arXiv subjects

Mario Veruete

Publications and source records attributed to Mario Veruete.

4 recordsLinked to original sources

arXiv2023

Artificial intelligence and the skill premium

What will likely be the effect of the emergence of ChatGPT and other forms of artificial intelligence (AI) on the skill premium? To address this question, we develop a nested constant elasticity of substitution production function that distinguishes between industrial robots and AI. Industrial robots predominantly substitute for low-skill workers, whereas AI mainly helps to perform the tasks of high-skill workers. We show that AI reduces the skill premium as long as it is more substitutable for high-skill workers than low-skill workers are for high-skill workers.

econ.TH↗

arXiv2019

Density dependent replicator-mutator models in directed evolution

We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal rescaling related to the Avron-Herbst formula [1] to give of a complete picture of the Cauchy problem. Besides its well-posedness, we provide an implicit/explicit expression of the solution, and analyze its large time behaviour. As a by product, we also solve a replicator-mutator model where the mutation coefficient is socially determined, in the sense that it is modulated by the mean-fitness. The latter model reveals concentration or anti diffusion/diffusion phenomena.

math.AP↗

arXiv2018

Evolutionary branching via replicator-mutator equations

We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some underlying Schrödinger spectral elements (for which we provide new and non-standard estimates). As a consequence, the long time behaviour is determined by the principal eigenfunction or ground state. Based on this, we discuss (rigorously and via numerical explorations) the conditions on the fitness function and the mutation rate for evolutionary branching to occur.

math.AP↗

arXiv2017

A new proof of the competitive exclusion principle in the chemostat

We give an new proof of the well-known competitive exclusion principle in the chemostat model with $n$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number of the species, after being ordered. It uses elementary analysis and comparisons of solutions of ordinary differential equations.

math.CA↗