arXiv subjects

Hélène Barcelo

Publications and source records attributed to Hélène Barcelo.

11 recordsLinked to original sources

arXiv2026

A memorial tribute: Adriano Garsia (1928--2024)

Adriano Mario Garsia was born in Tunis on August 20, 1928, to a Tunisian-Italian family. He lived on a farm there until the end of World War II, then moved to Rome. After finishing high school, he was sent to the United States to live with relatives in Woyming and eventually made his way to California, becoming a student of Charles Loewner at Stanford in the early 1950s. Following his Ph.D., Adriano held positions at MIT, the University of Minnesota, and Caltech before joining the nascent mathematics department at the University of California, San Diego, in 1966 where he spent the remainder of his career. He passed away in San Diego on October 6, 2024, at the age of 96.

math.HO↗

arXiv2021

Punishing defectors and rewarding cooperators: Do people discriminate between genders?

Do people discriminate between men and women when they have the option to punish defectors or reward cooperators? Here we report on four pre-registered experiments, that shed some light on this question. Study 1 (N=544) shows that people do not discriminate between genders when they have the option to punish (reward) defectors (cooperators) in a one-shot prisoner's dilemma with third-party punishment/reward. Study 2 (N=253) extends Study 1 to a different method of punishing/rewarding: participants are asked to rate the behaviour of a defector/cooperator on a scale of 1 to 5 stars. In this case too, we find that people do not discriminate between genders. Study 3a (N=331) and Study 3b (N=310) conceptually replicate Study 2 with a slightly different gender manipulation. These latter studies show that, in situations where they do not have specific beliefs about the gender of the defector/cooperator's partner, neither men nor women discriminate between genders.

physics.soc-ph↗

arXiv2020

Priming reasoning increases intentions to wear a face covering to slow down COVID-19 transmission

Finding mechanisms to promote the use of face masks is fundamental during the second phase of the COVID-19 pandemic response, when shelter-in-place rules are relaxed and some segments of the population are allowed to circulate more freely. Here we report three pre-registered studies (total N = 1,920), using an heterogenous sample of people living in the USA, showing that priming people to "rely on their reasoning" rather than to "rely on their emotions" significantly increases their intentions to wear a face covering. Compared to the baseline, priming reasoning promotes intentions to wear a face covering, whereas priming emotion has no significant effect. These findings have theoretical and practical implications. Practically, they offer a simple and scalable intervention to promote intentions to wear a face mask. Theoretically, they shed light on the cognitive basis of intentions to wear a face covering.

physics.soc-ph↗

arXiv2020

The effect of messaging and gender on intentions to wear a face covering to slow down COVID-19 transmission

Now that various countries are or will soon be moving towards relaxing shelter-in-place rules, it is important that people use a face covering, to avoid an exponential resurgence of the spreading of the coronavirus disease (COVID-19). Here we report a pre-registered online experiment (N=2,459) using a heterogenous, although not representative, sample of people living in the USA, where we test the relative effect of messages highlighting that the coronavirus is a threat to "you" vs "your family" vs "your community" vs "your country" on self-reported intentions to wear a face covering. Results show that focusing on "your community" promotes intentions to wear a face covering relative to the baseline; the trend is the same when comparing "your community" to the other conditions, but not significant. We also conducted pre-registered analyses of gender differences on intentions to wear a face covering. We find that men less than women intend to wear a face covering, but this difference almost disappears in counties where wearing a face covering is mandatory. We also find that men less than women believe that they will be seriously affected by the coronavirus, and this partly mediates gender differences in intentions to wear a face covering (this is particularly ironic because official statistics actually show that men are affected by the COVID-19 more seriously than women). Finally, we also find gender differences in self-reported negative emotions felt when wearing a face covering. Men more than women agree that wearing a face covering is shameful, not cool, a sign of weakness, and a stigma; and these gender differences also mediate gender differences in intentions to wear a face covering.

physics.soc-ph↗

arXiv2019

On the heterogeneity of people's (dis)honest behavior along two dimensions: Cost of lying and cost of acquiring information

