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Fernando Tohmé

Publications and source records attributed to Fernando Tohmé.

At least 19 recordsLinked to original sources
arXiv2026

From Type to Token: Petri Nets, Individual Token Philosophy, and Individualized Causal Effects

Structural Causal Models and Bayesian Networks are the dominant framework for representing causal relations. They are fundamentally type-level formalisms since their estimands, Average Treatment Effects and Conditional Average Treatment Effects, are properties of distributions over populations, not of individual units. When treatment effects exhibit unbounded heterogeneity, these estimands collapse. What persists is the structural, token-level core of causation. We argue that Petri Nets under the Individual Token Philosophy are the natural representation of these token-level causal structures. We develop a formal translation from Bayesian Networks to Petri Nets, providing a two-layer account of individualized causality. The PN layer provides a structural representation of causal mechanisms that does not rest on distributional assumptions. In turn, a conformal prediction layer quantifies causal effects with finite-sample coverage guarantees. Together they constitute a complete account of individual causal effects.

cs.AI↗
arXiv2026

Watermarking: from Impossibility to Auditable Compliance

Article 50 (2) of the EU Artificial Intelligence Act requires providers of generative systems to make synthetic outputs machine-readable and detectable, while qualifying the effectiveness, interoperability, robustness, and reliability by technical feasibility, cost, content-specific limits, and the state of the art. For free-form text, one important implementation route is the implementation of a generative watermarking procedure, which poses a compliance problem that is hard to address. Strong watermarking is impossible against adaptive removal, while ordinary edits attenuate statistical evidence, and unmarked human text may overlap distributionally with machine output. This article develops an auditable alternative. First, it defines a description-length robustness profile. A finite-sample bound shows that detectable bias decays and that the required sample size grows with the inverse square of the decay rate. This replaces an unidentified Shannon-entropy constant with collision entropy. Second, it constructs label-conditional conformal prediction sets with separate false-attribution and false-exclusion levels, reporting ``watermark supported,'' ``not supported,'' or ``inconclusive''. Coverage is obtained as a finite-sample result and is class-conditional under exchangeability. A small reproducible simulation of a tournament watermark confirms both claims and shows that the surviving-token rule overstates the tolerable edit rate roughly twofold. The resulting premarket certificate, signed detector report, and postmarket recalibration protocol operationalize the Commission's 2026 Code of Practice without claiming universal robustness.

cs.CR↗
arXiv2026

Sheaf Subcategories of Quiver Representations

Let $Q$ be a finite quiver without oriented cycles, $C$ its path category, and $k$ a field. This paper is expository. We assemble in one place, and in elementary combinatorial form, the dictionary between Grothendieck topologies on $C$ and subcategories of $\mathrm{mod}\text{-}kQ$. Every Grothendieck topology on $C$ is rigid, so the sheaf categories are presheaf categories on full subcategories and are indexed by subsets $Σ$ of the vertices; this is due to Murfet in the quiver case and, in far greater generality, to Di-Li-Liang. Passing to $k$-linear coefficients, each topology cuts out a full subcategory $\mathcal{S}_Σ\subseteq \mathrm{mod}\text{-}kQ$. We identify $\mathcal{S}_Σ$ as the perpendicular category, in the sense of Geigle-Lenzing, of the set of simples off $Σ$; it is therefore wide, and equivalent to $\mathrm{mod}\text{-}kQ_Σ$ for an explicit reduced quiver $Q_Σ$. We record when $\mathcal{S}_Σ$ is a Serre subcategory (exactly when $Σ$ is closed under successors), observe that $Σ\mapsto \mathcal{S}_Σ$ embeds the Boolean lattice $2^{Q_0}$ into the lattice of wide subcategories, and note that in Dynkin type $A_n$ this captures $2^n$ of the $C_{n+1}$ wide subcategories. Intrinsically, a wide subcategory $\mathcal{W}$ is a sheaf subcategory exactly when ${}^{\perp}\mathcal{W}$ is a Serre subcategory and $\mathcal{W} = ({}^{\perp}\mathcal{W})^{\perp}$. All of these results are known, or follow readily from known results; the aim is a concrete self-contained account of the quiver case, with attributions collected in Section 8.

math.CT↗
arXiv2026

Regional advantage in rugby sevens: Is there a home effect when nobody is home?

