On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.

Elastoplastic consolidation at finite strain. Part 2: finite element implementation and numerical examples

A mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. A two-field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations. The constitutive model for the solid phase is represented by modified Cam—Clay theory formulated in the Kirchhoff principal stress space, and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. The finite element model is fully amenable to exact linearization. Numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses. The paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability.

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Stabilization in a two-species chemotaxis system with logistic source

We study a system of three partial differential equations modelling the spatiotemporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. For a range of the parameters the system possesses a uniquely determined spatially homogeneous positive equilibrium (u?, v?) globally asymptotically stable within a certain nonempty range of the logistic growth coefficients.

Revisiting the method to obtain the mechanical properties of hydrided fuel cladding in the hoop direction

The method reported in the literature to calculate the stress–strain curve of nuclear fuel cladding from ring tensile test is revisited in this paper and a new alternative is presented. In the former method, two universal curves are introduced under the assumption of small strain. In this paper it is shown that these curves are not universal, but material-dependent if geometric nonlinearity is taken into account. The new method is valid beyond small strains, takes geometric nonlinearity into consideration and does not need universal curves. The stress–strain curves in the hoop direction are determined by combining numerical calculations with experimental results in a convergent loop. To this end, ring tensile tests were performed in unirradiated hydrogen-charged samples. The agreement among the simulations and the experimental results is excellent for the range of concentrations tested (up to 2000 wppm hydrogen). The calculated stress–strain curves show that the mechanical properties do not depend strongly on the hydrogen concentration, and that no noticeable strain hardening occurs. However, ductility decreases with the hydrogen concentration, especially beyond 500 wppm hydrogen. The fractographic results indicate that as-received samples fail in a ductile fashion, whereas quasicleavage is bserved in the hydrogen-charged samples.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

On a competitive system under chemotactic effects with non-local terms

In this paper, we study a system of partial differential equations describing the evolution of a population under chemotactic effects with non-local reaction terms. We consider an external application of chemoattractant in the system and study the cases of one and two populations in competition. By introducing global competitive/cooperative factors in terms of the total mass of the populations, weobtain, forarangeofparameters, thatanysolutionwithpositive and bounded initial data converges to a spatially homogeneous state with positive components. The proofs rely on the maximum principle for spatially homogeneous sub- and super-solutions.

Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Vector Boolean Functions: Applications in Symmetric Cryptography

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++ denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales (funciones que asocian un vector booleano a otro vector booleano) desde una perspectiva criptográfica. Esta nueva implementación emplea la librería NTL de Victor Shoup, incorporando nuevos módulos que complementan a las funciones de NTL, adecuándolas para el análisis criptográfico. La clase fundamental que representa una función booleana vectorial se puede inicializar de manera muy flexible mediante diferentes estructuras de datas tales como la Tabla de verdad, la Representación de traza y la Forma algebraica normal entre otras. De esta manera VBF permite evaluar los criterios criptográficos más relevantes de los algoritmos de cifra en bloque y de stream, así como funciones hash: por ejemplo, proporciona la no-linealidad, la distancia lineal, el grado algebraico, las estructuras lineales, la distribución de frecuencias de los valores absolutos del espectro Walsh o del espectro de autocorrelación, entre otros criterios. Adicionalmente, VBF puede llevar a cabo operaciones entre funciones booleanas vectoriales tales como la comprobación de igualdad, la composición, la inversión, la suma, la suma directa, el bricklayering (aplicación paralela de funciones booleanas vectoriales como la empleada en el algoritmo de cifra Rijndael), y la adición de funciones coordenada. La tesis también muestra el empleo de la librería VBF en dos aplicaciones prácticas. Por un lado, se han analizado las características más relevantes de los sistemas de cifra en bloque. Por otro lado, combinando VBF con algoritmos de optimización, se han diseñado funciones booleanas cuyas propiedades criptográficas son las mejores conocidas hasta la fecha. ABSTRACT This thesis develops the theoretical foundations and designs an open collection of C++ classes, called VBF, designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This new implementation uses the NTL library from Victor Shoup, adding new modules which complement the existing ones making VBF better suited for cryptography. The fundamental class representing a vector Boolean function can be initialized in a flexible way via several alternative types of data structures such as Truth Table, Trace Representation, Algebraic Normal Form (ANF) among others. This way, VBF allows the evaluation of the most relevant cryptographic criteria for block and stream ciphers as well as for hash functions: for instance, it provides the nonlinearity, the linearity distance, the algebraic degree, the linear structures, the frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, VBF can perform operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions. This thesis also illustrates the use of VBF in two practical applications. On the one hand, the most relevant properties of the existing block ciphers have been analysed. On the other hand, by combining VBF with optimization algorithms, new Boolean functions have been designed which have the best known cryptographic properties up-to-date.

