Applications of random sampling to virtual screening of combinatorial libraries

We describe statistical techniques for effective evaluation of large virtual combinatorial libraries (> 10(10) potential compounds). The methods described are used for computationally evaluating templates (prioritization of candidate libraries for synthesis and screening) and for the design of individual combinatorial libraries (e.g., for a given diversity site, reagents can be selected based on the estimated frequency with which they appear in products that pass a computational filter). These statistical methods are powerful because they provide a simple way to estimate the properties of the overall library without explicitly enumerating all of the possible products. In addition, they are fast and simple, and the amount of sampling required to achieve a desired precision is calculable. In this article, we discuss the computational methods that allow random product selection from a combinatorial library and the statistics involved in estimating errors from quantities obtained from such samples. We then describe three examples: (1) an estimate of average molecular weight for the several billion possible products in a four-component Ugi reaction, a quantity that can be calculated exactly for comparison; (2) the prioritization of four templates for combinatorial synthesis using a computational filter based on four-point pharmacophores; and (3) selection of reagents for the four-component Ugi reaction based on their frequency of occurrence in products that pass a pharmacophore filter.     

Transmission System Planning-The Old World Meets The New

Transmission systems in the United States and around the world have become more difficult to plan under deregulation. Uncertainties in generation type, location, and pricing coupled with market mechanisms that encourage transfers not designed for in the legacy transmission system have made the transmission planner's life difficult. This paper describes the planning process under regulation, some of the issues encountered during the present transition to a deregulated industry, and some of the open questions that need to be addressed in the United States.     

Parallel computational geometry of rectangles

Rectangles in a plane provide a very useful abstraction for a number of problems in diverse fields. In this paper we consider the problem of computing geometric properties of a set of rectangles in the plane. We give parallel algorithms for a number of problems usingn processors wheren is the number of upright rectangles. Specifically, we present algorithms for computing the area, perimeter, eccentricity, and moment of inertia of the region covered by the rectangles inO(logn) time. We also present algorithms for computing the maximum clique and connected components of the rectangles inO(logn) time. Finally, we give algorithms for finding the entire contour of the rectangles and the medial axis representation of a givenn × n binary image inO(n) time. Our results are faster than previous results and optimal (to within a constant factor).     

Hardness anisotropy of acetaminophen crystals

The anisotropy of acetaminophen hardness was demonstrated using both Vickers and Knoop indentation hardness measurements. Based on a model of Knoop hardness anisotropy proposed by Brookes et al. (1), it was concluded that plastic flow in acetaminophen crystals occurs primarily as a result of slip in the (010)<001> system. This conclusion was corroborated with the results of the Vickers indentation tests. The apparent brittleness of acetaminophen was rationalized because only one slip system appeared to be operative. Under these conditions generalized plastic flow cannot occur, since this requires the operation of at least five independent slip systems (2). The high stress concentrations that result from flow lead to fracture. Therefore acetaminophen is more precisely classified as being semiductile. When a material deforms plastically as a result of slip in only one slip system, considerable crystal realignment can occur during compaction. This in turn can facilitate capping during decompression and ejection, since the cleavage plane, (010), would become aligned with the direction of highest tensile stress.     

Theoretical analysis of chronoamperometric transients in electrochemical machining and characterization of titanium 6/4 and inconel 718 alloys

An analytical expression is derived for the current–time transient for electrochemical machining (ECM) using a planar tool and workpiece configuration. This is obtained as a function of such parameters as the initial interelectrode gap, applied voltage, electrolytic conductivity, valency, density and feed rate. Good theoretical fits to experimental data are found for the alloys titanium 6/4 (Ti6/4) and Inconel 718 (In718) using both sodium chloride and sodium nitrate electrolytes, demonstrating the applicability of this theory. The values of the electrolytic molar conductivity obtained for chloride and nitrate are consistent with the expected conductivity obtained from molar conductivity measurements. The mean valency values obtained for Ti6/4 and In718 are 3.5 ± 0.2 and 3.0 ± 0.2, respectively. The fraction of the applied voltage used to drive the electrochemical surface reactions, V₀, has also been obtained. The variation in V₀ between alloys when using the same electrolyte and also for each alloy when using different electrolytes is attributed to differences in the thermodynamics of the removal of the metal from the surface metal oxide. For In718 using chloride electrolyte, an increase in V₀ is observed at higher applied voltages, consistent with a change in the electrochemical dissolution reaction. Analysis of the variation of V₀ at low applied voltages throughout the current–time transient has enabled the current–voltage characteristics of these surfaces electrochemical reactions to be determined, indicating Tafel behaviour. These data show this analysis to be a powerful methodology for understanding and measuring ECM characteristics under realistic ECM conditions.     

Approximating large convolutions in digital images

Computing discrete two-dimensional (2-D) convolutions is an important problem in image processing. In mathematical morphology, an important variant is that of computing binary convolutions, where the kernel of the convolution is a 0-1 valued function. This operation can be quite costly, especially when large kernels are involved. We present an algorithm for computing convolutions of this form, where the kernel of the binary convolution is derived from a convex polygon. Because the kernel is a geometric object, we allow the algorithm some flexibility in how it elects to digitize the convex kernel at each placement, as long as the digitization satisfies certain reasonable requirements. We say that such a convolution is valid. Given this flexibility we show that it is possible to compute binary convolutions more efficiently than would normally be possible for large kernels. Our main result is an algorithm which, given an mxn image and a k-sided convex polygonal kernel K, computes a valid convolution in O(kmn) time. Unlike standard algorithms for computing correlations and convolutions, the running time is independent of the area or perimeter of K, and our techniques do not rely on computing fast Fourier transforms. Our algorithm is based on a novel use of Bresenham's (1965) line-drawing algorithm and prefix-sums to update the convolution incrementally as the kernel is moved from one position to another across the image.     

