Transformation Algorithm Research Articles

A unified strategy to compute some special functions of number-theoretic interest

We introduce an algorithm to compute the functions belonging to a suitable set F defined as follows: f∈F means that f(s,x), s∈A⊂R being fixed and x>0, has a power series expansion centred at x0=1 with convergence radius greater or equal than 1; moreover, it satisfies a functional equation of step 1 and the Euler-Maclaurin summation formula can be applied to f. Denoting the Euler gamma-function as Γ, we will show that, for x>0, log⁡Γ(x), the digamma function ψ(x), the polygamma functions ψ(w)(x), w∈N, w≥1, and, for s>1 being fixed, the Hurwitz ζ(s,x)-function and its first partial derivative ∂ζ∂s(s,x) are in F. In all these cases the coefficients of the involved power series will depend on the values of ζ(u), u>1, where ζ is the Riemann zeta-function. As a by-product, we will also show how to compute the Dirichlet L-functions L(s,χ) and L′(s,χ), s>1, χ being a primitive Dirichlet character, by inserting the reflection formulae of ζ(s,x) and ∂ζ∂s(s,x) into the first step of the Fast Fourier Transform algorithm. Moreover, we will obtain some new formulae and algorithms for the Dirichlet β-function and for the Catalan constant G. Finally, we will study the case of the Bateman G-function and of the alternating Hurwitz zeta-function, also known as the η-function; we will show that, even if they are not in F, our approach can be adapted to handle them too. In the last section we will also describe some tests that show a performance gain with respect to a standard multiprecision implementation of ζ(s,x) and ∂ζ∂s(s,x), s>1, x>0.

Real-time prediction of SO2 emission concentration under wide range of variable loads by convolution-LSTM VE-transformer

In this paper, a sulfur dioxide (SO2) emission concentration real-time dynamic prediction model is proposed to achieve the control target of ultra-low SO2 emissions and economical desulfurization system operation at a large-scale coal-fired power plant. First, a vision-expansion self-attention strategy is adopted on the Transformer algorithm structure for better time-series information feature extraction. Second, to adapt to the vision-expansion self-attention strategy, convolution and long short-term memory (LSTM) are combined to process input information position encoding, which can obtain long time-series information absolute position encoding. Then, a Convolution-LSTM VE-Transformer model is constructed by combining the above two proposed parts. The mutual information method and the differential evolution algorithm are combined to calculate correlations between variables and obtain the optimal delay time. Finally, a real-time dynamic prediction model of SO2 is established. In this model, the structure of the input and output variables is determined by the delay time and the influence of coal quality on the SO2 concentration. The quantitative comparison results show the superior accuracy and generalization ability of the proposed prediction model to related popular methods, indicating that the model has strong potential for use in further controller design and applications.

ViT-based Terrain Recognition System for wearable soft exosuit

Terrain classification and force assistance strategies in complex environments have always piqued the interest of many researchers. For wearable soft exosuits, inaccurate terrain recognition can easily introduce undesired assist forces that can easily injure the wearer. Because of these problems, we introduced a depth camera into the exosuit system, perform classification of terrain based on a Vision Transformer (ViT), and optimized the control algorithm, which is known as a ViT-Based Terrain Recognition System (TTRS). First, we used the Transformer algorithm to achieve a considerable classification effect in terrain recognition. We also introduced terrain recognition as prior knowledge into the force assistance strategy of the exosuit, providing different force assistance to the exosuit in different terrains. Subsequently, we performed human experiments with seven able-bodied people (six males and one female). The promising results demonstrate that our classification accuracy can reach 99.2% under six different terrains and that it can smoothly switch the force–assist curve in different terrains to better adapt to the complex terrain and improve the walking effect. The aforementioned terrain recognition algorithms and force–assist strategies may positively influence the study of soft exosuit, powered prostheses, and orthotics.

