Effect of coupling asymmetry on mean-field solutions of direct and inverse Sherrington-Kirkpatrick model

We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations. The three theories include the first and second order Plefka expansions, referred to as naive mean field (nMF) and TAP, respectively, and a mean field theory which is exact for fully asymmetric couplings. We call the last of these simply MF theory. We show that for the direct problem, nMF performs worse than the other two approximations, TAP outperforms MF when the coupling matrix is nearly symmetric, while MF works better when it is strongly asymmetric. For the inverse problem, MF performs better than both TAP and nMF, although an ad hoc adjustment of TAP can make it comparable to MF. For high temperatures the performance of TAP and MF approach each other

Development of novel 2D and 3D correlative microscopy to characterise the composition and multiscale structure of suspended sediment aggregates.

Suspended cohesive sediments form aggregates or 'flocs' and are often closely associated with carbo, nutrients, pathogens and pollutants, which makes understanding their composition, transport and fate highly desirable. Accurate prediction of floc behaviour requires the quantification of 3-dimensional (3D) properties (size, shoe and internal structure) that span several scales (i.e. nanometre [nm] to millimetre [mm]-scale). Traditional techniques (optical cameras and electron microscopy [EM]), however, can only provide 2-dimensional (2D) simplifications of 3D floc geometries. Additionally, the existence of a resolution gap between conventional optical microscopy (COM) and transmission EM (TEM) prevents an understanding of how floc nm-scale constituents and internal structure influence mm-scale floc properties. Here, we develop a novel correlative imaging workflow combining 3D X-ray micro-computed tomography (μCT), 3D focused ion beam nanotomography (FIB-nt) and 2D scanning EM (SEM) and TEM (STEM) which allows us to stabilise, visualise and quantify the composition and multi scale structure of sediment flocs for the first time. This new technique allowed the quantification of 3D floc geometries, the identification of individual floc components (e.g., clays, non-clay minerals and bacteria), and characterisation of particle-particle and structural associations across scales. This novel dataset demonstrates the truly complex structure of natural flocs at multiple scales. The integration of multiscale, state-of-the-art instrumentation/techniques offers the potential to generate fundamental new understanding of floc composition, structure and behaviour

Three-dimensional super-resolution microscopy of the inactive X chromosome territory reveals a collapse of its active nuclear compartment harboring distinct Xist RNA foci

Background: A Xist RNA decorated Barr body is the structural hallmark of the compacted inactive X territory in female mammals. Using super resolution three-dimensional structured illumination microscopy (3D-SIM) and quantitative image analysis, we compared its ultrastructure with active chromosome territories (CTs) in human and mouse somatic cells, and explored the spatio-temporal process of Barr body formation at onset of inactivation in early differentiating mouse embryonic stem cells (ESCs). Results: We demonstrate that all CTs are composed of structurally linked chromatin domain clusters (CDCs). In active CTs the periphery of CDCs harbors low-density chromatin enriched with transcriptionally competent markers, called the perichromatin region (PR). The PR borders on a contiguous channel system, the interchromatin compartment (IC), which starts at nuclear pores and pervades CTs. We propose that the PR and macromolecular complexes in IC channels together form the transcriptionally permissive active nuclear compartment (ANC). The Barr body differs from active CTs by a partially collapsed ANC with CDCs coming significantly closer together, although a rudimentary IC channel system connected to nuclear pores is maintained. Distinct Xist RNA foci, closely adjacent to the nuclear matrix scaffold attachment factor-A (SAF-A) localize throughout Xi along the rudimentary ANC. In early differentiating ESCs initial Xist RNA spreading precedes Barr body formation, which occurs concurrent with the subsequent exclusion of RNA polymerase II (RNAP II). Induction of a transgenic autosomal Xist RNA in a male ESC triggers the formation of an `autosomal Barr body' with less compacted chromatin and incomplete RNAP II exclusion. Conclusions: 3D-SIM provides experimental evidence for profound differences between the functional architecture of transcriptionally active CTs and the Barr body. Basic structural features of CT organization such as CDCs and IC channels are however still recognized, arguing against a uniform compaction of the Barr body at the nucleosome level. The localization of distinct Xist RNA foci at boundaries of the rudimentary ANC may be considered as snap-shots of a dynamic interaction with silenced genes. Enrichment of SAF-A within Xi territories and its close spatial association with Xist RNA suggests their cooperative function for structural organization of Xi

Advances in shape measurement in the digital world

The importance of particle shape in terms of its effects on the behaviour of powders and other particulate systems has long been recognised, but particle shape information has been rather difficult to obtain and use until fairly recently, unlike its better-known counterpart, particle size. However, advances in computing power and 3D image acquisition and analysis techniques have resulted in major progress being made in the measurement, description and application of particle shape information in recent years. Because we are now in a digital era, it is fitting that many of these advanced techniques are based on digital technology. This review article aims to trace the development of these new techniques, highlight their contributions to both academic and practical applications, and present a perspective for future developments