Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

Sound objects in time, space and action

SOUND OBJECTS IN TIME, SPACE AND ACTIONThe term "sound object" describes an auditory experience that is associated with an acoustic event produced by a sound source. At cortical level, sound objects are represented by temporo-spatial activity patterns within distributed neural networks. This investigation concerns temporal, spatial and action aspects as assessed in normal subjects using electrical imaging or measurement of motor activity induced by transcranial magnetic stimulation (TMS).Hearing the same sound again has been shown to facilitate behavioral responses (repetition priming) and to modulate neural activity (repetition suppression). In natural settings the same source is often heard again and again, with variations in spectro-temporal and spatial characteristics. I have investigated how such repeats influence response times in a living vs. non-living categorization task and the associated spatio-temporal patterns of brain activity in humans. Dynamic analysis of distributed source estimations revealed differential sound object representations within the auditory cortex as a function of the temporal history of exposure to these objects. Often heard sounds are coded by a modulation in a bilateral network. Recently heard sounds, independently of the number of previous exposures, are coded by a modulation of a left-sided network.With sound objects which carry spatial information, I have investigated how spatial aspects of the repeats influence neural representations. Dynamics analyses of distributed source estimations revealed an ultra rapid discrimination of sound objects which are characterized by spatial cues. This discrimination involved two temporo-spatially distinct cortical representations, one associated with position-independent and the other with position-linked representations within the auditory ventral/what stream.Action-related sounds were shown to increase the excitability of motoneurons within the primary motor cortex, possibly via an input from the mirror neuron system. The role of motor representations remains unclear. I have investigated repetition priming-induced plasticity of the motor representations of action sounds with the measurement of motor activity induced by TMS pulses applied on the hand motor cortex. TMS delivered to the hand area within the primary motor cortex yielded larger magnetic evoked potentials (MEPs) while the subject was listening to sounds associated with manual than non- manual actions. Repetition suppression was observed at motoneuron level, since during a repeated exposure to the same manual action sound the MEPs were smaller. I discuss these results in terms of specialized neural network involved in sound processing, which is characterized by repetition-induced plasticity.Thus, neural networks which underlie sound object representations are characterized by modulations which keep track of the temporal and spatial history of the sound and, in case of action related sounds, also of the way in which the sound is produced.LES OBJETS SONORES AU TRAVERS DU TEMPS, DE L'ESPACE ET DES ACTIONSLe terme "objet sonore" décrit une expérience auditive associée avec un événement acoustique produit par une source sonore. Au niveau cortical, les objets sonores sont représentés par des patterns d'activités dans des réseaux neuronaux distribués. Ce travail traite les aspects temporels, spatiaux et liés aux actions, évalués à l'aide de l'imagerie électrique ou par des mesures de l'activité motrice induite par stimulation magnétique trans-crânienne (SMT) chez des sujets sains. Entendre le même son de façon répétitive facilite la réponse comportementale (amorçage de répétition) et module l'activité neuronale (suppression liée à la répétition). Dans un cadre naturel, la même source est souvent entendue plusieurs fois, avec des variations spectro-temporelles et de ses caractéristiques spatiales. J'ai étudié la façon dont ces répétitions influencent le temps de réponse lors d'une tâche de catégorisation vivant vs. non-vivant, et les patterns d'activité cérébrale qui lui sont associés. Des analyses dynamiques d'estimations de sources ont révélé des représentations différenciées des objets sonores au niveau du cortex auditif en fonction de l'historique d'exposition à ces objets. Les sons souvent entendus sont codés par des modulations d'un réseau bilatéral. Les sons récemment entendus sont codé par des modulations d'un réseau du côté gauche, indépendamment du nombre d'expositions. Avec des objets sonores véhiculant de l'information spatiale, j'ai étudié la façon dont les aspects spatiaux des sons répétés influencent les représentations neuronales. Des analyses dynamiques d'estimations de sources ont révélé une discrimination ultra rapide des objets sonores caractérisés par des indices spatiaux. Cette discrimination implique deux représentations corticales temporellement et spatialement distinctes, l'une associée à des représentations indépendantes de la position et l'autre à des représentations liées à la position. Ces représentations sont localisées dans la voie auditive ventrale du "quoi".Des sons d'actions augmentent l'excitabilité des motoneurones dans le cortex moteur primaire, possiblement par une afférence du system des neurones miroir. Le rôle des représentations motrices des sons d'actions reste peu clair. J'ai étudié la plasticité des représentations motrices induites par l'amorçage de répétition à l'aide de mesures de potentiels moteurs évoqués (PMEs) induits par des pulsations de SMT sur le cortex moteur de la main. La SMT appliquée sur le cortex moteur primaire de la main produit de plus grands PMEs alors que les sujets écoutent des sons associée à des actions manuelles en comparaison avec des sons d'actions non manuelles. Une suppression liée à la répétition a été observée au niveau des motoneurones, étant donné que lors de l'exposition répétée au son de la même action manuelle les PMEs étaient plus petits. Ces résultats sont discuté en termes de réseaux neuronaux spécialisés impliqués dans le traitement des sons et caractérisés par de la plasticité induite par la répétition. Ainsi, les réseaux neuronaux qui sous-tendent les représentations des objets sonores sont caractérisés par des modulations qui gardent une trace de l'histoire temporelle et spatiale du son ainsi que de la manière dont le son a été produit, en cas de sons d'actions.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

