arXiv research

Critiques incorrect fixed point assertions in digital topology.

Corrects incorrect assertions about fixed points in digital topology.

Incorrect fixed point assertions in digital topology are discussed.

Incorrect fixed point assertions in digital topology are discussed.

Fixed point assertions in digital topology are often incorrect or poorly stated.

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality under "usual" conditions; or that we improve upon.

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases, researchers using these tools have derived conclusions that are incorrect or tr…

Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.

The paper addresses flaws in fixed point assertions for digital images.

Convolutional neural network improves assertion detection in multi-label clinical text.

The paper [10] incorrectly asserts that the digital image MSS_18, a digital model of the Euclidean 2-sphere S^2, is not 18-contractible. We show this assertion is false.

Study shows AD for neural nets with machine-representable numbers can be incorrect.

Develops a theory for equivariant networks with partial domain symmetry.

The paper highlights issues with fixed point claims in digital images.

The paper highlights issues in fixed point claims in digital topology.

Reliability is a critical consideration to DL-based systems. But the statistical nature of DL makes it quite vulnerable to invalid inputs, i.e., those cases that are not considered in the training phase of a DL model. This paper proposes to perform data sanity check to identify invalid inputs, so as to enhance the reli…

Paper finds previous work on submanifolds incorrect.

Improved text-to-image alignment using iterative VQA feedback.

Fine-tuning neural networks to guarantee performance on specific examples can also introduce incorrect inputs.

This paper was withdrawn as Lemma 2 is incorrect.

Withdrawn by the authors, the main theorem is incorrect

We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres to the larger class of reversible Finsler 2-spheres: Lusternik-Schnirelmann's theorem asserting the existence of three simple closed geodesics, and Bangert-Franks-Hingston's theorem asserting the existence of infinitely many closed geodesics.…

Study on numerical reliability of AD for MaxPool in neural nets.

This paper is not ready for public consumption, as the last step (Figure 20) is incorrect.

State-of-the-art approaches for Knowledge Base Completion (KBC) exploit deep neural networks trained with both false and true assertions: positive assertions are explicitly taken from the knowledge base, whereas negative ones are generated by random sampling of entities. In this paper, we argue that random sampling is …

Let $H$ be the quaternion algebra. Let $g$ be a complex Lie algebra and let $U(g)$ be the enveloping algebra of $g$. We define a Lie algebra structure on the tensor product space of $H$ and $U(g)$, and obtain the quaternification $g^H$ of $g$. Let $S^3g^H$ be the set of $g^H$-valued smooth mappings over $S^3$. The Lie …

Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.

We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every $n$-dimensional homogeneous ANR is a topological $n$-manifold, whereas the Busemann Conjecture asserts that every $n$-dimensional $G$-space is a topological $n$-manifold. The key object in bo…

In this paper we present a statistical analysis about the characteristics that we intend to influence in the performance of the neural networks in terms of assertiveness in the prediction of Brazilian stock returns. We created a population of architectures for analysis and extracted the sample that had the best asserti…

Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.

In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kaehler (or shortly l.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus, and a met…

The original Smale Conjecture asserted that the inclusion of the group O(4) of isometries of the round 3-sphere S into the full diffeomorphism group Diff(S) is a homotopy equivalence. The (Generalized) Smale Conjecture asserts that the inclusion of Isom(M) into Diff(M) is a homotopy equivalence whenever M is an ellipti…

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have…

The Slope Conjecture proposed by Garoufalidis asserts that the degree of the colored Jones polynomial determines a boundary slope, and its refinement, the Strong Slope Conjecture proposed by Kalfagianni and Tran asserts that the linear term in the degree determines the topology of an essential surface that satisfies th…

I show that Matsumoto conjectured inequality between relative length and Finsler length is false. The incorrectness of the claim is easily inferred from the geometry of the indicatrix.

Generalizes $π_2$-diffeomorphism finiteness to non-zero first homotopy groups.

A minimalist approach improves LLM reasoning by filtering incorrect responses.

The Comment cond-mat/0503325 is built around two core statements, both of which are plainly incorrect.

Improves estimation under model misspecification with fake features.

Our main theorem asserts that every Farey graph embedded in the 1-skeleton of the pants complex of any finite type surface is totally geodesic.

The results in the recently posted manuscript arXiv:math/0405153v3 are incorrect. The correct version of the aimed results is not original. The preprint contains material from references that are not properly quoted.

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for Kähler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any f…

New proof found for Khovanov's assertion about Frobenius algebra twists.

Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.

According to Courant's theorem, an eigenfunction as\-sociated with the $n$-th eigenvalue $λ\_n$ has at most $n$ nodal domains. A footnote in the book of Courant and Hilbert, states that the same assertion is true for any linear combination of eigenfunctions associated with eigenvalues less than or equal to $λ\_n$. We c…

Two rigidity theorems for manifolds with nonnegative Ricci curvature and specific volume growth.