result Directly estimates de-biasing corrections without auxiliary models.
We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of transition probabilities. We prove that such approximate corrections are sufficien…
In this paper the relation between the choice of a differential structure and a smooth connection in the tangential bundle is discussed. For the case of an exotic one obtains corrections to the curvature after the change of the differential structure, which can not be neglected by a gauge transformation. In the m…
According to a formula by Gordon and Litherland, the signature of a knot K can be computed as the signature of a Goeritz matrix of K minus a suitable correction term, read off from the diagram of K. In this article, we consider the family of two bridge knots K(p/q) and compute the signature of their Goeritz matrices in…
We show that the four derivative terms in the effective action of three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These terms receive both perturbative and non-perturbative corrections. Using our technique for constraining the effective action, we are able to determine the exact form of the eig…
In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms , are related to the -equivariant Floer homology . We show that the only interesting correction terms of a $\mathrm{Pin}…
The Gauss self-linking integral of an unframed knot is not a knot invariant, but it can be turned into an invariant by adding a correction term which requires adding extra structure to the knot. We collect the different definitions/theorems/proofs concerning this correction term, most of which are well-known (at least …
New invariants improve Heegaard Floer slice genus and clasp number bounds.
problem Improving bounds for knot concordance.
method Using knot Floer homology and involutive correction terms.
result Improved slice genus and clasp number bounds proved.
Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t_0 on Sigma(L), the 2-fold cover of S^3 branched along L. We prove, generalizing results of Manolescu-Owens and Donald-Owens, that for an oriented quasi-alternating link L the signature of L equals minus…
A method compares AI corrections to a base model for explaining predictions.
problem Creating explanations for AI predictions.
method Introduces a surrogate model to correct a simpler base model and provides criteria for accuracy and fidelity.
result Induces neighborhoods of instances with ideal accuracy and fidelity.
Classifies 3-manifolds bounding rational homology balls.
problem Identifying 3-manifolds that bound rational homology balls.
method Used constraints from Donaldson's diagonalization theorem and Heegaard Floer correction terms.
result Complete classification of spherical 3-manifolds bounding rational homology balls.
A method to correct binary classifier errors in multi-label pairwise models.
problem Improving the accuracy of binary classifiers in multi-label pairwise models.
method Computing competence and cross-competence measures to estimate and correct label errors.
result The proposed correction methods significantly outperform the reference method in terms of zero-one loss.
We show that the correction terms in Heegaard Floer homology give a lower bound to the the genus of one-sided Heegaard splittings and the --Thurston norm. Using a result of Jaco--Rubinstein--Tillmann, this gives a lower bound to the complexity of certain closed --manifolds. As an application, we compute…
New methods correct spectral distortions using known analyte concentrations.
problem Distorted spectral shapes from absorbing and scattering contributions.
method Modified penalized baseline correction methods that incorporate known analyte concentrations.
result Improved prediction performance on near infra-red data sets.
Relative Thom polynomials for maps around boundaries established.
problem Understanding singularities in maps around boundaries.
method Introducing and analyzing Thom polynomials relative to prescribed maps around boundaries, establishing structure theorems and correction terms.
result Unified framework for invariants of immersions and singularities of their extensions.
Study geodesic curvature in Heisenberg group, interpreting it as distance correction.
problem Interpreting geodesic curvature in the Heisenberg group.
method Analyzing smooth horizontal curves in the Heisenberg group, interpreting curvature as distance correction.
result Geodesic curvature in Heisenberg group is the first term in distance expansion.
Bias-corrected Cox regression with AI-extracted covariates via calibration summary statisticsstat.ME
Corrects bias in Cox models using AI-extracted covariates.
problem Bias in Cox regression models due to AI-extracted covariates.
method Unified multivariate calibration framework to decompose and correct bias.
result Corrected Cox estimator reduces bias and achieves near-nominal coverage.
A method for inferring ground-truth signals from degraded sensor data.
problem Inferring ground-truth signals from multiple degraded sensor signals.
method Iterative correction of degraded signals using a Bayesian multi-sensor data fusion method.
result The method effectively infers ground-truth signals from noisy and degraded sensor data.
The paper uses Heegaard Floer homology to study homology cobordism groups.
problem Understanding the structure of homology cobordism groups.
method Defined an invariant using Heegaard Floer homology, analogous to Stoffregen's connected Seiberg-Witten Floer homology.
result Computed involutive correction terms for certain three-manifolds.
Given an element in the first homology of a rational homology 3-sphere , one can consider the minimal rational genus of all knots in this homology class. This defines a function on , which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function usi…
Paper introduces deep neural decoders for near-term fault-tolerant quantum experiments.
problem Efficient decoders for quantum error correction under realistic noise.
method Deep neural decoders complemented by traditional algorithms.
result Deep neural decoders perform well in low noise regimes.
UCBMQ improves Q-learning by adding momentum to correct bias and limit regret.
problem Improving Q-learning's bias and regret in reinforcement learning.
method UCBMQ combines Q-learning with an upper confidence bound and momentum term.
result UCBMQ guarantees a regret of with a linear second-order term in .
New method combines machine learning with data assimilation for model error correction.
problem Correcting model errors using sparse and noisy observations.
method Hybrid machine learning and data assimilation methods.
result Tendency correction outperforms resolvent correction in data assimilation experiments.
We give a differential geometric construction of a connection in the bundle of quantum Hilbert spaces arising from half-form corrected geometric quantization of a prequantizable, symplectic manifold, endowed with a rigid, family of Kähler structures, all of which give vanishing first Dolbeault cohomology groups. In [An…
Study shows infinite rank in bipolar filtration of topologically slice knots.
problem Understanding deeper structures in the smooth concordance group of topologically slice knots.
method Used higher order amenable Cheeger-Gromov -invariants and infinitely many Heegaard Floer correction term -invariants.
result Graded quotient of bipolar filtration has infinite rank at each stage greater than one.
We discuss a concordance invariant constructed from Heegaard Floer homology "correction terms" and +/- 1 surgeries on knots in the three-sphere.
Paper proposes a new meta-learning approach for correcting noisy labels.
problem Learning with noisy labels in machine learning models.
method Meta-learned instance re-weighting approach extended to label correction problem.
result Proposed MLC (Meta Label Correction) framework achieves large improvements over previous methods.