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Whole-brain proton magnetic resonance spectroscopic imaging (1H-MRSI) is a non-invasive technique for assessing neurochemical distribution in the brain, offering valuable insights into brain functions and neural diseases. It greatly benefits from the improved SNR at ultrahigh field strengths ($\geq$7T). However, 1H-MRSI still faces several challenges, such as long acquisition time and severe signal contaminations from water and lipids. In this study, 2D and 3D short TR/TE 1H-FID-MRSI sequences using rosette trajectories were developed with spatial resolutions of 4.48$\times$4.48 mm$^2$ and 4.48$\times$4.48$\times$4.50 mm$^3$, respectively. Water signals were suppressed using an optimized Five-variable-Angle-gaussian-pulses-with-ShorT-total-duration of 76 ms (FAST) water suppression scheme, and lipid signals were removed using the L2 regularization method. Metabolic maps of major 1H metabolites were obtained within 5:40 min with 16 averages and 1 average for the 2D and 3D acquisitions, respectively. Excellent inter-session reproducibility was shown, with the coefficients of variance (CV) being lower than 6% for N-Acetyle-L-aspartic acid (NAA), Glutamate (Glu), Choline Chloride and glycerophosphocholine (tCho), Creatine and Phosphocreatine (tCr), and Glycine and Myo-inositol (Gly+Ins). To explore the potential of further accelerating the acquisition, compressed sensing was applied retrospectively to the 3D datasets. The structural similarity index (SSIM) remained above 0.85 and 0.8 until $R = 2$ and $R = 3$ for the metabolite maps of Glu, NAA, tCr, and tCho, indicating the possibility for further reduction of acquisition time to around 2min., Comment: 25 pages, 9 figures

Purpose. Proton Magnetic Resonance Spectroscopic Imaging (1H-MRSI) provides non-invasive spectral-spatial mapping of metabolism. However, long-standing problems in whole-brain 1H-MRSI are spectral overlap of metabolite peaks with large lipid signal from scalp, and overwhelming water signal that distorts spectra. Fast and effective methods are needed for high-resolution 1H-MRSI to accurately remove lipid and water signals while preserving the metabolite signal. The potential of supervised neural networks for this task remains unexplored, despite their success for other MRSI processing. Methods. We introduce a deep-learning method based on a modified Y-NET network for water and lipid removal in whole-brain 1H-MRSI. The WALINET (WAter and LIpid neural NETwork) was compared to conventional methods such as the state-of-the-art lipid L2 regularization and Hankel-Lanczos singular value decomposition (HLSVD) water suppression. Methods were evaluated on simulated and in-vivo whole-brain MRSI using NMRSE, SNR, CRLB, and FWHM metrics. Results. WALINET is significantly faster and needs 8s for high-resolution whole-brain MRSI, compared to 42 minutes for conventional HLSVD+L2. Quantitative analysis shows WALINET has better performance than HLSVD+L2: 1) more lipid removal with 41% lower NRMSE, 2) better metabolite signal preservation with 71% lower NRMSE in simulated data, 155% higher SNR and 50% lower CRLB in in-vivo data. Metabolic maps obtained by WALINET in healthy subjects and patients show better gray/white-matter contrast with more visible structural details. Conclusions. WALINET has superior performance for nuisance signal removal and metabolite quantification on whole-brain 1H-MRSI compared to conventional state-of-the-art techniques. This represents a new application of deep-learning for MRSI processing, with potential for automated high-throughput workflow.

Introduction: Altered neurometabolism is an important pathological mechanism in many neurological diseases and brain cancer, which can be mapped non-invasively by Magnetic Resonance Spectroscopic Imaging (MRSI). Advanced MRSI using non-cartesian compressed-sense acquisition enables fast high-resolution metabolic imaging but has lengthy reconstruction times that limits throughput and needs expert user interaction. Here, we present a robust and efficient Deep Learning reconstruction to obtain high-quality metabolic maps. Methods: Fast high-resolution whole-brain metabolic imaging was performed at 3.4 mm$^3$ isotropic resolution with acquisition times between 4:11-9:21 min:s using ECCENTRIC pulse sequence on a 7T MRI scanner. Data were acquired in a high-resolution phantom and 27 human participants, including 22 healthy volunteers and 5 glioma patients. A deep neural network using recurring interlaced convolutional layers with joint dual-space feature representation was developed for deep learning ECCENTRIC reconstruction (Deep-ER). 21 subjects were used for training and 6 subjects for testing. Deep-ER performance was compared to conventional iterative Total Generalized Variation reconstruction using image and spectral quality metrics. Results: Deep-ER demonstrated 600-fold faster reconstruction than conventional methods, providing improved spatial-spectral quality and metabolite quantification with 12%-45% (P<0.05) higher signal-to-noise and 8%-50% (P<0.05) smaller Cramer-Rao lower bounds. Metabolic images clearly visualize glioma tumor heterogeneity and boundary. Conclusion: Deep-ER provides efficient and robust reconstruction for sparse-sampled MRSI. The accelerated acquisition-reconstruction MRSI is compatible with high-throughput imaging workflow. It is expected that such improved performance will facilitate basic and clinical MRSI applications.

