High precision multifractal analysis in the 3D Anderson model of localisation

This work presents a large scale multifractal analysis of the electronic state in the vicinity of the localisation-delocalisation transition in the three-dimensional Anderson model of localisation using high-precision data and very large system sizes of up to L3 = 2403. The multifractal analysis is implemented using box- and system- size scaling of the generalized inverse participation ratios employing typical and ensemble averaging techniques. The statistical analysis in this study has shown that in the thermodynamic limit a proposed symmetry relation in the multifractal exponents is true for the 3D Anderson model in the orthogonal universality class. Better agreement with the symmetry is found when using system-size scaling with ensemble averaging in which a more complete picture of the multifractal spectrum f(α) is also obtained. A complete profile of f(α) has negative fractal dimensions and shows the contributions coming from the tails of the distribution. Various boxpartitioning approaches have been carefully studied such as the use of cubic and non-cubic boxes, periodic boundary conditions to enlarge the system, and single and multiple origins in the partitioning grid. The most reliable method is equal partitioning of a system into cubic boxes which has also been shown to be the least numerically expensive. Furthermore, this work gives an expression relating f(α) and the probability density function (PDF) of wavefunction intensities. The relation which contains a finite-size correction provides an alternative and simpler method to obtain f(α) directly from the PDF in which f(α) is interpreted as the scaleinvariant distribution at criticality. Finally, a generalization of standard multifractal analysis which is applicable to the critical regime and not just at the critical point is presented here. Using this generalization together with finite-size scaling analysis, estimates of critical disorder and critical exponent based on exact diagonalization have been obtained that are in excellent agreement, supporting for the first time previous results of transfer matrix calculations

Multifractal analysis with the probability density function at the three-dimensional Anderson transition

The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and we comment on the possible existence of termination points. A PDF-based multifractal analysis is hence shown to be a valid alternative to the standard approach based on the scaling of general inverse participation ratios.Comment: 4 pages, 7 figure

High precision multifractal analysis in the 3D Anderson model of localisation

This work presents a large scale multifractal analysis of the electronic state in the vicinity of the localisation-delocalisation transition in the three-dimensional Anderson model of localisation using high-precision data and very large system sizes of up to L3 = 2403. The multifractal analysis is implemented using box- and system- size scaling of the generalized inverse participation ratios employing typical and ensemble averaging techniques. The statistical analysis in this study has shown that in the thermodynamic limit a proposed symmetry relation in the multifractal exponents is true for the 3D Anderson model in the orthogonal universality class. Better agreement with the symmetry is found when using system-size scaling with ensemble averaging in which a more complete picture of the multifractal spectrum f(α) is also obtained. A complete profile of f(α) has negative fractal dimensions and shows the contributions coming from the tails of the distribution. Various boxpartitioning approaches have been carefully studied such as the use of cubic and non-cubic boxes, periodic boundary conditions to enlarge the system, and single and multiple origins in the partitioning grid. The most reliable method is equal partitioning of a system into cubic boxes which has also been shown to be the least numerically expensive. Furthermore, this work gives an expression relating f(α) and the probability density function (PDF) of wavefunction intensities. The relation which contains a finite-size correction provides an alternative and simpler method to obtain f(α) directly from the PDF in which f(α) is interpreted as the scaleinvariant distribution at criticality. Finally, a generalization of standard multifractal analysis which is applicable to the critical regime and not just at the critical point is presented here. Using this generalization together with finite-size scaling analysis, estimates of critical disorder and critical exponent based on exact diagonalization have been obtained that are in excellent agreement, supporting for the first time previous results of transfer matrix calculations.EThOS - Electronic Theses Online ServiceUniversity of WarwickEngineering and Physical Sciences Research Council (EPSRC) (EP/C007042/1)Ōsaka Daigaku [Osaka University]GBUnited Kingdo

Transcriptional diversity during lineage commitment of human blood progenitors.

