Chirok: a post-refinement tool to analyse absolute structure

Chirok is software for a post-refinement test of the absolute structure. The software allows a user to calculate a distribution of the measure of chirality based on intensity quotients and linked to the Flack parameter. The distribution is fitted by a set of peak functions, the refined centre of which gives an estimate of the Flack parameter with the same or better precision compared with the usual refinement schemes. The use of this software is illustrated with a collection of published data for chiral structures.

Exponentially Modified Peak Functions in Biomedical Sciences and Related Disciplines

In many cases relevant to biomedicine, a variable time, which features a certain distribution, is required for objects of interest to pass from an initial to an intermediate state, out of which they exit at random to a final state. In such cases, the distribution of variable times between exiting the initial and entering the final state must conform to the convolution of the first distribution and a negative exponential distribution. A common example is the exponentially modified Gaussian (EMG), which is widely used in chromatography for peak analysis and is long known as ex-Gaussian in psychophysiology, where it is applied to times from stimulus to response. In molecular and cell biology, EMG, compared with commonly used simple distributions, such as lognormal, gamma, and Wald, provides better fits to the variabilities of times between consecutive cell divisions and transcriptional bursts and has more straightforwardly interpreted parameters. However, since the range of definition of the Gaussian component of EMG is unlimited, data approximation with EMG may extend to the negative domain. This extension may seem negligible when the coefficient of variance of the Gaussian component is small but becomes considerable when the coefficient increases. Therefore, although in many cases an EMG may be an acceptable approximation of data, an exponentially modified nonnegative peak function, such as gamma-distribution, can make more sense in physical terms. In the present short review, EMG and exponentially modified gamma-distribution (EMGD) are discussed with regard to their applicability to data on cell cycle, gene expression, physiological responses to stimuli, and other cases, some of which may be interpreted as decision-making. In practical fitting terms, EMG and EMGD are equivalent in outperforming other functions; however, when the coefficient of variance of the Gaussian component of EMG is greater than ca. 0.4, EMGD is preferable.

Comparison of interval timing behaviour in mice following dorsal or ventral hippocampal lesions with mice having δ -opioid receptor gene deletion

Mice with cytotoxic lesions of the dorsal hippocampus (DH) underestimated 15 s and 45 s target durations in a bi-peak procedure as evidenced by proportional leftward shifts of the peak functions that emerged during training as a result of decreases in both ‘start’ and ‘stop’ times. In contrast, mice with lesions of the ventral hippocampus (VH) displayed rightward shifts that were immediately present and were largely limited to increases in the ‘stop’ time for the 45 s target duration. Moreover, the effects of the DH lesions were congruent with the scalar property of interval timing in that the 15 s and 45 s functions superimposed when plotted on a relative timescale, whereas the effects of the VH lesions violated the scalar property. Mice with DH lesions also showed enhanced reversal learning in comparison to control and VH lesioned mice. These results are compared with the timing distortions observed in mice lacking δ -opioid receptors (Oprd1 −/− ) which were similar to mice with DH lesions. Taken together, these results suggest a balance between hippocampal–striatal interactions for interval timing and demonstrate possible functional dissociations along the septotemporal axis of the hippocampus in terms of motivation, timed response thresholds and encoding in temporal memory.

Evaluation of peak functions on ultra-coarse grids

Integration of sampled data arises in many practical applications, where the integrand function is available from experimental measurements only. One extensive field of research is the problem of pest monitoring and control where an accurate evaluation of the population size from the spatial density distribution is required for a given pest species. High aggregation population density distributions (peak functions) are an important class of data that often appear in this problem. The main difficulty associated with the integration of such functions is that the function values are usually only available at a few locations; therefore, new techniques are required to evaluate the accuracy of integration as the standard approach based on convergence analysis does not work when the data are sparse. Thus, in this paper, we introduce the new concept of ultra-coarse grids for high aggregation density distributions. Integration of the density function on ultra-coarse grids cannot provide the prescribed accuracy because of insufficient information (uncertainty) about the integrand function. Instead, the results of the integration should be treated probabilistically by considering the integration error as a random variable, and we show how the corresponding probabilities can be calculated. Handling the integration error as a random variable allows us to evaluate the accuracy of integration on very coarse grids where asymptotic error estimates cannot be applied.

Parallel Swarms Oriented Particle Swarm Optimization

The particle swarm optimization (PSO) is a recently invented evolutionary computation technique which is gaining popularity owing to its simplicity in implementation and rapid convergence. In the case of single-peak functions, PSO rapidly converges to the peak; however, in the case of multimodal functions, the PSO particles are known to get trapped in the local optima. In this paper, we propose a variation of the algorithm called parallel swarms oriented particle swarm optimization (PSO-PSO) which consists of a multistage and a single stage of evolution. In the multi-stage of evolution, individual subswarms evolve independently in parallel, and in the single stage of evolution, the sub-swarms exchange information to search for the global-best. The two interweaved stages of evolution demonstrate better performance on test functions, especially of higher dimensions. The attractive feature of the PSO-PSO version of the algorithm is that it does not introduce any new parameters to improve its convergence performance. The strategy maintains the simple and intuitive structure as well as the implemental and computational advantages of the basic PSO.