A fast symbolic SNR computation method and its Verilog-A implementation for Sigma-Delta modulator design optimization

Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods

The authors show how to use symbolic computing methods to obtain an analytic representation of the solution of

By using symbolic computation methods, we systematically study a generalized (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-Boussinesq) equation, which can be used to explain some interesting physical phenomena in the fields of fluids. We first obtain bilinear representation of the equation by employing the properties of Bell's polynomials. Based on that, its a series of exact solutions, such as one kink soliton solutions, two kink soliton solutions and lump wave solutions, are constructed in detail. It is worth mentioning that we also study the interaction solutions between lump waves and kink waves. Moreover, in order to describe the dynamic behaviours of those solutions, some graphical analyses are given by selecting different parameter values in such solutions. Those analyses are helpful for enriching the physical phenomena in KP-type equations.

This paper investigates duopoly competition under both constant and decreasing returns to scale in a market characterized by an isoelastic demand function, where firms adjust their strategies using a gradient adjustment mechanism. To establish the stability conditions of the model, we adopt different analytical approaches depending on the type of returns to scale. Under constant returns to scale, we employ a traditional approach by deriving the closed-form solution of the Nash equilibrium and analyzing the Jacobian matrix to verify whether the moduli of all eigenvalues are less than one. In contrast, under decreasing returns to scale, we analyze the local stability of the Nash equilibrium using symbolic computation methods without deriving a closed-form solution. The results show that when firms have heterogeneous costs, the model can exhibit both period-doubling and Neimark–Sacker bifurcations under both types of returns to scale. However, when costs are homogeneous, only period-doubling bifurcations occur. Numerical simulations support these analytical results and further demonstrate the emergence of complex dynamics, including chaotic behavior.

Schwarz’s alternating method in a matrix form and its applications to composites

Stewart platform is a parallel linkage, which is widely used in the area of parallel robotics. Generalized Stewart Platform (GSP) consists of two rigid bodies connected with six constraints between six pairs of geometric primitives in the base and the moving platform respectively. Direct kinematics to GSP is to determine the pose of moving platform according to six constraints between the base and the moving platform. Strategies on direct kinematics to GSP were presented, which were based on graph theory and symbolic computation method. A GSP can be decomposed into smaller ones if possible, and the corresponding parameters conditions of real solutions to direct kinematics to the GSP can be obtained according to these strategies.

Under investigation in this paper is a (3 + 1)-dimensional generalized nonlinear Schrödinger equation with the distributed coefficients for the spatiotemporal optical solitons or light bullets. Through the symbolic computation and Hirota method, one- and two-soliton solutions are derived. We also present the Bäcklund transformation, through which we derive the soliton solutions. When the gain/loss coefficient is the monotonically decreasing function for the propagation coordinate [Formula: see text], amplitude for the spatiotemporal optical soliton or light bullet decreases along [Formula: see text], while when the gain/loss coefficient is the monotonically increasing function for [Formula: see text], amplitude for the spatiotemporal optical soliton or light bullet increases along [Formula: see text]. Directions of the solitons are different because the signs of imaginary parts of the frequencies are adverse. Based on the two-soliton solutions, elastic and inelastic collisions between the two spatiotemporal optical solitons or light bullets are derived under different conditions presented in the paper.

This paper presents a fast symbolic method for computation of the signal-to-noise ratio (SNR) of switched-capacitor sigma-delta modulators. The key idea is to use a Taylor expansion polynomial to approximate the rational expression of a noise transfer function (NTF). This new method can be used in automatic optimization tools developed for switched-capacitor sigma-delta modulator design.

