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We define two versions of the archimedean height pairing between certain Bloch higher cycles. Both pairings generalize the archimedean height pairing between ordinary cycles. To do this, we introduce the notion of framed mixed Hodge structures and define two heights of a framed mixed Hodge structure. Moreover, we show that, with a pair of properly intersecting refined higher cycles in complementary codimension, we can associate a framed mixed Hodge structure. As an interesting example, we compute both heights for the complex polylogarithm variation of mixed Hodge structures and show that each of them gives rise to a well known version of the single valued polylogarithm function.

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)

Blockchain technology, beyond cryptocurrencies, is called to be the new information exchange ecosystem due to its unique properties, such as immutability and transparency. The main objective of this work is to introduce the design of a decentralized rental system, which leverages smart contracts and the Ethereum public blockchain. The work started from an exhaustive investigation on the Ethereum platform, emphasizing the aspect of cryptography and all the technology behind this platform. In order to test the proposed scheme in a realistic use, the implementation of a web application for the rental of vehicles has been carried out. The application covers the entire vehicle rental process offered in traditional web applications, adding more autonomy and ease of use to users. Following Ethereum application development guidelines, all business logic is located in the smart contracts implemented in the Ethereum network, where these contracts control the entire vehicle rental system of customers. While this is a work in progress, the results obtained in the first proof of concept have been very promising.

A Mobile Ad hoc NETwork (MANET) is a type of wireless network without any infrastructure, where nodes must adapt to the changing dynamic situations that result from their mobility. Because of the decentralization of nodes and the security needs of communications, management of MANETs must be self-organized, which is a major research challenge. In order to cope with the intrinsic properties of MANETs, a new decentralized management system for MANETs called Self-organizing Life Cycle Management (SLCM), is here fully described and evaluated. Regarding security, node authentication is the most critical component of access control in any network, and in particular in MANETs. Broadcasting is also a fundamental data dissemination mechanism in these networks. Both aspects have received special attention when defining the proposed SLCM system. In particular, both a strong access control algorithm based on the cryptographic paradigm of zero-knowledge proofs, and a three-step broadcast protocol, are here defined. This work includes the performance evaluation of the scheme, and the obtained experimental results show that SLCM significantly improves both the quality and the security of life cycle management of self-organized MANETs., Comment: arXiv admin note: text overlap with arXiv:1005.3391, arXiv:1005.0106

Vehicular ad-hoc networks, where traffic information is distributed from many sources to many destinations, require data authentication mechanisms to detect any malicious behavior of users, such as modification or replay attacks. In this paper we propose a new data aggregation protocol that uses probabilistic verification to detect such attack attempts a posteriori in an efficient way, with minimal overhead and delay. The algorithm also contains an additional security mechanism based on reactive groups created on demand, which ensure a priori that vehicles generate trustworthy information. According to a comprehensive analysis including both a small-scale real device implementation and NS2 simulations, it is shown that the proposed protocol is robust.

A vehicular ad-hoc network is a type of communication network where the nodes are vehicles. Their aim is to manage traffic efficiently in order to prevent unwanted events such as accidents, jams, etc. The research on this type of networks assumes the use of additional infrastructure installed on the roads, and special devices installed in vehicles. In this paper we propose a novel solution for the deployment of vehicular networks, which uses only existing smartphones with technologies such as Wi-Fi, GPS and Bluetooth. This approach will save the costs of road infrastructure deployment and extra vehicles devices, making it possible to deploy the first real-world vehicular ad-hoc network with a low cost. In particular, the developed implementation of the proposal for the Symbian platform is here examined in full detail.