Application of scanning electron microscopy for pollution particle source determination in residential dust and soil

Many tons of electric furnace flue dust accumulated in an industrial area in Tifton, Georgia. Vehicles transporting the flue dust, classified as K061 hazardous waste because it contained lead and cadmium, initially dumped the material in a warehouse. Once the warehouse was full, the flue dust was dumped in uncovered piles. Run-off from the piles and wind-driven particles had the opportunity to contaminate nearby industries, residential buildings, and neighborhood soils over a period of many years. Scanning electron microscopy-energy dispersive x-ray spectrometry (SEM-EDS) was used to compare the morphology and chemical composition of fly ash dust from the suspect pile with samples collected from the surrounding buildings and soil. Adhesive samplers were used to collect dust that had accumulated in buildings surrounding the fly ash dump site. Suspect dust particles were analyzed by SEM-EDS and compared with known dust particles from the fly ash pile. Soil samples were dried, sieved, and the “fines” analyzed by SEM-EDS for comparison with samples from the fly ash pile. Fly ash particles similar in morphology and chemical composition to the fly ash in the suspect pile were identified in most of the buildings sampled surrounding the fly ash dump site and in all of the soil samples analyzed surrounding the dumpsite. This case study illustrates the usefulness of applying morphology and chemistry information acquired by SEM-EDS for pollution particle source determination.     

Formulation and Compaction of Nonfracturing Deformable Coated Beads

There has been considerable interest in making tablets from spheronized bead rather than through encapsulation. It is obvious that the forces present during compaction may break a coating intended to control drug release. This effect may be moderated by cushioning agents incorporated into the bead formulation or situation between the beads. Our work describes the latter method.     

Dynamic flow modelling of riverine amphibian habitat with application to regulated flow management

In regulated rivers, relicensing of hydropower projects can provide an opportunity to change flow regimes and reduce negative effects on sensitive aquatic biota. The volume of flow, timing and ramping rate of spring spills, and magnitude of aseasonal pulsed flows have potentially negative effects on the early life stages of amphibians, such as the Foothill yellow‐legged frog (Rana boylii). Two‐dimensional hydrodynamic modeling is one method to evaluate potential effects of flow variation on frog egg masses and tadpoles. We explored the usefulness of this technique by modeling habitat suitability under several pulsed flow scenarios in two river reaches in northern California, USA. We conducted analyses beyond simple weighted usable area calculations, such as quantifying the risk of scour or stranding, in order to quantify potential loss under different flow scenarios. The modeling results provided information on potential susceptibility to flow fluctuations as well as the influence of channel morphology on habitat suitability. Under each flow scenario, low percentages of suitable habitat remained suitable or were ‘buffered’ from the pulse, creating high potential for scour of egg masses or tadpoles. However, due to differences in channel morphologies, the wide, shallow study site provided 2‐3 times the buffering capacity of the entrenched study site. Additional analyses suggested that limited buffering capacity and lack of connectivity between suitable egg mass and tadpole habitats may explain why some hydraulically suitable habitats are unoccupied. This type of model‐based analysis would be useful for managing foothill yellow‐legged frogs or similar aquatic species in regulated river systems. Copyright © 2010 John Wiley & Sons, Ltd.     

NON‐UNIFORM CHANGES TO WHITEWATER RECREATION IN CALIFORNIA'S SIERRA NEVADA FROM REGIONAL CLIMATE WARMING

Whitewater recreation is an aesthetic ecosystem service potentially affected by climate warming alterations to runoff. In California's Sierra Nevada, climate change is likely to reduce water availability with warmer air temperatures and stationary or decreasing precipitation, which will likely alter whitewater recreation opportunities. In this study, we identified 128 whitewater runs on the west slope of the Sierra Nevada within a 13‐basin study area that ranged from serene float trips to remote, difficult, kayak expeditions. We used a spatially explicit, one‐dimensional rainfall‐runoff model to estimate the unregulated hydrology at specific locations within flow thresholds amenable to whitewater recreation. Climate warming scenarios were simulated by increasing air temperature by 2 °C, 4 °C and 6 °C and assuming no change in precipitation. With mild warming, the average number of boatable weeks per year increases, but more extreme warming decreases the average boatable weeks per year across the Sierra Nevada. Runs in low‐elevation drainages, such as the Cosumnes and the Tule River Basins, are most vulnerable to changes in boatable weeks. Yet, high‐elevation watersheds, such as the Kern River, also have a large reduction in boatable weeks. Watersheds in the central Sierra Nevada show an increase in boatable weeks. Overall, we found elevation and run type to be the best predictors of resiliency for Sierra Nevada whitewater runs. Recreation is important for management of rivers, yet it is difficult to quantify and to plan for. This research provides a sensitivity analysis approach to climate warming for the Sierra Nevada and presents a method that can be applied to other regions and whitewater rivers. The observed reduction in whitewater recreation opportunities in unregulated rivers because of climate warming and continued increases in population will likely increase the importance of whitewater boating on regulated rivers and thus the reliance on operations for meeting multiple demands. Copyright © 2011 John Wiley & Sons, Ltd.