Haces y teoría de la señal

Traballo Fin de Grao en Matemáticas. Curso 2019-2020[ES] En este trabajo haremos una introducción a la teoría de haces y expondremos sus recientes aplicaciones al control de sistemas de información. Para poder abordar estos dos puntos expondremos los elementos básicos de la teoría de categorías. Estos nos proporcionarán el lenguaje necesario para el entendimiento de la teoría de haces. Para las aplicaciones, será útil dar una descripción explicita de haces sobre un complejo celular mediante el concepto auxiliar de los haces celulares. Será entonces el momento de tratar la homología, centrada en el estudio de complejos simpliciales, y la cohomología con coeficientes en un haz, que se convertirá en el instrumento principal para el análisis de los sistemas del siguiente capítulo. Con todo esto mostraremos cómo esta teoría tiene aplicaciones prácticas. En este trabajo nos centraremos en es el estudio del buen funcionamiento de un sistema de sensores de control del tráfico en un aeropuerto.[EN] In this work we will make an introduction to sheaf theory and explain its recent applications to control of information systems. In order to address these two points, we will expose basic elements of category theory. These provide us with the necessary language for understanding sheaf theory. For applications, it will be useful to give an explicit description of sheaves on a cell complex using cell sheaves. Then, we will explain homology, focused on the study of simplicial complexes, and cohomology with coefficients in a sheaf, which will become the main instrument for the analysis of systems in the next chapter. All things considered, we will show how this theory has practical applications. In this work we will focus on the traffic control sensor system at an airport monitoring

Composition in Differential Privacy for General Granularity Notions

The composition theorems of differential privacy (DP) allow data curators to combine different algorithms to obtain a new algorithm that continues to satisfy DP. However, new granularity notions (i.e., neighborhood definitions), data domains, and composition settings have appeared in the literature that the classical composition theorems do not cover. For instance, the original parallel composition theorem does not translate well to general granularity notions. This complicates the opportunity of composing DP mechanisms in new settings and obtaining accurate estimates of the incurred privacy loss after composition. To overcome these limitations, we study the composability of DP in a general framework and for any kind of data domain or neighborhood definition. We give a general composition theorem in both independent and adaptive versions and we provide analogous composition results for approximate, zero-concentrated, and Gaussian DP. Besides, we study the hypothesis needed to obtain the best composition bounds. Our theorems cover both parallel and sequential composition settings. Importantly, they also cover every setting in between, allowing us to compute the final privacy loss of a composition with greatly improved accuracy

SoK: Differentially Private Publication of Trajectory Data

Trajectory analysis holds many promises, from improvements in traffic management to routing advice or infrastructure development. However, learning users\u27 paths is extremely privacy-invasive. Therefore, there is a necessity to protect trajectories such that we preserve the global properties, useful for analysis, while specific and private information of individuals remains inaccessible. Trajectories, however, are difficult to protect, since they are sequential, highly dimensional, correlated, bound to geophysical restrictions, and easily mapped to semantic points of interest. This paper aims to establish a systematic framework on protective masking and synthetic-generation measures for trajectory databases with syntactic and differentially private (DP) guarantees, including also utility properties, derived from ideas and limitations of existing proposals. To reach this goal, we systematize the utility metrics used throughout the literature, deeply analyze the DP granularity notions, explore and elaborate on the state of the art on privacy-enhancing mechanisms and their problems, and expose the main limitations of DP notions in the context of trajectories

