Cooling Fermions in an Optical Lattice by Adiabatic Demagnetization

The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'{e}el temperature. However, reaching this temperature in the lab has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system, and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the $SU(2)$ symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the $SU(2)$ symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard Model.Comment: References adde

MINE - A Game for the Analysis of Regional Water Policies in Open-Pit Lignite Mining Areas

The game MINE has been developed for the analysis of regional water policies in open-pit lignite mining areas. It is implemented for a GDR test area. The purpose of the game is above all to teach decision makers and their staff in mining regions in order to get a better understanding of the complex interrelated socio-economic processes with respect to water management in such regions. The game is designed to be played by five groups of players representing municipal and industrial water supply, agriculture, environmental protection and lignite mining. Two versions are available, one in BASIC for simple micro-computers as the Apple II combined with a gaming board, another one in FORTRAN for the VAX or ALTOS combined with sophisticated color graphics. The paper describes the game, its practical application and first experiences in playing the game

A System of Subroutines For Iteratively Reweighted Least Squares Computations

A description of a system of subroutines to compute solutions to the iteratively reweighted least squares problem is presented. The weights are determined from the data and linear fit and are computed as functions of the scaled residuals. Iteratively reweighted least squares is a part of robust statistics where "robustness" means relative insensitivity to moderate departures from assumptions. The software for iteratively reweighted least squares is cast as semi-portable Fortran code whose performance is unaffected (in the sense that performance will not be degraded) by the computer or operating-system environment in which it is used. An [ell sub1] start and an [ell sub2] start are provided. Eight weight functions, a numerical rank determination, convergence criterion, and a stem-and-leaf display are included.

Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging

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On the potential for mapping apparent neural soma density via a clinically viable diffusion MRI protocol

Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advances in measurement technology and modelling efforts, a clinically viable technique that reveals salient features of grey matter microstructure, such as the density of quasi-spherical cell bodies and quasi-cylindrical cell projections, is an exciting prospect. As a step towards capturing the microscopic architecture of grey matter in clinically feasible settings, this work uses a biophysical model that is designed to disentangle the diffusion signatures of spherical and cylindrical structures in the presence of orientation heterogeneity, and takes advantage of B-tensor encoding measurements, which provide additional sensitivity compared to standard single diffusion encoding sequences. For the fast and robust estimation of microstructural parameters, we leverage recent advances in machine learning and replace conventional fitting techniques with an artificial neural network that fits complex biophysical models within seconds. Our results demonstrate apparent markers of spherical and cylindrical geometries in healthy human subjects, and in particular an increased volume fraction of spherical compartments in grey matter compared to white matter. We evaluate the extent to which spherical and cylindrical geometries may be interpreted as correlates of neural soma and neural projections, respectively, and quantify parameter estimation errors in the presence of various departures from the modelling assumptions. While further work is necessary to translate the ideas presented in this work to the clinic, we suggest that biomarkers focussing on quasi-spherical cellular geometries may be valuable for the enhanced assessment of neurodevelopmental disorders and neurodegenerative diseases

Multi-compartment microscopic diffusion imaging

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay

Can T-spectroscopy resolve submicrometer axon diameters?

The microscopic geometry of white matter carries rich information about brain function in health and disease. A key challenge for medical imaging is to estimate microstructural features noninvasively. One important parameter is the axon diameter, which correlates with the conduction time delay of action potentials and is affected by various neurological disorders. Diffusion magnetic resonance (MR) experiments are the method of choice today when we aim to recover the axon diameter distribution, although the technique requires very high gradient strengths in order to assess nerve fibers with one micrometer or less in diameter. In practice in-vivo brain imaging is only sensitive to the largest axons, not least due to limitations in the human physiology which tolerates only moderate gradient strengths. This work studies, from a theoretical perspective, the feasibility of T-spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T -weighted signal, which is based on a surface-to-volume ratio approximation of the Bloch-Torrey equation. Under a certain regime of bulk and surface relaxation coefficients, our simulation results suggest that it might be possible to reveal axons smaller than one micrometer in diameter. © 2013 Springer-Verlag

Bayesian image quality transfer

Image quality transfer (IQT) aims to enhance clinical images of relatively low quality by learning and propagating high-quality structural information from expensive or rare data sets. However,the original framework gives no indication of confidence in its output,which is a significant barrier to adoption in clinical practice and downstream processing. In this article,we present a general Bayesian extension of IQT which enables efficient and accurate quantification of uncertainty,providing users with an essential prediction of the accuracy of enhanced images. We demonstrate the efficacy of the uncertainty quantification through super-resolution of diffusion tensor images of healthy and pathological brains. In addition,the new method displays improved performance over the original IQT and standard interpolation techniques in both reconstruction accuracy and robustness to anomalies in input images

Tractographic and Microstructural Analysis of the Dentato-Rubro-Thalamo-Cortical Tracts in Children Using Diffusion MRI

The dentato-rubro-thalamo-cortical tract (DRTC) is the main outflow pathway of the cerebellum, contributing to a finely balanced corticocerebellar loop involved in cognitive and sensorimotor functions. Damage to the DRTC has been implicated in cerebellar mutism syndrome seen in up to 25% of children after cerebellar tumor resection. Multi-shell diffusion MRI (dMRI) combined with quantitative constrained spherical deconvolution tractography and multi-compartment spherical mean technique modeling was used to explore the frontocerebellar connections and microstructural signature of the DRTC in 30 healthy children. The highest density of DRTC connections were to the precentral (M1) and superior frontal gyri (F1), and from cerebellar lobules I-IV and IX. The first evidence of a topographic organization of anterograde projections to the frontal cortex at the level of the superior cerebellar peduncle (SCP) is demonstrated, with streamlines terminating in F1 lying dorsomedially in the SCP compared to those terminating in M1. The orientation dispersion entropy of DRTC regions appears to exhibit greater contrast than that shown by fractional anisotropy. Analysis of a separate reproducibility cohort demonstrates good consistency in the dMRI metrics described. These novel anatomical insights into this well-studied pathway may prove to be of clinical relevance in the surgical resection of cerebellar tumors

Quantitative mapping of the per-axon diffusion coefficients in brain white matter.

This article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per-axon or microscopic diffusion coefficients