Extending stochastic resonance for neuron models to general Levy noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Levy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general Levy noise models. We achieve this by showing that �¿large jump�¿ discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a �¿forbidden intervals�¿ theorem as in Patel and Kosko's paper

Interpolation and Best Approximation for Spherical Radial Basis Function Networks

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and radial basis functions stemming from the smooth kernel are intended to approximate only functions from this small native space. In this paper, we embed the smooth radial basis functions in a larger native space generated by a less smooth kernel and use them to interpolate the samples. Our result shows that there exists a linear combination of spherical radial basis functions that can both exactly interpolate samples generated by functions in the larger native space and near best approximate the target function

Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.This research has been partially funded by the Spanish Ministry of Science, Innovation and Universities, grant number RTI2018-101148-B-I00

All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation

This paper introduces a new data representation and compression technique for precomputed radiance transfer (PRT). The light transfer functions and light sources are modeled with spherical radial basis functions (SRBFs). A SRBF is a rotation-invariant function that depends on the geodesic distance between two points on the unit sphere. Rotating functions in SRBF representation is as straightforward as rotating the centers of SRBFs. Moreover, highfrequency signals are handled by adjusting the bandwidth parameters of SRBFs. To exploit inter-vertex coherence, the light transfer functions are further classified iteratively into disjoint clusters, and tensor approximation is applied within each cluster. Compared with previous methods, the proposed approach enables real-time rendering with comparable quality under high-frequency lighting environments. The data storage is also more compact than previous all-frequency PRT algorithms. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture; G.1.2 [Numerical Analysis]: Approximation—Special function approximations; E.4 [Coding and Information Theory]: Data compaction and compressio

Natural ventilation design attributes application effect on, indoor natural ventilation performance of a double storey, single unit residential building

In establishing a good indoor thermal condition, air movement is one of the important parameter to be considered to provide indoor fresh air for occupants. Due to the public awareness on environment impact, people has been increasingly attentive to passive design in achieving good condition of indoor building ventilation. Throughout case studies, significant building attributes were found giving effect on building indoor natural ventilation performance. The studies were categorized under vernacular houses, contemporary houses with vernacular element and contemporary houses. The indoor air movement of every each spaces in the houses were compared with the outdoor air movement surrounding the houses to indicate the space’s indoor natural ventilation performance. Analysis found the wind catcher element appears to be the most significant attribute to contribute most to indoor natural ventilation. Wide opening was also found to be significant especially those with louvers. Whereas it is also interesting to find indoor layout design is also significantly giving impact on the performance. The finding indicates that a good indoor natural ventilation is not only dictated by having proper openings at proper location of a building, but also on how the incoming air movement is managed throughout the interior spaces by proper layout. Understanding on the air pressure distribution caused by indoor windward and leeward side is important in directing the air flow to desired spaces in producing an overall good indoor natural ventilation performance

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation

LightSkin: Globale Echtzeitbeleuchtung für Virtual und Augmented Reality

In nature, each interaction of light is bound to a global context. Thus, each observable natural light phenomenon is the result of global illumination. It is based on manifold laws of absorption, reflection, and refraction, which are mostly too complex to simulate given the real-time constraints of interactive applications. Therefore, many interactive applications do not support the simulation of those global illumination phenomena yet, which results in unrealistic and synthetic-looking renderings. This unrealistic rendering becomes especially a problem in the context of virtual reality and augmented reality applications, where the user should experience the simulation as realistic as possible. In this thesis we present a novel approach called LightSkin that calculates global illumination phenomena in real-time. The approach was especially developed for virtual reality and augmented reality applications satisfying several constraints coming along with those applications. As part of the approach we introduce a novel interpolation scheme, which is capable to calculate realistic indirect illumination results based on a few number of supporting points, distributed on model surfaces. Each supporting point creates its own proxy light sources, which are used to represent the whole indirect illumination for this point in a compact manner. These proxy light sources are then linearly interpolated to obtain dense results for the entire visible scene. Due to an efficient implementation on GPU, the method is very fast supporting complex and dynamic scenes. Based on the approach, it is possible to simulate diffuse and glossy indirect reflections, soft shadows, and multiple subsurface scattering phenomena without neglecting filigree surface details. Furthermore, the method can be adapted to augmented reality applications providing mutual global illumination effects between dynamic real and virtual objects using an active RGB-D sensor device. In contrast to existing interactive global illumination approaches, our approach supports all kinds of animations, handling them more efficient, not requiring extra calculations or leading to disturbing temporal artifacts. This thesis contains all information needed to understand, implement, and evaluate the novel LightSkin approach and also provides a comprehensive overview of the related field of research.In der Natur ist jede Interaktion des Lichts mit Materie in einen globalen Kontext eingebunden, weswegen alle natürlichen Beleuchtungsphänomene in unserer Umwelt das Resultat globaler Beleuchtung sind. Diese basiert auf der Anwendung mannigfaltiger Absorptions-, Reflexions- und Brechungsgesetze, deren Simulation so komplex ist, dass interaktive Anwendungen diese nicht in wenigen Millisekunden berechnen können. Deshalb wurde bisher in vielen interaktiven Systemen auf die Abbildung von solchen globalen Beleuchtungsphänomenen verzichtet, was jedoch zu einer unrealistischen und synthetisch-wirkenden Darstellung führte. Diese unrealistische Darstellung ist besonders für die Anwendungsfelder Virtual Reality und Augmented Reality, bei denen der Nutzer eine möglichst realitätsnahe Simulation erfahren soll, ein gewichtiger Nachteil. In dieser Arbeit wird das LightSkin-Verfahren vorgestellt, das es erlaubt, globale Beleuchtungsphänomene in einer Echtzeitanwendung darzustellen. Das Verfahren wurde speziell für die Anwendungsfelder Virtual Reality und Augmented Reality entwickelt und erfüllt spezifische Anforderungen, die diese an eine Echtzeitanwendung stellen. Bei dem Verfahren wird das indirekte Licht durch eine geringe Anzahl von Punktlichtquellen (Proxy-Lichtquellen) repräsentiert, die für eine lose Menge von Oberflächenpunkten (Caches) berechnet und anschließend über die komplette sichtbare Szene interpoliert werden. Diese neue Form der Repräsentation der indirekten Beleuchtung erlaubt eine effiziente Berechnung von diffusen und glänzenden indirekten Reflexionen, die Abbildung von weichen Schatten und die Simulation von Multiple-Subsurface-Scattering-Effekten in Echtzeit für komplexe und voll dynamische Szenen. Ferner wird gezeigt, wie das Verfahren modifiziert werden kann, um globale Lichtwechselwirkungen zwischen realen und virtuellen Objekten in einer Augmented-Reality-Anwendung zu simulieren. Im Gegensatz zu den meisten existierenden Echtzeitverfahren zur Simulation von globalen Beleuchtungseffekten benötigt der hier vorgestellte Ansatz keine aufwändigen zusätzlichen Berechnungen bei Animationen und erzeugt darüber hinaus für diese keine visuellen Artefakte. Diese Arbeit enthält alle Informationen, die zum Verständnis, zur Implementierung und zur Evaluation des LightSkin-Verfahrens benötigt werden und gibt darüber hinaus einen umfassenden Über- blick über das Forschungsfeld