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The aim of this note is to survey the results in some geometric problems related to the centroids and the static equilibrium points of convex bodies. In particular, we collect results related to Gr\"unbaum's inequality and the Busemann-Petty centroid inequality, describe classifications of convex bodies based on equilibrium points, and investigate the location and structure of equilibrium points, their number with respect to a general reference point as well as the static equilibrium properties of convex polyhedra., Comment: 27 pages, 1 table, 5 figures

In a recent paper published in Nature, Y.I. Sobolev et al. introduced the concept of trajectoids: convex, rigid objects, which roll without slip or spin on a flat plane along a prescribed periodic, unbounded planar path. A geometric construction method applicable to many paths was introduced, and the theory was experimentally verified using objects rolling downwards on slightly inclined planes. The construction method was applicable to many but not all curves. A possible extension of the method (referred to as period-n trajectoids) was also proposed, but the limits of applicability were not clarified. Here, a geometric proof is given for the existence of period-n trajectoids for any sufficiently smooth prescribed curve. A somewhat different proof was recently proposed by O. Muller independently from this work. We also highlight some related geometry problems.

Time-Series Forecasting is a powerful data modeling discipline that analyzes historical observations to predict future values of a time-series. It has been utilized in numerous applications, including but not limited to economics, meteorology, and health. In this paper, we use time-series forecasting techniques to model and predict the future incidence of chickenpox. To achieve this, we implement and simulate multiple models and data preprocessing techniques on a Hungary-collected dataset. We demonstrate that the LSTM model outperforms all other models in the vast majority of the experiments in terms of county-level forecasting, whereas the SARIMAX model performs best at the national level. We also demonstrate that the performance of the traditional data preprocessing method is inferior to that of the data preprocessing method that we have proposed.

Reliable quasi-static object manuipulation and robotic locomotion require verification of the stability of equilibria under rigid contacts and friction. In a recent paper, M. Posa, M. Tobenkin, and R. Tedrake demonstrated that sums-of-squares (SOS) programming can be used to verify Lyapunov stability via Lyapunov's direct method. This test was successfully applied to several simple problems with a single point contact. At the same time it has been found that this method is too conservative for several multi-contact systems. In this paper, an extension of Lyapunov's direct method is proposed, which makes use of several Lyapunov functions, and which allows \emph{temporary} increase of those Lyapunov function along a motion trajectory. The proposed method remains compatible with SOS programming techniques. The improved stability test is successfully applied to a rigid body with 2 point contacts, for which the exact conditions of Lyapunov stability are unknown.

We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n} \big)$ with high probability, assuming only certain partial independence of the letters. Our observation is motivated by Nicaud (2014) providing a near-linear bound in the case of two random mapping letters, among multiple other results. The upper bound for the latter case has been recently improved by the breakthrough work of Chapuy and Perarnau (2023) to $\mathcal{O}(\sqrt{n} \log n)$.

Answering a question of Conway and Guy in a 1968 paper, L\'angi in 2021 proved the existence of a monostable polyhedron with $n$-fold rotational symmetry for any $n \geq 3$, and arbitrarily close to a Euclidean ball. In this paper we strengthen this result by characterizing the possible symmetry groups of all mono-monostatic smooth convex bodies and convex polyhedra. Our result also answers a stronger version of the question of Conway and Guy, asked in the above paper of L\'angi., Comment: 17 pages, 6 figures

The recent developments of computer and electronic systems have made the use of intelligent systems for the automation of agricultural industries. In this study, the temperature variation of the mushroom growing room was modeled by multi-layered perceptron and radial basis function networks based on independent parameters including ambient temperature, water temperature, fresh air and circulation air dampers, and water tap. According to the obtained results from the networks, the best network for MLP was in the second repetition with 12 neurons in the hidden layer and in 20 neurons in the hidden layer for radial basis function network. The obtained results from comparative parameters for two networks showed the highest correlation coefficient (0.966), the lowest root mean square error (RMSE) (0.787) and the lowest mean absolute error (MAE) (0.02746) for radial basis function. Therefore, the neural network with radial basis function was selected as a predictor of the behavior of the system for the temperature of mushroom growing halls controlling system.