We study the existence of a \emph{Regional Differential} in rugby sevens: whether, in tournaments where no competing team enjoys formal home status, some national sides systematically over- or under-perform depending on \emph{where} the event is staged. Using the universe of 2672 men's and women's matches from international rugby sevens tournaments played between 2016 and 2025, principally the World Rugby Sevens Series, but also the World Cup Sevens and the Olympic Games, we replace the binary ``locality'' indicator of the classic home advantage literature with continuous measures of geographic, temporal, and cultural proximity between each team and the host country. We show that aggregate associations between proximity and performance (which appear large and highly significant in naive specifications) are almost entirely an artifact of \emph{team composition} and \emph{scheduling}: once team and opponent quality are absorbed through fixed effects in a symmetric team-match panel, no general regional advantage survives. However, this null aggregate masks substantial heterogeneity. For a well-defined subset of teams (most notably France, but also New Zealand, the United States, Canada, Spain, Ireland, Kenya, Samoa, and Brazil), performance declines significantly and monotonically with the distance separating the host city from home. Some of the established southern-hemisphere powers (Fiji, South Africa, Australia, Argentina) are essentially distance-neutral. We further show that for some teams the gradient operates through east-west jet lag rather than pure displacement. The Regional Differential in sevens is therefore real but \emph{team-specific} rather than universal, a distinction obscured by pooled estimation.

econ.EM↗
arXiv2026

The Best Are Always the Best: COVID-19 Lockdown Stringency and the Dispersion of Olympic Medal Outcomes

We ask whether COVID-19 lockdown stringency altered national Olympic performance between Rio 2016 and Tokyo 2020, using the Oxford Stringency Index and the 99 countries that won a medal in either edition. As in \citet{liu2024}, mean performance is unaffected: stringency is insignificant in every OLS and ANOVA specification. The distribution is not. Among the 84 non-traditionally dominant nations, medal changes are three to six times more dispersed in high-stringency countries; the difference is absent among dominant nations and concentrated in men's events. A common shock left the competitive hierarchy intact while sharply raising outcome uncertainty for smaller Olympic teams.

econ.EM↗
arXiv2026

Formation of Circular Directed Networks with Shared Link Costs

This paper develops a noncooperative model of directed network formation in which agents create links to access valuable information while sharing the costs generated along the paths through which information is obtained. Each agent is endowed with a positive amount of information and chooses, simultaneously, which other agents to contact. A directed link initiated by one agent allows her to access the information of the contacted agent and of the latter's reachable network, but each link in the resulting information path entails a unit cost. Payoffs therefore depend on the total value of accessible information net of the accumulated connection costs required to obtain it. The paper characterizes the relationship between strategy profiles and directed graphs, defines accessibility, paths, components, and minimal connectedness, and studies the Nash architectures induced by individual best responses. The central result is that strict Nash equilibria must take the form of circular directed networks. Moreover, circular networks are exactly the Nash networks that use the minimum number of links while allowing every agent to access all available information. Although noncircular weak Nash networks may exist, they are structurally redundant and do not satisfy the same minimality property. The model also shows that strict Nash networks are both Pareto optimal and efficient in terms of aggregate welfare. Finally, the paper compares this framework with Bala and Goyal's model, emphasizing that shared path costs and heterogeneous information values generate different equilibrium implications. The analysis supports the equivalence between strict stability and minimal connectivity in directed information networks.

cs.MA↗
arXiv2026

Optimal Networks with Accumulative Costs and Bidirectional Communication

This paper is an extension of the approach of Larrosa and Tohmé (2003), in which the payoff function is modified by allowing information to flow in both directions. Costs continue to be paid by the agent who initiates the connection, so this asymmetry reveals changes in the final equilibrium topology. We find that several optimal topologies persist as Nash networks, but that a strict Nash network corresponds to the sequential line network with intermediate active nodes; that is, agents are placed in a line and, every other agent, they connect with the predecessor agent and with the subsequent agent. In this way, cost accumulation is interrupted and benefits are maximized.

cs.GT↗
arXiv2025

Local and Global Optima: Sheaves and Polynomial Approximations

In this paper, we analyze how global optima of an agent's preferences can be reconstructed from the solutions found for local problems. A sheaf-theoretic analysis provides an abstract characterization of the global solution, and polynomial approximations are obtained when only a few local instances are available.

econ.TH↗
arXiv2025

A categorical representation of games

Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players $\mathbf{Gam}_I$ is built from this representation, and a more general category $\mathbf{Gam}$ is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of $\mathbf{Gam}$, $\mathbf{NE}$ and $\mathbf{Gam}^{NE}$ in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples.