The novel technique of frequency-offset separated oscillatory fields (FOSOF) has been originally proposed as a modification to Ramsey's method of separated oscillatory fields. It has recently been employed in precision measurements with atomic beams since it allows for an alternative approach to determine absolute resonance frequencies. We present results from a systematic investigation of the FOSOF technique adapted to a beam of cold neutrons.

MRI, a widespread non-invasive medical imaging modality, is highly sensitive to patient motion. Despite many attempts over the years, motion correction remains a difficult problem and there is no general method applicable to all situations. We propose a retrospective method for motion estimation and correction to tackle the problem of in-plane rigid-body motion, apt for classical 2D Spin-Echo scans of the brain, which are regularly used in clinical practice. Due to the sequential acquisition of k-space, motion artifacts are well localized. The method leverages the power of deep neural networks to estimate motion parameters in k-space and uses a model-based approach to restore degraded images to avoid ''hallucinations''. Notable advantages are its ability to estimate motion occurring in high spatial frequencies without the need of a motion-free reference. The proposed method operates on the whole k-space dynamic range and is moderately affected by the lower SNR of higher harmonics. As a proof of concept, we provide models trained using supervised learning on 600k motion simulations based on motion-free scans of 43 different subjects. Generalization performance was tested with simulations as well as in-vivo. Qualitative and quantitative evaluations are presented for motion parameter estimations and image reconstruction. Experimental results show that our approach is able to obtain good generalization performance on simulated data and in-vivo acquisitions. We provide a Python implementation at https://gitlab.unige.ch/Oscar.Dabrowski/sismik_mri/.

Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high-resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, the Marchenko-Pastur principal component analysis (MP-PCA) based denoising and the low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential and impact on preclinical 14.1T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte-Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio SNR while preserving noise properties in each spectrum for both in vivo and Monte-Carlo datasets. Relative metabolite concentrations were not significantly altered by either methods and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted on lower concentrated metabolites. Our study provided a framework on how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care especially for low-concentrated metabolites., Comment: Brayan Alves and Dunja Simicic are joint first authors. Currently in revision for NMR in Biomedicine

Magnetic resonance spectroscopic imaging (MRSI) enables the simultaneous non-invasive acquisition of MR spectra from multiple spatial locations inside the brain. While 1H-MRSI is increasingly used in the human brain, it is not yet widely applied in the preclinical settings, mostly because of difficulties specifically related to very small nominal voxel size in the rodent brain and low concentration of brain metabolites, resulting in low signal-to-noise ratio SNR. In this context, we implemented a free induction decay 1H-MRSI sequence (1H-FID-MRSI) in the rat brain at 14.1T. We combined the advantages of 1H-FID-MRSI with the ultra-high magnetic field to achieve higher SNR, coverage and spatial resolution in the rodent brain, and developed a custom dedicated processing pipeline with a graphical user interface: MRS4Brain toolbox. LCModel fit, using the simulated metabolite basis-set and in-vivo measured MM, provided reliable fits for the data at acquisition delays of 1.3 and 0.94 ms. The resulting Cram\'er-Rao lower bounds were sufficiently low (<30%) for eight metabolites of interest, leading to highly reproducible metabolic maps. Similar spectral quality and metabolic maps were obtained between 1 and 2 averages, with slightly better contrast and brain coverage due to increased SNR in the latter case. Furthermore, the obtained metabolic maps were accurate enough to confirm the previously known brain regional distribution of some metabolites. The acquisitions proved high reproducibility over time. We demonstrated that the increased SNR and spectral resolution at 14.1T can be translated into high spatial resolution in 1H-FID-MRSI of the rat brain in 13 minutes, using the sequence and processing pipeline described herein. High-resolution 1H-FID-MRSI at 14.1T provided reproducible and high-quality metabolic mapping of brain metabolites with significantly reduced technical limitations., Comment: Dunja Simicic and Brayan Alves are joint first authors

