On the frequency of gravitational waves

We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.Comment: 4 pages, 2 figures. In v2 minor corrections and a full sentence changed in section III in the paragraph about turbulence. Version accepted for publication by PR

Exotic Heavy Quarkonium Spectroscopy: A Mini-review

Since nine years experiments have been observing a host of exotic states decaying into heavy quarkonia. The interpretation of most of them still remains uncertain and, in some cases, controversial, notwithstanding a considerable progress has been made on the quality of the experimental information available and a number of ideas and models have been put forward to explain the observations. In this mini-review we will summarize the measurements, with the most recent updates, and list the useful ones yet to be done. We will discuss the problem of the spin of the X, which could hide some major surprise on its interpretation, and review some more phenomenological issues debated in the field.Comment: 14 pages, 2 figures, 5 tables. To appear in Mod. Phys. Lett.

Input-driven unsupervised learning in recurrent neural networks

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is an attractor neural network with Hebbian learning (e.g. the Hopfield model). The model simplicity and the locality of the synaptic update rules come at the cost of a limited storage capacity, compared with the capacity achieved with supervised learning algorithms, whose biological plausibility is questionable. Here, we present an on-line learning rule for a recurrent neural network that achieves near-optimal performance without an explicit supervisory error signal and using only locally accessible information, and which is therefore biologically plausible. The fully connected network consists of excitatory units with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the patterns to be memorized are presented on-line as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs ('local fields'). Synapses corresponding to active inputs are modified as a function of the position of the local field with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. An additional parameter of the model allows to trade storage capacity for robustness, i.e. increased size of the basins of attraction. We simulated a network of 1001 excitatory neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction: our results show that, for any given basin size, our network more than doubles the storage capacity, compared with a standard Hopfield network. Our learning rule is consistent with available experimental data documenting how plasticity depends on firing rate. It predicts that at high enough firing rates, no potentiation should occu

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

The final publication is available at Springer via http://dx.doi.org/ 10.1007/s00466-016-1305-zThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P1P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr–Coulomb and Drucker–Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.Peer ReviewedPostprint (author's final draft

Stabilized mixed explicit finite element formulation for compressible and nearly-incompressible solids

El presente estudio presenta una formulación mixta de elementos finitos capaz de abordar problemas quasiincompresibles en forma explícita. Esta formulación se aplica a elementos con interpolaciones independientes e iguales de desplazamientos y deformaciones, estabilizadas mediante subescalas variacionales (VMS). Como continuación del estudio presentado en la referencia [23] , en la que se introdujo la subescala de las deformaciones, en este trabajo se incluyen los efectos de la sub-escala de los desplazamientos, con el fin de estabilizar el campo de las presiones. La formulación evita la condición de Ladyzhenskaya-Babuska-Brezzi (LBB) y sólo requiere la resolución de un sistema diagonal de ecuaciones. En este artículo se tratan también los principales aspectos de implementación. Finalmente, ejemplos de validación numérica muestran el comportamiento de estos elementos en comparación con la formulación irreducible.This study presents a mixed finite element formulation able to address nearly-incompressible problems explicitly. This formulation is applied to elements with independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). As a continuation of the study presented in reference [23], in which the strains sub-scale was introduced, in this work the effects of sub-scale displacements are included, in order to stabilize the pressure field. The formulation avoids the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and only requires the solution of a diagonal system of equations. The main aspects of implementation are also discussed. Finally, numerical examples validate the behaviour of these elements compared with the irreductible formulation.Peer ReviewedPostprint (published version

Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coefficient

We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Coppi (2005), dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a non-zero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained profile has the typical oscillating feature of the crystalline structure, reconciled with the presence of viscosity, associated to the differential rotation of the disk, and with a net accretion rate. In fact, we provide a direct relation between the electromagnetic reaction of the disk and the (no longer zero) increasing of its mass per unit time. The radial accretion component of the velocity results to be few orders of magnitude below the equatorial sound velocity. Its oscillating-like character does not allow a real matter in-fall to the central object (an effect to be searched into non-linear MHD corrections), but it accounts for the out-coming of steady fluxes, favourable to the ring-like morphology of the disk.Comment: 15 pages, 1 figure, accepted for publication on Modern Physics Letters

An Agent-based Modelling Framework for Driving Policy Learning in Connected and Autonomous Vehicles

Due to the complexity of the natural world, a programmer cannot foresee all possible situations, a connected and autonomous vehicle (CAV) will face during its operation, and hence, CAVs will need to learn to make decisions autonomously. Due to the sensing of its surroundings and information exchanged with other vehicles and road infrastructure, a CAV will have access to large amounts of useful data. While different control algorithms have been proposed for CAVs, the benefits brought about by connectedness of autonomous vehicles to other vehicles and to the infrastructure, and its implications on policy learning has not been investigated in literature. This paper investigates a data driven driving policy learning framework through an agent-based modelling approaches. The contributions of the paper are two-fold. A dynamic programming framework is proposed for in-vehicle policy learning with and without connectivity to neighboring vehicles. The simulation results indicate that while a CAV can learn to make autonomous decisions, vehicle-to-vehicle (V2V) communication of information improves this capability. Furthermore, to overcome the limitations of sensing in a CAV, the paper proposes a novel concept for infrastructure-led policy learning and communication with autonomous vehicles. In infrastructure-led policy learning, road-side infrastructure senses and captures successful vehicle maneuvers and learns an optimal policy from those temporal sequences, and when a vehicle approaches the road-side unit, the policy is communicated to the CAV. Deep-imitation learning methodology is proposed to develop such an infrastructure-led policy learning framework

The galileon as a local modification of gravity

In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]Comment: 35 pages; minor modifications, a typo corrected in eq. (114

Limits and opportunities of risk analysis application in railway systems

Risk Analysis is a collection of methods widely used in many industrial sectors. In the transport sector it has been particularly used for air transport applications. The reasons for this wide use are well-known: risk analysis allows to approach the safety theme in a stochastic - rather than deterministic - way, it forces to break down the system in sub-components, last but not least it allows a comparison between solutions with different costs, introducing de facto an element of economic feasibility of the project alternatives in the safety field. Apart from the United Kingdom, in Europe the application of this tool in the railway sector is relatively recent. In particular Directive 2004/49/EC (the "railway safety directive") provides for compulsory risk assessment in relation to the activities of railway Infrastructure Managers (IMs) and of Railway Undertakings (RUs). Nevertheless the peculiarity of the railway system - in which human, procedural, environmental and technological components have a continuous interchange and in which human responsibilities and technological functions often overlap - induced the EC to allow wide margins of subjectivity in the interpretation of risk assessment. When enacting Commission Regulation (EC) No 352/2009 which further regulates this subject, a risk assessment is considered positive also if the IM or RU declare to take safety measures widely used in normal practice. The paper shows the results of a structured comparative analysis of the rail sector and other industrial sectors, which illustrate the difficulties, but also the opportunities, of a transfer towards the railway system of the risk analysis methods currently in use for the other systems