Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

International audienceThis chapter proposes a framework for dealing with two problems related to the analysis of shapes: the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [8], we consider the characteristic functions of the subsets of ℝ2 and their distance functions. The L 2 norm of the difference of characteristic functions and the L∞ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular that induced by the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ℝ2 of positive reach in the sense of Federer [12], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem. We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational de.nitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples

Histological Validation of in-vivo VERDICT MRI for Prostate using 3D Personalised Moulds

VERDICT analysis can successfully distinguish benign from malignant prostate tissue in-vivo showing promising results as a cancer diagnostic tool. However, the accuracy with which model parameters reflect the underlying tissue characteristics is unknown. In this study, we quantitatively compare the intracellular, extracellular-extravascular and vascular volume fractions derived from in-vivo VERDICT MRI against histological measurements from prostatectomies. We use 3D-printed personalised moulds designed from in-vivo MRI that help preserve the orientation and location of the gland and aid histological alignment. Results from the first samples using the 3D mould pipeline show good agreement between in-vivo VERDICT estimates and histology

Repair of Parastomal Hernias with Biologic Grafts: A Systematic Review

Contains fulltext : 98303.pdf (publisher's version ) (Open Access)BACKGROUND: Biologic grafts are increasingly used instead of synthetic mesh for parastomal hernia repair due to concerns of synthetic mesh-related complications. This systematic review was designed to evaluate the use of these collagen-based scaffolds for the repair of parastomal hernias. METHODS: Studies were retrieved after searching the electronic databases MEDLINE, EMBASE and Cochrane CENTRAL. The search terms 'paracolostomy', 'paraileostomy', 'parastomal', 'colostomy', 'ileostomy', 'hernia', 'defect', 'closure', 'repair' and 'reconstruction' were used. Selection of studies and assessment of methodological quality were performed with a modified MINORS index. All reports on repair of parastomal hernias using a collagen-based biologic scaffold to reinforce or bridge the defect were included. Outcomes were recurrence rate, mortality and morbidity. RESULTS: Four retrospective studies with a combined enrolment of 57 patients were included. Recurrence occurred in 15.7% (95% confidence interval [CI] 7.8-25.9) of patients and wound-related complications in 26.2% (95% CI 14.7-39.5). No mortality or graft infections were reported. CONCLUSIONS: The use of reinforcing or bridging biologic grafts during parastomal hernia repair results in acceptable rates of recurrence and complications. However, given the similar rates of recurrence and complications achieved using synthetic mesh in this scenario, the evidence does not support use of biologic grafts

Cross-scanner and cross-protocol multi-shell diffusion MRI data harmonization: algorithms and result

Cross-scanner and cross-protocol variability of diffusion magnetic resonance imaging (dMRI) data are known to be major obstacles in multi-site clinical studies since they limit the ability to aggregate dMRI data and derived measures. Computational algorithms that harmonize the data and minimize such variability are critical to reliably combine datasets acquired from different scanners and/or protocols, thus improving the statistical power and sensitivity of multi-site studies. Different computational approaches have been proposed to harmonize diffusion MRI data or remove scanner-specific differences. To date, these methods have mostly been developed for or evaluated on single b-value diffusion MRI data. In this work, we present the evaluation results of 19 algorithms that are developed to harmonize the cross-scanner and cross-protocol variability of multi-shell diffusion MRI using a benchmark database. The proposed algorithms rely on various signal representation approaches and computational tools, such as rotational invariant spherical harmonics, deep neural networks and hybrid biophysical and statistical approaches. The benchmark database consists of data acquired from the same subjects on two scanners with different maximum gradient strength (80 and 300 ​mT/m) and with two protocols. We evaluated the performance of these algorithms for mapping multi-shell diffusion MRI data across scanners and across protocols using several state-of-the-art imaging measures. The results show that data harmonization algorithms can reduce the cross-scanner and cross-protocol variabilities to a similar level as scan-rescan variability using the same scanner and protocol. In particular, the LinearRISH algorithm based on adaptive linear mapping of rotational invariant spherical harmonics features yields the lowest variability for our data in predicting the fractional anisotropy (FA), mean diffusivity (MD), mean kurtosis (MK) and the rotationally invariant spherical harmonic (RISH) features. But other algorithms, such as DIAMOND, SHResNet, DIQT, CMResNet show further improvement in harmonizing the return-to-origin probability (RTOP). The performance of different approaches provides useful guidelines on data harmonization in future multi-site studies

VERDICT MRI for Prostate Cancer: Intracellular Volume Fraction versus Apparent Diffusion Coefficient

