Related papers: The partial gossip problem revisited
We present a short proof of a celebrated result of G\'acs and K\"orner giving sufficient and necessary condition on the joint distribution of two discrete random variables $X$ and $Y$ for the case when their mutual information matches the…
In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing…
This paper addresses the issue of suppressing a rumor using the truth in a cost-effective way. First, an individual-level dynamical model capturing the rumor-truth mixed spreading processes is proposed. On this basis, the cost-effective…
In connection to a conjecture of W. L\"u. Q. Li and C. Yang we prove a result on small function sharing by a power of a meromorphic function with few poles and its derivative. Our results improve a number of known results.
In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest…
Large language models have advanced rapidly, but no single model excels in every area -- each has its strengths and weaknesses. Instead of relying on one model alone, we take inspiration from gossip protocols in distributed systems, where…
The pseudo-circle is known to be nonhomogeneous. The original proofs of this fact were discovered independently by L. Fearnley and J.T. Rogers, Jr. The purpose of this paper is to provide an alternative, very short proof based on a result…
Partially quenched theories are theories in which the valence- and sea-quark masses are different. Here, we will discuss the nonanalytic one-loop corrections to some physical quantities, using partially quenched chiral perturbation theory.…
In eprint gr-qc/9901053 Gen Yoneda and Hisa-aki Shinkai have made several claims disputing our results in gr-qc/9710004, and gr-qc/9804019. We show here that these claims are not correct.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
The G-normal distribution was introduced by Peng [2007] as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we…
An alternative proof is given for the main result of the article referred to in the title and published in ECP (2024). The proof exploits the theory of regenerative composition structures due to Gnedin and Pitman. The present article is a…
In the IoT era, information is more and more frequently picked up by connected smart sensors with increasing, though limited, storage, communication and computation abilities. Whether due to privacy constraints or to the structure of the…
In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was…
In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large…
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We give an introduction to the ideas behind G. S. Tseytin's 1958 construction of a seven-relation semigroup with undecidable word problem. We give a history of the ideas leading up to its construction, some intuition for the proof, and…
We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.