Positional Encoding by Robots with Non-Rigid Movements

Consider a set of autonomous computational entities, called \emph{robots}, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant $\delta > 0$, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than $\delta$ amount. This model is known in literature as \emph{non-rigid} movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having $O(1)$ bits of persistent memory and ability to make circular moves

Linear Time Distributed Swap Edge Algorithms

In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2-edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If one tree edge e = {x, y} fails, the communication network will be disconnected. However, since X is 2-edge connected, communication can be restored by replacing e by non-tree edge e′, called a swap edge of e, whose ends lie in different components of T − e. Of all possible swap edges of e, we would like to choose the best, as defined by the application. The all best swap edges problem is to identify the best swap edge for every tree edge, so that in case of any edge failure, the best swap edge can be activated quickly. There are solutions to this problem for a number of cases in the literature. A major concern for all these solutions is to minimize the number of messages. However, especially in fault-transient environments, time is a crucial factor. In this paper we present a novel technique that addresses this problem from a time perspective; in fact, we present a distributed solution that works in linear time with respect to the height h of T for a number of differentcriteria, while retaining the optimal number of messages. To the best of our knowledge, all previous solutions solve the problem in O(h^2) time in the cases we consider

Le scienziate dimenticate: Margaret Hamilton, le missioni sulla Luna, matematica e programmazione

Guerra fredda, 1961: l’Unione Sovietica ha dato un terribile smacco agli Stati Uniti, mandando il primo uomo nello spazio. Il presidente Kennedy decide di tentare la carta della missione di conquista della Luna, difficilissima ma di grandissimo impatto mediatico. La giovane matematica Margaret Hamilton si trova quasi per caso a essere un personaggio chiave della missione: assunta come programmatrice quando la sua esperienza era minima, diventa in breve tempo tanto esperta da essere messa a capo del gruppo NASA responsabile del software del computer di guida dell’Apollo 11. Inventa nuovi metodi di coordinamento e controllo del software che diventeranno importantissimi nell’immediato futuro, pioniera del software engineering, disciplina a cui lei stessa dà il nome. La complessità del programma Apollo 11 è enorme sia dal punto di vista ingegneristico che matematico e informatico, coinvolge centinaia di persone, può fallire in mille modi diversi, ma grazie anche alla scrupolosità di Margaret ha il successo che sappiamo. Il suo importantissimo contributo è premiato dal presidente Obama nel 2017.Cold War, 1961: the Soviet Union gave the United States a terrible blow by sending the first man into space. President Kennedy decides to try the road of the mission to conquer the Moon, very difficult but of great media impact. The young mathematician Margaret Hamilton finds herself almost by accident to be a key figure in the mission: hired as a programmer when her experience was minimal, she quickly becomes expert enough to be put in charge of the NASA team responsible for the software of the guidance computer of the Apollo 11. She invents new methods of software coordination and control that will become very important in the near future, she was a pioneer of software engineering, a discipline to which she herself gives her name. The complexity of the Apollo program is enormous both from an engineering, mathematical and computer science point of view, it involves hundreds of people, it can fail in a thousand different ways, but thanks to Margaret's scrupulousness it has the success we know. Her very important contribution is rewarded by President Obama

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure

Triggered fault slip on June 17, 2000 on the Reykjanes Peninsula, SW-Iceland captured by radar interferometry

Dynamically triggered seismicity followed shortly after a M-s 6.6 earthquake in Iceland on June 17, 2000. Smaller earthquakes occurred on the Reykjanes Peninsula up to 100 km from the mainshock rupture. Using interferometric analysis of Synthetic Aperture Radar images (InSAR), we measure crustal deformation associated with three triggered deformation events. The largest of these occurred at Lake Kleifarvatn, 85 km west of the mainshock epicenter. Modeling of the InSAR data reveals strikeslip on a north-striking fault, with a geodetic moment of 6.2 x 10(17) Nm, equivalent to magnitude M-w 5.8 earthquake. A seismological estimate of the moment is not yet available, because the seismic signature of this event is partly hidden by the mainshock waveform. The paucity of aftershocks on the triggered rupture plane suggests some aseismic slip there, compatible with a thin seismogenic crust, high heat-flow, hydrothermal alteration and the presence of fluids in the area

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Global link between deformation and volcanic eruption quantified by satellite imagery

A key challenge for volcanological science and hazard management is that few of the world’s volcanoes are effectively monitored. Satellite imagery covers volcanoes globally throughout their eruptive cycles, independent of ground-based monitoring, providing a multidecadal archive suitable for probabilistic analysis linking deformation with eruption. Here we show that, of the 198 volcanoes systematically observed for the past 18 years, 54 deformed, of which 25 also erupted. For assessing eruption potential, this high proportion of deforming volcanoes that also erupted (46%), together with the proportion of non-deforming volcanoes that did not erupt (94%), jointly represent indicators with ‘strong’ evidential worth. Using a larger catalogue of 540 volcanoes observed for 3 years, we demonstrate how this eruption–deformation relationship is influenced by tectonic, petrological and volcanic factors. Satellite technology is rapidly evolving and routine monitoring of the deformation status of all volcanoes from space is anticipated, meaning probabilistic approaches will increasingly inform hazard decisions and strategic development

Magma plumbing systems: a geophysical perspective

Over the last few decades, significant advances in using geophysical techniques to image the structure of magma plumbing systems have enabled the identification of zones of melt accumulation, crystal mush development, and magma migration. Combining advanced geophysical observations with petrological and geochemical data has arguably revolutionised our understanding of, and afforded exciting new insights into, the development of entire magma plumbing systems. However, divisions between the scales and physical settings over which these geophysical, petrological, and geochemical methods are applied still remain. To characterise some of these differences and promote the benefits of further integration between these methodologies, we provide a review of geophysical techniques and discuss how they can be utilised to provide a structural context for and place physical limits on the chemical evolution of magma plumbing systems. For example, we examine how Interferometric Synthetic Aperture Radar (InSAR), coupled with Global Positioning System (GPS) and Global Navigation Satellite System (GNSS) data, and seismicity may be used to track magma migration in near real-time. We also discuss how seismic imaging, gravimetry and electromagnetic data can identify contemporary melt zones, magma reservoirs and/or crystal mushes. These techniques complement seismic reflection data and rock magnetic analyses that delimit the structure and emplacement of ancient magma plumbing systems. For each of these techniques, with the addition of full-waveform inversion (FWI), the use of Unmanned Aerial Vehicles (UAVs) and the integration of geophysics with numerical modelling, we discuss potential future directions. We show that approaching problems concerning magma plumbing systems from an integrated petrological, geochemical, and geophysical perspective will undoubtedly yield important scientific advances, providing exciting future opportunities for the volcanological community