Rendering speed

Automatically creating a VR data set from the CAD solids reduces the preparation time for a tool review session to minutes. The required level of image-rendering speed tuid projection quality in this special application is medium, so the actual IPT system is moderate in price. 

Rendering speed is also processor dependent, although a typical render to any uncompressed format should take only a few tens of seconds. More complex and highly compressed formats may require significantly longer rendering times, sometimes measured in minutes instead of seconds. 

Although cSFC shows relatively poor figures of merit (speed, sensitivity, detection dynamic range and sample capacity) as well as a limited application area, its applications tend to be unique. These include solutes that can be solvated with pure SCCO2 and quantified with FID. Linear density programs typical in cSFC are ideal for homologous series found in surfactants, many prepolymers, etc. Selectivity in cSFC, which can be achieved by mobile phase density and temperature programming, relies on selective interactions with the stationary phase. Quantitative analysis in cSFC may be rendered difficult by small injected volumes the use of internal standards is recommended. 

The speed, sensitivity, high degree of automation and ability to quantitate protein bands directly render this system ideal for biopharmaceutical analysis. 

Generation of antibodies that can recognize and bind to specific viruses is straightforward. A sample of live or attenuated virus, or a purified component of the viral caspid, can be injected into animals to stimulate polyclonal antibody production (or to facilitate monoclonal antibody production by hybridoma technology). Harvested antibodies are then employed to develop specific immunoassays that can be used to screen test samples routinely for the presence of that specific virus. Immunoassays capable of detecting a wide range of viruses are available commercially. The sensitivity, ease, speed and relative inexpensiveness of these assays render them particularly attractive. 

There are a few points with respect to this procedure that merit discussion. First, there is the Hessian matrix. With elements, where n is the number of coordinates in the molecular geometry vector, it can grow somewhat expensive to construct this matrix at every step even for functions, like those used in most force fields, that have fairly simple analytical expressions for their second derivatives. Moreover, the matrix must be inverted at every step, and matrix inversion formally scales as where n is the dimensionality of the matrix. Thus, for purposes of efficiency (or in cases where analytic second derivatives are simply not available) approximate Hessian matrices are often used in the optimization process - after aU, the truncation of the Taylor expansion renders the Newton-Raphson method intrinsically approximate. As an optimization progresses, second derivatives can be estimated reasonably well from finite differences in the analytic first derivatives over the last few steps. For the first step, however, this is not an option, and one typically either accepts the cost of computing an initial Hessian analytically for the level of theory in use, or one employs a Hessian obtained at a less expensive level of theory, when such levels are available (which is typically not the case for force fields). To speed up slowly convergent optimizations, it is often helpful to compute an analytic Hessian every few steps and replace the approximate one in use up to that point. For really tricky cases (e.g., where the PES is fairly flat in many directions) one is occasionally forced to compute an analytic Hessian for every step. 

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