arXiv subjects

Javier Fernández

Publications and source records attributed to Javier Fernández.

13 recordsLinked to original sources

arXiv2026

Variational reduction of homogenous Lagrangian systems

In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of the system can be reconstructed up to quadratures from the critical points of the reduced variational principle. Also, we characterize the mentioned critical points in terms of a set of ordinary differential equations which are the scaling analogue of the Lagrange-Poincaré equations. Finally, we study if the homogeneous Lagrangian systems are naturally related or not with the Herglotz variational principle.

math.DG↗

arXiv2026

Robust certification of high-dimensional quantum devices

Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.

quant-ph↗

arXiv2026

Lagrangian reduction of symmetric discrete mechanical systems: a survey

In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction of DMSs with nonholonomic constraints, DMSs with external forcing, as well as a theory of reduction by stages for such systems. This line of work was inspired by the paper and the monograph written by H. Cendra, J. Marsden and T. Ratiu in 2001.

math.DG↗

arXiv2026

Remarks on structures and preservation in forced discrete mechanical systems of Routh type

We study a type of forced discrete mechanical system $(Q,L_d,f_d)$ -- that we name of Routh type -- whose (discrete) time-flow preserves a symplectic structure on $Q\times Q$. That structure arises as the pullback via the forced discrete Legendre transform of the canonical symplectic structure on $T^*Q$ modified by a "magnetic term". One example of this type of system is provided by the Lagrangian reduction of a symmetric (unforced) discrete mechanical system in the Routh style. In this particular case, we do not reduce by the full symmetry group but, rather, by an appropriate isotropy subgroup. In this context, the preserved symplectic structure can be alternatively seen as the Marsden-Weinstein reduction of the canonical symplectic structure $ω_{L_d}$ on $Q\times Q$.

math.DG↗

arXiv2023

Lagrangian reduction of forced discrete mechanical systems

In this paper we propose a process of Lagrangian reduction and reconstruction for symmetric discrete-time mechanical systems acted on by external forces, where the symmetry group action on the configuration manifold turns it into a principal bundle. We analyze the evolution of momentum maps and Poisson structures under different conditions.

math.DG↗

arXiv2022

Is it worth the effort? Understanding and contextualizing physical metrics in soccer

We present a framework that gives a deep insight into the link between physical and technical-tactical aspects of soccer and it allows associating physical performance with value generation thanks to a top-down approach. First, we estimate physical indicators from tracking data. Then, we contextualize each player's run to understand better the purpose and circumstances in which it is done, adding a new dimension to the creation of team and player profiles. Finally, we assess the value-added by off-ball high-intensity runs by linking with a possession-value model. This novel approach allows answering practical questions from very different profiles of practitioners within a soccer club, from analysts, coaches, and scouts to physical coaches and readaptation physiotherapists.

stat.ML↗

arXiv2022

Discrete Mechanical Systems in a Dirac Setting: a Proposal

In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is possible to recover discrete Lagrangian and Hamiltonian systems as particular cases. We also note that this approach allows for kinematic as well as variational constraints.

math.DG↗

arXiv2021

Error analysis of forced discrete mechanical systems

The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order $r$ of the Lagrangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over $TQ$, where we study the existence of flows, the construction and properties of discrete exact systems and the contact order of the flows (variational integrators) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over $Q\times Q$.

math.NA↗

arXiv2021

Motor-Imagery-Based Brain Computer Interface using Signal Derivation and Aggregation Functions

