Error Estimation for Moments Analysis in Heavy-Ion Collision Experiments

Fluctuations of conserved quantities are predicted to be sensitive to the correlation length and connected to the thermodynamic susceptibility. Thus, moments of net-baryon, net-charge and net-strangeness have been extensively studied theoretically and experimentally to explore phase structure and bulk properties of QCD matters created in heavy ion collision experiment. As the moments analysis is statistics hungry study, the error estimation is crucial to extract physics information from the limited experimental data. In this paper, we will derive the limit distributions and error formula based on Delta theorem in statistics for various order moments used in the experimental data analysis. The Monte Carlo simulation is also applied to test the error formula.Comment: 14 pages, 10 figure

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

B cell hyperresponsiveness and expansion of mature follicular B cells but not of marginal zone B cells in NFATc2/c3 double-deficient mice

Marginal zone (MZ) B cells and peritoneal B-I cells provide a first defense system of thymus-independent Ab responses against foreign pathogens and therefore share a number of functional properties. Recently, development of B-1a cells was shown to be controlled by the transcription factor NFATc1. We show here that mice deficient for NFATc2 and c3 display a distinct lower representation of MZ B cells, which is correlated with a reduced capturing of trinitrophenyl-Ficoll. In contrast, mature follicular B cells from NFATc2/c3(-/-) mice are strongly increased in number. NFATc2/c3-/- B cells exhibit a marked increase in BCR-induced intracellular Ca(2+) mobilization and proliferation. However, trinitrophenyl-Ficoll-specific IgM and IgG3 responses of NFATc2/c3-deficient mice are intact, and chimeric mice reconstituted with NFATc2/3-deficient B cells show a normal number of MZ B cells and normal BCR responses. These observations suggest that the strongly elevated Th2 cytokine milieu in NFATc2/c3-deficient mice leads to a hyperactivation of mature, follicular B cells, whereas MZ B cells are less responsive to these signals

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

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

Breakup Density in Spectator Fragmentation

Proton-proton correlations and correlations of protons, deuterons and tritons with alpha particles from spectator decays following 197Au + 197Au collisions at 1000 MeV per nucleon have been measured with two highly efficient detector hodoscopes. The constructed correlation functions, interpreted within the approximation of a simultaneous volume decay, indicate a moderate expansion and low breakup densities, similar to assumptions made in statistical multifragmentation models. PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn, 25.75.GzComment: 11 pages, LaTeX with 3 included figures; Also available from http://www-kp3.gsi.de/www/kp3/aladin_publications.htm

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

Geometrical Insights for Implicit Generative Modeling

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the $1$-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio

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