Blood cells derive from hematopoietic stem cells through stepwise fating events. To characterize gene expression programs driving lineage choice, we sequenced RNA from eight primary human hematopoietic progenitor populations representing the major myeloid commitment stages and the main lymphoid stage. We identified extensive cell type-specific expression changes: 6711 genes and 10,724 transcripts, enriched in non-protein-coding elements at early stages of differentiation. In addition, we found 7881 novel splice junctions and 2301 differentially used alternative splicing events, enriched in genes involved in regulatory processes. We demonstrated experimentally cell-specific isoform usage, identifying nuclear factor I/B (NFIB) as a regulator of megakaryocyte maturation-the platelet precursor. Our data highlight the complexity of fating events in closely related progenitor populations, the understanding of which is essential for the advancement of transplantation and regenerative medicine.The work described in this article was primarily supported by the European Commission Seventh Framework Program through the BLUEPRINT grant with code HEALTH-F5-2011-282510 (D.H., F.B., G.C., J.H.A.M., K.D., L.C., M.F., S.C., S.F., and S.P.G.). Research in the Ouwehand laboratory is further supported by program grants from the National Institute for Health Research (NIHR, www.nihr.ac.uk; to A.A., M.K., P.P., S.B.G.J., S.N., and W.H.O.) and the British Heart Foundation under nos. RP-PG-0310-1002 and RG/09/12/28096 (www.bhf.org.uk; to A.R. and W.J.A.). K.F. and M.K. were supported by Marie Curie funding from the NETSIM FP7 program funded by the European Commission. The laboratory receives funding from the NHS Blood and Transplant for facilities. The Cambridge BioResource (www.cambridgebioresource.org.uk), the Cell Phenotyping Hub, and the Cambridge Translational GenOmics laboratory (www.catgo.org.uk) are supported by an NIHR grant to the Cambridge NIHR Biomedical Research Centre (BRC). The BRIDGE-Bleeding and Platelet Disorders Consortium is supported by the NIHR BioResource—Rare Diseases (http://bioresource.nihr.ac.uk/; to E.T., N.F., and Whole Exome Sequencing effort). Research in the Soranzo laboratory (L.V., N.S., and S. Watt) is further supported by the Wellcome Trust (Grant Codes WT098051 and WT091310) and the EU FP7 EPIGENESYS initiative (Grant Code 257082). Research in the Cvejic laboratory (A. Cvejic and C.L.) is funded by the Cancer Research UK under grant no. C45041/A14953. S.J.S. is funded by NIHR. M.E.F. is supported by a British Heart Foundation Clinical Research Training Fellowship, no. FS/12/27/29405. E.B.-M. is supported by a Wellcome Trust grant, no. 084183/Z/07/Z. Research in the Laffan laboratory is supported by Imperial College BRC. F.A.C., C.L., and S. Westbury are supported by Medical Research Council Clinical Training Fellowships, and T.B. by a British Society of Haematology/NHS Blood and Transplant grant. R.J.R. is a Principal Research Fellow of the Wellcome Trust, grant no. 082961/Z/07/Z. Research in the Flicek laboratory is also supported by the Wellcome Trust (grant no. 095908) and EMBL. Research in the Bertone laboratory is supported by EMBL. K.F. and C.v.G. are supported by FWO-Vlaanderen through grant G.0B17.13N. P.F. is a compensated member of the Omicia Inc. Scientific Advisory Board. This study made use of data generated by the UK10K Consortium, derived from samples from the Cohorts arm of the project.This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on 26/9/14 in volume 345, number 6204, DOI: 10.1126/science.1251033. This version will be under embargo until the 26th of March 2015

The Allelic Landscape of Human Blood Cell Trait Variation and Links to Common Complex Disease

Many common variants have been associated with hematological traits, but identification of causal genes and pathways has proven challenging. We performed a genome-wide association analysis in the UK Biobank and INTERVAL studies, testing 29.5 million genetic variants for association with 36 red cell, white cell, and platelet properties in 173,480 European-ancestry participants. This effort yielded hundreds of low frequency (<5%) and rare (<1%) variants with a strong impact on blood cell phenotypes. Our data highlight general properties of the allelic architecture of complex traits, including the proportion of the heritable component of each blood trait explained by the polygenic signal across different genome regulatory domains. Finally, through Mendelian randomization, we provide evidence of shared genetic pathways linking blood cell indices with complex pathologies, including autoimmune diseases, schizophrenia, and coronary heart disease and evidence suggesting previously reported population associations between blood cell indices and cardiovascular disease may be non-causal.We thank members of the Cambridge BioResource Scientific Advisory Board and Management Committee for their support of our study and the National Institute for Health Research Cambridge Biomedical Research Centre for funding. K.D. is funded as a HSST trainee by NHS Health Education England. M.F. is funded from the BLUEPRINT Grant Code HEALTH-F5-2011-282510 and the BHF Cambridge Centre of Excellence [RE/13/6/30180]. J.R.S. is funded by a MRC CASE Industrial studentship, co-funded by Pfizer. J.D. is a British Heart Foundation Professor, European Research Council Senior Investigator, and National Institute for Health Research (NIHR) Senior Investigator. S.M., S.T, M.H, K.M. and L.D. are supported by the NIHR BioResource-Rare Diseases, which is funded by NIHR. Research in the Ouwehand laboratory is supported by program grants from the NIHR to W.H.O., the European Commission (HEALTH-F2-2012-279233), the British Heart Foundation (BHF) to W.J.A. and D.R. under numbers RP-PG-0310-1002 and RG/09/12/28096 and Bristol Myers-Squibb; the laboratory also receives funding from NHSBT. W.H.O is a NIHR Senior Investigator. The INTERVAL academic coordinating centre receives core support from the UK Medical Research Council (G0800270), the BHF (SP/09/002), the NIHR and Cambridge Biomedical Research Centre, as well as grants from the European Research Council (268834), the European Commission Framework Programme 7 (HEALTH-F2-2012-279233), Merck and Pfizer. DJR and DA were supported by the NIHR Programme ‘Erythropoiesis in Health and Disease’ (Ref. NIHR-RP-PG-0310-1004). N.S. is supported by the Wellcome Trust (Grant Codes WT098051 and WT091310), the EU FP7 (EPIGENESYS Grant Code 257082 and BLUEPRINT Grant Code HEALTH-F5-2011-282510). The INTERVAL study is funded by NHSBT and has been supported by the NIHR-BTRU in Donor Health and Genomics at the University of Cambridge in partnership with NHSBT. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR, the Department of Health of England or NHSBT. D.G. is supported by a “la Caixa”-Severo Ochoa pre-doctoral fellowship