PROMIS-29 and EORTC QLQ-C30: an empirical investigation towards a common conception of health

PurposeThe assessment of health-related quality of life (HRQOL) measured via patient-reported outcomes (PROs) is a key component in clinical trials and increasingly used in clinical routine worldwide. Two PRO measures (PROMs) that share the same definition of health and report outcomes on a comparable T-metric anchored to general population samples are the PROMIS-29 and the EORTC QLQ-C30. In this study, we investigate the empirical agreement of these underlying concepts.MethodsWe collected PROMIS-29 and EORTC QLQ-C30 data from 1,478 female patients at a breast cancer outpatient centre. We calculated descriptive statistics and correlations between the subscales of both instruments. We performed exploratory (EFA) and confirmatory factor analysis (CFA) in randomly split subsamples in order to assess the underlying psychometric structure of both instruments.ResultsThe cohort (mean age = 47.4, ± 14.49) reported comparable mean HRQOL scores between the corresponding subscales of both instruments similar to general population reference values. Correlation between the corresponding subscales of both instruments ranged between 0.59 (Social Role) and 0.78 (Physical Functioning). Both an exploratory and a theoretically driven confirmatory factor analysis provided further support for conceptual agreement of the scales.ConclusionEORTC QLQ-C30 and PROMIS-29 showed similar scores and satisfactory agreement in conceptional and statistical analysis. This suggests that the underlying conceptualization of health is reasonably close. Hence, the development of score transformation algorithms or calibration of both instruments on common scales could prospectively increase the comparability of clinical and research PRO data collected with either instrument.

Disaster cassification net: A disaster classification algorithm on remote sensing imagery

As we all know, natural disasters have a great impact on people’s lives and properties, and it is very necessary to deal with disaster categories in a timely and effective manner. In light of this, we propose using tandem stitching to create a new Disaster Cassification network D-Net (Disaster Cassification Net) using the D-Conv, D-Linear, D-model, and D-Layer modules. During the experiment, we compared the proposed method with “CNN” and “Transformer”, we found that disaster cassification net compared to CNN algorithm Params decreased by 26–608 times, FLOPs decreased by up to 21 times, Precision increased by 1.6%–43.5%; we found that disaster cassification net compared to Transformer algorithm Params decreased by 23–149 times, FLOPs decreased by 1.7–10 times, Precision increased by 3.9%–25.9%. Precision increased by 3.9%–25.9%. And found that disaster cassification net achieves the effect of SOTA(State-Of-The-Art) on the disaster dataset; After that, we compared the above-mentioned MobileNet_v2 with the best performance on the classification dataset and CCT network are compared with disaster cassification net on fashion_mnist and CIFAR_100 public datasets, respectively, and the results show that disaster cassification net can still achieve the state-of-the-art classification effect. Therefore, our proposed algorithm can be applied not only to disaster tasks, but also to other classification tasks.

The multi-AUV time-varying formation reconfiguration control based on rigid-graph theory and affine transformation

This paper studies the time-varying formation reconfiguration control for multiple underactuated autonomous underwater vehicles (AUVs) with an Euler–Lagrange-like model. The goal is to control a fleet of AUVs to achieve any desired formation shape using a distance-based graph rigidity and affine transformation (GR-AT) algorithm. Firstly, the distance-based graph rigidity with backstepping technology is utilized to solve the formation controlproblem, and we acquire the initial nominal formation. In the sequel, we transform the nominal formation into any desired formation shape using the properties of the affine transformation (including translation, scaling, rotation, shearing, or a combination of them). Even the geometric shapes formed can be constantly changed. The Lyapunov stability theory can ensure the uniform ultimate boundedness of whole distance errors. Finally, several simulation examples with formation reconfiguration are given to validate the efficacy of the designed control methods. Moreover, some experimental results are presented to confirm the validity and applicability of the scheme with four real bionic robot fish.

Cloud-Cluster: An uncertainty clustering algorithm based on cloud model

As a cornerstone of the world, uncertainty embodies the nature of data and knowledge. Existing uncertainty theory-based clustering algorithms learn fuzziness, i.e., the uncertainty of clustering objects belonging to different clusters. However, these algorithms do not refer to the fuzziness of objects themselves, i.e., the randomness of data. Here, we propose a clustering algorithm named Cloud-Cluster, which simultaneously characterizes the fuzziness and randomness of objects to reserve uncertain information, and to describe clusters into concepts. It embeds random uncertainty of concepts to extend the data distribution range for better data partitions and gradually constructs accurate concepts by an improved backward cloud transformation algorithm (MBCT-SR-Ex). Moreover, to ensure that the concept clustering process gradually converges, Cloud-Cluster introduces the Cluster Concept Drift Degree to evaluate the uncertainty of concepts during the clustering process. Experiments on UCI and OpenML clustering datasets show that Cloud-Cluster improves the average clustering accuracy by over 14% compared to K-Means and uncertainty theory-based clustering algorithms. Extensive experimental results on the evaluation of uncertainty show that Cloud-Cluster can handle the uncertainty of datasets in the clustering process well, in addition to exhibiting robustness with unclear clusters.