This paper studies lying in a novel context. Previous work has focused on situations in which people are either fully aware of the economic consequences of all available actions (e.g., die-under-cup paradigm), or they are uncertain, but this uncertainty cannot be cleared in any way (e.g., sender-receiver game). On the contrary, in reality, people oftentimes know that they will have a chance to lie, they are initially uncertain about the economic consequences of the available actions, but they can invest resources (e.g., time) to find them out. Here we capture the essence of this type of situations by means of a novel decision problem. Two experiments provide evidence of four empirical regularities regarding the distribution of choices, and suggest that participants vary along two dimensions: the moral cost of lying, and the cost of investing time to find out the payoffs associated to the available actions. Taking inspiration from these observations, we introduce a model that is consistent with the main empirical results.

physics.soc-ph↗

arXiv2018

Algebraic Voting Theory & Representations of $S_m \wr S_n$

We consider the problem of selecting an $n$-member committee made up of one of $m$ candidates from each of $n$ distinct departments. Using an algebraic approach, we analyze positional voting procedures, including the Borda count, as $\mathbb{Q}S_m \wr S_n$-module homomorphisms. In particular, we decompose the spaces of voter preferences and election results into simple $\mathbb{Q}S_m \wr S_n$-submodules and apply Schur's Lemma to determine the structure of the information lost in the voting process. We conclude with a voting paradox result, showing that for sufficiently different weighting vectors, applying the associated positional voting procedures to the same set of votes can yield arbitrarily different election outcomes.

math.CO↗

arXiv2015

Group size effect on cooperation in one-shot social dilemmas II. Curvilinear effect

In a world in which many pressing global issues require large scale cooperation, understanding the group size effect on cooperative behavior is a topic of central importance. Yet, the nature of this effect remains largely unknown, with lab experiments insisting that it is either positive or negative or null, and field experiments suggesting that it is instead curvilinear. Here we shed light on this apparent contradiction by considering a novel class of public goods games inspired to the realistic scenario in which the natural output limits of the public good imply that the benefit of cooperation increases fast for early contributions and then decelerates. We report on a large lab experiment providing evidence that, in this case, group size has a curvilinear effect on cooperation, according to which intermediate-size groups cooperate more than smaller groups and more than larger groups. In doing so, our findings help fill the gap between lab experiments and field experiments and suggest concrete ways to promote large scale cooperation among people.

q-bio.PE↗

arXiv2013

The Discrete Fundamental Group of the Associahedron, and the Exchange Module

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory. We study the abelianization of the discrete fundamental group, and show that it is free abelian of rank $\binom{n+2}{4}$. We also find a combinatorial description for a basis of this rank. We also introduce the exchange module of the type $A_n$ cluster algebra, used to model the relations in the cluster algebra. We use the discrete fundamental group to the study of exchange module, and show that it is also free abelian of rank $\binom{n+2}{3}$.

math.CO↗

arXiv2009

$k$-Parabolic Subspace Arrangements

In this paper, we study $k$-parabolic arrangements, a generalization of $k$-equal arrangements for finite real reflection groups. When $k=2$, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement, over $\mathbb{C}$, of the type $W$ Coxeter arrangement is isomorphic to the pure Artin group of type $W$. Khovanov (1996) gave an algebraic description for the fundamental group of the complement, over $\mathbb{R}$, of the 3-equal arrangement. We generalize Khovanov's result to obtain an algebraic description of the fundamental groups of the complements of 3-parabolic arrangements for arbitrary finite reflection groups. Our description is a real analogue to Brieskorn's description.

math.CO↗

arXiv2007

The Discrete Fundamental Group of the Order Complex of $B_n$

A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is equivalent to computing the discrete homotopy group of the 1-skeleton of the permutahedron. To compute this group we introduce combinatorial techniques that we believe will be helpful in computing discrete fundamental groups of other polytopes. More precisely, we use the language of words, over the alphabet of simple transpositions, to obtain conditions that are necessary and sufficient to characterize the equivalence classes of cycles. The proof requires only simple combinatorial arguments. As a corollary, we also obtain a combinatorial proof of the fact that the first Betti number of the complement of the 3-equal arrangement is equal to $2^{n-3}(n^2-5n+8)-1.$ This formula was originally obtained by Björner and Welker in 1995.

math.CO↗

arXiv1997

Combinatorial Representation Theory

We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is much important and beautiful work that we have not been able to mention.

math.RT↗