Optimization Under Uncertainty Using the Generalized Inverse Distribution Function

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows for the use of all the possible information available in the probabilistic domain. Furthermore, the use of a quantile based approach leads naturally to a multi-objective methodology which allows an a-posteriori selection of the candidate design based on risk/opportunity criteria defined by the designer. Finally, the error on the estimation of the objectives due to the resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure

Model selection in High-Dimensions: A Quadratic-risk based approach

In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quick-to-compute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion (AIC), but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to compute. The method is illustrated using the problem of selecting the number of components in a mixture model, where it is shown that, by using an appropriate kernel, the method is computationally straightforward in arbitrarily high data dimensions. In this same context it is shown that the method has some clear advantages over AIC and BIC.Comment: Updated with reviewer suggestion

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure

Somatostatin receptor-directed molecular imaging for therapeutic decision-making in patients with medullary thyroid carcinoma

BACKGROUND: Somatostatin receptor (SSTR) positron emission tomography/computed tomography (PET/CT) is increasingly deployed in the diagnostic algorithm of patients affected with medullary thyroid carcinoma (MTC). We aimed to assess the role of SSTR-PET/CT for therapeutic decision making upon restaging. METHODS: 23 pretreated MTC patients underwent SSTR-PET/CT and were discussed in our interdisciplinary tumor board. Treatment plans were initiated based on scan results. By comparing the therapeutic regimen before and after the scan, we assessed the impact of molecular imaging on therapy decision. SSTR-PET was also compared to CT portion of the SSTR-PET/CT (as part of hybrid imaging). RESULTS: SSTR-PET/CT was superior in 9/23 (39.1%) subjects when compared to conventional CT and equivalent in 14/23 (60.9%). Those findings were further corroborated on a lesion-based level with 27/73 (37%) metastases identified only by functional imaging (equivalent to CT in the remaining 46/73 (63%)). Investigating therapeutic decision making, no change in treatment was initiated after PET/CT in 7/23 (30.4%) patients (tyrosine kinase inhibitor (TKI), 4/7 (57.2%); surveillance, 3/7 (42.8%)). Imaging altered therapy in the remaining 16/23 (69.6%). Treatment prior to PET/CT included surgery in 6/16 (37.5%) cases, followed by TKI in 4/16 (25%), active surveillance in 4/16 (25%), and radiation therapy (RTx) in 2/16 (12.5%) subjects. After SSTR-PET/CT, the therapeutic regimen was changed as follows: In the surgery group, 4/6 (66.7%) patients underwent additional surgery, and 1/6 (16.7%) underwent surveillance and TKI, respectively. In the TKI group, 3/4 (75%) individuals received another TKI and the remaining subject (1/4, 25%) underwent peptide receptor radionuclide therapy. In the surveillance group, 3/4 (75%) underwent surgery (1/4, (25%), RTx). In the RTx group, one patient was switched to TKI and another individual was actively monitored (1/2, 50%, respectively). Moreover, in the 16 patients in whom treatment was changed by molecular imaging, control disease rate was achieved in 12/16 (75%) during follow-up. CONCLUSIONS: In patients with MTC, SSTR-PET/CT was superior to CT alone and provided relevant support in therapeutic decision-making in more than two thirds of cases, with most patients being switched to surgical interventions or systemic treatment with TKI. As such, SSTR-PET/CT can guide the referring treating physician towards disease-directed treatment in various clinical scenarios

Comparison of PET/CT-based eligibility according to VISION and TheraP trial criteria in end-stage prostate cancer patients undergoing radioligand therapy

Background Two randomized clinical trials demonstrated the efficacy of prostate-specific membrane antigen (PSMA) radioligand therapy (PSMA RLT) in metastatic castration-resistant prostate cancer (mCRPC). While the VISION trial used criteria within PSMA PET/CT for inclusion, the TheraP trial used dual tracer imaging including FDG PET/CT. Therefore, we investigated whether the application of the VISION criteria leads to a benefit in overall survival (OS) or progression-free survival (PFS) for men with mCRPC after PSMA RLT. Methods Thirty-five men with mCRPC who had received PSMA RLT as a last-line option and who had undergone pretherapeutic imaging with FDG and [68Ga]Ga-PSMA I&T or [18F]PSMA-1007 were studied. Therapeutic eligibility was retrospectively evaluated using the VISION and TheraP study criteria. Results 26 of 35 (74%) treated patients fulfilled the VISION criteria (= VISION+) and only 17 of 35 (49%) fulfilled the TheraP criteria (= TheraP+). Significantly reduced OS and PFS after PSMA RLT was observed in patients rated VISION− compared to VISION+ (OS: VISION−: 3 vs. VISION+: 12 months, hazard ratio (HR) 3.1, 95% confidence interval (CI) 1.0–9.1, p < 0.01; PFS: VISION−: 1 vs. VISION+: 5 months, HR 2.7, 95% CI 1.0–7.8, p < 0.01). For patients rated TheraP−, no significant difference in OS but in PFS was observed compared to TheraP+ patients (OS: TheraP−: 5.5 vs. TheraP+: 11 months, HR 1.6, 95% CI 0.8–3.3, p = 0.2; PFS: TheraP−: 1 vs. TheraP+: 6 months, HR 2.2, 95% CI 1.0–4.5, p < 0.01). Conclusion Retrospective application of the inclusion criteria of the VISION study leads to a benefit in OS and PFS after PSMA RL, whereas TheraP criteria appear to be too strict in patients with end-stage prostate cancer. Thus, performing PSMA PET/CT including a contrast-enhanced CT as proposed in the VISION trial might be sufficient for treatment eligibility of end-stage prostate cancer patients

Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units

Associations between normal organs and tumor burden in patients imaged with fibroblast activation protein inhibitor-directed positron emission tomography

Several radiolabeled fibroblast activation protein targeted inhibitors (FAPI) have been developed for molecular imaging and therapy. A potential correlation of radiotracer uptake in normal organs and extent of tumor burden may have consequences for a theranostic approach using ligands structurally associated with [68Ga]Ga-FAPI, as one may anticipate decreased doses to normal organs in patients with extensive tumor load. In the present proof-of-concept study investigating patients with solid tumors, we aimed to quantitatively determine the normal organ biodistribution of [68Ga]Ga-FAPI-04, depending on the extent of tumor. Except for a trend towards significance in the myocardium, we did not observe any relevant associations between PET-based tumor burden and normal organs. Those preliminary findings may trigger future studies to determine possible implications for theranostic approaches and FAP-directed drugs, as one may expect an unchanged dose for normal organs even in patients with higher tumor load. Abstract (1) Background: We aimed to quantitatively investigate [68Ga]Ga-FAPI-04 uptake in normal organs and to assess a relationship with the extent of FAPI-avid tumor burden. (2) Methods: In this single-center retrospective analysis, thirty-four patients with solid cancers underwent a total of 40 [68Ga]Ga-FAPI-04 PET/CT scans. Mean standardized uptake values (SUVmean) for normal organs were established by placing volumes of interest (VOIs) in the heart, liver, spleen, pancreas, kidneys, and bone marrow. Total tumor burden was determined by manual segmentation of tumor lesions with increased uptake. For tumor burden, quantitative assessment included maximum SUV (SUVmax), tumor volume (TV), and fractional tumor activity (FTA = TV × SUVmean). Associations between uptake in normal organs and tumor burden were investigated by applying Spearman’s rank correlation coefficient. (3) Results: Median SUVmean values were 2.15 in the pancreas (range, 1.05–9.91), 1.42 in the right (range, 0.57–3.06) and 1.41 in the left kidney (range, 0.73–2.97), 1.2 in the heart (range, 0.46–2.59), 0.86 in the spleen (range, 0.55–1.58), 0.65 in the liver (range, 0.31–2.11), and 0.57 in the bone marrow (range, 0.26–0.94). We observed a trend towards significance for uptake in the myocardium and tumor-derived SUVmax (ρ = 0.29, p = 0.07) and TV (ρ = −0.30, p = 0.06). No significant correlation was achieved for any of the other organs: SUVmax (ρ ≤ 0.1, p ≥ 0.42), TV (ρ ≤ 0.11, p ≥ 0.43), and FTA (ρ ≤ 0.14, p ≥ 0.38). In a sub-analysis exclusively investigating patients with high tumor burden, significant correlations of myocardial uptake with tumor SUVmax (ρ = 0.44; p = 0.03) and tumor-derived FTA with liver uptake (ρ = 0.47; p = 0.02) were recorded. (4) Conclusions: In this proof-of-concept study, quantification of [68Ga]Ga-FAPI-04 PET showed no significant correlation between normal organs and tumor burden, except for a trend in the myocardium. Those preliminary findings may trigger future studies to determine possible implications for treatment with radioactive FAP-targeted drugs, as higher tumor load or uptake may not lead to decreased doses in the majority of normal organs

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R

Liquid-Gas Phase Transition of Supernova Matter and Its Relation to Nucleosynthesis

We investigate the liquid-gas phase transition of dense matter in supernova explosion by the relativistic mean field approach and fragment based statistical model. The boiling temperature is found to be high (T_{boil} >= 0.7 MeV for rho_B >= 10^{-7} fm^{-3}), and adiabatic paths are shown to go across the boundary of coexisting region even with high entropy. This suggests that materials experienced phase transition can be ejected to outside. We calculated fragment mass and isotope distribution around the boiling point. We found that heavy elements at the iron, the first, second, and third peaks of r-process are abundantly formed at rho_B = 10^{-7}, 10^{-5}, 10^{-3} and 10^{-2} fm^{-3}, respectively.Comment: 29 pages, 13 figures. This article is submitted to Nucl. Phys.