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Nikolay N. Osipov

Publications and source records attributed to Nikolay N. Osipov.

8 recordsLinked to original sources
arXiv2026

Collective intelligence in science: direct elicitation of diverse information from experts with unknown information structure

Suppose we need a deep collective analysis of an open scientific problem: there is a complex scientific hypothesis and a large online group of mutually unrelated experts with relevant private information of a diverse and unpredictable nature. This information may be results of experts' individual experiments, original reasoning of some of them, results of AI systems they use, etc. We propose a simple mechanism based on a self-resolving play-money prediction market entangled with a chat. We show that such a system can easily be brought to an equilibrium where participants directly share their private information on the hypothesis through the chat and trade as if the market were resolved in accordance with the truth of the hypothesis. This approach will lead to efficient aggregation of relevant information in a completely interpretable form even if the ground truth cannot be established and experts initially know nothing about each other and cannot perform complex Bayesian calculations. Finally, by rewarding the experts with some real assets proportionally to the play money they end up with, we can get an innovative way to fund large-scale collaborative studies of any type.

cs.GT↗
arXiv2023

From prediction markets to interpretable collective intelligence

We outline how to create a mechanism that provides an optimal way to elicit, from an arbitrary group of experts, the probability of the truth of an arbitrary logical proposition together with collective information that has an explicit form and interprets this probability. Namely, we provide strong arguments for the possibility of the development of a self-resolving prediction market with play money that incentivizes direct information exchange between experts. Such a system could, in particular, motivate simultaneously many experts to collectively solve scientific or medical problems in a very efficient manner. We also note that in our considerations, experts are not assumed to be Bayesian.

cs.GT↗
arXiv2022

Bellman function method for general operators on martingales

It is shown that the Bellman function method can be applied to study the $L^p$-norms of general operators on martingales, i.e., of operators that are not necessarily martingale transforms. Informally, we provide a single Bellman-type function that "encodes" the $L^p$-boundedness of "almost all" operators from Gundy's extrapolation theorem. As examples of such operators, we consider the Haar transforms and the operator whose $L^p$-boundedness underlies Rubio de Francia's inequality for the Walsh system.

math.FA↗
arXiv2017

Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces

We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator are discussed: it is shown that a rotation factor is needed for the boundedness of the operator in some smooth spaces while it is not essential in other spaces. We study the operators on some "end" spaces of the Triebel--Lizorkin scale and then use usual interpolation methods.

math.FA↗
arXiv2014

Sharp estimates of integral functionals on classes of functions with small mean oscillation

We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $\mathbb{R}^2$). We show how the unit ball in the $\mathrm{BMO}$ space, or a Muckenhoupt class, or a Gehring class can be described in such a fashion. Finally, we consider a Bellman function problem on these classes, discuss its solution and related questions.

math.CA↗
arXiv2013

Littlewood--Paley--Rubio de Francia inequality in Morrey--Campanato spaces

Rubio de Francia proved the one-sided Littlewood--Paley inequality for arbitrary intervals in $L^p$, $2 \le p < \infty$. In this article, his methods are developed and employed to prove an analogue of such an inequality "beyond the index $p=\infty$", i.e., for spaces of Hölder functions and BMO.

math.CA↗