arXiv research

Corrects a flawed proof of the Kropholler Conjecture.

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clusterin…

This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.

The paper proves an obstruction to immersed curves with specific curvature.

In recent years several trading platforms appeared which provide a backtest engine to calculate historic performance of self designed trading strategies on underlying candle data. The construction of a correct working backtest engine is, however, a subtle task as shown by Maier-Paape and Platen (cf. arXiv:1412.5558 [q-…

There is a gap in the proof of the main theorem in the article [ShCh13a] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [ShCh13a] is correct. We also describe a computer certification of this result.

Corrected proof for 3D harmonic manifolds with minimal horospheres.

The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we …

This note gives a correction to the proof of the main result of "Harmonic representatives for cuspidal cohomology classes" by J. Dodziuk, J. McGowan and Peter Perry, an article that appeared in Serge Lang memorial volume.

Corrects a 1998 proof about free factors of free groups.

Corrects errors in previous work on linear elasticity calculations.

It has been pointed out to the author by David Glickenstein that the proof of the (closely related) Lemmas 1.2 and 3.2 in the title paper is incorrect. The statements of both Lemmas are correct, and the purpose of this note is to give a correct argument. The argument is of some interest in its own right.

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…

There are errors in the proof of the uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.

This replaces the previous version, by correcting an error in the proof of Theorem 1.4, that was pointed out by the referee.

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoret…

The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.

Corrects errors in previous work on spectral asymptotics in elasticity.

We correct the proof in the unoriented case of Theorem 1.2 in the paper "Cobordisms of maps with singularities of given class"

We present a new, more elementary proof of the Freedman-Teichner result that the geometric classification techniques (surgery, s-cobordism, and pseudoisotopy) hold for topological 4-manifolds with groups of subexponential growth. In an appendix Freedman and Teichner give a correction to their original proof, and reform…

We correct the proof of Theorem 5 of the paper Homology stability for outer automorphism groups of free groups, by the first two authors.

The paper corrects a proof and extends a theorem about linking pairings in 4-manifolds.

We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of $Out(F_N)$ acts on the projectivized space of geodesic currents $\mathbb{P}Curr(F_N)$ with uniform north-south dynamics. The first proof, using purely train-track methods, provides an elaborated and corr…

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 IRL algorithm for continuous state spaces with formal guarantees.

Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are interested in that the consensus BN structure only represents independences all the g…

It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable covering of a finite simplicial complex remains unproved. However, results and proofs of the first four sections (in particular, the approximation…

Counterexample and new proof for curvature varifolds.

We give geometric explanations and proofs of various mirror symmetry conjectures for $T^{n}$-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex stru…

In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then we redevelop the regularity theory for our problem accordingly. This means that m…

We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow on complete noncompact manifolds with bounded curvatures.

Corrected a false lemma in Cimasoni's work on linking theory.

This is the second part of the proof of the exact traiangles in Seiberg-Witten Floer theory. We analyse the splitting and gluing of flow lines of the Chern-Simons-Dirac functional when the underlying three-manifold splits along a torus. (two corrections added)

The paper corrects and improves previous assertions in digital topology.

Completes the proof of curvature tensor existence for Jacobi operators.

In my masters thesis I prove a square root bound on the distance of homological codes that come from two dimensional surfaces, as a result of the systolic inequality. I also give a detailed version of M.H. Freedman's proof that due to systolic freedom, this bound does not hold in higher dimensions.

Researchers found the maximum number of holes in polyominoes grows proportionally to the dimension.

The seminal paper of Caponnetto and de Vito (2007) provides minimax-optimal rates for kernel ridge regression in a very general setting. Its proof, however, contains an error in its bound on the effective dimensionality. In this note, we explain the mistake, provide a correct bound, and show that the main theorem remai…

In Thurston's notes, he gives two different definitions of the Gromov norm (also called simplicial volume) of a manifold and states that they are equal but does not prove it. Gromov proves it in the special case of hyperbolic manifolds as a consequence of his proof that simplicial volume is proportional to volume. We g…

Recently, a lot of effort has been paid to the efficient computation of Kriging predictors when observations are assimilated sequentially. In particular, Kriging update formulae enabling significant computational savings were derived in Barnes and Watson (1992), Gao et al. (1996), and Emery (2009). Taking advantage of …

In this paper we show that for a large class C of 4-manifolds each member of C has only finitely many simple homotopy type upto s-cobordism. This result generalizes a similar result of Hillman for certain complex surfaces. We also present a correction in the proof of Hillman's result.

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessar…

Paper corrects a proof about biharmonic hypersurfaces with three distinct curvatures.

Shorter proof for wave front length in Euclidean disk

In 1978 Brakke introduced the mean curvature flow in the setting of geometric measure theory. There exist multiple variants of the original definition. Here we prove that most of them are indeed equal. One central point is to correct the proof of Brakke's §3.5, where he develops an estimate for the evolution of the mea…

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery form…

We prove that the quotient map from Aut(F_n) to Out(F_n) induces an isomorphism on homology in dimension i for n at least 2i+4. This corrects an earlier proof by the first author and significantly improves the stability range. In the course of the proof, we also prove homology stability for a sequence of groups which a…