The Random Bit Complexity of Mobile Robots Scattering

We consider the problem of scattering $n$ robots in a two dimensional continuous space. As this problem is impossible to solve in a deterministic manner, all solutions must be probabilistic. We investigate the amount of randomness (that is, the number of random bits used by the robots) that is required to achieve scattering. We first prove that $n \log n$ random bits are necessary to scatter $n$ robots in any setting. Also, we give a sufficient condition for a scattering algorithm to be random bit optimal. As it turns out that previous solutions for scattering satisfy our condition, they are hence proved random bit optimal for the scattering problem. Then, we investigate the time complexity of scattering when strong multiplicity detection is not available. We prove that such algorithms cannot converge in constant time in the general case and in $o(\log \log n)$ rounds for random bits optimal scattering algorithms. However, we present a family of scattering algorithms that converge as fast as needed without using multiplicity detection. Also, we put forward a specific protocol of this family that is random bit optimal ($n \log n$ random bits are used) and time optimal ($\log \log n$ rounds are used). This improves the time complexity of previous results in the same setting by a $\log n$ factor. Aside from characterizing the random bit complexity of mobile robot scattering, our study also closes its time complexity gap with and without strong multiplicity detection (that is, $O(1)$ time complexity is only achievable when strong multiplicity detection is available, and it is possible to approach it as needed otherwise)

Uncovering the mesoscale structure of the credit default swap market to improve portfolio risk modelling

One of the most challenging aspects in the analysis and modelling of financial markets, including Credit Default Swap (CDS) markets, is the presence of an emergent, intermediate level of structure standing in between the microscopic dynamics of individual financial entities and the macroscopic dynamics of the market as a whole. This elusive, mesoscopic level of organisation is often sought for via factor models that ultimately decompose the market according to geographic regions and economic industries. However, at a more general level the presence of mesoscopic structure might be revealed in an entirely data-driven approach, looking for a modular and possibly hierarchical organisation of the empirical correlation matrix between financial time series. The crucial ingredient in such an approach is the definition of an appropriate null model for the correlation matrix. Recent research showed that community detection techniques developed for networks become intrinsically biased when applied to correlation matrices. For this reason, a method based on Random Matrix Theory has been developed, which identifies the optimal hierarchical decomposition of the system into internally correlated and mutually anti-correlated communities. Building upon this technique, here we resolve the mesoscopic structure of the CDS market and identify groups of issuers that cannot be traced back to standard industry/region taxonomies, thereby being inaccessible to standard factor models. We use this decomposition to introduce a novel default risk model that is shown to outperform more traditional alternatives.Comment: Quantitative Finance (2021

PRELIMINARY STUDIES ON SEDIMENT CORE FROM THE TYRO BASIN

Η παρούσα εργασία παρουσιάζει τα προκαταρκτικά αποτελέσματα της ορυκτολογικής και μικροπαλαιοντολογικής ανάλυσης που πραγματοποιήθηκε σε δείγματα ιζημάτων από τον πυρήνα TYR05 που συλλέχθηκε από την ανοξική και υπεράλμυρη λεκάνη Τύρου στην ανατολική Μεσόγειο. Ο πυρήνας αποτελεί μία σύνθετη λιθοστρωματογραφική ακολουθία που αποδίδεται στο ισχυρό γεωδυναμικό καθεστώς της περιοχής. Οι συγκεντρώσεις πλαγκτονικών τρηματοφόρων παρουσιάζουν διακυμάνσεις οι οποίες συμπίπτουν με αλλαγές στη λιθολογία του πυρήνα. Η ορυκτολογική σύσταση των ιζημάτων δείχνει επίδραση από τους εβαπορίτες που δημιουργούνται στον πυθμένα της λεκάνης. Τα ορυκτά συστατικά σε σχέση με τις συγκεντρώσεις της μικροπανίδας δείχνουν ότι τα ιζήματα περιλαμβάνουν σαπροπηλικά στρώματα. Χρειάζονται επιπλέον αναλύσεις για τον ασφαλή προσδιορισμό των σαπροπηλικών αποθέσεων.The present paper summarizes the preliminary results of the mineralogical and micropaleontological analysis conducted on sediment samples from core TYR05 retrieved from the anoxic and hypersaline Tyro basin in the eastern Mediterranean Sea. The core comprises a complex lithostratigraphic sequence attributed to the strong geodynamic regime of the area. The planktonic foraminifera associations present fluctuations which coincide with changes in the lithology of the core. The mineralogical composition of the sediments shows influence from the evaporites developed on the bottom of the basin. The mineral constituents in association to the microfauna assemblages suggest that the sediments include sapropelic layers. Further analyses are needed in order to determine safely the sapropelic deposits

Assessment of High-Resolution Satellite-Based Rainfall Estimates over the Mediterranean during Heavy Precipitation Events

Abstract Heavy precipitation events (HPE) can incur significant economic losses as well as losses of lives through catastrophic floods. Evidence of increasing heavy precipitation at continental and global scales clearly emphasizes the need to accurately quantify these phenomena. The current study focuses on the error analysis of two of the main quasi-global, high-resolution satellite products [Climate Prediction Center (CPC) morphing technique (CMORPH) and Precipitation Estimation from Remotely Sensed Imagery Using Artificial Neural Networks (PERSIANN)], using rainfall data derived from high-quality weather radar rainfall estimates as a reference. This analysis is based on seven major flood-inducing HPEs that developed over complex terrain areas in northern Italy (Fella and Sessia regions) and southern France (Cevennes–Vivarais region). The storm cases were categorized as convective or stratiform based on their characteristics, including rainfall intensity, duration, and area coverage. The results indicate that precipitation type has an effect on the algorithm's ability to capture rainfall effectively. Convective storm cases exhibited greater rain rate retrieval errors, while low rain rates in stratiform-type systems are not well captured by the satellite algorithms investigated in this study, thus leading to greater missed rainfall volumes. Overall, CMORPH exhibited better error statistics than PERSIANN for the HPEs of this study. Similarities are also shown in the two satellite products' error characteristics for the HPEs that occurred in the same geographical area