Notations and conventions in molecular spectroscopy: part 3. Permutation and permutation-inversion symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 3 in a series, deals with symmetry notation referring to groups that involve nuclear permutations and the inversion operation. Further parts will follow, dealing inter alia with vibration-rotation spectroscopy and electronic spectroscopy.

Sequentially testing for a gene-drug interaction in a genomewide analysis

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs. Copyright (c) 2007 John Wiley & Sons, Ltd.

Potential energy surface and MULTIMODE vibrational analysis of C2H3+

A full dimensional, ab initio-based semiglobal potential energy surface for C2H3+ is reported. The ab initio electronic energies for this molecule are calculated using the spin-restricted, coupled cluster method restricted to single and double excitations with triples corrections [RCCSD(T)]. The RCCSD(T) method is used with the correlation-consistent polarized valence triple-zeta basis augmented with diffuse functions (aug-cc-pVTZ). The ab initio potential energy surface is represented by a many-body (cluster) expansion, each term of which uses functions that are fully invariant under permutations of like nuclei. The fitted potential energy surface is validated by comparing normal mode frequencies at the global minimum and secondary minimum with previous and new direct ab initio frequencies. The potential surface is used in vibrational analysis using the "single-reference" and "reaction-path" versions of the code MULTIMODE. (c) 2006 American Institute of Physics.

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcal/mol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively. (C) 2008 American Institute of Physics.

Utopia Ltd

Utopia Ltd. explores the relationship between utopian ideas and commodification, bringing together artwork by Blaise Drummond, Brendan Earley, Pil and Galia Kollectiv, David Mabb, Lizi Sanchez and Mary-Ruth Walsh. The seven artists’ work opens up a debate on the utopian within painting, sculpture, architecture, design and video.The works in Utopia Ltd. represent modernist architecture and design in its various mutations within a spectacularised, commodified 20th century consumer society. In these works, the utopian dream seems to burst through again and again, despite rather than because of the permutations of commodity culture. By picturing the past, present and possible future, the works destabilize fixed linear time. By rescuing, reclaiming and re-picturing, Utopia Ltd. suggests that utopian ideas persist in contemporary art, making a provocative demand on the viewer’s capacity to produce utopian dreams of their own. The exhibition’s title Utopia Ltd. is a satirical echo of an operetta by Gilbert and Sullivan, Utopia (Limited) or, The Flowers of Progress (1893), in which a utopian colony is turned into a joint stock company.

Decision making for HVAC&R system selection for a typical office building in the UK

Demands for thermal comfort, better indoor air quality together with lower environmental impacts have had ascending trends in the last decade. In many circumstances, these demands could not be fully covered through the soft approach of bioclimatic design like optimisation of the building orientation and internal layout. This is mostly because of the dense urban environment and building internal energy loads. In such cases, heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems make a key role to fulfill the requirements of indoor environment. Therefore, it is required to select the most proper HVAC&R system. In this study, a robust decision making approach for HVAC&R system selection is proposed. Technical performance, economic aspect and environmental impacts of 36 permutations of primary and secondary systems are taken into account to choose the most proper HVAC&R system for a case study office building. The building is a representative for the dominant form of office buildings in the UK. Dynamic performance evaluation of HVAC&R alternatives using TRNSYS package together with life cycle energy cost analysis provides a reliable basis for decision making. Six scenarios broadly cover the decision makers' attitudes on HVAC&R system selection which are analysed through Analytical Hierarchy Process (AHP). One of the significant outcomes reveals that, despite both the higher energy demand and more investment requirements associated with compound heating, cooling and power system (CCHP); this system is one of the top ranked alternatives due to the lower energy cost and C02 emissions. The sensitivity analysis reveals that in all six scenarios, the first five top ranked alternatives are not changed. Finally, the proposed approach and the results could be used by researchers and designers especially in the early stages of a design process in which all involved bodies face the lack of time, information and tools for evaluation of a variety of systems.

