Searcharxiv⌕ Search

arXiv subjects

George Parfionov

Publications and source records attributed to George Parfionov.

4 recordsLinked to original sources
arXiv2009

Memento Ludi: Information Retrieval from a Game-Theoretic Perspective

We develop a macro-model of information retrieval process using Game Theory as a mathematical theory of conflicts. We represent the participants of the Information Retrieval process as a game of two abstract players. The first player is the `intellectual crowd' of users of search engines, the second is a community of information retrieval systems. In order to apply Game Theory, we treat search log data as Nash equilibrium strategies and solve the inverse problem of finding appropriate payoff functions. For that, we suggest a particular model, which we call Alpha model. Within this model, we suggest a method, called shifting, which makes it possible to partially control the behavior of massive users. This Note is addressed to researchers in both game theory (providing a new class of real life problems) and information retrieval, for whom we present new techniques to control the IR environment.

cs.IR↗
arXiv2006

How `hot' are mixed quantum states?

Given a mixed quantum state $ρ$ of a qudit, we consider any observable $M$ as a kind of `thermometer' in the following sense. Given a source which emits pure states with these or those distributions, we select such distributions that the appropriate average value of the observable $M$ is equal to the average Tr$Mρ$ of $M$ in the stare $ρ$. Among those distributions we find the most typical one, namely, having the highest differential entropy. We call this distribution conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter $β$. The expressions establishing the liaisons between the density operator $ρ$ and its temperature parameter $β$ are provided. Within this approach, the uniform mixed state has the highest `temperature', which tends to zero as the state in question approaches to a pure state.

quant-ph↗
arXiv2006

`Lazy' quantum ensembles

We compare different strategies aimed to prepare an ensemble with a given density matrix $ρ$. Preparing the ensemble of eigenstates of $ρ$ with appropriate probabilities can be treated as `generous' strategy: it provides maximal accessible information about the state. Another extremity is the so-called `Scrooge' ensemble, which is mostly stingy to share the information. We introduce `lazy' ensembles which require minimal efforts to prepare the density matrix by selecting pure states with respect to completely random choice. We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to guess which pure state is prepared by Alice. His null hypothesis, based on the lack of any information about Alice's intention, is that Alice prepares any pure state with equal probability. Then, the average quantum state measured by Bob turns out to be $ρ$, and he has to make a new hypothesis about Alice's intention solely based on the information that the observed density matrix is $ρ$. The arising `lazy' ensemble is shown to be the alternative hypothesis which minimizes the Type I error.

quant-ph↗