In a dual-inertia system based on permanent magnet synchronous motor (PMSM), the elastic transmission mechanism, such as reducer and coupling, is prone to mechanical resonance, which reduces the precision of servo system transmission. Model prediction and introduction of state feedback are effective methods to suppress mechanical resonance, but the control parameters de-pend on the mechanical parameters of the system. Therefore, mechanical parameter identification is very necessary. In this paper, a forgetting factor recursive least square method is used to identify the mechanical parameters of the dual-inertia elastic system. Firstly, the mathematical model of the dual-inertia system is established and reasonably simplified. Then, the discrete function of the identification algorithm is constructed, and the motor speed and electromagnetic torque are sam-pled to achieve the on-line identification of the main mechanical parameters of the dual-inertia system, and the influencing factors of the identification accuracy are analyzed. Finally, simulations and experiments are carried out to verify the effectiveness of the algorithm.

This work is developed over the question ”How to automatically create a good clustering on spatial dataset with high different local densities?” opened by previus work of Berzi [5]. To answer the main question, this work describe a approach of recursive clustering process based on a technique of finding ”vague-solution”, where the output is an hierarchical clustering of initial dataset. In particularly the the approach is developed and tested on DBSCAN algorithm [11] with large dataset gathered by Google Place in Metropolitan Area of Milan. The core solutions developed in this algorithm are condensed in the capacity of generation a Hierarchical Clustering with a recursive select the best solutions in according tothe our goals, previously dfined by some sets of rules. The algorithm described here, and developed in my Master Thesis, rosolve two problem: - When we use an algorithm of clustering that can create a set of differents clustering, but equally valid and don’t know exctly what we must have as good solution, we areled to ask ourselves: ”What are the better?” This obviously depends by our goals, sonow the question is: ”What are our goals?”; - The second problem is condensed in the sentence ”Not all clusters can be found in one-shot clustering process, more often we must reapply the process to some part of datataset”, so there we have a second question that this paper answering: ”How to create clustering of data with ad-hoc processing for each different part of input dataset?”; These questions are resolved by the approaches named in this work as: Space of Solutions, Vague-Solution, Vague-Solution finding Method and finaly Recursive Clustering. All of these approaches was drafted and tested in mine Master Thesis titled ”Geospatial data analysis for Urban informatics applications: the case of the Google Place of the City of Milan” [25].

In tele-monitoring, wireless body area networks (WBANs), sleep analysis and other applications involving electroencephalogram (EEG) signal, due to the high number of EEG recording channels, long recording time and several repetition of recordings to reach the highest signal-to-noise ratio, the amount of acquired data by the sensors is too large, demanding use of some compression procedure. Compressed sensing can be considered as one of the most effective compression methods in terms of compression ratio, which needs the underlying signal be sparse or have sparse representation in an appropriate domain. EEG signal is not sparse in time domain, therefore, in this paper correlation based weighted recursive least squares dictionary learning algorithm (CBW-RLS) is proposed that uses between-channel correlations to sparsify EEG signals. Due to the low-rank structure of EEG signals, exploiting between-channel correlations increase the sparsity level of the model while reducing the computational cost of dictionary learning procedure. This is done by merely updating the dictionary atoms which are involved in the sparse model of the previous data, reducing the total number of data used at each iteration and speeding up the dictionary learning algorithm. The simulation results show that the proposed method has better performance in terms of both quality of the EEG reconstruction and the computational cost compared to the other methods.

Multi-step ahead streamflow forecasting is of practical interest for the operation of hydropower reservoirs. We provide generalized results on the error evolution in multi-step ahead forecasting by conducting several large-scale experiments based on simulations. We also present a multiple-case study using monthly time series of streamflow. Our findings suggest that some forecasting methods are more useful than others. However, the errors computed at each time step of a forecast horizon within a specific case study strongly depend on the case examined and can be either small or large, regardless of the forecasting method used and the time step of interest.

