Likelihood, entropy and species diversity; some comparisons in a Sumatran forest

In attempts to conserve the species diversity of trees in tropical forests, monitoring of diversity in inventories is essential. For effective monitoring it is crucial to be able to make meaningful comparisons between different regions, or comparisons of the diversity of a region at different times. Many species diversity measures have been defined, including the well-known abundance and entropy measures. All such measures share a number of problems in their effective practical use. However, probably the most problematic is that they cannot be used to meaningfully assess changes, since thay are only concerned with the number of species or the proportions of the population/sample which they constitute. A natural (though simplistic) model of a species frequency distribution is the multinomial distribution. It is shown that the likelihood analysis of samples from such a distribution are closely related to a number of entropy-type measures of diversity. Hence a comparison of the species distribution on two plots, using the multinomial model and likelihood methods, leads to generalised cross-entropy as the LRT test statistic of the null that the species distributions are the same. Data from 30 contiguous plots in a forest in Sumatra are analysed using these methods. Significance tests between all pairs of plots yield extremely low p-values, indicating strongly that it ought to been "Obvious" that the observed species distributions are different on different plots. In terms of how different the plots are, and how these differences vary over the whole study site, a display of the degrees of freedom of the test, (equivalent to the number of shared species) seems to be the most revealing indicator, as well as the simplest.

Analysis of species hyper-diversity in the tropical rain forests of Indonesia: the problem of non-observance

The main interest in the assessment of forest species diversity for conservation purposes is in the rare species. The main problem in the tropical rain forests is that most of the species are rare. Assessment of species diversity in the tropical rain forests is therefore often concerned with estimating that which is not observed in recorded samples. Statistical methodology is therefore required to try to estimate the truncated tail of the species frequency distribution, or to estimate the asymptote of species/diversity-area curves. A Horvitz-Thompson estimator of the number of unobserved (“virtual”) species in each species intensity class is proposed. The approach allows a definition of an extended definition of diversity, ( or generalised Renyi entropy). The paper presents a case study from data collected in Jambi, Sumatra, and the “extended diversity measure” is used on the species data.

Minimizing total weighted completion time in a proportionate flow shop

We study the special case of the m machine flow shop problem in which the processing time of each operation of job j is equal to pj; this variant of the flow shop problem is known as the proportionate flow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that the problem of minimizing total weighted completion time is solvable in O(n2) time. © 1998 John Wiley & Sons, Ltd.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Two-machine flow shop scheduling problems with no-wait jobs

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 43-approximation algorithm.

Novel inclusion complex of ibuprofen tromethamine with cyclodextrins: Physico-chemical characterization

Guest-host interactions of ibuprofen tromethamine salt (Ibu.T) with native and modified cyclodextrins (CyDs) have been investigated using several techniques, namely phase solubility diagrams (PSDs), proton nuclear magnetic resonance (H-1 NMR), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray powder diffractometry (XRPD). scanning-electron microscopy (SEM) and molecular mechanics (MM). From the analysis of PSD data (A(L)-type) it is concluded that the anionic tromethamine salt of ibuprofen (pK(a) = 4.55) forms 1: 1 soluble complexes with all CyDs investigated in buffered water at pH 7.0, while the neutral form of Ibu forms an insoluble complex with beta-CyD (B-S-type) in buffered water at pH 2.0. Ibu.T has a lower tendency to complex with beta-CyD (K-11 = 58 M-1 at pH 7.0) compared with the neutral Ibu (K-11 = 4200 M (1)) in water. Complex formation of Ibu.T with beta-CyD (Delta G degrees = -20.4 kJ/mol) is enthalpy driven (Delta H degrees = -22.9 kJ/mol) and is accompanied by a small unfavorable entropy (Delta S degrees = -8.4 J/mol K) change. H-1 NMR studies and MM computations revealed that, on complexation, the hydrophobic central benzene ring of lbu.T and part of the isobutyl group reside within the beta-CyD cavity leaving the peripheral groups (carboxylate, tromethamine and methyl groups) located near the hydroxyl group networks at either rim of beta-CyD. PSD, H-1 NMR, DSC, FT-IR, XRPD, SEM and MM studies confirmed the formation of Ibu.T/beta-CyD inclusion complex in solution and the solid state. (C) 2009 Elsevier B.V. All rights reserved.

Determination of micelle/water partition coefficients and associated thermodynamic data for dialkyl phthalate esters

Micelle/water partition coefficients for three dialkyl phthalate esters - dimethyl phthalate ester (DMP), diethyl phthalate ester (DEP) and dipropyl phthalate ester (DPP) were obtained by micellar liquid chromatography (MLC). Experiments were conducted over a temperature range which led to calculation of a Gibbs free energy, enthalpy and entropy of transfer for the phthalate esters. In addition, small angle neutron scattering (SANS) experiments were conducted with no substantial change observed in micelle size before and after phthalate ester incorporation. Overall, a novel method for obtaining thermodynamic information, based on partitioning data, has been developed for dialkyl phthalate esters using micellar liquid chromatography.