Searcharxiv⌕ Search

arXiv subjects

Pedro Duarte

Publications and source records attributed to Pedro Duarte.

At least 19 recordsLinked to original sources
arXiv2026

A Vision-based Framework for Intelligent gNodeB Mobility Control

This paper proposes a vision-based framework for the intelligent control of mobile Open Radio Access Network (O-RAN) base stations (gNBs) operating in dynamic wireless environments. The framework comprises three innovative components. The first is the introduction of novel Service Models (SMs) within a vision-enabled O-RAN architecture, termed VisionRAN. These SMs extend state-of-the-art O-RAN-based architectures by enabling the transmission of vision-based sensing data and gNB positioning control messages. The second is an O-RAN xApp, VisionApp, which fuses vision and radio data, and uses this information to control the position of a mobile gNB, using a Deep Q-Network (DQN). The third is a digital twin environment, VisionTwin, which incorporates vision data and can emulate realistic wireless scenarios; this digital twin was used to train the DQN running in VisionApp and validate the overall system. Experimental results, obtained using real vision data and an emulated radio, demonstrate that the proposed approach reduces the duration of Line-of-Sight (LoS) blockages by up to 75% compared to a static gNB. These findings confirm the viability of integrating multimodal perception and learning-based control within RANs.

cs.NI↗
arXiv2025

The fibered rotation number

We provide an explicit formula for an increment of the fibered rotation number of a one-parameter family of circle cocycles over any ergodic transformation in terms of invariant measures. As an application, for a family of random dynamical systems on the circle, this gives a formula for an increment of the rotation number in terms of the stationary measures. In the case of projective Schr\"odinger cocycles associated with the Anderson Model, that provides a relation between the properties of the stationary measures on the projective space and the integrated density of states (IDS) of the corresponding family of operators. In particular, it gives a dynamical proof of H\"older regularity of the IDS in Anderson Model. Finally, we prove that the IDS for the Anderson Model with an ergodic background must be H\"older continuous.

math.DS↗
arXiv2025

A Reinforcement Learning Framework for Mobility Control of gNBs in Dynamic Radio Access Networks

The increasing complexity of wireless environments, characterized by user mobility and dynamic obstructions, poses challenges for the maintenance of Line-of-Sight (LoS) connectivity. Mobile base stations (gNBs) stand as a promising solution by physically relocating to restore or sustain LoS, thereby necessitating the development of intelligent algorithms for autonomous movement control. As part of the CONVERGE research project, which is developing an experimental chamber to integrate computer vision (CV) into mobile networks and enhance Quality of Service (QoS) in dynamic wireless environments, this paper presents two key contributions. First, we introduce the CONVERGE Chamber Simulator (CC-SIM), a 3D simulation environment for developing, training, and validating mobility control algorithms for mobile gNBs. CC-SIM models user and obstacle mobility, visual occlusion, and Radio Frequency (RF) propagation behavior. It supports both offline reinforcement learning and real-time testing through tight integration with a standalone 5G system via the OpenAirInterface (OAI) RF simulator, enabling validation under realistic network conditions. Second, leveraging CC-SIM, we develop a Deep Q-Network (DQN) agent that learns to reposition the gNB proactively in response to dynamic environmental changes. Experiments across three representative use cases show that the trained agent significantly reduces LoS blockage time - by up to 42% - when compared to static deployments. These results highlight the effectiveness of learning-based mobility control in adaptive next-generation wireless networks.

cs.NI↗
arXiv2025

H\"older continuity of Lyapunov exponents for non-invertible and non-compact random cocycles

We study the regularity of Lyapunov exponents for random linear cocycles taking values in $\Mat_m(\R)$ and driven by i.i.d. processes. Under three natural conditions - finite exponential moments, a spectral gap between the top two Lyapunov exponents, and quasi-irreducibility of the associated semigroup - we prove that the top Lyapunov exponent is H\"older continuous with respect to the Wasserstein distance. In the final section, we apply the main results to Schr\"odinger cocycles with unbounded potentials.

math.DS↗
arXiv2025

Random 2D linear cocycles II: statistical properties

Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit formula for the unique stationary measure associated to such cocycles and establish a Furstenberg-type formula characterizing the Lyapunov exponent. Using the spectral properties of the corresponding Markov operator and a parameter elimination argument, we prove that Lebesgue almost every cocycle in this space satisfies large deviations estimates and a central limit theorem.

math.DS↗
arXiv2025

Random 2D linear cocycles I: dichotomic behavior

In this paper we establish a Bochi-Ma\~n\'e type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or Markov shift. Moreover, we prove that Lebesgue almost every such cocycle has finite first Lyapunov exponent, which then implies a break in the regularity of the Lyapunov exponent, from analyticity to discontinuity.

