Covariance matrix estimation for stationary time series

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms of the covariances. We develop a large deviation result for quadratic forms of stationary processes using m-dependence approximation, under the framework of causal representation and physical dependence measures.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Controlling Multiple COVID-19 Epidemic Waves: An Insight from a Multi-scale Model Linking the Behaviour Change Dynamics to the Disease Transmission Dynamics

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves

Linking key intervention timing to rapid decline of the COVID-19 effective reproductive number to quantify lessons from mainland China

Effective reproductive numbers (Rt) were calculated from data on the COVID-19 outbreak in China and linked to dates in 2020 when different interventions were enacted. From a maximum of 3.98 before the lockdown in Wuhan City, the values of Rt declined to below 1 by the second week of February, after the construction of hospitals dedicated to COVID-19 patients. The Rt continued to decline following additional measures in line with the policy of “early detection, early report, early quarantine, and early treatment.” The results provide quantitative evaluations of how intervention measures and their timings succeeded, from which lessons can be learned by other countries dealing with future outbreaks

Interpetrosal sphingosine-1-phosphate ratio predicting Cushing’s disease tumor laterality and remission after surgery

BackgroundCushing’s disease (CD) poses significant challenges in its treatment due to the lack of reliable biomarkers for predicting tumor localization or postoperative clinical outcomes. Sphingosine-1-phosphate (S1P) has been shown to increase cortisol biosynthesis and is regulated by adrenocorticotropic hormone (ACTH).MethodsWe employed bilateral inferior petrosal sinus sampling (BIPSS), which is considered the gold standard for diagnosing pituitary sources of CD, to obtain blood samples and explore the clinical predictive value of the S1P concentration ratio in determining tumor laterality and postoperative remission. We evaluated 50 samples from 25 patients who underwent BIPSS to measure S1P levels in the inferior petrosal sinuses bilaterally.ResultsSerum S1P levels in patients with CD were significantly higher on the adenoma side of the inferior petrosal sinus than on the nonadenoma side (397.7 ± 15.4 vs. 261.9 ± 14.88; P < 0.05). The accuracy of diagnosing tumor laterality with the interpetrosal S1P and ACTH ratios and the combination of the two was 64%, 56% and 73%, respectively. The receiver operating characteristic curve analysis revealed that the combination of interpetrosal S1P and ACTH ratios, as a predictor of tumor laterality, exhibited a sensitivity of 81.82% and a specificity of 75%, with an area under the curve value of 84.09%. Moreover, we observed that a high interpetrosal S1P ratio was associated with nonremission after surgery. Correlation analyses demonstrated that the interpetrosal S1P ratio was associated with preoperative follicle-stimulating hormone (FSH), luteinizing hormone (LH), and postoperative ACTH 8 am levels (P < 0.05).ConclusionOur study demonstrated a significant association between the interpetrosal S1P ratio and tumor laterality, as well as postoperative remission in CD, suggesting that the interpetrosal S1P ratio could serve as a valuable biomarker in clinical practice

Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.Fil: Tang, Biao. University of York; Reino Unido. University of Toronto; CanadáFil: Xiao, Yanni. Xi'an Jiaotong University; ChinaFil: Sander, Beate. University of Toronto; CanadáFil: Kulkarni, Manisha A.. University of Ottawa; CanadáFil: Wu, Jianhong. University of York; Reino UnidoFil: Miretti, Marcos Mateo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas | Universidad Nacional de Misiones. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas; Argentin

Influencing factors and clinical significance of the metastatic lymph nodes ratio in gastric adenocarcinoma

<p>Abstract</p> <p>Background</p> <p>To investigate influencing factors of the metastatic lymph nodes ratio (MLR) and whether it is related to survival in patients with gastric adenocarcinoma.</p> <p>Methods</p> <p>We retrospectively evaluated the clinical features of 121 patients with gastric adenocarcinoma enrolled in our hospital between 2000 and 2007. The receiver operating characteristic (ROC) curve was used to determine the cutoff of the MLR, and CK20 immunohistochemical staining was used to detect micrometastasis of the lymph nodes.</p> <p>Results</p> <p>The areas under the ROC curve of MLR used to predict the death of 3-year and 5-year postoperative patients were 0.826 ± 0.053 and 0.896 ± 0.046. Thus MLR = 30.95% and MLR = 3.15% were designated as cutoffs. The MLR was then classified into three groups: MLR₁(MLR<3.15%); MLR₂(3.15% ≤ MLR ≤ 30.95%); and MLR₃(MLR>30.95%). We found that patients with a higher MLR demonstrated a much poorer survival period after radical operation than those patients with a lower MLR (P = 0.000). The COX model showed that MLR was an independent prognostic factor (P = 0.000). The MLR could also discriminate between subsets of patients with different 5-year survival periods within the same N stage (P < 0.05). The MLR has been shown to be 34.7% (242/697) by HE staining and 43.5% (303/697) by CK staining (P = 0.001). The clinicopathological characteristics of lymph vessel invasion and the depth of invasion could significantly affect the MLR.</p> <p>Conclusion</p> <p>MLR is an independent prognostic factor in gastric cancer. The combined ROC curve with MLR is an effective strategy to produce a curve to predict the 3-year and 5-year survival rates.</p

Cyclotrimerization of alkynes catalyzed by a self-supported cyclic tri-nuclear nickel(0) complex with α-diimine ligands

A cyclic tri-nuclear α-diimine nickel(0) complex [{Ni(μ-L Me-2,4 )} 3 ] (2) was synthesized from a “pre-organized”, trimerized trigonal LNiBr 2 -type precursor [Ni 3 (μ 2 -Br) 3 (μ 3 -Br) 2 (L Me-2,4 ) 3 ]·Br (1; L Me-2,4 = [(2,4-Me 2 C 6 H 3 )NC(Me)] 2 ). In complex 2, the α-diimine ligands not only exhibit the normal N,N′-chelating mode, but they also act as bridges between the Ni atoms through an unusual π-coordination of a C═N bond to Ni. Complex 2 is able to catalyze the cyclotrimerization of alkynes to form substituted benzenes in good yield and regio-selectivity for the 1,3,5-isomers, which is found to vary with the nature of the alkyne employed. This complex represents a convenient self-supported nickel(0) catalyst with no need for additional ligands and reducing agent

Analytic formula for the proton radioactivity spectroscopic factor

In the present work, we systematically study the spectroscopic factor of proton radioactivity ($S_p$) with $A>100$ using the deformed two-potential approach (D-TPA). It is found that there is a link between the quadrupole deformation parameter of proton emitter and $S_p$. Based on this result, we propose a simple analytic formula for estimating the spectroscopic factor of proton radioactivity. With the help of this formula, the calculated half-lives of proton radioactivity can reproduce the experimental data successfully within a factor of 2.77. Furthermore, we extend the D-TPA with this formula for evaluating the spectroscopic factor to predict the proton radioactivity half-lives of 12 proton radioactivity candidates whose radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the universal decay law for proton radioactivity (UDLP) and the new Geiger-Nuttall law (NG-N) are also used. It turns out that all of the predicted results are basically consistent with each other