Non-Gaussian features from the inverse volume corrections in loop quantum cosmology

In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make $f_{{\rm NL}}$ of the inflationary models increase 0.1%. Moreover, we find that two new shapes arise, namely $\mathcal F_{1}$ and $\mathcal F_{2}$. The former gives a unique loop quantum feature which is less correlated with the local, equilateral and single types, while the latter is highly correlated with the local one.Comment: matched to the published version. 30 pages, 4 figure

Landau-Zener Tunnelling in a Nonlinear Three-level System

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.Comment: 8 pages, 8 figure

Explainable machine learning-based prediction model for diabetic nephropathy

The aim of this study is to analyze the effect of serum metabolites on diabetic nephropathy (DN) and predict the prevalence of DN through a machine learning approach. The dataset consists of 548 patients from April 2018 to April 2019 in Second Affiliated Hospital of Dalian Medical University (SAHDMU). We select the optimal 38 features through a Least absolute shrinkage and selection operator (LASSO) regression model and a 10-fold cross-validation. We compare four machine learning algorithms, including eXtreme Gradient Boosting (XGB), random forest, decision tree and logistic regression, by AUC-ROC curves, decision curves, calibration curves. We quantify feature importance and interaction effects in the optimal predictive model by Shapley Additive exPlanations (SHAP) method. The XGB model has the best performance to screen for DN with the highest AUC value of 0.966. The XGB model also gains more clinical net benefits than others and the fitting degree is better. In addition, there are significant interactions between serum metabolites and duration of diabetes. We develop a predictive model by XGB algorithm to screen for DN. C2, C5DC, Tyr, Ser, Met, C24, C4DC, and Cys have great contribution in the model, and can possibly be biomarkers for DN

Wigner solution of the quark gap equation

Solutions and their evolutions of the quark gap equation are studied within the Nambu-Jona--Lasinio model, which is a basic issue for studying the QCD phase structure and locating the possible critical end point. It is shown that in the chiral limit case of the vacuum, chiral symmetry will hold if the coupling strength $G$ is small, then the system only has the Wigner solution at $M=0$. If increasing $G$, two symmetric minima will appear as the positive and `negative' Nambu solutions, however, the solution $M=0$ now corresponds to a maximum instead of a minimum of the thermodynamical potential, so is not a physically stable state anymore (we call it `pseudo-Wigner solution'). Besides, it is shown that as the current quark mass $m$ increases, the pseudo-Wigner solution will become negative, and disappear together with the negative Nambu solution if $m$ is large enough. Similar things happen if we increase the temperature or quark chemical potential $\mu$. Some interesting phenomenon is, from some $\mu$ a second local minimum will show up. As $\mu$ increases gradually, it will be stabler than the Nambu solution, survives even the Nambu solution disappears, and approaches $m$, which are just the features of the Wigner solution we expect.Comment: version accepted for publication in the European Physical Journal

FXR1P but not FMRP regulates the levels of mammalian brain-specific microRNA-9 and microRNA-124

Mammalian brain-specific miR-9 and miR-124 have been implicated in several aspects of neuronal development and function. However, it is not known how their expression levels are regulated in vivo. We found that the levels of miR-9 and miR-124 are regulated by FXR1P but not by the loss of FXR2P or FMRP in vivo, a mouse model of fragile X syndrome. Surprisingly, the levels of miR-9 and miR-124 are elevated in fmr1/fxr2 double-knock-out mice, in part reflecting posttranscriptional upregulation of FXR1P. Indeed, FXR1P is required for efficient processing of pre-miR-9 and pre-miR-124 in vitro and forms a complex with Dicer and pre-miRNAs. These findings reveal differential roles of FMRP family proteins in controlling the expression levels of brain-specific miRNAs