math.DS↗
arXiv2024

Obstacle-Aware Positioning of a Mobile Robotic Platform for 6G Networks

The 6G paradigm and the massive usage of interconnected wireless devices introduced the need for flexible wireless networks. A promising approach lies in employing Mobile Robotic Platforms (MRPs) to create communications cells on-demand. The challenge consists in positioning the MRPs to improve the wireless connectivity offered. This is exacerbated in millimeter wave (mmWave), Terahertz (THz), and visible light-based networks, which imply the establishment of short-range, Line of Sight (LoS) wireless links to take advantage of the ultra-high bandwidth channels available. This paper proposes a solution to enable the obstacle-aware, autonomous positioning of MRPs and provide LoS wireless connectivity to communications devices. It consists of 1) a Vision Module that uses video data gathered by the MRP to determine the location of obstacles, wireless devices and users, and 2) a Control Module, which autonomously positions the MRP based on the information provided by the Vision Module. The proposed solution was validated in simulation and through experimental testing, showing that it is able to position an MRP while ensuring LoS wireless links between a mobile communications cell and wireless devices or users.

cs.NI↗
arXiv2023

Isospectral Reductions of Non-negative Matrices

Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic scheme to approximate the stationary measure of a stochastic matrix based on isospectral reductions. We run numerical experiments that indicate this scheme is advantageous when there is more than one eigenvalue near 1, precisely the case where iterative methods perform poorly. We give a partial explanation why this scheme should work well, showing that in some situations isospectral reduction improves the spectral gap.

math.DS↗
arXiv2022

Statistical properties for mixing Markov chains with applications to dynamical systems

We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics, including systems for which the spectral gap property for the transition or the transfer operator does not hold.

math.DS↗
arXiv2022

A dynamical Thouless formula

In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the integrated density of states of a Schr\"odinger operator. Here, the role of the integrated density of states will be played by a more geometrical quantity, the fibered rotation number. As an application of this formula we present limitations on the modulus of continuity of random linear cocycles. Moreover, we derive H\"older-type continuity properties of the fibered rotation number for linear cocycles over various base dynamics.

math.DS↗
arXiv2022

Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles

We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result is applicable to cocycles corresponding to Schr\"odinger operators with randomly perturbed quasiperiodic potentials. Moreover, we establish an average uniform convergence to the Lyapunov exponent in the Oseledets theorem.

math.DS↗
arXiv2021

H\"older continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps

Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are H\"older continuous and whose projective actions are partially hyperbolic dynamical systems. We prove that locally near any typical cocycle, the Lyapunov exponents are H\"older continuous functions relative to the uniform topology. This result is obtained as a consequence of a uniform large deviations type estimate in the space of cocycles. As a byproduct of our approach, we also establish other statistical properties for the iterates of such cocycles, namely a central limit theorem and a large deviations principle.

math.DS↗
arXiv2021

Mixed Random-Quasiperiodic Cocycles

We introduce the concept of mixed random-quasiperiodic linear cocycles. We characterize the ergodicity of the base dynamics and establish a large deviations type estimate for certain types of observables. For the fiber dynamics we prove the uniform upper semicontinuity of the maximal Lyapunov exponent. This paper is meant to introduce a model to be studied in depth in further projects.

math.DS↗
arXiv2021

Asymptotic Dynamics of Hamiltonian Polymatrix Replicators

In a previous paper [3] we have studied flows defined on polytopes, presenting a new method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. These results apply to the class of polymatrix replicator systems, which contains several important models in Evolutionary Game Theory. Here we establish the Hamiltonian character of the asymptotic dynamics of Hamiltonian polymatrix replicators.

math.DS↗
arXiv2019

Scattering amplitudes and contour deformations

We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system. The integrals produce branch cuts in the complex plane of the integrand which prohibit a naive Euclidean integration path. By employing contour deformations, we can also access the kinematical regions associated with the scattering amplitude in Minkowski space. We show that in principle a homogeneous Bethe-Salpeter equation, together with analytic continuation methods such as the Resonances-via-Pad\'e method, is sufficient to determine the resonance pole locations on the second Riemann sheet. However, the scalar model investigated here does not produce resonance poles above threshold but instead virtual states on the real axis of the second sheet, which pose difficulties for analytic continuation methods. To address this, we calculate the scattering amplitude on the second sheet directly using the two-body unitarity relation which follows from the scattering equation.

hep-ph↗