arXiv subjects

Pedro Souza

Publications and source records attributed to Pedro Souza.

5 recordsLinked to original sources

arXiv2026

On Bands and Limit Theorems in Tropical Geometry

We review the basic theory of bands and band schemes introduced by Baker-Jin-Lorscheid, which is an algebraic framework for tropicalization, analytification, and $\mathbb{F}_1$-geometry. For an affine scheme $X$ over a non-Archimedean valued field $k$, one can associate to every affine embedding $\iota$ of $X$ a naturally defined affine band scheme $Y_\iota$ whose rational points over the tropical band $\mathbb{T}$ recover the tropicalization $Trop(X,\iota)$. We prove that $X$ is the limit of the $Y_\iota$ in the category of band schemes, thereby obtaining a scheme-theoretic enhancement of Payne's limit theorem. By taking $\mathbb{T}$-rational points, this recovers Payne's theorem for affine tropicalizations from the perspective of band scheme theory and the same method provides an analogous result in the real tropical setting.

math.AG↗

arXiv2026

Enabling Real-Time Programmability for RAN Functions: A Wasm-Based Approach for Robust and High-Performance dApps

While the Open Radio Access Network Alliance (O-RAN) architecture enables third-party applications to optimize radio access networks at multiple timescales, real-time distributed applications (dApps) that demand low latency, high performance, and strong isolation remain underexplored. Existing approaches propose colocating a new RAN Intelligent Controller (RIC) at the edge, or deploying dApps in bare metal along with RAN functions. While the former approach increases network complexity and requires additional edge computing resources, the latter raises serious security concerns due to the lack of native mechanisms to isolate dApps and RAN functions. Meanwhile, WebAssembly (Wasm) has emerged as a lightweight, fast technology for robust execution of external, untrusted code. In this work, we propose a new approach to executing dApps using Wasm to isolate applications in real-time in O-RAN. Results show that our lightweight and robust approach ensures predictable, deterministic performance, strong isolation, and low latency, enabling real-time control loops.

cs.NI↗

arXiv2024

On the topology of the moduli of tropical unramified p-covers

We study the topology of the moduli space of unramified $\mathbb{Z}/p$-covers of tropical curves of genus $g \geq 2$, where $p$ is a prime number. We use recent techniques by Chan--Galatius--Payne to identify contractible subcomplexes of the moduli space. We then use this contractibility result to show that this moduli space is simply connected. In the case of genus 2, we determine the homotopy type of this moduli space for all primes $p$. This work is motivated by prospective applications to the top-weight cohomology of the space of prime cyclic étale covers of smooth algebraic curves.

math.AG↗

arXiv2021

Tropicalization of toric prevarieties

The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schröer) always admits an embedding into a toric variety that is not necessarily separated, a so-called toric prevariety. In order to have a convenient framework to study the tropicalization of homogeneous spectra we propose a tropicalization procedure for toric prevarieties and study its basic properties. With these tools at hand, we prove a generalization of Payne's and Foster--Gross--Payne's tropical limit theorem for divisorial schemes.

math.AG↗

arXiv2019

Identifying Network Ties from Panel Data: Theory and an Application to Tax Competition

Social interactions determine many economic behaviors, but information on social ties does not exist in most publicly available and widely used datasets. We present results on the identification of social networks from observational panel data that contains no information on social ties between agents. In the context of a canonical social interactions model, we provide sufficient conditions under which the social interactions matrix, endogenous and exogenous social effect parameters are all globally identified. While this result is relevant across different estimation strategies, we then describe how high-dimensional estimation techniques can be used to estimate the interactions model based on the Adaptive Elastic Net GMM method. We employ the method to study tax competition across US states. We find the identified social interactions matrix implies tax competition differs markedly from the common assumption of competition between geographically neighboring states, providing further insights for the long-standing debate on the relative roles of factor mobility and yardstick competition in driving tax setting behavior across states. Most broadly, our identification and application show the analysis of social interactions can be extended to economic realms where no network data exists.

econ.EM↗