The Method Of Quasi-specular Elements To Reduce Stochastic Noise During Illuminance Simulation

When simulating the propagation of light, luminance/ radiance brought by a ray is calculated from the optical properties of the scene objects it interacts with. According to their optical properties, objects can be roughly divided into diffuse and specular. In Monte Carlo ray tracing luminance/radiance is calculated only for diffuse surfaces. When a ray hits a specular a surface, it is reflected (or refracted) until it reaches a diffuse surface, and only then the luminance/radiance is calculated. In the proposed approach, diffuse elements are further divided into genuine diffuse and quasi-specular elements. The most natural criterion for the latter is that it scatters light in a narrow cone about the specular direction. An element of the scene can also be a superposition of both types when its scattering function is a sum of the genuine diffuse and quasi-specular parts. This article shows how different components of illuminance/irradiance interact with quasi-specular objects and describe how this works in the bi-directional stochastic ray tracing. The proposed approach significantly reduces stochastic noise for multiple scenes. This method is also applicable for simulation of volume scattering, treating the phase function of the medium as quasi-specular. In this case, the choice of quasi-specular objects is not based on the nature of the bidirectional scattering distribution function (BSDF): the medium is treated as completely quasi-specular while the surfaces, even if their BSDFs are narrower, remain genuine diffuse. The article shows the advantage of this approach.

Theologizing for the Yoga Community?

Stephanie Corigliano addresses the issues of religious belonging and commitment by comparing and contrasting “rooted” and “aerial” modes of comparative theology. Corigliano first examines the “rooted” comparative theological methods of four founding scholar-practitioners and then attends to the differently configured experiences and theological potentials of a younger generation that is “aerial,” more agile, and fluid in its instincts. Even if initially religious commitment or “rootedness” sensibly formed a natural criterion for comparative theology, nevertheless, as the scope of the field expands, this criterion must cede some space to the fact of less rooted, more fluid realities in one’s own community and life, and in those of our religious others. Testing comparative theology in the classroom and using it as a tool for examining new religious and spiritual movements suggests that it can no longer be limited to exchanges between persons from established religious traditions.

Cost Estimation for Process Selection

In selecting a process to make a given component, it is first necessary to screen available processes to find those which can make the desired shape from the desired material with the desired precision and finish. Commonly, many processes survive this screening, and it is then desirable to rank them approximately so that the most promising are explored first. The natural criterion for ranking is that of relative cost. This paper describes an approximate relative cost model, applicable to all processes, designed to give this approximate ranking. It is based on summing the costs of material, energy, time, capital and other resources. The values for equipment cost, tooling cost and production rate depend on component size and complexity. Approximate scaling methods are used to include these dependencies. The model has been implemented in a Process Selector (the CPS) and fills its intended function adequately.

Applications of Borovkov's Renovation Theory to Non-Stationary Stochastic Recursive Sequences and Their Control

We investigate in this paper the stability of non-stationary stochastic processes, arising typically in applications of control. The setting is known as stochastic recursive sequences, which allows us to construct on one probability space stochastic processes that correspond to different initial states and even different control policies. It does not require any Markovian assumptions. A natural criterion for stability for such processes is that the influence of the initial state disappears after some finite time; in other words, starting from different initial states, the process will couple after some finite time to the same limiting (not necessarily stationary nor ergodic) stochastic process. We investigate this as well as other types of coupling, and present conditions for them to occur uniformly in some class of control policies. We then use the coupling results to establish new theoretical aspects in the theory of non-Markovian control.

Applications of Borovkov's Renovation Theory to Non-Stationary Stochastic Recursive Sequences and Their Control

We investigate in this paper the stability of non-stationary stochastic processes, arising typically in applications of control. The setting is known as stochastic recursive sequences, which allows us to construct on one probability space stochastic processes that correspond to different initial states and even different control policies. It does not require any Markovian assumptions. A natural criterion for stability for such processes is that the influence of the initial state disappears after some finite time; in other words, starting from different initial states, the process will couple after some finite time to the same limiting (not necessarily stationary nor ergodic) stochastic process. We investigate this as well as other types of coupling, and present conditions for them to occur uniformly in some class of control policies. We then use the coupling results to establish new theoretical aspects in the theory of non-Markovian control.

Prediction of level crossings for normal processes containing deterministic components

A level crossing predictor is a predictor process Y(t) which can be used to predict whether a specific process X(t) will cross a predetermined level or not. A natural criterion of how good a predictor is can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm.Suppose the process X(t) consists of a deterministic part A(t) which can be calculated with sufficient accuracy, and a stochastic part Xe(t) which can be predicted by some statistically based predictor An example of this is the prediction of water level near a coast, when A(t) is a sum of known tide components.The paper develops a tool to handle the detection properties of such predictor processes when used to predict level crossings for the case when A(t) is periodic or is a sum of such functions.

Prediction of level crossings for normal processes containing deterministic components

A level crossing predictor is a predictor process Y(t) which can be used to predict whether a specific process X(t) will cross a predetermined level or not. A natural criterion of how good a predictor is can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm. Suppose the process X(t) consists of a deterministic part A(t) which can be calculated with sufficient accuracy, and a stochastic part Xe (t) which can be predicted by some statistically based predictor An example of this is the prediction of water level near a coast, when A(t) is a sum of known tide components. The paper develops a tool to handle the detection properties of such predictor processes when used to predict level crossings for the case when A(t) is periodic or is a sum of such functions.