相关论文: Martin Gardner's Mistake

This work is a modern revisitation of a classical paper by Alessandro Terracini, going back to 1915, which suggests an elementary but powerful method for studing Grassmann defective varieties. In particular, the case of Veronese surfaces is…

The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…

The problem of enumerating meanders -- pairs of simple plane curves with transverse intersections -- was formulated about forty years ago and is still far from solved. Recently, it was discovered that meanders admit a factorization into…

This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…

Cardinal's factorization algorithm of 1996 splits a univariate polynomial into two factors with root sets separated by the imaginary axis, which is an important goal itself and a basic step toward root-finding. The novelty of the algorithm…

Cardinal scores (numeric ratings) collected from people are well known to suffer from miscalibrations. A popular approach to address this issue is to assume simplistic models of miscalibration (such as linear biases) to de-bias the scores.…

Microtask crowdsourcing has enabled dataset advances in social science and machine learning, but existing crowdsourcing schemes are too expensive to scale up with the expanding volume of data. To scale and widen the applicability of…

The shuffle lattice was introduced by Greene in 1988 as an idealized model for DNA mutation, when he revealed remarkable combinatorial properties of this structure. In this paper, we prove an explicit formula for the $M$-triangle of the…

This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the action of GL(2,Z) on the Macdonald polynomials at…

In this paper a twofold inverse problem for orthogonal matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the problem is…

The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…

The work presented in this article suggests a solution to the two sample problem. Keywords: Two sample problem, Welch-Aspin solution, Fisher-Behrens problem, nuisance parameter, similarity, the Linnik phenomenon.

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper's self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is…

Many questions that we ask about the world do not have a single clear answer, yet typical human annotation set-ups in machine learning assume there must be a single ground truth label for all examples in every task. The divergence between…

An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…

We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete

Moment problems and orthogonal polynomials, both meant in a single real variable, belong to the oldest problems in Classical Analysis. They have been developing for over a century in two parallel, mostly independent streams. During the last…

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…

Legendre published the first attempted proof of the law of Quadratic Reciprocity. But, in its final form (1797), it had a gap. Some 125 years later Herman Teege published the first rigorous proof of the unproven hypothesis which formed that…