A common rule for integration and suppression of luminance contrast across eyes, space, time, and pattern

Visual perception begins by dissecting the retinal image into millions of small patches for local analyses by local receptive fields. However, image structures extend well beyond these receptive fields and so further processes must be involved in sewing the image fragments back together to derive representations of higher order (more global) structures. To investigate the integration process, we also need to understand the opposite process of suppression. To investigate both processes together, we measured triplets of dipper functions for targets and pedestals involving interdigitated stimulus pairs (A, B). Previous work has shown that summation and suppression operate over the full contrast range for the domains of ocularity and space. Here, we extend that work to include orientation and time domains. Temporal stimuli were 15-Hz counter-phase sine-wave gratings, where A and B were the positive and negative phases of the oscillation, respectively. For orientation, we used orthogonally oriented contrast patches (A, B) whose sum was an isotropic difference of Gaussians. Results from all four domains could be understood within a common framework in which summation operates separately within the numerator and denominator of a contrast gain control equation. This simple arrangement of summation and counter-suppression achieves integration of various stimulus attributes without distorting the underlying contrast code.

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Mathematics Subject Classification: 26A33, 93B51, 93C95

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

Fractional order of poling period for broadly tunable second harmonic generation

We demonstrate the possibility to use a fractional order of poling period of nonlinear crystal waveguides for tunable second harmonic generation. This approach allows one to extend wavelength coverage in the visible spectral range by frequency doubling in a single crystal waveguide.

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.

The Palace of Quinta do Marquês do Alegrete: restitution strategies for space, time and memory

Palaces, as an architectural typology, can be found in recreation Quintas that surrounded the main cities in Portugal, which preserved its rural character since the 16th century until the middle of the 19th century. Consisting of cultivated land and farm buildings, the palace of the Quinta was the owner´s temporary residence, for summer holidays and festive events, with gardens, pavilions, fountains and lakes for recreational purposes and leisure. The focus on palaces, as a historic building and as in need of new uses, clearly shows how current the debate on contemporary interventions in this heritage typology is. Interventions in architectural heritage require multidisciplinary teams to identify conservation strategies which enable a qualified use of its spaces, such as for example the experience of security and well-being, which can contribute to a better quality of life and simultaneously to the quality of the urban environment. This paper presents the Palace of Quinta Alegre and its rehabilitation project for contemporary use and public esteem, both of which are considered fundamental prerequisites for its sustainable maintenance in space, in time and in memory. [versão Portuguesa] Sob a denominação de tipologia arquitectónica, o edifício Palácio pode ser encontrado nas Quintas de Recreio que rodeavam as principais cidades Portuguesas, tendo preservado o seu carácter rural, desde o século XVI até metade do século XIX. Consistindo as Quintas em terra cultivada e edifícios rurais, o Palácio da Quinta consistia na residência temporária do proprietário, para férias de verão e eventos comemorativos, dispondo de jardins, pavilhões, fontes e lagos para recreação e lazer. O tema dos Palácios, entendido como edifício histórico que procura novos usos, demonstra como é actual o debate sobre intervenções contemporâneas nesta tipologia de valor patrimonial. A intervenção em património arquitectónico requer a definição de estratégias de conservação por equipas multidisciplinares que permitam estabelecer um uso qualificado dos seus espaços, proporcionando experiências sensoriais de bem-estar e segurança, contribuindo para uma melhor qualidade de vida e, simultaneamente, para a qualidade do ambiente urbano em que se insere. Este artigo tem por objectivo apresentar o Palácio da Quinta Alegre e o projecto de reabilitação, devolvendo-o a um uso contemporâneo e à estima pública, factores fundamentais para a sua manutenção sustentável no espaço, no tempo e na memória.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Fractional state space analysis of economic systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Stability of the Iteration Method for non Expansive Mappings

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.