Performance of a multi-level TDR system exposed to tropical field conditions - A time-space comparison with tensiometry

Time-domain reflectometry (TDR) is an important technique to obtain series of soil water content measurements in the field. Diode-segmented probes represent an improvement in TDR applicability, allowing measurements of the soil water content profile with a single probe. In this paper we explore an extensive soil water content dataset obtained by tensiometry and TDR from internal drainage experiments in two consecutive years in a tropical soil in Brazil. Comparisons between the variation patterns of the water content estimated by both methods exhibited evidences of deterioration of the TDR system during this two year period at field conditions. The results showed consistency in the variation pattern for the tensiometry data, whereas TDR estimates were inconsistent, with sensitivity decreasing over time. This suggests that difficulties may arise for the long-term use of this TDR system under tropical field conditions. (c) 2008 Elsevier B.V. All rights reserved.

The new economy: Essays in network economics and two-sided markets

Following the Introduction, which surveys existing literature on the technology advances and regulation in telecommunications and on two-sided markets, we address specific issues on the industries of the New Economy, featured by the existence of network effects. We seek to explore how each one of these industries work, identify potential market failures and find new solutions at the economic regulation level promoting social welfare. In Chapter 1 we analyze a regulatory issue on access prices and investments in the telecommunications market. The existing literature on access prices and investment has pointed out that networks underinvest under a regime of mandatory access provision with a fixed access price per end-user. We propose a new access pricing rule, the indexation approach, i.e., the access price, per end-user, that network i pays to network j is function of the investment levels set by both networks. We show that the indexation can enhance economic efficiency beyond what is achieved with a fixed access price. In particular, access price indexation can simultaneously induce lower retail prices and higher investment and social welfare as compared to a fixed access pricing or a regulatory holidays regime. Furthermore, we provide sufficient conditions under which the indexation can implement the socially optimal investment or the Ramsey solution, which would be impossible to obtain under fixed access pricing. Our results contradict the notion that investment efficiency must be sacrificed for gains in pricing efficiency. In Chapter 2 we investigate the effect of regulations that limit advertising airtime on advertising quality and on social welfare. We show, first, that advertising time regulation may reduce the average quality of advertising broadcast on TV networks. Second, an advertising cap may reduce media platforms and firms' profits, while the net effect on viewers (subscribers) welfare is ambiguous because the ad quality reduction resulting from a regulatory cap o¤sets the subscribers direct gain from watching fewer ads. We find that if subscribers are sufficiently sensitive to ad quality, i.e., the ad quality reduction outweighs the direct effect of the cap, a cap may reduce social welfare. The welfare results suggest that a regulatory authority that is trying to increase welfare via regulation of the volume of advertising on TV might necessitate to also regulate advertising quality or, if regulating quality proves impractical, take the effect of advertising quality into consideration. 3 In Chapter 3 we investigate the rules that govern Electronic Payment Networks (EPNs). In EPNs the No-Surcharge Rule (NSR) requires that merchants charge at most the same amount for a payment card transaction as for cash. In this chapter, we analyze a three- party model (consumers, merchants, and a proprietary EPN) with endogenous transaction volumes and heterogenous merchants' transactional benefits of accepting cards to assess the welfare impacts of the NSR. We show that, if merchants are local monopolists and the network externalities from merchants to cardholders are sufficiently strong, with the exception of the EPN, all agents will be worse o¤ with the NSR, and therefore the NSR is socially undesirable. The positive role of the NSR in terms of improvement of retail price efficiency for cardholders is also highlighted.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