Purpose:Our center's clinical outcome data so far indicated that excellent local control for the head and neck patients treated using multiple field optimized (MFO) IMPT technique have been achieved. The purpose is to determine the robustness of those IMPT plans and provide the clinician the knowledge of the degree of the robustness which will not compromise the local control and is safe for the normal tissue.Methods:A fast and approximate dose calculation method is developed to calculate the dose for the IMPT plan under different setup and range uncertainties. The dosimetric index evaluated using this method are compared with those calculated using the dose calculation model in TPS. A worst case scenario robustness analysis method is implemented using the fast dose calculation method. 100 head neck plans treated using MFO IMPT were retrospectively analyzed using implemented robustness analysis method. The lowest dose received by 95% target (D95) and the highest dose received by 5% target (D5) of GTV, CTV1, CTV2, CTV3, mean dose of parotid glands, cochlea and brain and the minimum dose in the most radiated 1 cm3 volume (D1cc) of spinal cord and brain stem were compared between nominal plans and plans in the worst case scenario.Results:For GTV, CTV1 CTV2 and CTV3, D95 in worst scenario are lower by 2.08, 4.59, 5.25 and 5.46 Gy than nominal plan, while D5 are higher by 1.14, 0.98, 0.85 and 1.21 Gy. D1cc of brain stem and spinal in worst scenario are higher by 3.37 and 1.95 Gy than nominal plan. The mean dose of parotid glands, cochlea and brain are higher by 3.52, 3.69 and 0.64 Gy respectively.Conclusion:The robustness analysis data from the clinically treated patients enables the clinician to gauge the degree of robustness in their clinical practice when adopting MFO IMPT technique for patient treatment.

The increasing frequency and severity of tsunamis in coastal areas underscore the urgent need for efficient Tsunami Early Warning Systems (TEWS). This research aims to optimize TEWS by integrating fast computational tsunami wave modeling to enhance prediction speed and accuracy. The study utilizes numerical simulations employing finite volume methods, along with GPU acceleration, to model tsunami wave propagation and its impact on coastal areas. Machine learning techniques, such as regression trees, are incorporated to analyze large datasets of pre-computed tsunami simulations for accurate forecasting. The results reveal that by applying rapid computational methods, detection time can be reduced by up to 7 minutes, particularly for near-field tsunamis. This significant time-saving enables more effective evacuation procedures and better disaster mitigation efforts. In comparison to conventional systems, the fast computation model also provides more accurate predictions, including tsunami heights and arrival times. The implications of these findings suggest that fast computational methods can substantially improve the current TEWS, allowing for quicker and more reliable tsunami warnings. Moreover, the integration of advanced machine learning techniques ensures the system's adaptability and robustness in predicting tsunami behaviors based on varying data inputs. The potential for implementing this model in tsunami-prone regions worldwide is considerable, offering an improved approach to tsunami disaster preparedness and response. By reducing detection time and enhancing prediction accuracy, the optimized TEWS can significantly minimize loss of life and infrastructure damage, making it a valuable tool for global disaster management strategies.

Autonomous underwater vehicle based mobile networks (AUV-MNs) are utilized in a wide range of marine applications and are likely to play a key role in the implementation of beyond 5G mobile space, air, ground, and sea networks. Communication technology and positioning technology are two key technologies for AUV-MNs, both of which are dependent on the accurate measurement of the underwater acoustic range. Furthermore, with the development of artificial intelligence, the rapid and accurate calculation of underwater acoustic range becomes more important, which affects the decision-making performance of AUV-MNs. In this paper, we propose a fast calculation method of the underwater acoustic horizontal range to guarantee a low-cost, long-endurance AUV-MN ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l^2$</tex-math></inline-formula> -AUV-MN-2.0). Using this fast calculation method, we can obtain an accurate horizontal range for the AUV-MNs in a simple manner, thus ensuring the performance of the AUV-MNs. We verify the feasibility and the robustness of the proposed method via simulations. Furthermore, this fast calculation method can be used in other types of ocean networks or systems, such as leader-follower based multi-AUVs collaborative operation networks, and underwater cellular-type networks.

