Parameterization of written signatures based on EFD

In this work we propose a method to quantify written signatures from digitalized images based on the use of Elliptical Fourier Descriptors (EFD). As usually signatures are not represented as a closed contour, and being that a necessary condition in order to apply EFD, we have developed a method that represents the signatures by means of a set of closed contours. One of the advantages of this method is that it can reconstruct the original shape from all the coefficients, or an approximated shape from a reduced set of them finding the appropriate number of EFD coefficients required for preserving the important information in each application. EFD provides accurate frequency information, thus the use of EFD opens many possibilities. The method can be extended to represent other kind of shapes

Affine equivalences of trigonometric curves

We provide an efficient algorithm to detect whether two given trigonometric curves, i.e. two parametrized curves whose components are truncated Fourier series, in any dimension, are affinely equivalent, i.e. whether there exists an affine mapping transforming one of the curves onto the other. If the coefficients of the parametrizations are known exactly (the exact case), the algorithm boils down to univariate gcd computation, so it is efficient and fast. If the coefficients of the parametrizations are known with finite precision, e.g. floating point numbers (the approximate case), the univariate gcd computation is replaced by the computation of singular values of an appropriate matrix. Our experiments show that the method works well, even for high degrees.Agencia Estatal de Investigació

Subgroup security in pairing-based cryptography

Pairings are typically implemented using ordinary pairing-friendly elliptic curves. The two input groups of the pairing function are groups of elliptic curve points, while the target group lies in the multiplicative group of a large finite field. At moderate levels of security, at least two of the three pairing groups are necessarily proper subgroups of a much larger composite-order group, which makes pairing implementations potentially susceptible to small-subgroup attacks. To minimize the chances of such attacks, or the effort required to thwart them, we put forward a property for ordinary pairing-friendly curves called subgroup security. We point out that existing curves in the literature and in publicly available pairing libraries fail to achieve this notion, and propose a list of replacement curves that do offer subgroup security. These curves were chosen to drop into existing libraries with minimal code change, and to sustain state-of-the-art performance numbers. In fact, there are scenarios in which the replacement curves could facilitate faster implementations of protocols because they can remove the need for expensive group exponentiations that test subgroup membership

General Relativity as a Biconformal Gauge Theory

We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to a curved 2n-dim geometry admits an action functional linear in the curvatures. Because symmetry is maintained between the translations and the special conformal transformations in the construction, these spaces are called biconformal; this same symmetry gives biconformal spaces overlapping structures with double field theories, including manifest T-duality. We establish that biconformal geometry is a form of double field theory, showing how general relativity with integrable local scale invariance arises from its field equations. While we discuss the relationship between biconformal geometries and the double field theories of T-dual string theories, our principal interest is the study of the gravity theory. We show that vanishing torsion and vanishing co-torsion solutions to the field equations overconstrain the system, implying a trivial biconformal space. With co-torsion unconstrained, we show that (1) the torsion-free solutions are foliated by copies of an n-dim Lie group, (2) torsion-free solutions generically describe locally scale-covariant general relativity with symmetric, divergence-free sources on either the co-tangent bundle of n-dim (p,q)-spacetime or the torus of double field theory, and (3) torsion-free solutions admit a subclass of spacetimes with n-dim non-abelian Lie symmetry. These latter cases include the possibility of a gravity-electroweak unification. It is notable that the field equations reduce all curvature components to dependence only on the solder form of an n-dim Lagrangian submanifold, despite the increased number of curvature components and doubled number of initial independent variables

Self-Consistent Model of Magnetospheric Electric Field, Ring Current, Plasmasphere, and Electromagnetic Ion Cyclotron Waves: Initial Results

Further development of our self-consistent model of interacting ring current (RC) ions and electromagnetic ion cyclotron (EMIC) waves is presented. This model incorporates large scale magnetosphere-ionosphere coupling and treats self-consistently not only EMIC waves and RC ions, but also the magnetospheric electric field, RC, and plasmasphere. Initial simulations indicate that the region beyond geostationary orbit should be included in the simulation of the magnetosphere-ionosphere coupling. Additionally, a self-consistent description, based on first principles, of the ionospheric conductance is required. These initial simulations further show that in order to model the EMIC wave distribution and wave spectral properties accurately, the plasmasphere should also be simulated self-consistently, since its fine structure requires as much care as that of the RC. Finally, an effect of the finite time needed to reestablish a new potential pattern throughout the ionosphere and to communicate between the ionosphere and the equatorial magnetosphere cannot be ignored

Decentralized and Fault-Tolerant Control of Power Systems with High Levels of Renewables