math.CT↗
arXiv2023

Visitors Out! The Absence of Away Team Supporters as a Source of Home Advantage in Football

We seek to gain more insight into the effect of the crowds on the Home Advantage by analyzing the particular case of Argentinean football (also known as soccer), where for more than ten years, the visiting team fans were not allowed to attend the games. Additionally, during the COVID-19 lockdown, a significant number of games were played without both away and home team fans. The analysis of more than 20 years of matches of the Argentinean tournament indicates that the absence of the away team crowds was beneficial for the Top 5 teams during the first two years after their attendance was forbidden. An additional intriguing finding is that the lack of both crowds affects significantly all the teams, to the point of turning the home advantage into home `disadvantage' for most of the teams.

econ.GN↗
arXiv2023

Dynamic Arrangements in Economic Theory: Level-Agnostic Representations

If Economics is understood as the study of the interactions among intentional agents, being rationality the main source of intentional behavior, the mathematical tools that it requires must be extended to capture systemic effects. Here we choose an alternative toolbox based on Category Theory. We examine potential {\em level-agnostic} formalisms, presenting three categories, $\mathcal{PR}$, $\mathcal{G}$ and an encompassing one, $\mathcal{PR-G}$. The latter allows for representing dynamic rearrangements of the interactions among different agents.

econ.TH↗
arXiv2023

Individualized Conformal

The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the observations that may be relevant for a given question and then using simulated controls to yield the intervals for the predicted values. This method is shown to be adaptive and able to detect the presence of latent relevant variables.

stat.ME↗
arXiv2022

An Assessment Tool for Academic Research Managers in the Third World

The academic evaluation of the publication record of researchers is relevant for identifying talented candidates for promotion and funding. A key tool for this is the use of the indexes provided by Web of Science and SCOPUS, costly databases that sometimes exceed the possibilities of academic institutions in many parts of the world. We show here how the data in one of the bases can be used to infer the main index of the other one. Methods of data analysis used in Machine Learning allow us to select just a few of the hundreds of variables in a database, which later are used in a panel regression, yielding a good approximation to the main index in the other database. Since the information of SCOPUS can be freely scraped from the Web, this approach allows to infer for free the Impact Factor of publications, the main index used in research assessments around the globe.

econ.EM↗
arXiv2022

The Relative Importance of Ability, Luck and Motivation in Team Sports: a Bayesian Model of Performance in the English Rugby Premiership

Results in contact sports like Rugby are mainly interpreted in terms of the ability and/or luck of teams. But this neglects the important role of the {\em motivation} of players, reflected in the effort exerted in the game. Here we present a Bayesian hierarchical model to infer the main features that explain score differences in rugby matches of the English Premiership Rugby 2020/2021 season. The main result is that, indeed, {\em effort} (seen as a ratio between the number of tries and the scoring kick attempts) is highly relevant to explain outcomes in those matches.

stat.AP↗
arXiv2021

Fuzzy Group Identification Problems

We present a fuzzy version of the Group Identification Problem ("Who is a J?") introduced by Kasher and Rubinstein (1997). We consider a class $N = \{1,2,\ldots,n\}$ of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function $π: N \to [0; 1]$, indicating for each agent, including herself, the degree of membership to J. We consider the problem of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. While some results are analogous to those of the originally crisp model, the fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein.

econ.TH↗
arXiv2021

Home advantage and crowd attendance: Evidence from rugby during the Covid 19 pandemic

The COVID-19 pandemic forced almost all professional and amateur sports to be played without attending crowds. Thus, it induced a large-scale natural experiment on the impact of social pressure on decision making and behavior in sports fields. Using a data set of 1027 rugby union matches from 11 tournaments in 10 countries, we find that home teams have won less matches and their points difference decreased during the pandemics, shedding light on the impact of crowd attendance on the {\em home advantage} of sports teams.

econ.GN↗
arXiv2021

A Graph-based Similarity Function for CBDT: Acquiring and Using New Information

One of the consequences of persistent technological change is that it force individuals to make decisions under extreme uncertainty. This means that traditional decision-making frameworks cannot be applied. To address this issue we introduce a variant of Case-Based Decision Theory, in which the solution to a problem obtains in terms of the distance to previous problems. We formalize this by defining a space based on an orthogonal basis of features of problems. We show how this framework evolves upon the acquisition of new information, namely features or values of them arising in new problems. We discuss how this can be useful to evaluate decisions based on not yet existing data.

econ.TH↗