Stability of equilibrium states in mechanical systems with multiple unilateral frictional contacts is an important practical requirement, with high relevance for robotic applications. In our previous work, we theoretically analyzed finite-time Lyapunov stability for a minimal model of planar rigid body with two frictional point contacts. Assuming inelastic impacts and Coulomb friction, conditions for stability and instability of an equilibrium configuration have been derived. In this work, we present for the first time an experimental demonstration of this stability theory, using a variable-structure rigid ''biped'' with frictional footpads on an inclined plane. By changing the biped's center-of-mass location, we attain different equilibrium states, which respond to small perturbations by divergence or convergence, showing remarkable agreement with the predictions of the stability theory. Using high-speed recording of video movies, good quantitative agreement between experiments and numerical simulations is obtained, and limitations of the rigid-body model and inelastic impact assumptions are also studied. The results prove the utility and practical value of our stability theory., Comment: Accepted for publication by IEEE Transactions on Robotics

Prediction models in mobility and transportation maintenance systems have been dramatically improved through using machine learning methods. This paper proposes novel machine learning models for intelligent road inspection. The traditional road inspection systems based on the pavement condition index (PCI) are often associated with the critical safety, energy and cost issues. Alternatively, the proposed models utilize surface deflection data from falling weight deflectometer (FWD) tests to predict the PCI. Machine learning methods are the single multi-layer perceptron (MLP) and radial basis function (RBF) neural networks as well as their hybrids, i.e., Levenberg-Marquardt (MLP-LM), scaled conjugate gradient (MLP-SCG), imperialist competitive (RBF-ICA), and genetic algorithms (RBF-GA). Furthermore, the committee machine intelligent systems (CMIS) method was adopted to combine the results and improve the accuracy of the modeling. The results of the analysis have been verified through using four criteria of average percent relative error (APRE), average absolute percent relative error (AAPRE), root mean square error (RMSE), and standard error (SD). The CMIS model outperforms other models with the promising results of APRE=2.3303, AAPRE=11.6768, RMSE=12.0056, and SD=0.0210., Comment: 23 pages, 10 figures

In the present work, a novel and the robust computational investigation is carried out to estimate solubility of different acids in supercritical carbon dioxide. Four different algorithms such as radial basis function artificial neural network, Multi-layer Perceptron (MLP) artificial neural network (ANN), Least squares support vector machine (LSSVM) and adaptive neuro-fuzzy inference system (ANFIS) are developed to predict the solubility of different acids in carbon dioxide based on the temperature, pressure, hydrogen number, carbon number, molecular weight, and acid dissociation constant of acid. In the purpose of best evaluation of proposed models, different graphical and statistical analyses and also a novel sensitivity analysis are carried out. The present study proposed the great manners for best acid solubility estimation in supercritical carbon dioxide, which can be helpful for engineers and chemists to predict operational conditions in industries., Comment: 37 pages, 9 figure

Accurate prediction of mercury content emitted from fossil fueled power stations is of utmost important for environmental pollution assessment and hazard mitigation. In this paper, mercury content in the output gas of power stations boilers was predicted using adaptive neuro fuzzy inference system method integrated with particle swarm optimization. The input parameters of the model include coal characteristics and the operational parameters of the boilers. The dataset has been collected from a number of power plants and employed to educate and examine the proposed model. To evaluate the performance of the proposed ANFIS PSO model the statistical meter of MARE was implemented. Furthermore, relative errors between acquired data and predicted values presented, which confirm the accuracy of the model to deal nonlinearity and representing the dependency of flue gas mercury content into the specifications of coal and the boiler type., Comment: 31 pages, 7 figures

Emotion detection from the text is an important and challenging problem in text analytics. The opinion-mining experts are focusing on the development of emotion detection applications as they have received considerable attention of online community including users and business organization for collecting and interpreting public emotions. However, most of the existing works on emotion detection used less efficient machine learning classifiers with limited datasets, resulting in performance degradation. To overcome this issue, this work aims at the evaluation of the performance of different machine learning classifiers on a benchmark emotion dataset. The experimental results show the performance of different machine learning classifiers in terms of different evaluation metrics like precision, recall ad f-measure. Finally, a classifier with the best performance is recommended for the emotion classification., Comment: 30 pages, 13 tables, 1 figure

Evaporation is one of the main processes in the hydrological cycle, and it is one of the most critical factors in agricultural, hydrological, and meteorological studies. Due to the interactions of multiple climatic factors, the evaporation is a complex and nonlinear phenomenon; therefore, the data-based methods can be used to have precise estimations of it. In this regard, in the present study, Gaussian Process Regression, Nearest-Neighbor, Random Forest and Support Vector Regression were used to estimate the pan evaporation in the meteorological stations of Golestan Province, Iran. For this purpose, meteorological data including PE, temperature, relative humidity, wind speed and sunny hours collected from the Gonbad-e Kavus, Gorgan and Bandar Torkman stations from 2011 through 2017. The accuracy of the studied methods was determined using the statistical indices of Root Mean Squared Error, correlation coefficient and Mean Absolute Error. Furthermore, the Taylor charts utilized for evaluating the accuracy of the mentioned models. We report that GPR for Gonbad-e Kavus Station with input parameters of T, W and S and GPR for Gorgan and Bandar Torkmen stations with input parameters of T, RH, W, and S had the most accurate performances and proposed for precise estimation of PE. Due to the high rate of evaporation in Iran and the lack of measurement instruments, the findings of the current study indicated that the PE values might be estimated with few easily measured meteorological parameters accurately., Comment: 21 pages, 5 figures