Inter-area oscillations have been identified as a major problem faced by most power systems and stability of these oscillations are of vital concern due to the potential for equipment damage and resulting restrictions on available transmission capacity. In recent years, wide-area measurement systems (WAMSs) have been deployed that allow inter-area modes to be observed and identified.Power grids consist of interconnections of many subsystems which may interact with their neighbors and include several sensors and actuator arrays. Modern grids are spatially distributed and centralized strategies are computationally expensive and might be impractical in terms of hardware limitations such as communication speed. Hence, decentralized control strategies are more desirable.Recently, the use of HVDC links, FACTS devices and renewable sources for damping of inter-area oscillations have been discussed in the literature. However, very few such systems have been deployed in practice partly due to the high level of robustness and reliability requirements for any closed loop power system controls. For instance, weather dependent sources such as distributed winds have the ability to provide services only within a narrow range and might not always be available due to weather, maintenance or communication failures.Given this background, the motivation of this work is to ensure power grid resiliency and improve overall grid reliability. The first consideration is the design of optimal decentralized controllers where decisions are based on a subset of total information. The second consideration is to design controllers that incorporate actuator limitations to guarantee the stability and performance of the system. The third consideration is to build robust controllers to ensure resiliency to different actuator failures and availabilities. The fourth consideration is to design distributed, fault-tolerant and cooperative controllers to address above issues at the same time. Finally, stability problem of these controllers with intermittent information transmission is investigated.To validate the feasibility and demonstrate the design principles, a set of comprehensive case studies are conducted based on different power system models including 39-bus New England system and modified Western Electricity Coordinating Council (WECC) system with different operating points, renewable penetration and failures

Determining the Mass Composition of Ultra-high Energy Cosmic Rays Using Air Shower Universality

Ultra-high energy cosmic rays are accelerated via the most energetic and powerful processes in the Universe. For over a hundred years, the study of these particles has elicited great interest. While our knowledge and theoretical models have vastly improved over the last century, the exact sites at which and physical mechanisms by which the acceleration of these charged nuclei occurs remain elusive. In order to elucidate their origins, it is critical for us to better understand the energy spectrum and mass composition of cosmic rays. By doing so, we can come to more fully understand the astrophysical conditions needed to accelerate them and the interactions by which they are affected by during their propagation to Earth. Human-made accelerators and low-energy cosmic ray experiments provide insight into proposed acceleration and propagation models. Nevertheless, the most energetic ultra-high energy cosmic rays have a flux of around 1 particle per km 2 per century at an energy of around 10 20 eV. This energy is roughly a factor of one hundred more energetic than the center-of-mass energies attainable at the Large Hadron Collider (and over a factor of a thousand more energetic than the energies at which the charge and nuclear mass of a cosmic ray may be directly measured). While models from the Large Hadron Collider may be extrapolated to the highest energies, it is critical that large-scale detectors be used to measure the macroscopic properties of cosmic rays. The Pierre Auger Observatory (Auger), located in the Argentine Province of Mendoza, is the largest ultra-high energy cosmic ray detector, extending over 3000 km^2 . As an ultra-high energy cosmic ray traverses Earth’s atmosphere, it will interact with the atmospheric nuclei to generate electromagnetic and hadronic cascades, which will continue to develop until the remaining energy of a constituent particle is too small for further particle generation. Thus, the Auger observatory uses the atmosphere as a calorimeter to measure the development of an air shower cascade. The fluorescence detector measures the fluorescence light induced by the interacting cascades (the longitudinal profile), and the surface detector samples the footprint of the shower at the ground level (the lateral distribution). The depth at which the cascade is fully developed may be determined from the longitudinal profile, which is used to infer the primary mass. Due to its sensitivity to ambient light, the duty cycle, however, of the fluorescence detector is limited to around 15 %, whereas the surface detector is active around 100 % of the time. Thus, in order to measure enough events to test astrophysical scenarios at the highest energy, the reconstruction of the surface detector must be augmented to be able to infer the primary mass, which is not directly accessible from the lateral distribution. This is possible with the air shower universality approach. Within this method, the unique timing and signal distributions of different particle components in the cosmic-ray-induced cascade are exploited to describe air showers as a function of their primary energy, mass, and geometry. The universality approach is easily extendable to other detector types and is of essential importance for the upgrade of Auger and future analyses. The major focus of this work is to determine the mass composition derived with the universality approach. The results found are compatible with those found by the fluores- cence detector and provide insight into the mass composition above 10^19.5 eV. At the highest energies, the mass composition determined using the universality approach trends towards a lighter composition, which is a promising signal for point-source anisotropy. To achieve these results, a new reconstruction procedure was developed which exhibits minimal depen- dence on the arrival direction, has an efficiency across all energies of more than 90 %, and fully includes correlations between the reconstructed physics observables. Reconstructed air shower simulations using contemporary hadronic interaction models were individually studied and compared. Similarities and differences between reconstructed simulations and data are highlighted throughout this work. The methods developed in this work are of great interest for the data analysis of the forthcoming upgrade to Auger (AugerPrime)

The Pierre Auger Observatory: Contributions to the 34th International Cosmic Ray Conference (ICRC 2015)

Contributions of the Pierre Auger Collaboration to the 34th International Cosmic Ray Conference, 30 July - 6 August 2015, The Hague, The NetherlandsComment: 24 proceedings, the 34th International Cosmic Ray Conference, 30 July - 6 August 2015, The Hague, The Netherlands; will appear in PoS(ICRC2015

Measurement of the Energy Spectrum and Mass Composition of Ultra-high Energy Cosmic Rays

In this work, ultra-high energy cosmic rays are studied based on ten years of data taken with the Pierre Auger Observatory in Argentina. The all-particle flux of cosmic rays and the mass composition are derived using dedicated reconstruction algorithms and modern statistical methods. Simulation studies to aid these procedures are further developed and discussed in detail. Features in the derived energy spectrum and mass composition, and their impact on the physics of cosmic rays are detailed