Mild behavioral impairment linked to progression to Alzheimer's disease and cortical thinning in amnestic mild cognitive impairment.

Mild behavioral impairment (MBI) is a neurobehavioral syndrome characterized by later life emergence of sustained neuropsychiatric symptoms, as an at-risk state for dementia. However, the associations between MBI and a risk of progression to Alzheimer's disease (AD) and its neuroanatomical correlates in mild cognitive impairment (MCI) are still unclear. A total 1,184 older adults with amnestic MCI was followed for a mean of 3.1 ± 2.0 years. MBI was approximated using a transformation algorithm for the Neuropsychiatric Inventory at baseline. A two-step cluster analysis was used to identify subgroups of individuals with amnestic MCI based on profiles of 5 MBI domain symptoms (decreased motivation, affective dysregulation, impulse dyscontrol, social inappropriateness, abnormal perception/thought content). A Cox regression analysis was applied to investigate differences in the risk of progression to AD between subgroups. A subset of participants (n = 202) underwent 3D T1-weighted MRI scans at baseline and cortical thickness was compared between the subgroups of amnestic MCI patients. The cluster analysis classified the patients into 3 groups: (1) patients without any MBI domain symptoms (47.4%, asymptomatic group); (2) those with only affective dysregulation (29.4%, affective dysregulation group); (3) those with multiple MBI domain symptoms, particularly affective dysregulation, decreased motivation and impulse dyscontrol (23.2%, complex group). Compared to the asymptomatic group, the complex group was associated with a higher risk of progression to AD (hazard ratio = 2.541 [1.904-3.392], p < 0.001), but the affective dysregulation group was not (1.214 [0.883-1.670], p = 0.232). In cortical thickness analysis, the complex group revealed cortical thinning bilaterally in the inferior parietal, lateral occipital, lateral superior temporal, and frontopolar regions compared with the affective dysregulation group. The multiple co-occuring MBI domains in individuals with amnestic MCI are associated with a higher risk of progression to AD and cortical thinning in temporal, parietal and frontal areas. These results suggest that evaluation of MBI could be useful for risk stratification for AD and appropriate intervention in MCI individuals.

Drift analysis and sectional post-processing of indoor simultaneous localization and mapping (SLAM)-based laser scanning data

Even though the SLAM laser scanners (LSs) have the required resolution for construction analysis, a drift error has been detected in georeferencing phase of the data processing. The reduction of drift error in SLAM LSs with third-party software has not been studied. This paper demonstrates the drift error behavior of commercial SLAM LSs and their correction with sectional post-processing methods, and shows that the drift error is mainly in a vertical direction, and it is largest in the middle of the trajectory. The drift error was reduced from 10.6 cm to 0.2 cm. Circa 30 s length sections have better results than larger sections with non-rigid transformation algorithm. The method has shown potential to improve the quality and cost-effectiveness of multitemporal construction documentation. In addition, locations of additional control points were analyzed to prevent drift error, with adjustments to the walking path.