Detectores monolíticos y sensores compatibles con altos campos magnéticos para tomografía por emisión de positrones

Esta tesis recoje un trabajo experimental centrado en profundizar sobre el conocimiento de los bloques detectores monolíticos como alternativa a los detectores segmentados para tomografía por emisión de positrones (Positron Emission Tomography, PET). El trabajo llevado a cabo incluye el desarrollo, la caracterización, la puesta a punto y la evaluación de prototipos demostradores PET utilizando bloques monolíticos de ortosilicato de lutecio ytrio dopado con cerio (Cerium-Doped Lutetium Yttrium Orthosilicate, LYSO:Ce) usando sensores compatibles con altos campos magnéticos, tanto fotodiodos de avalancha (Avalanche Photodiodes, APDs) como fotomultiplicadores de silicio (Silicon Photomultipliers, SiPMs). Los prototipos implementados con APDs se construyeron para estudiar la viabilidad de un prototipo PET de alta sensibilidad previamente simulado, denominado BrainPET. En esta memoria se describe y caracteriza la electrónica frontal integrada utilizada en estos prototipos junto con la electrónica de lectura desarrollada específicamente para los mismos. Se muestran los montajes experimentales para la obtención de las imágenes tomográficas PET y para el entrenamiento de los algoritmos de red neuronal utilizados para la estimación de las posiciones de incidencia de los fotones γ sobre la superficie de los bloques monolíticos. Con el prototipo BrainPET se obtuvieron resultados satisfactorios de resolución energética (13 % FWHM), precisión espacial de los bloques monolíticos (~ 2 mm FWHM) y resolución espacial de la imagen PET de 1,5 - 1,7 mm FWHM. Además se demostró una capacidad resolutiva en la imagen PET de ~ 2 mm al adquirir simultáneamente imágenes de fuentes radiactivas separadas a distancias conocidas. Sin embargo, con este prototipo se detectaron también dos limitaciones importantes. En primer lugar, se constató una falta de flexibilidad a la hora de trabajar con un circuito integrado de aplicación específica (Application Specific Integrated Circuit, ASIC) cuyo diseño electrónico no era propio sino comercial, unido al elevado coste que requieren las modificaciones del diseño de un ASIC con tales características. Por otra parte, la caracterización final de la electrónica integrada del BrainPET mostró una resolución temporal con amplio margen de mejora (~ 13 ns FWHM). Tomando en cuenta estas limitaciones obtenidas con los prototipos BrainPET, junto con la evolución tecnológica hacia matrices de SiPM, el conocimiento adquirido con los bloques monolíticos se trasladó a la nueva tecnología de sensores disponible, los SiPMs. A su vez se inició una nueva estrategia para la electrónica frontal, con el ASIC FlexToT, un ASIC de diseño propio basado en un esquema de medida del tiempo sobre umbral (Time over Threshold, ToT), en donde la duración del pulso de salida es proporcional a la energía depositada. Una de las características más interesantes de este esquema es la posibilidad de manejar directamente señales de pulsos digitales, en lugar de procesar la amplitud de las señales analógicas. Con esta arquitectura electrónica se sustituyen los conversores analógicos digitales (Analog to Digital Converter, ADCs) por conversores de tiempo digitales (Time to Digital Converter, TDCs), pudiendo implementar éstos de forma sencilla en matrices de puertas programmable ‘in situ’ (Field Programmable Gate Array, FPGA), reduciendo con ello el consumo y la complejidad del diseño. Se construyó un nuevo prototipo demostrador FlexToT para validar dicho ASIC para bloques monolíticos o segmentados. Se ha llevado a cabo el diseño y caracterización de la electrónica frontal necesaria para la lectura del ASIC FlexToT, evaluando su linealidad y rango dinámico, el comportamiento frente a ruido así como la no linealidad diferencial obtenida con los TDCs implementados en la FPGA. Además, la electrónica presentada en este trabajo es capaz de trabajar con altas tasas de actividad y de discriminar diferentes centelleadores para aplicaciones phoswich. El ASIC FlexToT proporciona una excelente resolución temporal en coincidencia para los eventos correspondientes con el fotopico de 511 keV (128 ps FWHM), solventando las limitaciones de resolución temporal del prototipo BrainPET. Por otra parte, la