Expanding on a Heisenberg group case for a mathematical proposition.
problem Open case in the Heisenberg group .
method Expanding on Proposition 3.6[1] in the Heisenberg group.
result Foster curiosity for its resolution.
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Corrects conditions in Fissler and Ziegel's 2016 paper.
problem Clarifying conditions in Fissler and Ziegel's 2016 paper.
method None, as it is a correction of existing results.
result Corrects conditions in Proposition 3.4 and Theorem 5.2(ii) of Fissler and Ziegel (2016).
This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. ([7] = arXiv:1809.00593, [13] = arXiv:15…
There is an error in the proof of Proposition 3.7. Proposition 3.7 is needed for the proof of the main theorem.
Proposes a link between randomness and compression in deep learning.
problem Improving efficiency in deep learning training.
method Introduces a novel tomographic compression framework called Dual Tomographic Compression (DTC).
result Demonstrates high correlation between learning performance and Gibbs entropy over compression ratios.
Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.
New heat dispersion laws established for smooth compact manifolds.
problem Understanding heat dispersion in smooth compact manifolds.
method Established new heat dispersion laws through Theorem 1.1 and explored them further with Propositions 3.1 and 3.2.
result New heat dispersion laws for smooth compact manifolds.
About a Proposition on Escobar's paper "The Geometry of the First Non-zero Stekloff Eigenvalue"math.DG
The inequality involving Stekloff eigenvalues is tighter than previously thought.
problem The scope of a previously stated inequality involving Stekloff eigenvalues is narrowed.
method Analyzing conformally related manifolds and the equality condition.
result The equality in the inequality is only possible when the function is constant on the boundary.
The paper extends orthogonal decomposition results to hermitian Higgs bundles.
problem Classical propositions on holomorphic vector bundles do not always extend to Higgs bundles.
method The approach involves extending propositions on orthogonal decompositions and the second fundamental form to hermitian Higgs bundles.
result Extended propositions concerning orthogonal decompositions and the second fundamental form have applications in Higgs bundles.
We study geometric structures of -type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion is a closed 1-form (Proposition \ref{dGamma} and Theorem \ref{Fixspinor}). Using …
Paper shows statistical learning can't always lead to true knowledge.
problem Statistical learning and knowledge acquisition.
method Bayesian approach, Gibbs distribution, active information.
result Full learning and knowledge acquisition are not always possible.
Evaluating Conformance Measures in Process Mining using Conformance Propositions (Extended version)cs.AI
This paper evaluates conformance measures in process mining using conformance propositions.
problem Lack of formal definition and evaluation of conformance measures in process mining.
method Formulated 21 conformance propositions to evaluate existing measures.
result Identified challenges and requirements for conformance measures in process mining.
This paper has been withdrawn by the author, due to an error in Proposition 2.2.
HKT improves sequence processing with multi-scale attention and kernel analysis.
problem Processing sequences at multiple scales with efficient attention mechanisms.
method Trainable causal downsampling and convex weights for level-specific score matrices.
result HKT achieves consistent gains over standard attention across various tasks.
This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.
New algorithm for Riemannian barycentre from Markov chain samples.
problem Computing Riemannian barycentre from non-i.i.d. Markov chain samples.
method Proposes a new Markov chain Monte Carlo algorithm for Riemannian barycentre computation.
result Algorithm converges to Riemannian barycentre of stationary distribution.
In this paper, we will study the existence problem of minmax minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of minmax minimal torus in Theorem 5.1. Firstly we prove a strong uniformization result(Proposition 3.1) using method of [1]. Then we use…
This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as…
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.
We show a few propositions in favour of relations between the phase space of 3D gravity, moduli of quasi-Fuchsian groups, global solutions of cosh-Gordon equations and minimal surfaces in hyperbolic spaces.
We describe an error in the proof of a key proposition, which was necessary for the proof of the main result. Alternate proofs of the main result are given by Ozsvath-Stipsicz-Szabo and Dai-Hom-Stoffregen-Truong.
Paper withdrawn due to errors (superseded by math.AG/0604303). Proposition 11.4 is false, Section 12 is false, and the main statement is true only for bundles with SU(2)-invariant.
We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal intersections. We discuss some applications of the theory, with special emphasis o…
FOCA method prevents co-adaptation between feature extractor and classifier.
problem Co-adaptation between feature extractor and classifier degrades neural network performance.
method FOCA method uses randomly-generated, weak classifiers to optimize feature extractor without explicit co-adaptation.
result FOCA features form a point-like distribution within the same class under special conditions.
Formula for renormalized area of hypersurfaces in hyperbolic spaces.
problem Calculating the renormalized area of asymptotically minimal hypersurfaces in hyperbolic spaces.
method Combining Chen's conformal invariant quantity and Chern-Gauss-Bonnet formulas.
result Extension of renormalized area formulas to higher dimensions and non-minimal cases.