Modeling plant transpiration under limited soil water: comparison of different plant and soil hydraulic parameterizations and preliminary implications for their use in land surface models

Accurate estimates of how soil water stress affects plant transpiration are crucial for reliable land surface model (LSM) predictions. Current LSMs generally use a water stress factor, β, dependent on soil moisture content, θ, that ranges linearly between β = 1 for unstressed vegetation and β = 0 when wilting point is reached. This paper explores the feasibility of replacing the current approach with equations that use soil water potential as their independent variable, or with a set of equations that involve hydraulic and chemical signaling, thereby ensuring feedbacks between the entire soil–root–xylem–leaf system. A comparison with the original linear θ-based water stress parameterization, and with its improved curvi-linear version, was conducted. Assessment of model suitability was focused on their ability to simulate the correct (as derived from experimental data) curve shape of relative transpiration versus fraction of transpirable soil water. We used model sensitivity analyses under progressive soil drying conditions, employing two commonly used approaches to calculate water retention and hydraulic conductivity curves. Furthermore, for each of these hydraulic parameterizations we used two different parameter sets, for 3 soil texture types; a total of 12 soil hydraulic permutations. Results showed that the resulting transpiration reduction functions (TRFs) varied considerably among the models. The fact that soil hydraulic conductivity played a major role in the model that involved hydraulic and chemical signaling led to unrealistic values of β, and hence TRF, for many soil hydraulic parameter sets. However, this model is much better equipped to simulate the behavior of different plant species. Based on these findings, we only recommend implementation of this approach into LSMs if great care with choice of soil hydraulic parameters is taken

Phylogeny and ecology determine morphological structure in a snake assemblage in the central Brazilian Cerrado

To investigate the role of ecological and historical factors in the organization of communities, we describe the ecomorphological structure of an assemblage of snakes (61 species in six families) in the Cerrado (a savanna-like grassland) of Distrito Federal, Brazil. These snakes vary in habits, with some being fossorial, cryptozoic, terrestrial, semi-aquatic, or arboreal. Periods of activity also vary. A multivariate analysis identified distinct morphological groups associated with patterns of resource use. We report higher niche diversification compared to snakes in the Caatinga (a semi-arid region in northeastern Brazil), with fossorial and cryptozoic species occupying morphological space that is not occupied in the Caatinga. Monte Carlo permutations from canonical phylogenetic ordination revealed a significant phylogenetic effect on morphology for Colubridae, Colubrinae, Viperidae, Elapidae, and Boidae indicating that morphological divergence occurred in the distant past. We conclude that phylogeny is the most important factor determining structure of this Neotropical assemblage. Nevertheless, our results also suggest a strong ecological component characterizes a peculiar snake fauna.

Testing permutation properties through subpermutations

There has been great interest in deciding whether a combinatorial structure satisfies some property, or in estimating the value of some numerical function associated with this combinatorial structure, by considering only a randomly chosen substructure of sufficiently large, but constant size. These problems are called property testing and parameter testing, where a property or parameter is said to be testable if it can be estimated accurately in this way. The algorithmic appeal is evident, as, conditional on sampling, this leads to reliable constant-time randomized estimators. Our paper addresses property testing and parameter testing for permutations in a subpermutation perspective; more precisely, we investigate permutation properties and parameters that can be well approximated based on a randomly chosen subpermutation of much smaller size. In this context, we use a theory of convergence of permutation sequences developed by the present authors [C. Hoppen, Y. Kohayakawa, C.G. Moreira, R.M. Sampaio, Limits of permutation sequences through permutation regularity, Manuscript, 2010, 34pp.] to characterize testable permutation parameters along the lines of the work of Borgs et al. [C. Borgs, J. Chayes, L Lovasz, V.T. Sos, B. Szegedy, K. Vesztergombi, Graph limits and parameter testing, in: STOC`06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, ACM, New York, 2006, pp. 261-270.] in the case of graphs. Moreover, we obtain a permutation result in the direction of a famous result of Alon and Shapira [N. Alon, A. Shapira, A characterization of the (natural) graph properties testable with one-sided error, SIAM J. Comput. 37 (6) (2008) 1703-1727.] stating that every hereditary graph property is testable. (C) 2011 Elsevier B.V. All rights reserved.