Optimisation of multifractal analysis at the 3D Anderson transition using box-size scaling

We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(alpha), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation. The typical and ensemble averaged scaling laws of the generalised inverse participation ratios are considered. In pursuit of a numerical optimisation of the box-scaling technique we discuss different box-partitioning schemes including cubic and non-cubic boxes, use of periodic boundary conditions to enlarge the system and single and multiple origins for the partitioning grid are also implemented. We show that the numerically most reliable method is to divide a system of linear size L equally into cubic boxes of size l for which L/l is an integer. This method is the least numerically expensive while having a good reliability

Multifractal analysis of the metal-insulator transition in the three-dimensional Anderson model. II. Symmetry relation under ensemble averaging

We study the multifractal analysis (MFA) of electronic wave functions at the localization-delocalization transition in the three-dimensional Anderson model for very large system sizes up to 240(3). The singularity spectrum f(alpha) is numerically obtained using the ensemble average of the scaling law for the generalized inverse participation ratios P-q, employing box-size and system-size scaling. The validity of a recently reported symmetry law [Mirlin , Phys. Rev. Lett. 97, 046803 (2006)] for the multifractal spectrum is carefully analyzed at the metal-insulator transition. The results are compared to those obtained using different approaches, in particular the typical average of the scaling law. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA

İslâm dünyasında bilimin doğuşu

From the 8th century, the center of scientific activities had been the Islamic world in the historical process of scientific activities between the period of Ancient Greece and the Renaissance period. This is the common view of both eastern and western science historians. The success of scientific activities in the regions dominated by the Islam is no coincidence. It is for sure that the civilization created by Islam was much influential on this success. In addition, one cannot deny the efforts of many Muslim and non-Muslim people living in that period, from politicians to scientists. The scientific activities emerging as an inseparable part of the Islamic civilization have an important share in the universal culture as they constituted a step for the development of science and philosophy in the West. Hence, the rise of science in the Islamic world is an inseparable part of the scientific progress.Bilimsel faaliyetlerin tarihsel sürecinde Antik Yunan ve Rönesans dönemi arasındaki geçen zaman diliminde bilimsel etkinliklerin merkezini 8. Yüzyıldan itibaren İslam dünyası oluşturmuştur. Bu tespit hem doğulu hem de batılı bilim tarihçilerinin ortak kanaatidir. İslam dinin hakim olduğu coğrafyada gerçekleşen bilimsel etkinliklerin başarısı tesadüfi değildir. Bu başarının arkasında elbet ki İslam dininin oluşturduğu medeniyetin büyük etkisi vardır. Aynı zaman da o dönemde yaşayan siyasetçilerden bilim adamlarına kadar Müslüman olan ya da olmayan pek çok insanında emeği göz ardı edilemez. İslam uygarlığının ayrılmaz bir parçası olarak ortaya çıkan bilimsel aktiviteler, Batıda bilim ve felsefesinin gelişmesinde bir basamağı oluşturması bakımından evrensel kültür içinde de önemli yere sahiptir. Bu nedenle İslam dünyasında bilimin doğuşu bilimsel gelişmelerinde ayrılmaz bir parçasıdır

Critical parameters from a generalized multifractal analysis at the Anderson transition

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wave function amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wave function statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent nu = 1.58 +/- 0.03

Multifractal finite-size scaling and universality at the Anderson transition

We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L3=1203 and involving nearly 106 independent wave functions have yielded unprecedented precision for the critical disorder Wc=16.530(16.524,16.536) and the critical exponent ν=1.590(1.579,1.602). We find that the multifractal exponents Δq exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [ Phys. Rev. Lett. 105 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point