We investigate the response of a Ramsey-type experiment on an additional oscillating magnetic field. This superimposed field is oriented in the same direction as the static main magnetic field and causes a modulation of the original Larmor spin precession frequency. The observable magnitude of this modulation reduces at higher frequencies of the oscillating field. It disappears completely if the interaction time of the particles matches the oscillation period, which we call resonant cancellation. We present an analytical approach that describes the effect and compare it to a measurement using a monochromatic cold neutron beam.

The Gemini High-resolution Optical SpecTrograph (GHOST) is the newest high resolution spectrograph to be developed for a large aperture telescope, recently deployed and commissioned at the Gemini-South telescope. In this paper, we present the first science results from the GHOST spectrograph taking during its commissioning runs. We have observed the bright metal-poor benchmark star HD 122563, along with two stars in the ultra faint dwarf galaxy, Ret II, one of which was previously identified as a candidate member, but did not have a previous detailed chemical abundance analysis. This star (GDR3 0928) is found to be a bona fide member of Ret II, and from a spectral synthesis analysis, it is also revealed to be a CEMP-r star, with significant enhancements in the several light elements (C, N, O, Na, Mg, and Si), in addition to featuring an r-process enhancement like many other Ret II stars. The light-element enhancements in this star resemble the abundance patterns seen in the CEMP-no stars of other ultra faint dwarf galaxies, and are thought to have been produced by an independent source from the r-process. These unusual abundance patterns are thought to be produced by faint supernovae, which may be produced by some of the earliest generations of stars., Comment: 23 pages, 9 figures, 7 tables, submitted to the AAS Journals

A novel method for fast and high-resolution metabolic imaging, called ECcentric Circle ENcoding TRajectorIes for Compressed sensing (ECCENTRIC), has been developed and implemented at 7 Tesla MRI. ECCENTRIC is a non-Cartesian spatial-spectral encoding method optimized to accelerate magnetic resonance spectroscopic imaging (MRSI) with high signal-to-noise at ultra-high field. The approach provides flexible and random ($k,t$) sampling without temporal interleaving to improve spatial response function and spectral quality. ECCENTRIC needs low gradient amplitudes and slew-rates that reduces electrical, mechanical and thermal stress of the scanner hardware, and is robust to timing imperfection and eddy-current delays. Combined with a model-based low-rank reconstruction, this approach enables simultaneous imaging of up to 14 metabolites over the whole-brain at 2-3mm isotropic resolution in 4-10 minutes. In healthy volunteers ECCENTRIC demonstrated unprecedented spatial mapping of fine structural details of human brain neurochemistry. This innovative tool introduces a novel approach to neuroscience, providing new insights into the exploration of brain activity and physiology., Comment: 21 pages, 6 figures,3 tables, 4 pages supplementary material

Incomplete cancellation of collinear antiparallel spins gives rise to ferrimagnetism. Even if the oppositely polarized spins are owing to the equal number of a single magnetic element having the same valence state, in principle, a ferrimagnetic state can still arise from the crystallographic inequivalence of the host ions. However, experimental identification of such a state as ferrimagnetic is not straightforward because of the tiny magnitude expected for M and the requirement for a sophisticated technique to differentiate similar magnetic sites. We report a synchrotron-based resonant x-ray investigation at the Fe L2,3 edges on an epitaxial film of CaFe2O4, which exhibits two magnetic phases with similar energies. We find that while one phase of CaFe2O4 is antiferromagnetic, the other one is ferrimagnetic with an antiparallel arrangement of an equal number of spins between two distinct crystallographic sites with very similar local coordination environments. Our results further indicate two distinct origins of an overall minute M; one is intrinsic, from distinct Fe3+ sites, and the other one is extrinsic, arising from defective Fe2+ likely forming weakly-coupled ferrimagnetic clusters. These two origins are uncorrelated and have very different coercive fields. Hence, this work provides a direct experimental demonstration of ferrimagnetism solely due to crystallographic inequivalence of the Fe3+ as the origin of the weak M of CaFe2O4., Comment: 14 pages, 8 figures

