Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning

Approximation and inference methods for stochastic biochemical kinetics-a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics

Model Reduction for the Chemical Master Equation: an Information-Theoretic Approach

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, the Linear Mapping Approximation and state-space lumping. Despite the success of these techniques, they appear to be rather disparate and at present no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimising a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimisation approaches. In addition we derive general expressions for the propensities of a reduced system that generalise those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system and a genetic oscillator

Next-to-leading order multi-leg processes for the Large Hadron Collider

In this talk we discuss recent progress concerning precise predictions for the LHC. We give a status report of three applications of our method to deal with multi-leg one-loop amplitudes: The interference term of Higgs production by gluon- and weak boson fusion to order O(alpha^2 alpha_s^3) and the next-to-leading order corrections to the two processes pp -> ZZ jet and u ubar -> d dbar s sbar. The latter is a subprocess of the four jet cross section at the LHC.Comment: 6 pages, 5 figures. Talk given at the 8th international Symposium on Radiative Corrections (RADCOR), October 1-5 2007, Florence, Ital

Effects of random alloy disorder, shape deformation, and substrate misorientation on the exciton lifetime and fine structure splitting of GaAs/AlxGa1-xAs(111) quantum dots

Using atomistic, million-atom screened pseudopotential theory together with configuration interaction, as well as atomically resolved structures based on experimental characterization, we perform numerical calculations on self-assembled GaAs/AlxGa1-xAs(111) quantum dots that we compare with our experimental data. We show that random alloy disorder in the barrier can cause a symmetry breaking at the single-particle level (distortions of wave functions and lifting of degeneracies) which translates into the appearance of a nonzero exciton fine structure splitting (FSS) at the many-body level. Nevertheless, our results indicate that varying the concentration of aluminum in the random alloyed barrier allows simultaneous tuning of the exciton fine structure splitting and emission wavelength without altering its radiative lifetime tau approximate to 200 ps. Additionally, the optical properties of these quantum dots are predicted to be very robust against both symmetric and asymmetric shape elongation (with FSS 2.2 mu eV), rendering postselection less essential under well-controlled growth conditions. On the other hand, the growth on miscut substrates introduces a structural anisotropy along the quantization axis to which the system is very sensitive: the FSS ranges between 5 and 50 mu eV while the radiative lifetime of the transition is increased up to tau = 400 ps. The numerical results for the FSS are in perfect agreement with our experimental measurements which give FSS = 10 +/- 9 mu eV for 2 degrees miscut angle at x = 0.15

Comparison of Bond Character in Hydrocarbons and Fullerenes

We present a comparison of the bond polarizabilities for carbon-carbon bonds in hydrocarbons and fullerenes, using two different models for the fullerene Raman spectrum and the results of Raman measurements on ethane and ethylene. We find that the polarizabilities for single bonds in fullerenes and hydrocarbons compare well, while the double bonds in fullerenes have greater polarizability than in ethylene.Comment: 7 pages, no figures, uses RevTeX. (To appear in Phys. Rev. B.

Picosecond Nonlinear Relaxation of Photoinjected Carriers in a Single GaAs/AlGaAs Quantum Dot

Photoemission from a single self-organized GaAs/AlGaAs quantum dot (QD) is temporally resolved with picosecond time resolution. The emission spectra consisting of the multiexciton structures are observed to depend on the delay time and the excitation intensity. Quantitative agreement is found between the experimental data and the calculation based on a model which characterizes the successive relaxation of multiexcitons. Through the analysis we can determine the carrier relaxation time as a function of population of photoinjected carriers. Enhancement of the intra-dot carrier relaxation is demonstrated to be due to the carrier-carrier scattering inside a single QD.Comment: 4 pages, 4 figures, to be published in Phys. Rev. B, Rapid

New Data on the In Vitro Activity of Fenticonazole against Fluconazole-Resistant Candida Species.

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Risk factors for recurrence in patients with Clostridium difficile infection due to 027 and non-027 ribotypes

Objectives: Our objective was to evaluate factors associated with recurrence in patients with 027+ and 027– Clostridium difficile infection (CDI). Methods: Patients with CDI observed between January and December 2014 in six hospitals were consecutively included in the study. The 027 ribotype was deduced by the presence of tcdB, tcdB, cdt genes and the deletion Δ117 in tcdC (Xpert® C. difficile/Epi). Recurrence was defined as a positive laboratory test result for C. difficile more than 14 days but within 8 weeks after the initial diagnosis date with reappearance of symptoms. To identify factors associated with recurrence in 027+ and 027– CDI, a multivariate analysis was performed in each patient group. Subdistributional hazard ratios (sHRs) and 95% confidence intervals (95%CIs) were calculated. Results: Overall, 238 patients with 027+ CDI and 267 with 027– CDI were analysed. On multivariate analysis metronidazole monotherapy (sHR 2.380, 95%CI 1.549–3.60, p <0.001) and immunosuppressive treatment (sHR 3.116, 95%CI 1.906–5.090, p <0.001) were factors associated with recurrence in patients with 027+ CDI. In this patient group, metronidazole monotherapy was independently associated with recurrence in both mild/moderate (sHR 1.894, 95%CI 1.051–3.410, p 0.033) and severe CDI (sHR 2.476, 95%CI 1.281–4.790, p 0.007). Conversely, non-severe disease (sHR 3.704, 95%CI 1.437–9.524, p 0.007) and absence of chronic renal failure (sHR 16.129, 95%CI 2.155–125.000, p 0.007) were associated with recurrence in 027– CDI. Conclusions: Compared to vancomycin, metronidazole monotherapy appears less effective in curing CDI without relapse in the 027+ patient group, independently of disease severity