The choice between delta and shift operators for low-precision data representation

Low-precision data types for embedded applications reduce the power consumption and enhance the price-performance ratio. Inconsistence between the specified accuracy of a designed filter or controller and an imprecise data type can be overcome using the δ-operator, an alternative to the traditional discrete-time z-operator. Though in many cases it significantly increases accuracy, sometimes it shows no advantage over the shift operator. So the problem of choice between delta and shift operator arises. Therefore, a study on δ-operator applicability bounds is needed to solve this problem and provide δ-operator efficient practical use. In this paper we introduce a concept of the δ-operator applicability criterion. The discrete system implementation technique with discrete-time operator choice is given for the low-precision machine arithmetic

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems

Intraoperative Sphenoid Sinus Volume Measurement as an Alternative Technique to Intraoperative Computer Tomography

Isolated sphenoid sinus disease (ISSD) is where there is a group of pathologies characterized by inflammation in one or both sphenoid sinuses. Although computer tomography (CT)-based 3D reconstruction remains the gold standard among noninvasive approaches to ISSD diagnostics, no standardized techniques for direct intraoperative measurements of the sphenoid sinus volume in ISSD patients have been documented. We suggest a novel technique for the intraoperative measurement of the sphenoid sinus volume. Our technique is based on filling the sinus with 0.01% methylene blue solution after an endoscopic endonasal sphenoidotomy. The proposed technique was applied to 40 ISSD patients during surgery. Obtained intraoperative measurements were compared to noninvasive measurements from 3D reconstructions based on preoperative CT scans. Our results demonstrated that the obtained measurements did not exhibit significant differences exceeding 0.4 cm3, with CT-scan-based measurements in 39 out of 40 cases (p < 10−6, Wilcoxon sign-rank nonparametric test), thus confirming the accuracy of the proposed technique. Disagreements between direct intraoperative and CT-based measurements in a single case have been attributed to the presence of remaining pathological masses in the sinus, which was further confirmed during the secondary check of the operated sinus. Accordingly, we suggest that the agreement between the CT-based and intraoperative volume measurements can be used as an indicator of the successful elimination of all pathological masses from the sinus without having to perform an adequate exposure of the entire sphenoid sinus to reduce intraoperative bleeding. The proposed technique is accurate and does not require the involvement of specialized intraoperative CT scanners and avoids additional radiation exposure for the patient during an additional postoperation CT scan to confirm the success of the surgery

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems

Three-Dimensional (3D) Model-Based Lower Limb Stump Automatic Orientation

Modern prosthetics largely relies upon visual data processing and implementation technologies such as 3D scanning, mathematical modeling, computer-aided design (CAD) tools, and 3D-printing during all stages from design to fabrication. Despite the intensive advancement of these technologies, once the prosthetic socket model is obtained by 3D scanning, its appropriate orientation and positioning remain largely the responsibility of an expert requiring substantial manual effort. In this paper, an automated orientation algorithm based on the adjustment of the 3D-model virtual anatomical axis of the tibia along with the vertical axis of the rectangular coordinates in three-dimensional space is proposed. The suggested algorithm is implemented, tested for performance and experimentally validated by explicit comparisons against an expert assessment

Phase matching in RT KTP crystal for down-conversion into the THz range

Dispersion of refractive index and absorption coefficients in flux-grown high-resistivity KTiOPO4 crystals between 0.2–2.5 THz are verified at room temperature by a THz-TDS. Measured dispersion components n x , n y and n z are approximated for the first time in the form of Sellmeier equations. Phase matching for down-conversion into the THz range under a visible and near IR pump is found possible only in the principle plane by and types of three-wave interactions. Low frequency THz generation is favorable due to the low absorption coefficient down to 0.2 cm−1, below 0.5 THz

Phase matching in RT KTP crystal for down-conversion into the THz range

Dispersion of refractive index and absorption coefficients in flux-grown high-resistivity KTiOPO4 crystals between 0.2–2.5 THz are verified at room temperature by a THz-TDS. Measured dispersion components n x , n y and n z are approximated for the first time in the form of Sellmeier equations. Phase matching for down-conversion into the THz range under a visible and near IR pump is found possible only in the principle plane by and types of three-wave interactions. Low frequency THz generation is favorable due to the low absorption coefficient down to 0.2 cm−1, below 0.5 THz