Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 mu m and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems, Our simulations studies three different profiles, linear, hyperbolic. and constant, One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show my oscillation in the CE value (log eta), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C-i for the generated FWM signal at omega(3) was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems. (c) 2005 Elsevier B.V. All rights reserved.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Desenvolvimento e estudo em microcanais de fluidos inovadores análogos ao sangue baseados em vesículas unilamelares gigantes

O escoamento sanguíneo é um dos temas de grande interesse para a comunidade científica. Assim, a busca de fluidos que sejam análogos ao sangue bem como o estudo do seu escoamento em microcanais, tal como acontece com o sangue nos capilares, continua a ser alvo de investigação. Numa primeira fase deste trabalho, procedeu-se ao desenvolvimento de um modelo inovador para produzir glóbulos vermelhos artificiais, constituído por Vesículas Unilamelares Gigantes, vulgarmente designadas Giant Unilamellar Vesicles (GUVs), com três concentrações diferentes. Pretende-se que estas vesículas tenham um comportamento reológico idêntico ao escoamento dos glóbulos vermelhos (GVs) em microcanais, permitindo assim proceder a vários estudos hemodinâmicos. No desenvolvimento destas vesículas, foi verificado que as mais adequadas são constituídas por uma mistura natural de lípidos e lecitina de soja. Foi realizado um estudo relativamente à sua concentração, onde se verificou que, com o aumento da quantidade da lecitina de soja nas soluções, a concentração de GUVs tende a aumentar. Foi também realizado um estudo relativo aos diâmetros dos GUVs para verificar se estes se aproximavam em termos de tamanho dos GVs, onde foi verificado que a maioria dos GUVs possuem diâmetros com dimensões entre os 5 e 7 μm, tal como os GVs. Foi ainda verificado que a solução com a menor concentração de lecitina de soja possui uma maior quantidade de GUVs com diâmetros entre os 5 e 7 μm. Na segunda fase, foi estudado experimentalmente o escoamento das três soluções de GUVs em microcanais hiperbólicos, com três caudais diferentes, com o objetivo de visualizar a Camada Livre de Células (CLC), determinar a deformação e estudar as velocidades destes. Foi verificado que existe a formação de CLC em todas as concentrações e que aumenta com o aumento do caudal. Relativamente à deformação, esta é bastante mais evidente na contração do microcanal onde a taxa deformação é máxima. Para o caso da velocidade, foi observado um aumento bastante significativo e linear da velocidade na região da contração do microcanal hiperbólico e uma velocidade baixa e aproximadamente constante a montante e jusante da contração. vi Por fim, foi também realizado o estudo reológico dos GUVs, de forma a investigar se estes têm uma viscosidade próxima do sangue. Foi verificado que os GUVs apresentam uma viscosidade inferior à do sangue total e que existe um ligeiro aumento da viscosidade dos GUVs com o aumento da sua concentração. Por último, também foi efetuada uma comparação da viscosidade da solução de GUVs com uma solução de 5% de Hematócrito (Hct) em soro fisiológico, onde foi verificado que ambas as viscosidades são muito próximas.

Rare sex or out of reach equilibrium? The dynamics of F-IS in partially clonal organisms

Background: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient (F-IS) over bar < 0. Yet in partially clonal species, both F-IS < 0 and F-IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F-IS over time under increasing rates of clonality. Results: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F-IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F-IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F-IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean (F-IS,F-infinity) over bar value expected at equilibrium. Conclusion: Our results argue for a dynamical interpretation of F-IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean (F-IS) over bar values deviating from zero and/or a large variation of F-IS over loci are observed.

Previsão do índice bovespa por meio de redes neurais artificiais: uma análise comparada aos métodos tradicionais de séries de tempo

Forecast is the basis for making strategic, tactical and operational business decisions. In financial economics, several techniques have been used to predict the behavior of assets over the past decades.Thus, there are several methods to assist in the task of time series forecasting, however, conventional modeling techniques such as statistical models and those based on theoretical mathematical models have produced unsatisfactory predictions, increasing the number of studies in more advanced methods of prediction. Among these, the Artificial Neural Networks (ANN) are a relatively new and promising method for predicting business that shows a technique that has caused much interest in the financial environment and has been used successfully in a wide variety of financial modeling systems applications, in many cases proving its superiority over the statistical models ARIMA-GARCH. In this context, this study aimed to examine whether the ANNs are a more appropriate method for predicting the behavior of Indices in Capital Markets than the traditional methods of time series analysis. For this purpose we developed an quantitative study, from financial economic indices, and developed two models of RNA-type feedfoward supervised learning, whose structures consisted of 20 data in the input layer, 90 neurons in one hidden layer and one given as the output layer (Ibovespa). These models used backpropagation, an input activation function based on the tangent sigmoid and a linear output function. Since the aim of analyzing the adherence of the Method of Artificial Neural Networks to carry out predictions of the Ibovespa, we chose to perform this analysis by comparing results between this and Time Series Predictive Model GARCH, developing a GARCH model (1.1).Once applied both methods (ANN and GARCH) we conducted the results' analysis by comparing the results of the forecast with the historical data and by studying the forecast errors by the MSE, RMSE, MAE, Standard Deviation, the Theil's U and forecasting encompassing tests. It was found that the models developed by means of ANNs had lower MSE, RMSE and MAE than the GARCH (1,1) model and Theil U test indicated that the three models have smaller errors than those of a naïve forecast. Although the ANN based on returns have lower precision indicator values than those of ANN based on prices, the forecast encompassing test rejected the hypothesis that this model is better than that, indicating that the ANN models have a similar level of accuracy . It was concluded that for the data series studied the ANN models show a more appropriate Ibovespa forecasting than the traditional models of time series, represented by the GARCH model