A symbolic analysis of Archimedes’ periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented,, by remarking the cruciality of this topic in number theory. Periods of ordinal numbers, and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship among numbers and information, which shed new light on a red line passing through the whole history of mathematics

Toby Walsh in “The Singularity May Never Be Near” gives six arguments to support his point of view that technological singularity may happen but that it is unlikely. In this paper, we provide analysis of each one of his arguments and arrive at similar conclusions, but with more weight given to the “likely to happen” probability.

Vibration monitoring is a critical aspect of assessing the health and performance of machinery and industrial processes. This study explores the application of machine learning techniques, specifically the Random Forest (RF) classification model, to predict and classify chatter—a detrimental self-excited vibration phenomenon—during machining operations. While sophisticated methods have been employed to address chatter, this research investigates the efficacy of a simplified RF model. The study leverages simulated vibration data, bypassing resource-intensive real-world data collection, to develop a versatile chatter detection model applicable across diverse machining configurations. The feature extraction process combines time-series features and Fast Fourier Transform (FFT) data features, streamlining the model while addressing challenges posed by feature selection. By focusing on the RF model’s simplicity and efficiency, this research advances chatter detection techniques, offering a practical tool with improved generalizability, computational efficiency, and ease of interpretation. The study demonstrates that innovation can reside in simplicity, opening avenues for wider applicability and accelerated progress in the machining industry.

An ambitious per capita GDP target has been envisioned by the Chinese government since 2020 to project its sustainable economic growth rate by 2035. Can China fully achieve its goal? This is a question worth investigating. By inserting relevant TABLO modules of the final goods trade, the intermediate goods trade, and factor-strengthening technology spillovers, along with technology absorption thresholds effects of the global value chain, this study builds a global dynamic recursive computational general equilibrium (CGE ) model on basis of GTAP-RD. This approach allows considering the 'dual circulation' system strongly advocated and pointed out as the sole way to realize China’s technological (total factor productivity (TFP)) progress by the Chinese government, which integrates both domestic internal and international external circulations (trade and foreign direct investment (FDI)). We simulate China's technological progress under eight scenarios, and use the latest GTAP Version 11 production and trade data (released in April 2023) for 141 countries and regions and results are aggregated into 10 countries groups with 9 activity sectors and 10 commodities. Main conclusions are as follows: (1) If China maintains its trade opening policy, the 2035 vision goal can be achieved, with external circulation being more important than internal circulation for technological spillovers. (2) The economic growth impacts of external and internal circulation operate relatively independently. However, FDI provides a relatively larger synergistic effect for all forms of external trade circulation than to the internal one. Regarding factor-strengthening effects, spillovers are more favorable to 'capital' than to labor factors. (3) We find that the Regional Comprehensive Economic Partnership Agreement is the most important strategic partner for China. (4) It appears that FDI is not an effective way to lift the productive services sector's total factor productivity (TFP), and more realistic for China is to open up the productive services market more widely, as its efficiency is a pivotal reflection of China's independent innovation capability. (5) China–US decoupling has an enormous global impact. In all the Scenarios we consider, the United States is always the country that loses the most, and Europe would be the group of countries that benefits when there is a large increase in TFP in the US.

In this article we have constructed a basic methodology from which important perspectives for both the Collatz conjecture and Beal's conjecture can be derived. We falsified the conjecture we previously developed on Beal's conjecture and made the falsified conjecture usable for Collatz conjecture. In this regard, we have clearly expressed the numbers that can reach 1 in the Collatz conjecture. Then, using this, we created a limit for the numbers that should be considered for the Collatz conjecture. Thanks to the analysis of this limit, we have clearly expressed the recursive Collatz function in an equation. Using this structure, we wrote a function that indicates how many times the Collatz function repeats certain numbers to reach 1.

