Free Vibration Characteristics of the Conical Shells Based on Precise Integration Transfer Matrix Method

<div><p>Abstract Based on transfer matrix theory and precise integration method, precise integration transfer matrix method (PITMM) is advanced to research free vibration characteristics of the conical shells. The influences of the boundary conditions, the shell thickness and the semi-vertex conical angle on vibration characteristics are discussed. Based on Flügge thin shell theory and transfer matrix method, field transfer matrix of conical shells is obtained. According to the boundary conditions at ends of the conical shell, natural frequencies of the conical shell are solved by precise integration method. The approach of studying free vibration characteristics of the conical shells is obtained. Contrast of natural frequencies from the paper and previous literature, the method of the paper is confirmed. On this basis, the effects of the boundary conditions, the shell thickness and the semi-vertex conical angle on vibration characteristics are presented.</p></div

DNF of the patient mortality.

<p>DNF of the patient mortality.</p

Comparative performance of models on predicting 90-day mortality.

<p>NB-Naive Bayes, SVM-Support vector machine, NN-neural network, LOG-Logistic regression, BL-Boosted logistic regression, RT-Random tree, RF-Random forest, DNF-Disjunctive Normal Form learning.</p

Interpreting DNF models on three patients.

<p>The prediction procedure of DNF is represented in three layers: the top layer is the DNF itself; the middle layer is the clause level; and the bottom layer is the final outcome. Red color rectangles indicate that patient data is above the threshold and a severity condition is met; green rectangles indicate that patient data is below and the condition is not met. Three example patients are shown. For patient A, , and are all above the threshold and results in a positive Clause 2 so the predicted outcome is mortality. For patient B, Clause 2 is negative due to the low (procalcitonin in the lowest quartile); however high turns on Clause 1 and predicts mortality too. Patient C has high but it is not sufficient to turn on either Clause 1 or 2 and she is therefore predicted to survive.</p

Prediction performance of DNF learning on hospital and 90-day mortality data.

<p>10-fold cross validation is applied to assess the prediction performance of DNF learning on hospital and 90-day mortality, and compare the performance when using the whole feature set (Model 8, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089053#pone-0089053-t001" target="_blank">Table 1</a>) and only day 1 (Model 7) and/or day 2 cytokine (Model 7 + day 2 cytokines).</p

Availability of data across physiologic domains.

<p>Of 1815 patients with cytokine data on day 1, much smaller numbers of patients had single nucleotide profiles (SNP), Fluorescent-Antibody Cell Sorting (FACS) measurements of surface markers, or full coagulation studies (Coags)performed.</p

Predictors (features) inluded in the different models.

<p>Predictors (features) inluded in the different models.</p

DNF literals explanation.

<p>Note.</p><p>*: when missing values present in the data, they are treated as a literal, but they are never selected in the DNF learning.</p

Clinical characteristics and immunohistochemical scores in tissue array.

Clinical characteristics and immunohistochemical scores in tissue array.</p

Cell migration assay was conducted in DU-145 and 22RV1.

(A) The migration of DU-145 was displayed at 0h and 48h with the treatment of NC, S1and S2 siRNA. Wound-healing distances were analyzed within 48 hours; (B) The migration of 22RV1 was shown at 0h and 48h with treatment of NC, S1 and S2 siRNA. Wound-healing distances were analyzed within 48 hours. (**, P P < 0.001. T-test was used for data analysis and plotted by GraphPad Prism 9.0).</p