# Santiago Quintero's research while affiliated with École Polytechnique and other places

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## Publications (11)

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard family of polarization measures from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinion...

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for $\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \mathcal{E}(\mathbf{M}_n) | =n!\m...

Let $L$ be a distributive lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of finding $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ given $L$ and $f,g\in \mathcal{E}(L)$ as inputs. (1) We show that it can be solved in time $O(n)$ where $n=| L |$. The previous upper bound was $O(n^2)$. (2) We characterize t...

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of age...

Let L be a distributive lattice and E(L) be the set of join endomorphisms of L. We consider the problem of finding f⊓E(L)g given L and f,g∈E(L) as inputs. (1) We show that it can be solved in time O(n) where n=|L|. The previous upper bound was O(n2). (2) We characterize the standard notion of distributed knowledge of a group as the greatest lower b...

We describe a model for polarization in multi-agent systems based on Esteban and Ray’s standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of age...

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of age...

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-pr...

We describe a model for polarization in multi-agent systems based on Esteban and Ray's classic measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on the beliefs of others and an underlying influence graph. We show that polarization eventually disappears (converges to zero) if the influence graph is stro...

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-pr...

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set \({\mathcal {E}}(L)\) of all join-endomorphisms of a given finite lattice \(L\). In particular, we show that when \(L\) is \(\mathbf {M}_n\), the discrete order of n elements extended with top and bottom, \(| {\mathcal...

## Citations

... Our goal when implementing nudges as interventions should be to encourage and imply. Providing information, in the form of nudges, which heavily support the dissuade from one side, may cause heavy strengthening of preexisting radical beliefs due to the weight carried by the confirmation bias in polarized individuals [6], [7]. Instead of providing propaganda/counter-propaganda, we need to merely confuse or provoke thought amongst our targets. ...

... Their work explores the dependence of knowledge in a distributed system on the way processes communicate with one another. Guzmán et al. [23] introduce the theory of group space functions to reason about the information distributed among the members of a potentially infinite group. They develop the semantic foundations and algorithms to reason about distributed knowledge in multi-agent systems and analyze the properties of distributed spaces for reasoning about the distributed knowledge of such systems. ...

... using equation (16). Then, for f , g cotight, we have ...

Reference: Unitless Frobenius Quantales