Small Target Detection Model in Aerial Images Based on TCA-YOLOv5m

Target detection in aerial images taken by unmanned aerial vehicles is the most widely used scene at present. Compared with ordinary images, the background of aerial images is more complex, and the target size is smaller, which results in inferior detection precision and a high false detection rate. This paper proposes a new small target detection model TCA-YOLOv5m, which is based on YOLOv5m and combines the Transformer algorithm and the Coordinate Attention (CA) mechanism. In this model, the transformer algorithm is added to the end of the backbone of the YOLOv5, which enables the model to mine more features information of images. In the neck layer of the TCA-YOLOv5m, the Path Aggregation Network (PANet) and transformer algorithm are combined to enhance the expression capacity for the feature pyramid and improve the detection precision of occluded high-density small targets, and CA is introduced to more accurately locate targets in high-density scenes. In addition, the TCA-YOLOv5m adds a detection layer to improve the ability to capture small targets. This paper uses VisDrone 2019 as experimental data, and takes experiments to compare the detection precision and detection speed of the proposed model with baseline models. The experiment results indicate that the detection precision of the TCA-YOLOv5m reaches 97.4%, which is 5.2% higher than that of YOLOv5; the value of MAP @ 50 reaches 58.5%, which is 14.8% higher than YOLOv5. The Frames Per Second (FPS) of the TCA-YOLOv5m is 12.96 f/s, which ensures a certain real-time performance. Therefore, the TCA-YOLOv5m is suitable for the task of detecting dense small targets in aerial images.

Time-Domain Protection Scheme for Microgrids With Aggregated Inverter-Based Distributed Energy Resources

This paper proposes a time-domain-based protection scheme for radial and loop microgrid systems with inverter-based resources (IBRs), such as solar photovoltaic (PV) and type-4 wind turbines. The protection scheme is designed to function during both grid-interconnected and grid-isolated modes. The proposed scheme provides an ultra-high-speed sub-cycle directional element aided with low bandwidth communication between relays. Like directional comparison schemes, relays identify whether faults are in-zone or out-zone. The directional element is based on time-domain superimposed quantities and Park’s transformation algorithms. More specifically, the element calculates the superimposed positive-sequence direct component of transient energy during faults. Superimposed voltage and current quantities are calculated using delta filters and decoupled double synchronous reference frame (DDSRF) filters. The proposed filtering method improves the reliability of the superimposed directional element when IBRs are present. The protection scheme is evaluated on a modified IEEE 34-bus distribution system simulated using an electromagnetic transients program.

Obtaining 3D super-resolution images by utilizing rotationally symmetric structures and 2D-to-3D transformation

Super-resolution imaging techniques have provided unprecedentedly detailed information by surpassing the diffraction-limited resolution of light microscopy. However, in order to derive high quality spatial resolution, many of these techniques require high laser power, extended imaging time, dedicated sample preparation, or some combination of the three. These constraints are particularly evident when considering three-dimensional (3D) super-resolution imaging. As a result, high-speed capture of 3D super-resolution information of structures and dynamic processes within live cells remains both desirable and challenging. Recently, a highly effective approach to obtain 3D super-resolution information was developed that can be employed in commonly available laboratory microscopes. This development makes it both scientifically possible and financially feasible to obtain super-resolution 3D information under certain conditions. This is accomplished by converting 2D single-molecule localization data captured at high speed within subcellular structures and rotationally symmetric organelles. Here, a high-speed 2D single-molecule tracking and post-localization technique, known as single-point edge-excitation sub-diffraction (SPEED) microcopy, along with its 2D-to-3D transformation algorithm is detailed with special emphasis on the mathematical principles and Monte Carlo simulation validation of the technique.

СТЕГАНОГРАФІЧНА СИСТЕМА ПРИХОВУВАННЯ ТЕКСТОВОЇ ІНФОРМАЦІЇ В АУДІОФАЙЛАХ

Audio file steganography can be used as an effective and efficient method to hide messages, but it is a complex process because the human auditory system is sensitive to small changes in audio data. In this article an improved approach for hiding secret text message in audio is presented, combining steganography and cryptography. The Least Significant Bits (LSB) technique, one of the most common and basic methods of steganography, is used as an algorithm for steganographic transformation. The described point of this method is to replace the least significant bits of the audio container with message bits that contain not very useful information, so filling them with additional information has little effect on the quality of perception. Such a significant disadvantage as the low level of reliability is improved by the introduction of a cryptographic layer, the feasibility of which is justified in the article. Cryptographic protection has been added in the form of one of the modern symmetric encryption algorithms – the AES algorithm in the CBC mode. Pseudo-random numbers are used to create a stable cryptokey. The cryptoalgorithm is used to protect the message, which after cryptographic conversion is hidden in the audio file using the steganographic LSB method. The main characteristics of the stegosystem are analyzed. In this paper, the application system of steganographic protection of information in audio files using a cryptographic algorithm is implemented using the environment of Microsoft Visual Studio 2019 and cryptographic libraries, the programming language is C ++. A WAV audio file was used as the digital container. NIST tests were used to assess resistance to stegoanalysis, which according to the results is better using an improved method compared to the classical LSB approach. In addition, the steganographic algorithm is evaluated by visual analysis by comparing the original audio file and the stegofile with the hidden message. The results of the analysis indicate the absence of traces of steganography. Based on the obtained results, it can be argued about the reliability and efficiency of the proposed approach, so the use of LSB-AES technique can be proposed to ensure secure data transmission.