BACKGROUND: Biologic specificity of diffusion MRI in relation to prostate cancer aggressiveness may improve by examining separate components of the diffusion MRI signal. The Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumors (VERDICT) model estimates three distinct signal components and associates them to (a) intracellular water, (b) water in the extracellular extravascular space, and (c) water in the microvasculature. PURPOSE: To evaluate the repeatability, image quality, and diagnostic utility of intracellular volume fraction (FIC) maps obtained with VERDICT prostate MRI and to compare those maps with apparent diffusion coefficient (ADC) maps for Gleason grade differentiation. MATERIALS AND METHODS: Seventy men (median age, 62.2 years; range, 49.5–82.0 years) suspected of having prostate cancer or undergoing active surveillance were recruited to a prospective study between April 2016 and October 2017. All men underwent multiparametric prostate and VERDICT MRI. Forty-two of the 70 men (median age, 67.7 years; range, 50.0–82.0 years) underwent two VERDICT MRI acquisitions to assess repeatability of FIC measurements obtained with VERDICT MRI. Repeatability was measured with use of intraclass correlation coefficients (ICCs). The image quality of FIC and ADC maps was independently evaluated by two board-certified radiologists. Forty-two men (median age, 64.8 years; range, 49.5–79.6 years) underwent targeted biopsy, which enabled comparison of FIC and ADC metrics in the differentiation between Gleason grades. RESULTS: VERDICT MRI FIC demonstrated ICCs of 0.87–0.95. There was no significant difference between image quality of ADC and FIC maps (score, 3.1 vs 3.3, respectively; P = .90). FIC was higher in lesions with a Gleason grade of at least 3+4 compared with benign and/or Gleason grade 3+3 lesions (mean, 0.49 ± 0.17 vs 0.31 ± 0.12, respectively; P = .002). The difference in ADC between these groups did not reach statistical significance (mean, 1.42 vs 1.16 × 10^{-3} mm^{2}/sec; P = .26). CONCLUSION: Fractional intracellular volume demonstrates high repeatability and image quality and enables better differentiation of a Gleason 4 component cancer from benign and/or Gleason 3+3 histology than apparent diffusion coefficient

Evaluation of PSA and PSA Density in a Multiparametric Magnetic Resonance Imaging-Directed Diagnostic Pathway for Suspected Prostate Cancer: The INNOVATE Trial.

Objectives: To assess the clinical outcomes of mpMRI before biopsy and evaluate the space remaining for novel biomarkers. Methods: The INNOVATE study was set up to evaluate the validity of novel fluidic biomarkers in men with suspected prostate cancer who undergo pre-biopsy mpMRI. We report the characteristics of this clinical cohort, the distribution of clinical serum biomarkers, PSA and PSA density (PSAD), and compare the mpMRI Likert scoring system to the Prostate Imaging-Reporting and Data System v2.1 (PI-RADS) in men undergoing biopsy. Results: 340 men underwent mpMRI to evaluate suspected prostate cancer. 193/340 (57%) men had subsequent MRI-targeted prostate biopsy. Clinically significant prostate cancer (csigPCa), i.e., overall Gleason ≥ 3 + 4 of any length OR maximum cancer core length (MCCL) ≥4 mm of any grade including any 3 + 3, was found in 96/195 (49%) of biopsied patients. Median PSA (and PSAD) was 4.7 (0.20), 8.0 (0.17), and 9.7 (0.31) ng/mL (ng/mL/mL) in mpMRI scored Likert 3,4,5 respectively for men with csigPCa on biopsy. The space for novel biomarkers was shown to be within the group of men with mpMRI scored Likert3 (178/340) and 4 (70/350), in whom an additional of 40% (70/178) men with mpMRI-scored Likert3, and 37% (26/70) Likert4 could have been spared biopsy. PSAD is already considered clinically in this cohort to risk stratify patients for biopsy, despite this 67% (55/82) of men with mpMRI-scored Likert3, and 55% (36/65) Likert4, who underwent prostate biopsy had a PSAD below a clinical threshold of 0.15 (or 0.12 for men aged <50 years). Different thresholds of PSA and PSAD were assessed in mpMRI-scored Likert4 to predict csigPCa on biopsy, to achieve false negative levels of ≤5% the proportion of patients whom who test as above the threshold were unsuitably high at 86 and 92% of patients for PSAD and PSA respectively. When PSA was re tested in a sub cohort of men repeated PSAD showed its poor reproducibility with 43% (41/95) of patients being reclassified. After PI-RADS rescoring of the biopsied lesions, 66% (54/82) of the Likert3 lesions received a different PI-RADS score. Conclusions: The addition of simple biochemical and radiological markers (Likert and PSAD) facilitate the streamlining of the mpMRI-diagnostic pathway for suspected prostate cancer but there remains scope for improvement, in the introduction of novel biomarkers for risk assessment in Likert3 and 4 patients, future application of novel biomarkers tested in a Likert cohort would also require re-optimization around Likert3/PI-RADS2, as well as reproducibility testing