This paper reviews the pioneering work related to the generation of a sequence of prompts in Pretrained Language Models (PLMs) to automatically complete a complex writing task. The paper identifies the main categories of automated multi-step prompting and discusses their advantages and disadvantages. The paper also proposes an additional approach for automated multi-step prompting with iterative four main phases: in the first phase a sequence of prompts is geared to elicit the structure of the requested task. This is done by identifying the task’s main parts, the general contents of the different parts and their precedence relations. The structure of each main part is iteratively explored to find secondary and tertiary parts if they exist. A second phase is followed by a sequence of prompts that fill in the primary, secondary, and tertiary parts, and seek to fine-tune the result. The third phase reviews the generated text and criticizes it. Based on this criticism a revision is prepared. The fourth phase is fine-tuning the document, with emphasis on section length and text tone. Future research could deal with the system identification of points where the system should initiate interaction with the user for desired feedback and guidance.

In recent years, the emergence of spatiotemporal big data has made the transition of functional identification from the physical dimension to socioeconomic or human activities becoming more common. In the identification of urban functional areas, most studies considered only a single data source and a single division scale, the research results have problems such as low update frequency or incomplete information in a single data set, and overfitting or underfitting in a single spatial resolution. Using taxi trajectory data and point of interest (POI) data as the main data source, this study proposes a multi-scale recursive identification method for urban functional areas based on cross-validation. First, used the dynamic time warping (DTW) algorithm generates a time series similarity matrix, the CA-RFM model combines the clustering algorithm and random forest model is constructed, the model uses a clustering algorithm (K-MEDOIDS) to extract sig-nificant feature regions as input, which are imported into the random forest model for UFZ identification. Then, to overcome the shortcomings of single scale in expressing urban structural characteristics, a recursive model of different levels of urban road networks is established to classify multi-scale functional areas. Finally, cross-validation using the CA-RFM model and POI quantitative identification method, obtains the final identification results of urban functional areas. This paper selects Shenzhen as the study area for the case study, the results show that the com-bination of clustering algorithm and random forest model greatly reduces the error of manual selection of training samples. In addition, the research shows the superiority of the multi-scale recursive identification method that fuses multi-source data and performs cross-validation from two aspects, that is, the division speed of urban functional area identification results is accelerated and the accuracy is improved.

Nutrient regulation in aquaponic environments has been the topic of research for many years. Most have focused on appropriate control of nutrients in an aquaponic set-up, but very little research has been done on commercial scale applications. In our model, the input data was sourced on a weekly basis from three commercial aquaponic farms in South-East Texas over the course of a year. Due to limited number of data points, dimensionality reduction techniques like pair-wise correlation matrix was used to remove the highly correlated predictors. Feature selection techniques like the XGBoost classifier and Recursive Feature Elimination with ExtraTreesClassifier were used to rank the features in order of their relative importance. Ammonium and calcium were found to be the top two nutrient predictors and based on the months in which lettuce was cultivated, the median of these nutrient values from the historical dataset served as the optimal concentrations to be maintained in the aquaponic solution. To accomplish this, Vernier sensors were used to measure the nutrient values and actuator systems were built to dispense the appropriate nutrient into the ecosystem via a closed loop.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Firstly, we present a more explicit formulation of the complete system $D(N)$ of representatives of Manin's symbols over $\mathbb{Q}$, which was initially given by Shimura. Then we establish a bijection between $D(M)\times D(N)$ and $D(MN)$ for $(M,N)=1$, which reveals a recursive structure between Manin's symbols of different levels. Based on Manin's complete system $\Pi (N)$ of representatives of cusps on $X_0(N)$ and Cremona's characterization of the equivalence between cusps, we establish a bijection between a subset $C(N)$ of $D(N)$ and $\Pi (N)$, and then establish a bijection between $C(M)\times C(N)$ and $C(MN)$ for $(M,N)=1$. We also provide a recursive structure for elliptical points on $X_0(N)$. Based on these recursive structures, we obtain recursive algorithms for constructing Manin symbols over $\mathbb{Q}$, cusps and elliptical points on $X_0(N)$. This gives rise to a more efficient algorithms for modular elliptic curve. As direct corollaries of these recursive structures, we present a recursive version of the genus formula and an elementary proof of formulas of the numbers of $D(N)$, cusps and elliptical points on $X_0(N)$.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