Delay discounting in mild cognitive impairment

Introduction : Patients with mild cognitive impairme nt (MCI) may make suboptimal decisions particularly in complex situations, and thi s could be due to temporal discounting, the tendency to prefer immediate rewards over delayed but larger rewards. The present study proposes to evaluate intertemporal prefere nces in MCI patients as compared to healthy controls. Method : Fifty-five patients with MCI and 57 h ealthy controls underwent neuropsy- chological evaluation and a delay discounting questionnaire, which evaluates three para- meters: hyperbolic discounting ( k ), the percentage of choices for delayed and later rewards (%LL), and response consistency (Acc). Results : No significant differences were found in the delay discounting questionnaire between MC I patients and controls for the three reward sizes considered, small, medium, and large, using both k and %LL parameters. There were also no differences in the response consistency, Acc, between the two groups. Conclusions : Patients with MCI perform similarly to healthy controls in a delay discounting task. Memory deficits do not notably affect intertemporal preferences.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

Charge transport in poly(3-methylthiophene) schottky barrier diodes

Schottky-barrier devices were formed from electropolymerised films of poly (3-methylthiophene) (PMeT). Thermal annealing of a partially undoped film led to diodes with rectification ratios as high as 5900 at 1 V and 50,000 at 2.5 V and ideality factors slightly above 2. The temperature dependence of ac loss tangent and forward currents are identical suggesting that bulk effects dominate device behaviour event at very low forward voltages. Below 250 K forward currents are essentially independent of temperature. Preliminary TSC measurements show the presence of at least two trapping levels in the devices. © 1993.

Electrical characterization of CVD diamond-n(+) silicon junctions

The electrical characteristics of CVD-diamond/n(+)-Si heterojunction devices are reported. Below 250 K the diodes show an unusual inversion of their rectification properties. This behavior is attributed to an enhanced tunneling component due to interface states, which change their occupation with the applied bias. The temperature dependence of the loss tangent shows two relaxation processes with different activation energies. These processes are likely related with two parallel charge transport mechanisms, one through the diamond grain, and the other through the grain boundary. (C) 2001 Elsevier Science B.V. Ah rights reserved.

Charge transport in poly(3-methylthiophene) schottky barrier diodes

Schottky-barrier devices were formed from electropolymerised films of poly (3-methylthiophene) (PMeT). Thermal annealing of a partially undoped film led to diodes with rectification ratios as high as 5900 at 1 V and 50,000 at 2.5 V and ideality factors slightly above 2. The temperature dependence of ac loss tangent and forward currents are identical suggesting that bulk effects dominate device behaviour event at very low forward voltages. Below 250 K forward currents are essentially independent of temperature. Preliminary TSC measurements show the presence of at least two trapping levels in the devices. © 1993.

Electrical characterization of pn-junctions of PPV and silicon

Poly(phenylene vinylene) (PPV) grown via the precursor route, deposited on top of heavily doped n-type silicon, was studied using electrical measurement techniques. The results are compared to PPV grown via deposition of soluble derivative (MEH-PPV). The two types are very similar. They have comparable free carrier densities and both show minority-carrier effects. The activation energy found via the loss tangent is 0.13 eV. The effect of exposure to oxygen is visible in the capacitance and the current.

Electrical AC behaviour of MPCVD diamond Schottky diodes

The present work reports some experimental results on the electrical AC behaviour of metal-undoped diamond Schottky diodes fabricated with a free-standing MPCVD diamond film (5 mum thick). The metals are gold for the ohmic contact and aluminium for the rectifier. The capacitance and loss tangent vs, frequency shows that capacitance presents a relaxation maximum at frequencies near 10 kHz at room temperature. Although the simple model (small equivalent circuit) can justify the values for the relaxation, it cannot justify the departure from the Debye model, also verified in the Cole-Cole plot. Taking into account the existence of traps in the depletion region, a best fit to the experimental results was obtained. The difference between the Fermi level and the band edge of 0.2-0.3 eV is in agreement with the activation energy found from the loss tangent analysis. The capacitance with applied voltage (Mott-Schottky plots) gives a defect density of 10(16) cm(-3) with contact potentials near 0.5 V and the profile of defect density obtained shows a major density (approx. 10(17) cm(-3)) in a layer with a thickness less than 50 nm from the junction, decreasing by one order of magnitude with increasing distance. Finally a structural model is proposed to explain the AC behaviour found. (C) 2001 Elsevier Science B.V. All rights reserved.