arXiv subjects

Adriana Lara

Publications and source records attributed to Adriana Lara.

4 recordsLinked to original sources

arXiv2026

Tackling air quality with SAPIENS

Air pollution is a chronic problem in large cities worldwide and awareness is rising as the long-term health implications become clearer. Vehicular traffic has been identified as a major contributor to poor air quality. In a lot of cities the publicly available air quality measurements and forecasts are coarse-grained both in space and time. However, in general, real-time traffic intensity data is openly available in various forms and is fine-grained. In this paper, we present an in-depth study of pollution sensor measurements combined with traffic data from Mexico City. We analyse and model the relationship between traffic intensity and air quality with the aim to provide hyper-local, dynamic air quality forecasts. We developed an innovative method to represent traffic intensities by transforming simple colour-coded traffic maps into concentric ring-based descriptions, enabling improved characterisation of traffic conditions. Using Partial Least Squares Regression, we predict pollution levels based on these newly defined traffic intensities. The model was optimised with various training samples to achieve the best predictive performance and gain insights into the relationship between pollutants and traffic. The workflow we have designed is straightforward and adaptable to other contexts, like other cities beyond the specifics of our dataset.

cs.LG↗

arXiv2021

A randomized greedy algorithm for piecewise linear motion planning

We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle $\mathcal{R}$, and outputs an explicit system of piecewise linear motion planners for $\mathcal{R}$. The algorithm is designed in such a way that the cardinality of the outputed system is probabilistically close (with parameters chosen by the user) to minimal possible. This yields the first automated solution for robust-to-noise robot motion planning in terms of simplicial complexity (SC) techniques, a discretization of Farber's topological complexity TC. Besides its relevance toward technological applications, our work revels that, unlike other discrete approaches to TC, the SC model can recast Farber's invariant without having to introduce costly subdivisions. We develop and implement our algorithm by actually discretizing Macías-Virgós and Mosquera-Lois' notion of homotopic distance, thus encompassing computer estimations of other sectional category invariants as well, such as the Lusternik-Schnirelmann category of polyhedra.

math.AT↗

arXiv2016

Projective product coverings and sequential motion planning algorithms in real projective spaces

For positive integers $m$ and $s$, let $\mathbf{m}_s$ stand for the $s$-th tuple $(m,\ldots,m)$. We show that, for large enough $s$, the higher topological complexity $TC_s$ of an even dimensional real projective space $RP^m$ is characterized as the smallest positive integer $k=k(m,s)$ for which there is a $(\mathbb{Z}_2)^{s-1}$-equivariant map from Davis' projective product space $P_{\mathbf{m}_s}$ to the $(k+1)$-th join-power $((\mathbb{Z}_2)^{s-1})^{\ast(k+1)}$. This is a (partial) generalization of Farber-Tabachnikov-Yuzvinsky's work relating $TC_2$ to the immersion dimension of real projective spaces. In addition, we compute the exact value of $TC_s(RP^m)$ for $m$ even and $s$ large enough.

math.AT↗

arXiv2015

Motion planning in real flag manifolds

Starting from Borel's description of the mod-2 cohomology of real flag manifolds, we give a minimal presentation of the cohomology ring for semi complete flag manifolds $F_{k,m}:=F(1,\ldots,1,m)$ where $1$ is repeated $k$ times. The information is used in order to estimate Farber's topological complexity of these spaces when $m$ approaches (from below) a 2-power. In particular, we get almost sharp estimates for $F_{2,2^e-1}$ which resemble the known situation for the real projective spaces $F_{1,2^e}$. Our results indicate that the agreement between the topological complexity and the immersion dimension of real projective spaces no longer holds for other flag manifolds. More interestingly, we also get corresponding results for the $s$-th (higher) topological complexity of these spaces. Actually, we prove the surprising fact that, as $s$ increases, the estimates become stronger. Indeed, we get several full computations of the higher motion planning problem of these manifolds. This property is also shown to hold for surfaces: we get a complete computation of the higher topological complexity of all closed surfaces (orientable or not). A homotopy-obstruction explanation is included for the phenomenon of having a cohomologically accessible higher topological complexity even when the regular topological complexity is not so accessible.

math.AT↗