A new technique for detection of slow neutrons with gaseous detectors using ultra-thin layers with 10B atoms is presented. The reaction between a thermal neutron and a 10B atom releases 2 secondary particles, namely a 7Li ion and an alpha particle, which due to momentum conservation are emitted in opposite directions, along the same line (back to back). Current boron coated neutron detectors are equipped with 10B films with thicknesses of several micrometers, deposited on very thick substrate plates. However, since the ranges of the 7Li ion and the alpha particle are of few micrometeres in most materials, one of these particles is always lost in the 10B layer or substrate. As such, these detectors lose the ability to reconstruct the reaction line of action and to precisely determine the neutron position, as only one of the two secondary particles track can be measured. With the technique now presented, the sum of the 10B layer and the substrate thicknesses is small enough to allow for both secondary particles to escape and ionize the gas in opposite sides of the 10B converter foil. Independent readout structures, one on each side of the 10B converter foil, detect each secondary particle and determine its track centroid and the deposited energy. Since the two secondary particles are emitted back to back, the neutron position can be obtained by combining the information recorded by the two readout structures. Through GEANT4 simulations, we verified that the spatial resolution can be significantly improved: our results show that, by using a B4C layer with a thickness of 1 micron on a 0.9 micron Mylar substrate, the spatial resolution can by improved by a factor of 8, compared to conventional detectors with thick 10B detection layers.

Neutron guides are used to transport slow neutrons from sources to experiments. Conventional neutron supermirror guides use alternating thin layers based on nickel and titanium. Due to the magnetic properties of nickel, their neutron reflection properties are spin-dependent, in particular when exposed to high magnetic fields. Motivated by the requirements of precision experiments on neutron beta decay, we present novel supermirrors based on copper and titanium, which preserve the neutron beam polarization. These show excellent reflectivity and prove to be very stable even when exposed to high temperatures.

The PERC (Proton and Electron Radiation Channel) facility is currently under construction at the research reactor FRM II, Garching. It will serve as an intense and clean source of electrons and protons from neutron beta decay for precision studies. It aims to contribute to the determination of the Cabibbo-Kobayashi-Maskawa quark-mixing element $V_{ud}$ from neutron decay data and to search for new physics via new effective couplings. PERC's central component is a 12m long superconducting magnet system. It hosts an 8m long decay region in a uniform field. An additional high-field region selects the phase space of electrons and protons which can reach the detectors and largely improves systematic uncertainties. We discuss the design of the magnet system and the resulting properties of the magnetic field., Comment: Proceedings of the International Workshop on Particle Physics at Neutron Sources PPNS 2018, Grenoble, France, May 24-26, 2018

We introduce the 4-metre Multi-Object Spectroscopic Telescope (4MOST), a new high-multiplex, wide-field spectroscopic survey facility under development for the four-metre-class Visible and Infrared Survey Telescope for Astronomy (VISTA) at Paranal. Its key specifications are: a large field of view (FoV) of 4.2 square degrees and a high multiplex capability, with 1624 fibres feeding two low-resolution spectrographs ($R = \lambda/\Delta\lambda \sim 6500$), and 812 fibres transferring light to the high-resolution spectrograph ($R \sim 20\,000$). After a description of the instrument and its expected performance, a short overview is given of its operational scheme and planned 4MOST Consortium science; these aspects are covered in more detail in other articles in this edition of The Messenger. Finally, the processes, schedules, and policies concerning the selection of ESO Community Surveys are presented, commencing with a singular opportunity to submit Letters of Intent for Public Surveys during the first five years of 4MOST operations., Comment: Part of the 4MOST issue of The Messenger, published in preparation of 4MOST Community Workshop, see http://www.eso.org/sci/meetings/2019/4MOST.html

The High Efficiency and Resolution Multi Element Spectrograph, HERMES, is a facility-class optical spectrograph for the Anglo-Australian Telescope (AAT). It is designed primarily for Galactic Archaeology, the first major attempt to create a detailed understanding of galaxy formation and evolution by studying the history of our own galaxy, the Milky Way. The goal of the GALAH survey is to reconstruct the mass assembly history of the Milky Way through a detailed chemical abundance study of one million stars. The spectrograph is based at the AAT and is fed by the existing 2dF robotic fiber positioning system. The spectrograph uses volume phase holographic gratings to achieve a spectral resolving power of 28,000 in standard mode and also provides a high-resolution mode ranging between 40,000 and 50,000 using a slit mask. The GALAH survey requires an SNR greater than 100 for a star brightness of V ?= 14 in an exposure time of one hour. The total spectral coverage of the four channels is about 100 nm between 370 and 1000 nm for up to 392 simultaneous targets within the 2-degree field of view. HERMES has been commissioned over three runs, during bright time in October, November, and December 2013, in parallel with the beginning of the GALAH pilot survey, which started in November 2013. We present the first-light results from the commissioning run and the beginning of the GALAH survey, including performance results such as throughput and resolution, as well as instrument reliability., Comment: 22 pages, 28 figures. AAT, 2dF, HERMES