resolución energética con bloques monolíticos leidos por ASICs FlexToT proporciona una resolución energética de 15,4 % FWHM a 511 keV. Finalmente, se obtuvieron buenos resultados en la calidad de la imagen PET y en la capacidad resolutiva del demostrador FlexToT, proporcionando resoluciones espaciales en el centro del FoV en torno a 1,4 mm FWHM. ABSTRACT This thesis is focused on the development of experimental activities used to deepen the knowledge of monolithic detector blocks as an alternative to segmented detectors for Positron Emission Tomography (PET). It includes the development, characterization, setting up, running and evaluation of PET demonstrator prototypes with monolithic detector blocks of Cerium-doped Lutetium Yttrium Orthosilicate (LYSO:Ce) using magnetically compatible sensors such as Avalanche Photodiodes (APDs) and Silicon Photomultipliers (SiPMs). The prototypes implemented with APDs were constructed to validate the viability of a high-sensitivity PET prototype that had previously been simulated, denominated BrainPET. This work describes and characterizes the integrated front-end electronics used in these prototypes, as well as the electronic readout system developed especially for them. It shows the experimental set-ups to obtain the tomographic PET images and to train neural networks algorithms used for position estimation of photons impinging on the surface of monolithic blocks. Using the BrainPET prototype, satisfactory energy resolution (13 % FWHM), spatial precision of monolithic blocks (~ 2 mm FWHM) and spatial resolution of the PET image (1.5 – 1.7 mm FWHM) in the center of the Field of View (FoV) were obtained. Moreover, we proved the imaging capabilities of this demonstrator with extended sources, considering the acquisition of two simultaneous sources of 1 mm diameter placed at known distances. However, some important limitations were also detected with the BrainPET prototype. In the first place, it was confirmed that there was a lack of flexibility working with an Application Specific Integrated Circuit (ASIC) whose electronic design was not own but commercial, along with the high cost required to modify an ASIC design with such features. Furthermore, the final characterization of the BrainPET ASIC showed a timing resolution with room for improvement (~ 13 ns FWHM). Taking into consideration the limitations obtained with the BrainPET prototype, along with the technological evolution in magnetically compatible devices, the knowledge acquired with the monolithic blocks were transferred to the new technology available, the SiPMs. Moreover, we opted for a new strategy in the front-end electronics, the FlexToT ASIC, an own design ASIC based on a Time over Threshold (ToT) scheme. One of the most interesting features underlying a ToT architecture is the encoding of the analog input signal amplitude information into the duration of the output signals, delivering directly digital pulses. The electronic architecture helps substitute the Analog to Digital Converters (ADCs) for Time to Digital Converters (TDCs), and they are easily implemented in Field Programmable Gate Arrays (FPGA), reducing the consumption and the complexity of the design. A new prototype demonstrator based on SiPMs was implemented to validate the FlexToT ASIC for monolithic or segmented blocks. The design and characterization of the necessary front-end electronic to read-out the signals from the ASIC was carried out by evaluating its linearity and dynamic range, its performance with an external noise signal, as well as the differential nonlinearity obtained with the TDCs implemented in the FPGA. Furthermore, the electronic presented in this work is capable of working at high count rates and discriminates different phoswich scintillators. The FlexToT ASIC provides an excellent coincidence time resolution for events that correspond to 511 keV photopeak (128 ps FWHM), resolving the limitations of the poor timing resolution of the BrainPET prototype. Furthermore, the energy resolution with monolithic blocks read by FlexToT ASICs provides an energy resolution of 15.4 % FWHM at 511 keV. Finally, good results were obtained in the quality of the PET image and the resolving power of the FlexToT demonstrator, providing spatial resolutions in the centre of the FoV at about 1.4 mm FWHM.