Flow networks: A characterization of geophysical fluid transport

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is useful to analyze fluid dynamics in geophysical contexts, as illustrated by the construction of a flow network associated to the surface circulation in the Mediterranean sea. We use network-theory tools to analyze the flow network and gain insights into transport processes. In particular we quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix, and related to the statistics of stretching in the fluid, in particular to the Lyapunov exponent field. Finally we use a network community detection algorithm, Infomap, to partition the Mediterranean network into coherent regions, i.e. areas internally well mixed, but with little fluid interchange between them.Comment: 16 pages, 15 figures. v2: published versio

A Markov model for inferring flows in directed contact networks

Directed contact networks (DCNs) are a particularly flexible and convenient class of temporal networks, useful for modeling and analyzing the transfer of discrete quantities in communications, transportation, epidemiology, etc. Transfers modeled by contacts typically underlie flows that associate multiple contacts based on their spatiotemporal relationships. To infer these flows, we introduce a simple inhomogeneous Markov model associated to a DCN and show how it can be effectively used for data reduction and anomaly detection through an example of kernel-level information transfers within a computer.Comment: 12 page

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Beyond Speculative Robot Ethics

In this article we develop a dialogue model for robot technology experts and designated users to discuss visions on the future of robotics in long-term care. Our vision assessment study aims for more distinguished and more informed visions on future robots. Surprisingly, our experiment also lead to some promising co-designed robot concepts in which jointly articulated moral guidelines are embedded. With our model we think to have designed an interesting response on a recent call for a less speculative ethics of technology by encouraging discussions about the quality of positive and negative visions on the future of robotics.

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

TFAW survey II: 6 Newly Validated Planets and 13 Planet Candidates from K2

Searching for Earth-sized planets in data from Kepler's extended mission (K2) is a niche that still remains to be fully exploited. The TFAW survey is an ongoing project that aims to re-analyze all light curves in K2 C1-C8 and C12-C18 campaigns with a wavelet-based detrending and denoising method, and the period search algorithm TLS to search for new transit candidates not detected in previous works. We have analyzed a first subset of 24 candidate planetary systems around relatively faint host stars (10.9 < $K_{p}$ < 15.4) to allow for follow-up speckle imaging observations. Using VESPA and TRICERATOPS, we statistically validate six candidates orbiting four unique host stars by obtaining false-positive probabilities smaller than 1% with both methods. We also present 13 vetted planet candidates that might benefit from other, more precise follow-up observations. All of these planets are sub-Neptune-sized, with two validated planets and three candidates with sub-Earth sizes, and have orbital periods between 0.81 and 23.98 days. Some interesting systems include two ultra-short-period planets, three multi-planetary systems, three sub-Neptunes that appear to be within the small planet Radius Gap, and two validated and one candidate sub-Earths (EPIC 210706310, EPIC 210768568, and EPIC 246078343) orbiting metal-poor stars.Comment: Submitted to Monthly Notices of the Royal Astronomical Society. 25 pages, 14 figure

Vision-based Semantic Segmentation in Scene Understanding for Autonomous Driving: Recent Achievements, Challenges, and Outlooks

Scene understanding plays a crucial role in autonomous driving by utilizing sensory data for contextual information extraction and decision making. Beyond modeling advances, the enabler for vehicles to become aware of their surroundings is the availability of visual sensory data, which expand the vehicular perception and realizes vehicular contextual awareness in real-world environments. Research directions for scene understanding pursued by related studies include person/vehicle detection and segmentation, their transition analysis, lane change, and turns detection, among many others Unfortunately, these tasks seem insufficient to completely develop fully-autonomous vehicles i.e. achieving level-5 autonomy, travelling just like human-controlled cars. This latter statement is among the conclusions drawn from this review paper: scene understanding for autonomous driving cars using vision sensors still requires significant improvements. With this motivation, this survey defines, analyzes, and reviews the current achievements of the scene understanding research area that mostly rely on computationally complex deep learning models. Furthermore, it covers the generic scene understanding pipeline, investigates the performance reported by the state-of-the-art, informs about the time complexity analysis of avant garde modeling choices, and highlights major triumphs and noted limitations encountered by current research efforts. The survey also includes a comprehensive discussion on the available datasets, and the challenges that, even if lately confronted by researchers, still remain open to date. Finally, our work outlines future research directions to welcome researchers and practitioners to this exciting domain.This work was supported by the European Commission through European Union (EU) and Japan for Artificial Intelligence (AI) under Grant 957339

Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz

We compute the first curvature corrections to the spectrum of light-cone gauge type IIA string theory that arise in the expansion of $AdS_4\times \mathbb{CP}^3$ about a plane-wave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the self-energy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate two-oscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finite-size corrections, at the order 1/J, where $J$ is the length of the chain, in the two-magnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in $\lambda' =\lambda/J^2$. We conjecture that the equivalence extends to all orders in $\lambda$ and to higher orders in 1/J.Comment: 32 pages. Published version; journal reference adde

Data harmonisation for information fusion in digital healthcare: A state-of-the-art systematic review, meta-analysis and future research directions

Removing the bias and variance of multicentre data has always been a challenge in large scale digital healthcare studies, which requires the ability to integrate clinical features extracted from data acquired by different scanners and protocols to improve stability and robustness. Previous studies have described various computational approaches to fuse single modality multicentre datasets. However, these surveys rarely focused on evaluation metrics and lacked a checklist for computational data harmonisation studies. In this systematic review, we summarise the computational data harmonisation approaches for multi-modality data in the digital healthcare field, including harmonisation strategies and evaluation metrics based on different theories. In addition, a comprehensive checklist that summarises common practices for data harmonisation studies is proposed to guide researchers to report their research findings more effectively. Last but not least, flowcharts presenting possible ways for methodology and metric selection are proposed and the limitations of different methods have been surveyed for future research