Markerless attenuation correction for carotid MRI surface receiver coils in combined PET/MR imaging.

The purpose of the study was to evaluate the effect of attenuation of MR coils on quantitative carotid PET/MR exams. Additionally, an automated attenuation correction method for flexible carotid MR coils was developed and evaluated.The attenuation of the carotid coil was measured by imaging a uniform water phantom injected with 37 MBq of 18F-FDG in a combined PET/MR scanner for 24 min with and without the coil. In the same session, an ultra-short echo time (UTE) image of the coil on top of the phantom was acquired. Using a combination of rigid and non-rigid registration, a CT-based attenuation map was registered to the UTE image of the coil for attenuation and scatter correction. After phantom validation, the effect of the carotid coil attenuation and the attenuation correction method were evaluated in five subjects.Phantom studies indicated that the overall loss of PET counts due to the coil was 6.3% with local region-of-interest (ROI) errors reaching up to 18.8%. Our registration method to correct for attenuation from the coil decreased the global error and local error (ROI) to 0.8% and 3.8%, respectively. The proposed registration method accurately captured the location and shape of the coil with a maximum spatial error of 2.6 mm. Quantitative analysis in human studies correlated with the phantom findings, but was dependent on the size of the ROI used in the analysis.MR coils result in significant error in PET quantification and thus attenuation correction is needed. The proposed strategy provides an operator-free method for attenuation and scatter correction for a flexible MRI carotid surface coil for routine clinical use

Stability of closed gaps for the alternating Kronig-Penney Hamiltonian

We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions. \ua9 2015, Springer Basel

Automatic Verification of Finite Precision Implementations of Linear Controllers

We consider the problem of verifying finite precision implementation of linear time-invariant controllers against mathematical specifications. A specification may have multiple correct implementations which are different from each other in controller state representation, but equivalent from a perspective of input-output behavior (e.g., due to optimization in a code generator). The implementations may use finite precision computations (e.g. floating-point arithmetic) which cause quantization (i.e., roundoff) errors. To address these challenges, we first extract a controller\u27s mathematical model from the implementation via symbolic execution and floating-point error analysis, and then check approximate input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of floating-point controller implementation in C language using the combination of techniques such as symbolic execution and convex optimization problem solving. We demonstrate the scalability of our approach through evaluation with randomly generated controller specifications of realistic size

Scalable Verification of Linear Controller Software

We consider the problem of verifying software implementations of linear time-invariant controllers against mathematical specifications. Given a controller specification, multiple correct implementations may exist, each of which uses a different representation of controller state (e.g., due to optimizations in a third-party code generator). To accommodate this variation, we first extract a controller\u27s mathematical model from the implementation via symbolic execution, and then check input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of C code controller implementation using the combination of techniques such as symbolic execution, satisfiability solving and convex optimization. Through evaluation using randomly generated controller specifications of realistic size, we demonstrate that the scalability of this approach has significantly improved compared to our own earlier work based on the invariant checking method

Kinetics and thermodynamics of salt-dependent T7 gene 2.5 protein binding to single- and double-stranded DNA

Bacteriophage T7 gene 2.5 protein (gp2.5) is a single-stranded DNA (ssDNA)-binding protein that has essential roles in DNA replication, recombination and repair. However, it differs from other ssDNA-binding proteins by its weaker binding to ssDNA and lack of cooperative ssDNA binding. By studying the rate-dependent DNA melting force in the presence of gp2.5 and its deletion mutant lacking 26 C-terminal residues, we probe the kinetics and thermodynamics of gp2.5 binding to ssDNA and double-stranded DNA (dsDNA). These force measurements allow us to determine the binding rate of both proteins to ssDNA, as well as their equilibrium association constants to dsDNA. The salt dependence of dsDNA binding parallels that of ssDNA binding. We attribute the four orders of magnitude salt-independent differences between ssDNA and dsDNA binding to nonelectrostatic interactions involved only in ssDNA binding, in contrast to T4 gene 32 protein, which achieves preferential ssDNA binding primarily through cooperative interactions. The results support a model in which dimerization interactions must be broken for DNA binding, and gp2.5 monomers search dsDNA by 1D diffusion to bind ssDNA. We also quantitatively compare the salt-dependent ssDNA- and dsDNA-binding properties of the T4 and T7 ssDNA-binding proteins for the first time

Formal Verification of Masked Hardware Implementations in the Presence of Glitches

Masking provides a high level of resistance against side-channel analysis. However, in practice there are many possible pitfalls when masking schemes are applied, and implementation flaws are easily overlooked. Over the recent years, the formal verification of masked software implementations has made substantial progress. In contrast to software implementations, hardware implementations are inherently susceptible to glitches. Therefore, the same methods tailored for software implementations are not readily applicable. In this work, we introduce a method to formally verify the security of masked hardware implementations that takes glitches into account. Our approach does not require any intermediate modeling steps of the targeted implementation and is not bound to a certain leakage model. The verification is performed directly on the circuit’s netlist, and covers also higher-order and multivariate flaws. Therefore, a sound but conservative estimation of the Fourier coefficients of each gate in the netlist is calculated, which characterize statistical dependence of the gates on the inputs and thus allow to predict possible leakages. In contrast to existing practical evaluations, like t-tests, this formal verification approach makes security statements beyond specific measurement methods, the number of evaluated leakage traces, and the evaluated devices. Furthermore, flaws detected by the verifier are automatically localized. We have implemented our method on the basis of an SMT solver and demonstrate the suitability on a range of correctly and incorrectly protected circuits of different masking schemes and for different protection orders. Our verifier is efficient enough to prove the security of a full masked AES S-box, and of the Keccak S-box up to the third protection order