Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

A new multivariable 6-psi-6 summation formula

By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynomial argument this 8-phi-7 summation is transformed to another multivariable 8-phi-7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6-phi-5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6-psi-6 summation formula.Comment: 16 page

Generic properties of a quasi-one dimensional classical Wigner crystal

We studied the structural, dynamical properties and melting of a quasi-one-dimensional system of charged particles, interacting through a screened Coulomb potential. The ground state energy was calculated and, depending on the density and the screening length, the system crystallizes in a number of chains. As a function of the density (or the confining potential), the ground state configurations and the structural transitions between them were analyzed both by analytical and Monte Carlo calculations. The system exhibits a rich phase diagram at zero temperature with continuous and discontinuous structural transitions. We calculated the normal modes of the Wigner crystal and the magneto-phonons when an external constant magnetic field $B$ is applied. At finite temperature the melting of the system was studied via Monte Carlo simulations using the $modified$ $Lindemann$ $criterion$ (MLC). The melting temperature as a function of the density was obtained for different screening parameters. Reentrant melting as a function of the density was found as well as evidence of directional dependent melting. The single chain regime exhibits anomalous melting temperatures according to the MLC and as a check we study the pair correlation function at different densities and different temperatures, formulating a different criterion. Possible connection with recent theoretical and experimental results are discussed and experiments are proposed.Comment: 13 pages text, 21 picture

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Reply to: New Meta- and Mega-analyses of Magnetic Resonance Imaging Findings in Schizophrenia: Do They Really Increase Our Knowledge About the Nature of the Disease Process?

This work was supported by National Institute of Biomedical Imaging and Bioengineering Grant No. U54EB020403 (to the ENIGMA consortium)

Cortical brain abnormalities in 4474 individuals with schizophrenia and 5098 control subjects via the enhancing neuro Imaging genetics through meta analysis (ENIGMA) Consortium

BACKGROUND: The profile of cortical neuroanatomical abnormalities in schizophrenia is not fully understood, despite hundreds of published structural brain imaging studies. This study presents the first meta-analysis of cortical thickness and surface area abnormalities in schizophrenia conducted by the ENIGMA (Enhancing Neuro Imaging Genetics through Meta Analysis) Schizophrenia Working Group. METHODS: The study included data from 4474 individuals with schizophrenia (mean age, 32.3 years; range, 11-78 years; 66% male) and 5098 healthy volunteers (mean age, 32.8 years; range, 10-87 years; 53% male) assessed with standardized methods at 39 centers worldwide. RESULTS: Compared with healthy volunteers, individuals with schizophrenia have widespread thinner cortex (left/right hemisphere: Cohen's d = -0.530/-0.516) and smaller surface area (left/right hemisphere: Cohen's d = -0.251/-0.254), with the largest effect sizes for both in frontal and temporal lobe regions. Regional group differences in cortical thickness remained significant when statistically controlling for global cortical thickness, suggesting regional specificity. In contrast, effects for cortical surface area appear global. Case-control, negative, cortical thickness effect sizes were two to three times larger in individuals receiving antipsychotic medication relative to unmedicated individuals. Negative correlations between age and bilateral temporal pole thickness were stronger in individuals with schizophrenia than in healthy volunteers. Regional cortical thickness showed significant negative correlations with normalized medication dose, symptom severity, and duration of illness and positive correlations with age at onset. CONCLUSIONS: The findings indicate that the ENIGMA meta-analysis approach can achieve robust findings in clinical neuroscience studies; also, medication effects should be taken into account in future genetic association studies of cortical thickness in schizophrenia

Reproducibility in the absence of selective reporting: An illustration from large‐scale brain asymmetry research

The problem of poor reproducibility of scientific findings has received much attention over recent years, in a variety of fields including psychology and neuroscience. The problem has been partly attributed to publication bias and unwanted practices such as p‐hacking. Low statistical power in individual studies is also understood to be an important factor. In a recent multisite collaborative study, we mapped brain anatomical left–right asymmetries for regional measures of surface area and cortical thickness, in 99 MRI datasets from around the world, for a total of over 17,000 participants. In the present study, we revisited these hemispheric effects from the perspective of reproducibility. Within each dataset, we considered that an effect had been reproduced when it matched the meta‐analytic effect from the 98 other datasets, in terms of effect direction and significance threshold. In this sense, the results within each dataset were viewed as coming from separate studies in an “ideal publishing environment,” that is, free from selective reporting and p hacking. We found an average reproducibility rate of 63.2% (SD = 22.9%, min = 22.2%, max = 97.0%). As expected, reproducibility was higher for larger effects and in larger datasets. Reproducibility was not obviously related to the age of participants, scanner field strength, FreeSurfer software version, cortical regional measurement reliability, or regional size. These findings constitute an empirical illustration of reproducibility in the absence of publication bias or p hacking, when assessing realistic biological effects in heterogeneous neuroscience data, and given typically‐used sample sizes

Learning from Post-project Reviews : A Cross-Case Analysis

Every new product development (NPD) project should not only deliver a successful new product but also should generate learning for the organization. Postproject reviews (PPRs) are recognized by both practitioners and academics as an appropriate mechanism to stimulate and capture learning in NPD teams. However, relatively few companies use PPRs, and those that do use them often fail to do so effectively. Although they are widely perceived to be a useful tool, empirical research on how PPRs are typically organized and the learning that results is limited. The present article addresses this gap in the extant knowledge and describes five in-depth case studies, which were conducted at leading companies in Germany. A detailed investigation was made of how PPRs are conducted and of the type of learning that can result. Three main sources of data were used for each case: company documentation, in-depth interviews with managers responsible for NPD, and observation of an actual PPR. The different data sources enabled extensive triangulation of data to be conducted and a high degree of reliability and validity to be achieved. The analysis enabled a number of key characteristics of the way PPRs are managed to be identified. Various characteristics of PPRs influence their utility, such as the time at which they take place and the way discussions are moderated. In addition, the data show that participants in the discussions at PPRs often use metaphors and stories, which indicates that PPRs have the potential to generate tacit knowledge. Interestingly, the data also show that there are various different ways in which metaphors and stories appear to stimulate discussions on NPD projects. Based on the cross-case analysis, a wide range of implications are identified. Researchers need to investigate PPRs further to identify how they can generate tacit and explicit knowledge and support project-to-project learning. The generation of tacit knowledge in NPD is a topic that particularly needs further investigation. The research also led to a range of recommendations for practitioners. Companies need to strongly communicate the purpose and value of PPRs, to run them effectively to stimulate the maximum possible learning, and to disseminate the findings widely. PPRs have the potential to create and transfer knowledge amongst NPD professionals, but, as they are seldom currently used, many companies are missing an important opportunity