GRAVITY+ is the upgrade of GRAVITY and the Very Large Telescope Interferometer (VLTI) with wide-separation fringe tracking, new adaptive optics, and laser guide stars on all four 8~m Unit Telescopes (UTs), for ever fainter, all-sky, high contrast, milliarcsecond interferometry. Here we present the design and first results of the first phase of GRAVITY+, called GRAVITY Wide. GRAVITY Wide combines the dual-beam capabilities of the VLTI and the GRAVITY instrument to increase the maximum separation between the science target and the reference star from 2 arcseconds with the 8 m UTs up to several 10 arcseconds, limited only by the Earth's turbulent atmosphere. This increases the sky-coverage of GRAVITY by two orders of magnitude, opening up milliarcsecond resolution observations of faint objects, and in particular the extragalactic sky. The first observations in 2019 - 2022 include first infrared interferometry of two redshift $z\sim2$ quasars, interferometric imaging on the binary system HD 105913A, and repeated observations of multiple star systems in the Orion Trapezium Cluster. We find the coherence loss between the science object and fringe-tracking reference star well described by the turbulence of the Earth's atmosphere. We confirm that the larger apertures of the UTs result in higher visibilities for a given separation due to larger overlap of the projected pupils on sky and give predictions for visibility loss as a function of separation to be used for future planning., Comment: 15 pages, 12 figures, 5 tables. Accepted by A&A

Radiative shocks (RS) are complex phenomena which are ubiquitous in astrophysical environments. The study of such hypersonic shocks in the laboratory, under controlled conditions, is of primary interest to understand the physics at play and also to check the ability of numerical simulations to reproduce the experimental results. In this context, we conducted, at the Prague Asterix Laser System facility (PALS), the first experiments dedicated to the study of two counter-propagating radiative shocks propagating at non-equal speeds up to 25-50 km/s in noble gases at pressures ranging between 0.1 and 0.6 bar. These experiments highlighted the interaction between the two radiative precursors. This interaction is qualitatively but not quantitatively described by 1D simulations. Preliminary results obtained with XUV spectroscopy leading to the estimation of shock temperature and ion charge of the plasma are also presented.

We study the weak interaction processes taking place within a combustion flame that converts dense hadronic matter into quark matter in a compact star. Using the Boltzmann equation we follow the evolution of a small element of just deconfined quark matter all along the flame interior until it reaches chemical equilibrium at the back boundary of the flame. We obtain the reaction rates and neutrino emissivities of all the relevant weak interaction processes without making any assumption about the neutrino degeneracy. We analyse systematically the role the initial conditions of unburnt hadronic matter, such as density, temperature, neutrino trapping and composition, focusing on typical astrophysical scenarios such as cold neutron stars, protoneutron stars, and post merger compact objects. We find that the temperature within the flame rises significantly in a timescale of 1 nanosecond. The increase in $T$ strongly depends on the initial strangeness of hadronic matter and tends to be more drastic at larger densities. Typical final values range between $20$ and $60 \, \mathrm{MeV}$. The nonleptonic process $u + d \rightarrow u + s$ is always dominant in cold stars, but in hot objects the process $u + e^{-} \leftrightarrow d + {\nu_e}$ becomes relevant, and in some cases dominant, near chemical equilibrium. The rates for the other processes are orders of magnitude smaller. We find that the neutrino emissivity per baryon is very large, leading to a total energy release per baryon of $2-60 \, \mathrm{MeV}$ in the form of neutrinos along the flame. We discuss some astrophysical consequences of the results., Comment: 19 pages, 16 figures

For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized complex and intersect properly. In a special case, this mixed Hodge structure is an oriented biextension, and its height agrees with the higher archimedean height pairing introduced in a previous paper by the first two authors. We also compute a non-trivial example of this height given by Bloch-Wigner dilogarithm function. Finally we study the variation of mixed Hodge structures of Hodge-Tate type, and show that the height extends continuously to degenerate situations., Comment: A few typos were corrected to increase data accuracy. To appear in the Proceedings of the London Math Society

Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford-Taylor theory of plurisubharmonic functions on the tropicalization., Comment: Final version, 50 pages, 1 figure, to appear in Mathematische Zeitschrift