SoK: differentially private publication of trajectory data

Trajectory analysis holds many promises, from improvements in traffic management to routing advice or infrastructure development. However, learning users’ paths is extremely privacy-invasive. Therefore, there is a necessity to protect trajectories such that we preserve the global properties, useful for analysis, while specific and private information of individuals remains inaccessible. Trajectories, however, are difficult to protect, since they are sequential, highly dimensional, correlated, bound to geophysical restrictions, and easily mapped to semantic points of interest. This paper aims to establish a systematic framework on protective masking measures for trajectory databases with differentially private (DP) guarantees, including also utility properties, derived from ideas and limitations of existing proposals. To reach this goal, we systematize the utility metrics used throughout the literature, deeply analyze the DP granularity notions, explore and elaborate on the state of the art on privacy-enhancing mechanisms and their problems, and expose the main limitations of DP notions in the context of trajectories.We would like to thank the reviewers and shepherd for their useful comments and suggestions in the improvement of this paper. Javier Parra-Arnau is the recipient of a “Ramón y Cajal” fellowship funded by the Spanish Ministry of Science and Innovation. This work also received support from “la Caixa” Foundation (fellowship code LCF/BQ/PR20/11770009), the European Union’s H2020 program (Marie Skłodowska-Curie grant agreement № 847648) from the Government of Spain under the project “COMPROMISE” (PID2020-113795RB-C31/AEI/10.13039/501100011033), and from the BMBF project “PROPOLIS” (16KIS1393K). The authors at KIT are supported by KASTEL Security Research Labs (Topic 46.23 of the Helmholtz Association) and Germany’s Excellence Strategy (EXC 2050/1 ‘CeTI’; ID 390696704).Peer ReviewedPostprint (published version

La publicación de trayectorias: un estudio sobre la protección de la privacidad

El analisis de las trayectorias encierra numerosas ´ promesas, desde mejoras en la gestion del tr ´ afico hasta recomen- ´ daciones de ruta, o incluso en el desarrollo de infraestructuras. Sin embargo, conocer los lugares en los que uno ha estado es extremadamente invasivo. Por ello, surge la necesidad de anonimizar bases de datos de trayectorias, preservando las estadísticas globales utiles para el an ´ alisis, mientras que la ínformacion espec ´ ífica y privada de los individuos permanece inaccesible. En este trabajo analizamos el estado del arte en la publicacion´ de trayectorias con garantías de privacidad, revisando nociones, mecanismos y metricas de utilidad. De este an ´ alisis concluimos ´ limitaciones de las propuestas actuales y teniendo en cuenta tanto los problemas de privacidad como los de utilidad, esbozamos oportunidades de investigacion para el desarrollo de mecanismos éficaces bajo una proteccion espec ´ ífica y rigurosa. Index Terms—privacidad de trayectorias, anonimizacion, no- ´ ciones sintacticas y sem ´ anticas, utilidad, privacidad diferencial.Este trabajo tam- ´ bien ha recibido el apoyo de la Fundaci ´ on “la Caixa” ´ (codigo de beca LCF/BQ/PR20/11770009), del programa ´ H2020 de la Union Europea (acuerdo de subvenci ´ on Marie ´ Skłodowska-Curie n.º 847648), del Gobierno de Espana en el ˜ marco del proyecto “COMPROMISE” (PID2020-113795RBC31/AEI/10.13039/501100011033), y del proyecto BMBF “PROPOLIS” (16KIS1393K). Los autores del KIT cuentan con el apoyo de KASTEL Security Research Labs (Tema 46.23 de la Asociacion Helmholtz) y de la Estrategia de ´ Excelencia de Alemania (EXC 2050/1 ‘CeTI’).Peer ReviewedPostprint (published version

Anonymizing trajectory data: limitations and opportunities

A variety of conditions and limiting properties complicate the anonymization of trajectory data, since they are sequential, high-dimensional, bound to geophysical restrictions and easily mapped to semantic points of interest and regions with known properties like suburban neighborhoods, industrial areas or city-centers. Learning the places where one has been is extremely privacy-invasive. However, analyzing real trajectories holds numerous promises, ranging from better informed traffic management, to location recommendations or computational social science, infrastructure and even urban development planning. The aim of this paper is to establish various challenges, stemming from ideas and also limitations of existing proposals for the anonymization of trajectories, and subsequently identify research opportunities. Keeping both utility and privacy challenges prominent, we sketch the way towards establishing a useful research framework and propose possible research venues towards privacy-preserving trajectory publication.Peer ReviewedPostprint (author's final draft