NLN learns logical reasoning from neural networks.
problem Lack of logical reasoning in deep neural networks.
method Dynamic neural architecture that builds computational graph based on logical expressions, learns logical operations as neural modules, conducts propositional logical reasoning.
result NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks.
In this paper, we prove that a Gorenstein toric Fano variety is asymptotically Chow semistable then it is Ding polystable with respect to toric test configurations (Theorem 1.3). This extends the known result obtained by others (Theorem 1.2) to the case where admits Gorenstein singularity. We also sho…
Corrigendum to "Chern connection of a pseudo-Finsler metric as a family of affine connections"math.DG
In this note, we give the correct statements of [2,Proposition 3.3 and Theorem 3.4] and a formula of the Chern curvature in terms of the curvature tensor of the affine connection and the Chern tensor .
Paper proposes a sparse synthetic control method to select important predictors.
problem Choosing and weighting predictors affects synthetic control estimator performance.
method Sparse synthetic control procedure that penalizes predictors, derived in a linear factor model.
result Sparse synthetic control achieves lower bias and better post-treatment performance.
This is a corrected version of my paper "Application of integral geometry to minimal surfaces" appeared in International J. Math. vol. 4 Nr. 1 (1993), 89-111. The correction concerns Proposition 3.5. We discuss this correction in Appendix to the original version of my published paper by reproducing our correspondence w…
The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more g…
Study improves dividend discount model using VAR process.
problem Improving dividend discount models for better predictions.
method Introduced a Gordon growth model based on Vector Autoregressive Process (VAR).
result Two Propositions related to the new model.
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a nove…
The main results of the paper are Proposition 3 and 4 which provide an effective way to construct minimal hypersurfaces in a Euclidean space. We demonstrate our technique by several new examples. This note is English translation of an earlier draft version written (in Russian) in September 1999. The final version of th…
Szabó recently introduced a combinatorially-defined spectral sequence in Khovanov homology. After reviewing its construction and explaining our methodology for computing it, we present results of computations of the spectral sequence. Based on these computations, we make a number of conjectures concerning the structure…
Neuro# learns heuristics to speed up #SAT solvers.
problem Efficiently solving #SAT problems for large industrial instances.
method Learning branching heuristics to improve #SAT solver performance.
result Neuro# reduces step count and wall-clock time on diverse problem families.
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…
Paper provides seven Gauss diagram formulas for degree three long virtual knots.
problem Tackles the complete list of seven distinct Gauss diagram formulas for degree three long virtual knots.
method Gives seven Gauss diagram formulas for degree three long virtual knots and 23 for classical knots.
result Each Gauss diagram formula for degree three long virtual knots is represented as classical knots formulas, supporting Goussarov-Polyak-Viro conjecture.
Algorithm of construction of all knots, links with given number of crosses on diagram of knot, link is offered. This algorithm is based on simple proposition, that there is a representation of knot (link) as closure of braid with n threads and length of this braid does not exceed n(4n-5)+2.
For an embedded submanifold , Belkin and Niyogi showed that one can approximate the Laplacian operator using heat kernels. Using a definition of coarse Ricci curvature derived by iterating Laplacians, we approximate the coarse Ricci curvature of submanifolds in the same way. For this purpose…
Deep RL for ATP in intuitionistic logic, outperforming existing methods.
problem Automated theorem proving in intuitionistic propositional logic.
method Deep reinforcement learning with novel data augmentation and graph neural networks.
result Our prover outperforms Coq's tauto tactic, solving 84% of the theorems in a benchmark library.
Given a Riemannian metric on the 2-sphere, sweep the 2-sphere out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as possible yet preserving the sweepout. We show the following useful property (see Th…
Proposes using logical specifications for multi-objective reinforcement learning to improve agent behavior.
problem Difficulties in controlling reinforcement learning agents and the need for better generalization.
method Uses propositional logic to specify the importance of multiple objectives, encoding these specifications using a recurrent neural network.
result MORL agents parameterized by logical specifications can generalize to novel combinations of objectives and achieve comparable performance.
The article explains Rao distances and conformal mappings for 3D objects.
problem Calculating distances and preserving angles in 3D objects.
method Proposed constructions of distances and angle-preserving mappings.
result Application to virtual tourism and line integrals in complex planes.
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M …
New knot invariant defined without holomorphic theory.
problem Defining knot invariants without holomorphic theory.
method Developed grid homology theory to define .
result is a well-defined knot invariant and provides a lower bound on unknotting number.
Study uses ML to analyze financial behavior in big data.
problem Challenges in analyzing financial big data.
method Applied machine learning to financial behavioral data.
result ML models can effectively estimate performance in financial markets.
How do we assign value to economic transactions? To answer this question, we must consider whether the value of objects is inherent, is a product of social interaction, or involves other mechanisms. Economic theory predicts that there is an optimal price for any market transaction, and can be observed during auctions o…