Optical observations of the type IIb SN 2013df from a few days to about 250 days after explosion are presented. These observations are complemented with UV photometry taken by \textit{SWIFT} up to 60 days post-explosion. The double-peak optical light curve is similar to those of SNe 1993J and 2011fu although with different decline and rise rates. From the modelling of the bolometric light curve, we have estimated that the total mass of synthesised $^{56}$Ni in the explosion is $\sim0.1$ M$_{\odot}$, while the ejecta mass is $0.8-1.4$ M$_{\odot}$ and the explosion energy $0.4-1.2 \times 10^{51}$erg. In addition, we have estimated a lower limit to the progenitor radius ranging from $64-169$ $R_{\odot}$. The spectral evolution indicates that SN 2013df had a hydrogen envelope similar to SN 1993J ($\sim 0.2$ M$_{\odot}$). The line profiles in nebular spectra suggest that the explosion was asymmetric with the presence of clumps in the ejecta, while the [O\,{\sc i}] $\lambda$$\lambda$$6300$, $6364$ luminosities, may indicate that the progenitor of SN 2013df was a relatively low mass star ( $\sim 12-13 $ M$_{\odot}$)., Comment: 18 pages, 11 figures, 9 tables, accepted for publication in MNRAS

Considering the adjacent spin operators $S^z_jS^z_{j+1}$ and $S^-_jS^-_{j+1}$ in the S=1/2 Heisenberg chain, we give a determinant representation of their form factors. The dynamical structure factors of the respective operators are computed over the whole Brillouin zone in several magnetic fields and the resulting signal is analyzed in terms of excitation types. Among other results, we find that the $S^z_jS^z_{j+1}$ dynamical structure factor carries a large weight of the 4-spinon excitations which are distinguishable from the 2-spinon signal because they are located outside the 2-spinon spectrum., Comment: 16 pages

The interplay of quantum statistics, interactions and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe Ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential and either the total chemical potential or a fixed number of particles, allowing to quantify the full crossover behaviour of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction., Comment: 17 pages, 8 figures

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect Resonant Inelastic X-ray Scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into *two spinon* states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type., Comment: 4 pages, 4 figures

We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities and local density correlation numerically as a function of all physical parameters (interaction, temperature and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single-component, Lieb-Liniger gas, nonmonotonic behaviour of the local density correlation as a function of temperature is observed., Comment: 4 pages, 6 figures

We analyze nuclear spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction ("J-coupling" in NMR). Our analysis shows that the Overhauser field generated by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson series expansion and a generalized master equation approach, that for a nuclear spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount on the order of the inverse number of nuclear spins interacting with the electron., Comment: 11 pages, 3 figures

In this article we review our work on the dynamics and decoherence of electron and hole spins in single and double quantum dots. The first part, on electron spins, focuses on decoherence induced via the hyperfine interaction while the second part covers decoherence and relaxation of heavy-hole spins due to spin-orbit interaction as well as the manipulation of heavy-hole spin using electric dipole spin resonance., Comment: 19 pages, 4 figures, review article to appear in a book on semiconductor quantum bits, edited by O. Benson and F. Henneberger, published by Pan Stanford Publishing

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear spin bath. Due to the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of ~pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit., Comment: Main text: 4 pages, 3 figures, Supplementary material: 2 pages, 3 figures

We review our investigation of the spin dynamics for two electrons confined to a double quantum dot under the influence of the hyperfine interaction between the electron spins and the surrounding nuclei. Further we propose a scheme to narrow the distribution of difference in polarization between the two dots in order to suppress hyperfine induced decoherence., Comment: 12 pages, 3 figures; Presented as plenary talk at the annual DPG meeting 2006, Dresden (to appear in Advances in Solid State Physics vol. 46, 2006)

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the $\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ket{\uparrow\downarrow}$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity., Comment: v1:9 pages, 1 figure; v2: 13 pages, 2 figures, added section on measurement, to appear in Phys. Rev. B