Brain Computer Interface technologies are popular methods of communication between the human brain and external devices. One of the most popular approaches to BCI is Motor Imagery. In BCI applications, the ElectroEncephaloGraphy is a very popular measurement for brain dynamics because of its non-invasive nature. Although there is a high interest in the BCI topic, the performance of existing systems is still far from ideal, due to the difficulty of performing pattern recognition tasks in EEG signals. BCI systems are composed of a wide range of components that perform signal pre-processing, feature extraction and decision making. In this paper, we define a BCI Framework, named Enhanced Fusion Framework, where we propose three different ideas to improve the existing MI-based BCI frameworks. Firstly, we include aan additional pre-processing step of the signal: a differentiation of the EEG signal that makes it time-invariant. Secondly, we add an additional frequency band as feature for the system and we show its effect on the performance of the system. Finally, we make a profound study of how to make the final decision in the system. We propose the usage of both up to six types of different classifiers and a wide range of aggregation functions (including classical aggregations, Choquet and Sugeno integrals and their extensions and overlap functions) to fuse the information given by the considered classifiers. We have tested this new system on a dataset of 20 volunteers performing motor imagery-based brain-computer interface experiments. On this dataset, the new system achieved a 88.80% of accuracy. We also propose an optimized version of our system that is able to obtain up to 90,76%. Furthermore, we find that the pair Choquet/Sugeno integrals and overlap functions are the ones providing the best results.

cs.HC↗

arXiv2020

SoccerMap: A Deep Learning Architecture for Visually-Interpretable Analysis in Soccer

We present a fully convolutional neural network architecture that is capable of estimating full probability surfaces of potential passes in soccer, derived from high-frequency spatiotemporal data. The network receives layers of low-level inputs and learns a feature hierarchy that produces predictions at different sampling levels, capturing both coarse and fine spatial details. By merging these predictions, we can produce visually-rich probability surfaces for any game situation that allows coaches to develop a fine-grained analysis of players' positioning and decision-making, an as-yet little-explored area in sports. We show the network can perform remarkably well in the estimation of pass success probability, and present how it can be adapted easily to approach two other challenging problems: the estimation of pass-selection likelihood and the prediction of the expected value of a pass. Our approach provides a novel solution for learning a full prediction surface when there is only a single-pixel correspondence between ground-truth outcomes and the predicted probability map. The flexibility of this architecture allows its adaptation to a great variety of practical problems in soccer. We also present a set of practical applications, including the evaluation of passing risk at a player level, the identification of the best potential passing options, and the differentiation of passing tendencies between teams.

cs.LG↗

arXiv2020

Always Look on the Bright Side of the Field: Merging Pose and Contextual Data to Estimate Orientation of Soccer Players

Although orientation has proven to be a key skill of soccer players in order to succeed in a broad spectrum of plays, body orientation is a yet-little-explored area in sports analytics' research. Despite being an inherently ambiguous concept, player orientation can be defined as the projection (2D) of the normal vector placed in the center of the upper-torso of players (3D). This research presents a novel technique to obtain player orientation from monocular video recordings by mapping pose parts (shoulders and hips) in a 2D field by combining OpenPose with a super-resolution network, and merging the obtained estimation with contextual information (ball position). Results have been validated with players-held EPTS devices, obtaining a median error of 27 degrees/player. Moreover, three novel types of orientation maps are proposed in order to make raw orientation data easy to visualize and understand, thus allowing further analysis at team- or player-level.

cs.CV↗

arXiv2020

Using Player's Body-Orientation to Model Pass Feasibility in Soccer

Given a monocular video of a soccer match, this paper presents a computational model to estimate the most feasible pass at any given time. The method leverages offensive player's orientation (plus their location) and opponents' spatial configuration to compute the feasibility of pass events within players of the same team. Orientation data is gathered from body pose estimations that are properly projected onto the 2D game field; moreover, a geometrical solution is provided, through the definition of a feasibility measure, to determine which players are better oriented towards each other. Once analyzed more than 6000 pass events, results show that, by including orientation as a feasibility measure, a robust computational model can be built, reaching more than 0.7 Top-3 accuracy. Finally, the combination of the orientation feasibility measure with the recently introduced Expected Possession Value metric is studied; promising results are obtained, thus showing that existing models can be refined by using orientation as a key feature. These models could help both coaches and analysts to have a better understanding of the game and to improve the players' decision-making process.

cs.CV↗

arXiv2008

Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model

The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less $8π$, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar variables.

math.AP↗