Generic Large Cardinals and Systems of Filters

We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and concise way. In this framework we investigate the topic of definability of generic large cardinals properties.Comment: 36 page

Resilient Blocks for Summarising Distributed Data

Summarising distributed data is a central routine for parallel programming, lying at the core of widely used frameworks such as the map/reduce paradigm. In the IoT context it is even more crucial, being a privileged mean to allow long-range interactions: in fact, summarising is needed to avoid data explosion in each computational unit. We introduce a new algorithm for dynamic summarising of distributed data, weighted multi-path, improving over the state-of-the-art multi-path algorithm. We validate the new algorithm in an archetypal scenario, taking into account sources of volatility of many sorts and comparing it to other existing implementations. We thus show that weighted multi-path retains adequate accuracy even in high-variability scenarios where the other algorithms are diverging significantly from the correct values.Comment: In Proceedings ALP4IoT 2017, arXiv:1802.0097

Absoluteness via Resurrection

The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Velickovi\'c. We introduce a stronger form of resurrection axioms (the \emph{iterated} resurrection axioms $\textrm{RA}_\alpha(\Gamma)$ for a class of forcings $\Gamma$ and a given ordinal $\alpha$), and show that $\textrm{RA}_\omega(\Gamma)$ implies generic absoluteness for the first-order theory of $H_{\gamma^+}$ with respect to forcings in $\Gamma$ preserving the axiom, where $\gamma=\gamma_\Gamma$ is a cardinal which depends on $\Gamma$ ($\gamma_\Gamma=\omega_1$ if $\Gamma$ is any among the classes of countably closed, proper, semiproper, stationary set preserving forcings). We also prove that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover we outline that simultaneous generic absoluteness for $H_{\gamma_0^+}$ with respect to $\Gamma_0$ and for $H_{\gamma_1^+}$ with respect to $\Gamma_1$ with $\gamma_0=\gamma_{\Gamma_0}\neq\gamma_{\Gamma_1}=\gamma_1$ is in principle possible, and we present several natural models of the Morse Kelley set theory where this phenomenon occurs (even for all $H_\gamma$ simultaneously). Finally, we compare the iterated resurrection axioms (and the generic absoluteness results we can draw from them) with a variety of other forcing axioms, and also with the generic absoluteness results by Woodin and the second author.Comment: 34 page

Aggregate Drone Monitoring of Wildfires

Wildfires are an ever-increasing problem, exacerbated by the current global warming trends. Accordingly, it is becoming more and more relevant to monitor factors influencing their outbreaks and spreading to preemptively act on the riskiest areas and guide interventions in case an outbreak occurs. Different approaches have been proposed during the decades tackling this issue, which however require large datasets that are difficult and expensive to gather. In this paper, we propose to address the management of wildfires by empowering existing centralised models with a decentralised component. Leveraging dedicated monitoring drones together with smartphones held by experts and intervention corps, a decentralised system could both enhance data collection and assist interventions. As conditions near wildfires require strong fault-tolerance guarantees, we propose to develop such an application through aggregate programming, a novel approach to the resilient programming of decentralised systems

Engineering Resilient Collective Adaptive Systems by Self-Stabilisation

Collective adaptive systems are an emerging class of networked computational systems, particularly suited in application domains such as smart cities, complex sensor networks, and the Internet of Things. These systems tend to feature large scale, heterogeneity of communication model (including opportunistic peer-to-peer wireless interaction), and require inherent self-adaptiveness properties to address unforeseen changes in operating conditions. In this context, it is extremely difficult (if not seemingly intractable) to engineer reusable pieces of distributed behaviour so as to make them provably correct and smoothly composable. Building on the field calculus, a computational model (and associated toolchain) capturing the notion of aggregate network-level computation, we address this problem with an engineering methodology coupling formal theory and computer simulation. On the one hand, functional properties are addressed by identifying the largest-to-date field calculus fragment generating self-stabilising behaviour, guaranteed to eventually attain a correct and stable final state despite any transient perturbation in state or topology, and including highly reusable building blocks for information spreading, aggregation, and time evolution. On the other hand, dynamical properties are addressed by simulation, empirically evaluating the different performances that can be obtained by switching between implementations of building blocks with provably equivalent functional properties. Overall, our methodology sheds light on how to identify core building blocks of collective behaviour, and how to select implementations that improve system performance while leaving overall system function and resiliency properties unchanged.Comment: To appear on ACM Transactions on Modeling and Computer Simulatio