Bounded solutions of kk-dimensional system of nonlinear difference equations of neutral type

The $k$-dimensional system of neutral type nonlinear difference equations with delays in the following form \begin{equation*} \begin{cases} \Delta \Big(x_i(n)+p_i(n)\,x_i(n-\tau_i)\Big)=a_i(n)\,f_i(x_{i+1}(n-\sigma_i))+g_i(n),\\ \Delta \Big(x_k(n)+p_k(n)\,x_k(n-\tau_k)\Big)=a_k(n)\,f_k(x_1(n-\sigma_k))+g_k(n), \end{cases} \end{equation*} where $i=1,\dots,k-1$, is considered. The aim of this paper is to present sufficient conditions for the existence of nonoscillatory bounded solutions of the above system with various $(p_i(n))$, $i=1,\dots,k$, $k\geq 2$

Unstable neutral differential equations involving the maximum function

A nonlinear differential equation involving the maximum function is studied. The existence and asymptotic behavior of nonoscillatory solutions are considered. The difference between the positive and negative solutions is illustrated by some examples. Oscillation of solutions is also studied

Qualitative approximation of solutions to discrete Volterra equations

We present a new approach to the theory of asymptotic properties of solutions to discrete Volterra equations of the form \begin{equation*} \Delta^m x_n=b_n+\sum_{k=1}^{n}K(n,k)f(k,x_{\sigma(k)}). \end{equation*} Our method is based on using the iterated remainder operator and asymptotic difference pairs. This approach allows us to control the degree of approximation

S-Detect Software vs. EU-TIRADS Classification: A Dual-Center Validation of Diagnostic Performance in Differentiation of Thyroid Nodules

Computer-aided diagnosis (CAD) and other risk stratification systems may improve ultrasound image interpretation. This prospective study aimed to compare the diagnostic performance of CAD and the European Thyroid Imaging Reporting and Data System (EU-TIRADS) classification applied by physicians with S-Detect 2 software CAD based on Korean Thyroid Imaging Reporting and Data System (K-TIRADS) and combinations of both methods (MODELs 1 to 5). In all, 133 nodules from 88 patients referred to thyroidectomy with available histopathology or with unambiguous results of cytology were included. The S-Detect system, EU-TIRADS, and mixed MODELs 1–5 for the diagnosis of thyroid cancer showed a sensitivity of 89.4%, 90.9%, 84.9%, 95.5%, 93.9%, 78.9% and 93.9%; a specificity of 80.6%, 61.2%, 88.1%, 53.7%, 73.1%, 89.6% and 80.6%; a positive predictive value of 81.9%, 69.8%, 87.5%, 67%, 77.5%, 88.1% and 82.7%; a negative predictive value of 88.5%, 87.2%, 85.5%, 92.3%, 92.5%, 81.1% and 93.1%; and an accuracy of 85%, 75.9%, 86.5%, 74.4%, 83.5%, 84.2%, and 87.2%, respectively. Comparison showed superiority of the similar MODELs 1 and 5 over other mixed models as well as EU-TIRADS and S-Detect used alone (p-value < 0.05). S-Detect software is characterized with high sensitivity and good specificity, whereas EU-TIRADS has high sensitivity, but rather low specificity. The best diagnostic performance in malignant thyroid nodule (TN) risk stratification was obtained for the combined model of S-Detect (“possibly malignant” nodule) and simultaneously obtaining 4 or 5 points (MODEL 1) or exactly 5 points (MODEL 5) on the EU-TIRADS scale