This manuscript compares deterministic artificial intelligence to model following control applied to DC motor control, including evaluation of the threshold computation rate to let unmanned underwater vehicles correctly follow the challenging discontinuous square wave command signal. The approaches presented in the main text are validated in MATLAB®, where the motor process is discretized at multiple step sizes, which is inversely proportional to the computation rate. The performance is evaluated by the error mean and standard deviation. With a large step size, discrete deterministic artificial intelligence shows a larger error mean than the model-following self-turning regulator approach (benchmark selection). However, the performance gets optimized with the step size decreased. The error mean is close to the continuous deterministic artificial intelligence when the step size is reduced to 0.2 seconds, which means that the computation rate and the sampling period restrict discrete deterministic artificial intelligence. In that case, the continuous deterministic artificial intelligence is the most feasible and reliable selection for future applications on unmanned underwater vehicles since it is superior to all the approaches with multiple computation rates.

Table detection is a preliminary step in extracting reliable information from tables in scanned document images. We present CasTabDetectoRS, a novel end-to-end trainable table detection framework that operates on Cascade Mask R-CNN, including Recursive Feature Pyramid network and Switchable Atrous Convolution in the existing backbone architecture. By utilizing a comparatively lightweight backbone of ResNet-50, this paper demonstrates that superior results are attainable without relying on pre and post-processing methods, heavier backbone networks (ResNet-101, ResNeXt-152), and memory-intensive deformable convolutions. We evaluate the proposed approach on five different publicly available table detection datasets. Our CasTabDetectoRS outperforms the previous state-of-the-art results on four datasets (ICDAR-19, TableBank, UNLV, and Marmot) and accomplishes comparable results on ICDAR-17 POD. Upon comparing with previous state-of-the-art results, we obtain a significant relative error reduction of 56.36%, 20%, 4.5%, and 3.5% on the datasets of ICDAR-19, TableBank, UNLV, and Marmot, respectively. Furthermore, this paper sets a new benchmark by performing exhaustive cross-datasets evaluations to exhibit the generalization capabilities of the proposed method.

Goals: To use visual logistics for interpreting COVID-19 molecular and rapid antigen test (RAgT) performance, determine prevalence boundaries where risk exceeds expectations, and evaluate benefits of recursive testing along home, community, and emergency spatial care paths. Methods: Mathematica/open access software helped graph relationships, compare performance patterns, and perform recursive computations. Results: Tiered sensitivity/specificity comprise: T1) 90%/95%; T2) 95%/97.5%; and T3) 100%/≥99%, respectively. In emergency medicine, median RAgT performance peaks at 13.2% prevalence, then falls below T1, generating risky prevalence boundaries. RAgTs in pediatric ERs/EDs parallel this pattern with asymptomatic worse than symptomatic performance. In communities, RAgTs display large uncertainty with median prevalence boundary of 14.8% for 1/20 missed diagnoses, and at prevalence >33.3-36.9% risk 10% false omissions for symptomatic subjects. Recursive testing improves home RAgT performance. Home molecular tests elevate performance above T1, but lack adequate validation. Conclusions: Widespread RAgT availability encourages self-testing. Asymptomatic RAgT and PCR-based saliva testing present the highest chance of missed diagnoses. Home testing twice, once just before mingling, and molecular-based self-testing help avoid false omissions. Community and ER/ED RAgTs can identify contagiousness in low prevalence (<22%). Real-world trials of performance, cost-effectiveness, and public health impact could identify home molecular diagnostics as the optimal diagnostic portal.

The Van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Because of its chaotic nature, controlling, or forcing, the behavior of a Van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two Van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the Van der Pol oscillator. Deterministic AI (DAI) is an adaptive feedback control method that leverages the known physics of the Van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of DAI employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error (MAE) between the target trajectory and the response oscillator trajectory over time. RLS with exponential forgetting (RLS-EF) had the lowest MAE overall, with a 2.46% reduction in error. However, another method was notable. Least Mean Squares with normalized gradient adaptation (LMS-NG) had worse initial error in the first 10% of the simulation, but after that point had consistently better performance. We found that over the last 90% of the simulation, DAI with LMS-NG had a 48.7% reduction in MAE compared to feedforward alone.