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…
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48 results for “correction terms”
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 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.
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…
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…
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.
We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer a non-parametric correction to the misspecified driving term such as to faithful…
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.
Let L be a nonunimodular definite lattice. Using a theorem of Elkies we show that whether L embeds in the standard definite lattice of the same rank is completely determined by a collection of lattice correction terms, one for each metabolizing subgroup of the discriminant group. As a topological application this gives…
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}…
We show that if the connected sum of two knots with coprime Alexander polynomials is doubly slice, then the Ozsváth-Szabó correction terms as smooth double sliceness obstructions vanish for both knots. Recently, Jeffrey Meier gave smoothly slice knots that are topologically doubly slice, but not smoothly doubly slice. …
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…
Análisis de cointegración con una aplicación al mercado de deuda en Estados Unidos, Canadá y Méxicoq-fin.GN
Certain theoretical aspects of vector autoregression (VAR) as tools to model economic time series are revised, in particular their capacity to include both short term and long term information. The VAR model, in its error correction form, is derived and the permanent-transitory decomposition of factors proposed by Gonz…
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.
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.
In this work, we addressed the issue of applying a stochastic classifier and a local, fuzzy confusion matrix under the framework of multi-label classification. We proposed a novel solution to the problem of correcting label pairwise ensembles. The main step of the correction procedure is to compute classifier- specific…
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…
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.
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 .
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…
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.
We derive new obstructions to periodicity of classical knots by employing the Heegaard Floer correction terms of the finite cyclic branched covers of the knots. Applying our results to two fold covers, we demonstrate through numerous examples that our obstructions are successful where many existing periodicity obstruct…
Bias correction improves language model training performance.
problem Stochastic update bias in preconditioned optimizers.
method Cross-fitted preconditioning and variance-corrected inversion.
result Reduces held-out pretraining loss by 0.15 nats.
Physics-Informed Inference Time Scaling for Solving High-Dimensional PDE via Defect Correctionmath.NA
SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
Paper tackles continual reinforcement learning challenges with diversity exploration and adversarial self-correction.
problem Challenges in learning new tasks sequentially due to catastrophic forgetting.
method Develops an end-to-end framework (CDAN) combining unsupervised diversity exploration and adversarial self-correction.
result Final result outperforms baseline by 18.35% in NSD and 0.61 in average reward.
Study of Brown--York mass for four-dimensional asymptotically flat manifolds.
problem Calculating mass for hypersurfaces in four-dimensional asymptotically flat manifolds.
method Intrinsic definition of mean curvature, expansion analysis for large uniformly convex hypersurfaces.
result Shape-dependent correction to ADM mass for nearly round surfaces vanishes under certain conditions.
The resolved conifold geometry is linked to a special Kähler manifold and an instanton-corrected hyperkähler manifold.
problem Understanding the geometry of the resolved conifold and its associated structures.
method Explicit description of ASK and instanton-corrected HK manifolds, relating them to twistor coordinates and solving Riemann-Hilbert problems.
result The instanton-corrected hyperkähler manifold realizes a smoothing of the semi-flat HK metric associated with the ASK geometry.
DSM on manifolds removes singularities and computes small-noise expansions.
problem DSM on manifolds with singular noise.
method Rao-Blackwellized score matching, nearest-point projection, intrinsic Riemannian score.
result Canonical target equals intrinsic Riemannian score up to a small correction.
Mitigates overfitting in UU classification from two unlabeled datasets.
problem Overfitting in the UU classification method.
method Wrapping negative empirical risk terms with correction functions and proving consistency.
result Successfully mitigates overfitting and improves classification accuracy.
The correctness of Harrods model in the differential form is studied. The inadequacy of exponential growth of economy is shown; an alternative result is obtained. By example of Phillips model, an approach to correction of macroeconomic models (in terms of initial prerequisites) is generalized. A methodology based on ba…