The Role of Online Platforms for Media Markets – Two‐Dimensional Spatial Competition in a Two‐Sided Market

We analyze the market for online and offline media in a model of two-dimensional spatial competition where media outlets sell content and advertising space. Consumer preferences are distributed along the style and type of news coverage where the distance costs may vary across dimensions. For integrated provision of online and offline platforms we show that entering the online market reduces average profits and may even constitute a prisoner's dilemma. Specialized provision may yield polarization in the style and type dimensions. This is in contrast to the maximum–minimum differentiation result previously established in the literature on multidimensional horizontal competition. We show that maximal differentiation in both dimensions occurs due to the discrete nature of the type dimension and asymmetric advertising markets.

Consumerism in urban Russia in the 1880s and 90s: Exploring conceptions of time, space, and modernity through bicycle and watch advertisements

This paper discusses the urban consumer culture in Moscow and Petersburg during the 1880s and 1890s and uses the consumption of bicycles and watches as a lens through which to explore changing perceptions of time and space within the experience of modernity at the end of the nineteenth century. Specifically, I argue that the way in which consumers and merchants constructed a dialogue of meaning around particular objects; the way in which objects are consumed by a culture gives insight into the values, morals, and tenure of that culture. The paper preferences newspaper ads and photographs as the mouthpieces of merchants and consumers respectively as they constructed a dialogue in the language of consumerism, and explores the ways in which both parties sought to assign meaning to objects during the experience of modernity. I am particularly interested in the way consumers perform elements of cultural modernity in photographs and how these instances of performance relate to their negotiation of modernity. The paper takes as its focus large section of the urban Russian population, much of whom can traditionally be called “middle class” but whose diversity has led me to the adoption of the term “consumer community,” and whose makeup is described in detail. The paper contributes to the continuing scholarly discourse on the makeup of the middle class in Russia and the social boundaries of late tsarist society. It speaks to the the developing sensibilities and values of a generation struggling to define itself in a rapidly changing world, to the ways in which conceptualizations of public and private space, as well as feminine and masculine space were redefined, and to the developing visual culture of the Russian consumer society, largely predicated on the display of objects to signify socially desirable traits. Whereas other explorations of consumer culture and advertisements have portrayed the relationship between merchants and consumers as a one-sided monologue in which merchants convince consumers that certain objects have cultural value, I emphasis the dialogue between merchants and consumers, and their mutual negotiation of cultural meaning through objects.

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.

Two cooperating manipulators with fractional controllers

This paper analyzes the dynamic performance of two cooperative robot manipulators. It is studied the implementation of fractional-order algorithms in the position/force control of two cooperating robotic manipulators holding an object. The simulations reveal that fractional algorithms lead to performances superior to classical integer-order controllers.

Both Sides of the Story: Skill-biased Technological Change, Labour Market Frictions, and Endogenous Two-Sided Heterogeneity

This paper presents a stylised framework to examine how skill-biased technological change and labour market frictions affect the relationship between economic expansion and unskilled unemployment. The first part of the analysis focuses on the investment decisions in skill-acquisition and technology adoption activities faced by workers and firms in response to the introduction of an innovative technology. The second part examines how endogenous two-sided heterogeneity in the labour market affects the macroeconomic outcomes in terms of unemployment, technological diffusion, and economic expansion. To conclude, the framework is used to discuss the effects of alternative forms of policy intervention on agents' investment decisions and on the macroeconomic outcomes.