Related papers: Proving Conjectures Acquired by Composing Multiple…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
In a sequence of four papers, we prove the following results (via a unified approach) for all sufficiently large $n$: (i) [1-factorization conjecture] Suppose that $n$ is even and $D\geq 2\lceil n/4\rceil -1$. Then every $D$-regular graph…
One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
In this paper, we give an expository presentation of the paper of Olivier Mathieu. The paper of Mathieu proves that a Lie group-theoretic conjecture implies the Jacobian Conjecture. To give Mathieu's proof, we first review the required…
Stephan (Prove or Disprove 100 Conjectures from the OES, arXiv:math/0409509v4 [math.CO])enumerates a number of conjectures regarding integer sequences contained in Sloane's On-line Encyclopedia of Integer Sequences (N. J. A. Sloane, editor,…
The large volume of scientific publications is likely to have hidden knowledge that can be used for suggesting new research topics. We propose an automatic method that is helpful for generating research hypotheses in the field of physics…
We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).
We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].
We study the problem of multiple hypothesis testing for multidimensional data when inter-correlations are present. The problem of multiple comparisons is common in many applications. When the data is multivariate and correlated, existing…
We prove decoupling inequalities for mixed-homogeneous bivariate polynomials, which partially answers a conjecture of Bourgain, Demeter and Kemp.
In this paper, we prove a conjecture by Aas and Linusson on the two-point correlations of adjacent particles in a continuous multispecies TASEP on a ring (AIHPD, 2018). We use the theory of multiline queues as devised by Ferrari and Martin…
Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive…
In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite. In some cases, we are able to prove the conjectured recurrence. In some cases, we are not able to…
Uncertainty plays a crucial role in the machine learning field. Both model trustworthiness and performance require the understanding of uncertainty, especially for models used in high-stake applications where errors can cause cataclysmic…
In an era increasingly dominated by digital platforms, the spread of misinformation poses a significant challenge, highlighting the need for solutions capable of assessing information veracity. Our research contributes to the field of…
The ability to understand logical relationships between sentences is an important task in language understanding. To aid in progress for this task, researchers have collected datasets for machine learning and evaluation of current systems.…
Recently, Andrews and EI Bachraoui obtained several iden tities on two-colored partitions. While solving open problems they posed, Chen and Zhou derived a number of identities using analytic methods and asked for combinatorial proofs. In…