Delta Sigma Analog to Digital Converters (ADCs) are superior to their counterparts in achieving high resolution for low to medium bandwidth applications. This paper discusses an improved digital calibration technique for enhancing Signal to Noise ratio (SNR) of Delta Sigma ADC which is directly related to Effective Number of Bits (ENOB). The proposed method uses the Adaptive Line Enhancer (ALE) for improving the SNR of the modulator. Adaptive Line Enhancer filters out the estimate of signal of interest from noisy input signal by updating filter coefficients using Least Mean Square (LMS) Algorithm. Variable step size (VSS) LMS is used for updating filter coefficients in Adaptive Line Enhancer instead of Fixed step size (FSS) LMS to reduce the required number of iterations. The simulation results for second order single loop Delta Sigma modulator show approximately 20dB improvement in SNR after calibration and substitution of VSS LMS with FSS LMS has reduced approximately 4000 iterations.

The safety and clinical efficacy of 125 I seed-loaded stent for the treatment of portal vein tumor thrombosis (PVTT) have been shown. Accurate and fast dose calculation of the 125 I seeds with the presence of the stent is necessary for the plan optimization and evaluation. However, the dosimetric characteristics of the seed-loaded stents remain unclear and there is no fast dose calculation technique available. This paper aims to explore a fast and accurate analytical dose calculation method based on Monte Carlo (MC) dose calculation, which takes into account the effect of stent and tissue inhomogeneity. A detailed model of the seed-loaded stent was developed using 3D modeling software and subsequently used in MC simulations to calculate the dose distribution around the stent. The dose perturbation caused by the presence of the stent was analyzed, and dose perturbation kernels (DPKs) were derived and stored for future use. Then, the dose calculation method from AAPM TG-43 was adapted by integrating the DPK and appropriate inhomogeneity correction factors (ICF) to calculate dose distributions analytically. To validate the proposed method, several comparisons were performed with other methods in water phantom and voxelized CT phantoms for three patients. The stent has a considerable dosimetric effect reducing the dose up to 47.2% for single-seed stent and 11.9%-16.1% for 16-seed stent. In a water phantom, dose distributions from MC simulations and TG-43-DP-ICF showed a good agreement with the relative error less than 3.3%. In voxelized CT phantoms, taking MC results as the reference, the relative errors of TG-43 method can be up to 33%, while those of TG-43-DP-ICF method were less than 5%. For a dose matrix with 256 × 256 × 46 grid (corresponding to a phantom of 17.2 × 17.2 × 11.5cm3 ) for 16-seed-loaded stent, it only takes 17s for TG-43-DP-ICF to compute, compared to 25h for the full MC calculation. The combination of DPK and inhomogeneity corrections is an effective approach to handle both the presence of stent and tissue heterogeneity. Exhibiting good agreement with MC calculation and computational efficiency, the proposed TG-43-DP-ICF method is adequate for dose evaluation and optimization in seed-loaded stent implantation treatment planning.

The successful design of delta-sigma modulator (DSM)-based A/D or D/A converters depends heavily on the speed and flexibility of the methods used to determine important system parameters. A Markov model of a general-purpose DSM topology has been developed to calculate the stability range, the output signal-to-noise ratio (SNR), and the amount of harmonic distortion of a DSM. The results generated with the Markov-based approach compare favorably with the output of a DSM simulator which uses difference equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A delta-sigma modulator (DSM) is proposed for the direct connection to micro-electro-mechanical systems (MEMS) microphone. To reduce power, both the DAC reference voltage (VREF) and the DSM supply voltage (VDD) are reduced to 700 mV by limiting the maximum linear acoustic input range to 110 dB SPL (sound pressure level). For the low VDD operation, the switched capacitor (SC) integrators of DSM employ CMOS inverters as amplifiers. A unity-gain buffer compensates the pole error of the SC integrator; it reduces chip area by replacing the auto-zero capacitor of conventional inverter-based SC integrator. Compared to the conventional integrator, the integrator of this brief reduces the pole error from 0.3% to 0.06%, reduces the chip area and the power by 32.4% and 24.8%, respectively. The 3rd order DSM in a 65 nm CMOS process was measured to have Walden-figure of merit (FoMw) 89.3fJ/step, dynamic range (DR) 90.1 dB, signal-to-noise ratio (SNR) 87.2 dB, signal-to-noise and distortion ratio (SNDR) 86.4 dB, and power 122 uW at 10 MHz clock frequency (Fs).