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Pedro Cardoso

Publications and source records attributed to Pedro Cardoso.

14 recordsLinked to original sources
arXiv2026

Equilibrium fluctuations for a multi-species particle system with long jumps

In the present paper, we study the equilibrium fluctuations of a particle system in infinite volume with two conserved quantities and long-range dependence. More specifically, the model of interest is the so-called ABC model, in which three types of particles (A, B and C) exchange their locations between $x\in\mathbb{Z}$ and $x+z\in\mathbb{Z}$ at a rate that depends on the type of particles involved and is proportional to $|z|^{-\gamma-1}$ for $\gamma>0$. After rigorously identifying the normal modes associated to the conserved quantities (the density of particles of types $A$ and $B$, say), we prove that their fluctuations converge to independent fractional stochastic partial differential equations (SPDEs), which are either Gaussian or the Stochastic Burgers equation, and whose nature is determined by the microscopic range of dependence and the strength of the asymmetry.

math.PR↗
arXiv2025

ARETE: an R package for Automated REtrieval from TExt with large language models

1. A hard stop for the implementation of rigorous conservation initiatives is our lack of key species data, especially occurrence data. Furthermore, researchers have to contend with an accelerated speed at which new information must be collected and processed due to anthropogenic activity. Publications ranging from scientific papers to gray literature contain this crucial information but their data are often not machine-readable, requiring extensive human work to be retrieved. 2. We present the ARETE R package, an open-source software aiming to automate data extraction of species occurrences powered by large language models, namely using the chatGPT Application Programming Interface. This R package integrates all steps of the data extraction and validation process, from Optical Character Recognition to detection of outliers and output in tabular format. Furthermore, we validate ARETE through systematic comparison between what is modelled and the work of human annotators. 3. We demonstrate the usefulness of the approach by comparing range maps produced using GBIF data and with those automatically extracted for 100 species of spiders. Newly extracted data allowed to expand the known Extent of Occurrence by a mean three orders of magnitude, revealing new areas where the species were found in the past, which mayhave important implications for spatial conservation planning and extinction risk assessments. 4. ARETE allows faster access to hitherto untapped occurrence data, a potential game changer in projects requiring such data. Researchers will be able to better prioritize resources, manually verifying selected species while maintaining automated extraction for the majority. This workflow also allows predicting available bibliographic data during project planning.

cs.LG↗
arXiv2024

Derivation of non-polynomial fractional diffusions from the generalized exclusion with a slow barrier

In this article we derive in the hydrodynamic limit a generalized fractional porous medium equation, in the sense that the regional fractional Laplacian is applied to a function of the density given in terms of a power series, instead of a polynomial. The hydrodynamic limit is obtained considering a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place. This system is also studied in the presence of a "slow barrier" that hinders the flow of mass between two half-spaces.

math.PR↗
arXiv2024

Regional Fractional Stochastic Burgers from random interactions

The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional fractional Laplacian. The approach is to consider a boundary driven exclusion process with long jumps and asymmetric jump rates. Depending on the strength of the asymmetry we prove the convergence to stationary solutions of either the Ornstein-Uhlenbeck equation, or the stochastic Burgers equation. In the later setting, the convergence in some regimes is guaranteed by the recent proof of uniqueness of energy solutions derived in [16].

math.PR↗
arXiv2024

Linear and Nonlinear Fractional PDEs from interacting particle systems

In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For $m \in \mathbb{N}:=\{1, 2, \ldots\}$ fixed, the hydrodynamic equation is $\partial_t \rho(t,u)= [-(-\Delta)^{\gamma /2} \rho^m](t,u) $. For $m=1$, this {is} the fractional equation, which is linear. On the other hand, for $m \geq 2$, this is the fractional porous medium equation (which is nonlinear), obtained by choosing a rate which depends on the number of particles next to the initial and final position of a jump.

math.PR↗
arXiv2023

Hydrodynamics of a $d$-dimensional long jumps symmetric exclusion with a slow barrier

We obtain the hydrodynamic limit of symmetric long-jumps exclusion in $\mathbb{Z}^d$ (for $d \geq 1$), where the jump rate is inversely proportional to a power of the jump's length with exponent $\gamma+1$, where $\gamma \geq 2$. Moreover, movements between $\mathbb{Z}^{d-1} \times \mathbb{Z}_{-}^{*}$ and $\mathbb{Z}^{d-1} \times \mathbb N$ are slowed down by a factor $\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$). In the hydrodynamic limit we obtain the heat equation in $\mathbb{R}^d$ without boundary conditions or with Neumann boundary conditions, depending on the values of $\beta$ and $\gamma$. The (rather restrictive) condition in \cite{casodif} (for $d=1$) about the initial distribution satisfying an entropy bound with respect to a Bernoulli product measure with constant parameter is weakened or completely dropped.