Price discovery in dual-class shares across multiple markets

We extend the standard price discovery analysis to estimate the information share of dual-class shares across domestic and foreign markets. By examining both common and preferred shares, we aim to extract information not only about the fundamental value of the rm, but also about the dual-class premium. In particular, our interest lies on the price discovery mechanism regulating the prices of common and preferred shares in the BM&FBovespa as well as the prices of their ADR counterparts in the NYSE and in the Arca platform. However, in the presence of contemporaneous correlation between the innovations, the standard information share measure depends heavily on the ordering we attribute to prices in the system. To remain agnostic about which are the leading share class and market, one could for instance compute some weighted average information share across all possible orderings. This is extremely inconvenient given that we are dealing with 2 share prices in Brazil, 4 share prices in the US, plus the exchange rate (and hence over 5,000 permutations!). We thus develop a novel methodology to carry out price discovery analyses that does not impose any ex-ante assumption about which share class or trading platform conveys more information about shocks in the fundamental price. As such, our procedure yields a single measure of information share, which is invariant to the ordering of the variables in the system. Simulations of a simple market microstructure model show that our information share estimator works pretty well in practice. We then employ transactions data to study price discovery in two dual-class Brazilian stocks and their ADRs. We uncover two interesting ndings. First, the foreign market is at least as informative as the home market. Second, shocks in the dual-class premium entail a permanent e ect in normal times, but transitory in periods of nancial distress. We argue that the latter is consistent with the expropriation of preferred shareholders as a class.

3D calculation of Tucson-Melbourne 3NF effect in triton binding energy

As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both, novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF.

The use of nonparametric contrasts in one-way layouts and random block designs

Nonparametric simple-contrast estimates for one-way layouts based on Hodges-Lehmann estimators for two samples and confidence intervals for all contrasts involving only two treatments are found in the literature.Tests for such contrasts are performed from the distribution of the maximum of the rank sum between two treatments. For random block designs, simple contrast estimates based on Hodges-Lehmann estimators for one sample are presented. However, discussions concerning the significance levels of more complex contrast tests in nonparametric statistics are not well outlined.This work aims at presenting a methodology to obtain p-values for any contrast types based on the construction of the permutations required by each design model using a C-language program for each design type. For small samples, all possible treatment configurations are performed in order to obtain the desired p-value. For large samples, a fixed number of random configurations are used. The program prompts the input of contrast coefficients, but does not assume the existence or orthogonality among them.In orthogonal contrasts, the decomposition of the value of the suitable statistic for each case is performed and it is observed that the same procedure used in the parametric analysis of variance can be applied in the nonparametric case, that is, each of the orthogonal contrasts has a chi(2) distribution with one degree of freedom. Also, the similarities between the p-values obtained for nonparametric contrasts and those obtained through approximations suggested in the literature are discussed.

Optimization of Amplifier Placements in Switch-Based Optical Networks

Wavelength division multiplexing (WDM) offers a solution to the problem of exploiting the large bandwidth on optical links; it is the current favorite multiplexing technology for optical communication networks. Due to the high cost of an optical amplifier, it is desirable to strategically place the amplifiers throughout the network in a way that guarantees that all the signals are adequately amplified while minimizing the total number amplifiers being used. Previous studies all consider a star-based network. This paper demonstrates an original approach for solving the problem in switch-based WDM optical network assuming the traffic matrix is always the permutation of the nodes. First we formulate the problem by choosing typical permutations which can maximize traffic load on individual links; then a GA (Genetic Algorithm) is used to search for feasible amplifier placements. Finally, by setting up all the lightpaths without violating the power constaints we confirm the feasibility of the solution.

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.