HYDRA: Hybrid Deep Magnetic Resonance Fingerprinting

Purpose: Magnetic resonance fingerprinting (MRF) methods typically rely on dictio-nary matching to map the temporal MRF signals to quantitative tissue parameters. Such approaches suffer from inherent discretization errors, as well as high computational complexity as the dictionary size grows. To alleviate these issues, we propose a HYbrid Deep magnetic ResonAnce fingerprinting approach, referred to as HYDRA. Methods: HYDRA involves two stages: a model-based signature restoration phase and a learning-based parameter restoration phase. Signal restoration is implemented using low-rank based de-aliasing techniques while parameter restoration is performed using a deep nonlocal residual convolutional neural network. The designed network is trained on synthesized MRF data simulated with the Bloch equations and fast imaging with steady state precession (FISP) sequences. In test mode, it takes a temporal MRF signal as input and produces the corresponding tissue parameters. Results: We validated our approach on both synthetic data and anatomical data generated from a healthy subject. The results demonstrate that, in contrast to conventional dictionary-matching based MRF techniques, our approach significantly improves inference speed by eliminating the time-consuming dictionary matching operation, and alleviates discretization errors by outputting continuous-valued parameters. We further avoid the need to store a large dictionary, thus reducing memory requirements. Conclusions: Our approach demonstrates advantages in terms of inference speed, accuracy and storage requirements over competing MRF method

Measurement does not always aid state discrimination

We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to always assign the most commonly occurring state. Conditions which describe such sets of states have been derived.Comment: 3 page

Minimum-error discrimination between symmetric mixed quantum states

We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in the basis of the eigenstates of the symmetry operator.Comment: 10 page

Robust formation of morphogen gradients

We discuss the formation of graded morphogen profiles in a cell layer by nonlinear transport phenomena, important for patterning developing organisms. We focus on a process termed transcytosis, where morphogen transport results from binding of ligands to receptors on the cell surface, incorporation into the cell and subsequent externalization. Starting from a microscopic model, we derive effective transport equations. We show that, in contrast to morphogen transport by extracellular diffusion, transcytosis leads to robust ligand profiles which are insensitive to the rate of ligand production

IRAS versus POTENT Density Fields on Large Scales: Biasing and Omega

The galaxy density field as extracted from the IRAS 1.2 Jy redshift survey is compared to the mass density field as reconstructed by the POTENT method from the Mark III catalog of peculiar velocities. The reconstruction is done with Gaussian smoothing of radius 12 h^{-1}Mpc, and the comparison is carried out within volumes of effective radii 31-46 h^{-1}Mpc, containing approximately 10-26 independent samples. Random and systematic errors are estimated from multiple realizations of mock catalogs drawn from a simulation that mimics the observed density field in the local universe. The relationship between the two density fields is found to be consistent with gravitational instability theory in the mildly nonlinear regime and a linear biasing relation between galaxies and mass. We measure beta = Omega^{0.6}/b_I = 0.89 \pm 0.12 within a volume of effective radius 40 h^{-1}Mpc, where b_I is the IRAS galaxy biasing parameter at 12 h^{-1}Mpc. This result is only weakly dependent on the comparison volume, suggesting that cosmic scatter is no greater than \pm 0.1. These data are thus consistent with Omega=1 and b_I\approx 1. If b_I>0.75, as theoretical models of biasing indicate, then Omega>0.33 at 95% confidence. A comparison with other estimates of beta suggests scale-dependence in the biasing relation for IRAS galaxies.Comment: 35 pages including 10 figures, AAS Latex, Submitted to The Astrophysical Journa

Partial penetrance facilitates developmental evolution in bacteria

Development normally occurs similarly in all individuals within an isogenic population, but mutations often affect the fates of individual organisms differently. This phenomenon, known as partial penetrance, has been observed in diverse developmental systems. However, it remains unclear how the underlying genetic network specifies the set of possible alternative fates and how the relative frequencies of these fates evolve. Here we identify a stochastic cell fate determination process that operates in Bacillus subtilis sporulation mutants and show how it allows genetic control of the penetrance of multiple fates. Mutations in an intercompartmental signalling process generate a set of discrete alternative fates not observed in wild-type cells, including rare formation of two viable 'twin' spores, rather than one within a single cell. By genetically modulating chromosome replication and septation, we can systematically tune the penetrance of each mutant fate. Furthermore, signalling and replication perturbations synergize to significantly increase the penetrance of twin sporulation. These results suggest a potential pathway for developmental evolution between monosporulation and twin sporulation through states of intermediate twin penetrance. Furthermore, time-lapse microscopy of twin sporulation in wild-type Clostridium oceanicum shows a strong resemblance to twin sporulation in these B. subtilis mutants. Together the results suggest that noise can facilitate developmental evolution by enabling the initial expression of discrete morphological traits at low penetrance, and allowing their stabilization by gradual adjustment of genetic parameters