math.PR↗
arXiv2022

Diffusive fluctuations of long-range symmetric exclusion with a slow barrier

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-γ-1}$. Here we restrict to the choice $γ\geq 2$ so that the system has a diffusive behavior. Moreover, when particles move between $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, the jump rates are slowed down by a factor $αn^{-β}$, where $α>0$, $β\geq 0$ and $n$ is the scaling parameter. Depending on the values of $β$ and $γ$, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.

math.PR↗
arXiv2022

Lightweight Automated Feature Monitoring for Data Streams

Monitoring the behavior of automated real-time stream processing systems has become one of the most relevant problems in real world applications. Such systems have grown in complexity relying heavily on high dimensional input data, and data hungry Machine Learning (ML) algorithms. We propose a flexible system, Feature Monitoring (FM), that detects data drifts in such data sets, with a small and constant memory footprint and a small computational cost in streaming applications. The method is based on a multi-variate statistical test and is data driven by design (full reference distributions are estimated from the data). It monitors all features that are used by the system, while providing an interpretable features ranking whenever an alarm occurs (to aid in root cause analysis). The computational and memory lightness of the system results from the use of Exponential Moving Histograms. In our experimental study, we analyze the system's behavior with its parameters and, more importantly, show examples where it detects problems that are not directly related to a single feature. This illustrates how FM eliminates the need to add custom signals to detect specific types of problems and that monitoring the available space of features is often enough.

cs.LG↗
arXiv2022

Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion

We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators that are given by the regional fractional Laplacian with some additional reaction terms and various boundary conditions. This work solves some questions left open in \cite{BJGO2} about the same model.

math.PR↗
arXiv2022

Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: diffusive regime

In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(\cdot)$ which is symmetric and has finite variance, while for slow bonds the jump rates are given $p(\cdot)αn^{-β}$ (with $α>0$ and $β\geq 0$), and correspond to jumps from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$. We prove that: if there is a fast bond from $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, then the hydrodynamic limit is given by the heat equation with no boundary conditions; otherwise, it is given by the previous equation if $0\leq β<1$, but for $β\geq 1$ boundary conditions appear, namely, we get Robin (linear) boundary conditions if $β=1$ and Neumann boundary conditions if $β>1$.

math.PR↗
arXiv2022

Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime

We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$ the rates are slowed down by a factor $αn^{-β}$ (with $α>0$ and $β\geq 0$). We obtain several partial differential equations given in terms of the regional fractional Laplacian on $\mathbb R^*$ and with different boundary conditions. Surprisingly, in opposition to the diffusive regime, we get different regimes depending on whether $α=1$ (all bonds with the same rate) or $α\neq 1$.

math-ph↗
arXiv2021

Railgun: managing large streaming windows under MAD requirements

Some mission critical systems, e.g., fraud detection, require accurate, real-time metrics over long time sliding windows on applications that demand high throughput and low latencies. As these applications need to run 'forever' and cope with large, spiky data loads, they further require to be run in a distributed setting. We are unaware of any streaming system that provides all those properties. Instead, existing systems take large simplifications, such as implementing sliding windows as a fixed set of overlapping windows, jeopardizing metric accuracy (violating regulatory rules) or latency (breaching service agreements). In this paper, we propose Railgun, a fault-tolerant, elastic, and distributed streaming system supporting real-time sliding windows for scenarios requiring high loads and millisecond-level latencies. We benchmarked an initial prototype of Railgun using real data, showing significant lower latency than Flink and low memory usage independent of window size. Further, we show that Railgun scales nearly linearly, respecting our msec-level latencies at high percentiles (<250ms @ 99.9%) even under a load of 1 million events per second.

cs.DC↗
arXiv2020

Railgun: streaming windows for mission critical systems

Some mission critical systems, such as fraud detection, require accurate, real-time metrics over long time windows on applications that demand high throughputs and low latencies. As these applications need to run "forever", cope with large and spiky data loads, they further require to be run in a distributed setting. Unsurprisingly, we are unaware of any distributed streaming system that provides all those properties. Instead, existing systems take large simplifications, such as implementing sliding windows as a fixed set of partially overlapping windows, jeopardizing metric accuracy (violating financial regulator rules) or latency (breaching service agreements). In this paper, we propose Railgun, a fault-tolerant, elastic, and distributed streaming system supporting real-time sliding windows for scenarios requiring high loads and millisecond-level latencies. We benchmarked an initial prototype of Railgun using real data, showing significant lower latency than Flink, and low memory usage, independent of window size.

cs.DC↗