The formation of self-organized laser induced periodic surface structures (LIPSS) in metals, semiconductors and dielectrics upon pulsed laser irradiation is a well-known phenomenon, receiving increased attention due to its huge technological potential. For the case of metals, a major role in this process is played by surface plasmon polaritons (SPPs) propagating at the interface of the metal with the medium of incidence. Yet, simple and advanced models based on SPP propagation sometimes fail to explain experimental results, even of basic features as the LIPSS period. We experimentally demonstrate, for the particular case of LIPSS on Cu, that significant deviations of the structure period from the predictions of the standard model are observed, which are very pronounced for elevated angles of laser incidence. In order to explain this deviation, we introduce a model based on the propagation of a SPP on a rough surface that takes into account the influence of the specific roughness properties on the SPP wave vector. Good agreement of the modelling results with the experimental data is observed, which highlights the potential of this model for the general understanding of LIPSS in other metals., Comment: 14 pages, 5 figures

In this work the development results of the TRITIUM project is presented. The main objective of the project is the construction of a near real-time monitor for low activity tritium in water, aimed at in-situ surveillance and radiological protection of river water in the vicinity of nuclear power plants. The European Council Directive 2013/51/Euratom requires that the maximum level of tritium in water for human consumption to be lower than 100 Bq/L. Tritium levels in the cooling water of nuclear power plants in normal operation are much higher than the levels caused by the natural and cosmogenic components, and may easily surmount the limit required by the Directive. The current liquid-scintillation measuring systems in environmental radioactivity laboratories are sensitive to such low levels, but they are not suitable for real-time monitoring. Moreover, there is no currently available device with enough sensitivity and monitoring capabilities that could be used for surveillance of the cooling water of nuclear power plants. A detector system based on scintillation fibers read out by photomultiplier tubes (PMTs) or silicon photomultiplier (SiPM) arrays is under development for in-water tritium measurement. This detector will be installed in the vicinity of Almaraz nuclear power plant (Spain) in Spring 2019. An overview of the project development and the results of first prototypes are presented., Comment: 6 pages, 11 figures, IEEE NSS-MIC Conf Record 2018

In recent years, extraordinary spin angular momenta have been investigated in a variety of structured electromagnetic waves, being of especial interest in sub-wavelength evanescent fields. Here we demonstrate analytically that, in planar and cylindrical waveguides supporting transverse electric/magnetic modes, transverse spin density arises inside the waveguide (different from the spin induced in the evanescent region outside the waveguide), carrying indeed longitudinal extraordinary (so-called) Belinfante's spin momentum. Such contribution depends linearly on the mode transverse wave vector, and is thus induced by mode confinement. Cylindrical waveguides support in addition hybrid modes that exhibit a richer phenomenology with not only azimuthal (confinement-related) spin, but also an intrinsic helicity which leads to longitudinal spin density and transverse helicity-dependent spin momentum. Results are indeed presented for configurations relevant to spin-orbit coupling in nanophotonic waveguides and to manipulating optical forces in IR-to-microwave water-filled channels. Thus guided modes intrinsically carrying confinement-induced transverse spin, combined with intrinsic-helicity-induced longitudinal spin (when hybrid), hold promise of superb devices to control spin-orbit interaction and optical forces within confined geometries throughout the electromagnetic spectra.

Let $f:\mathbb{R}^n\to\mathbb{R}$ be a function. Assume that for a measurable set $\Omega$ and almost every $x\in\Omega$ there exists a vector $\xi_x\in\mathbb{R}^n$ such that $$\liminf_{h\to 0}\frac{f(x+h)-f(x)-\langle \xi_x, h\rangle}{|h|^2}>-\infty.$$ Then we show that $f$ satisfies a Lusin-type property of order $2$ in $\Omega$, that is to say, for every $\varepsilon>0$ there exists a function $g\in C^2(\mathbb{R}^n)$ such that $\mathcal{L}^{n}\left(\{x\in\Omega : f(x)\neq g(x)\}\right)\leq\varepsilon$. In particular every function which has a nonempty proximal subdifferential almost everywhere also has the Lusin property of class $C^2$. We also obtain a similar result (replacing $C^2$ with $C^1$) for the Fr\'echet subdifferential. Finally we provide some examples showing that this kind of results are no longer true for "Taylor subexpansions" of higher order., Comment: The example showing that the main results fail for $C^{k}$ with $k\geq 3$ has been changed. An example showing that the main results fail if we replace the Frechet subdifferential or the proximal subdifferential with the limiting subdifferential has been added