РАЗРАБОТКА АЛГОРИТМОВ ДЛЯ ВЫБОРКИ ДАННЫХ В КОМПОНЕНТАХ ОБЛАЧНОЙ ИНФРАСТРУКТУРЫ

The digital transformation of companies leads to the transfer of many technological and business processes to the cloud, which leads to new risks of confidential information presented in different data formats in the cloud infrastructure, as well as the complexity and heterogeneity of the cloud infrastructure. Cloud infocommunication systems built upon open-source software components expose variabilities in data formats and structures. Such data formats and structures may be convenient and reasonable when developing cloud components, although working with it during operation and maintenance is accompanied with the problem of a mismatch between the varieties and with the lack of special tools to query among the multiple data formats. In the article such data formats as YAML, JSON and XML are considered and thus an opportunity of its transformation into a single format is taken as a hypothesis. Considering analysis results of original data samples taken from OpenStack components three typical data structures are proposed. The other hypothesis is about the opportunity to join data taken from multiple sources. In order to verify assumptions, the algorithms for data transformation into a tabular format are developed. The quickness of transformations is verified on a large sample and obtained results are acceptable for usage while operating and maintaining cloud infocommunication systems. After applying the proposed algorithms to the original data samples an SQL query and a way to query on multiple data sources are proposed. The results of research may have an application for the cloud infrastructure availability solutions when working with multiple data formats.

Remote Sensing Object Detection Based on Convolution and Swin Transformer

Remote sensing object detection is an essential task for surveying the earth. It is challenging for the target detection algorithm in natural scenes to obtain satisfactory detection results in remote sensing images. In this paper, the RAST-YOLO (You only look once with Regin Attention and Swin Transformer) algorithm is proposed to address the problems of remote sensing object detection, such as significant differences in target scales, complex backgrounds, and tightly arranged small-size targets. To increase the information interaction range of the feature map, make full use of the background information of the object, and improve the detection accuracy of the object with a complex background, the Regin Attention (RA) mechanism combined with Swin Transformer as the backbone is proposed to extract features. To improve the detection accuracy of small objects, the C3D module is used to fuse deep and shallow semantic information and optimize the multi-scale problem of remote sensing targets. To evaluate the performance of RAST-YOLO, extensive experiments are performed on DIOR and TGRS-HRRSD datasets. The experimental results show that RAST achieves state-of-the-art detection accuracy with high efficiency and robustness. Specifically, compared with the baseline network, the mean average precision (mAP) of detection results is improved by 5% and 2.3% on DIOR and TGRS-HRRSD datasets, respectively, which demonstrates RAST-YOLO is effective and superior. Moreover, the lightweight structure of RAST-YOLO can ensure the real-time detection speed and obtain excellent detection results.

Wide-temperature-range multispectral camouflage enabled by orientation-gradient co-optimized microwave blackbody metastructure coupled with conformal MXene coating.

Cloaking against electromagnetic detection is a well-researched topic; yet achieving multispectral camouflage over a wide temperature range remains challenging. Herein, an orientation-gradient co-optimized graded Gyroid-shellular (GGS) SiOC-based metastructure with a conformal MXene coating (M@SiOC) is proposed to achieve wide-temperature-range microwave/infrared/visible-light-compatible camouflage. Firstly, the combination of coordinate transformation and genetic algorithm endows the GGS architecture with optimal orientation and gradient, allowing superior microwave blackbody-like behavior. Secondly, a microwave-transparent, low-infrared-emissivity MXene metasurface is constructed in situ to permit wide-temperature-range infrared camouflage. Finally, the outstanding spectral selectivity of MXene enables camouflage against 1.06 μm-lidar and visible-light detection. As a result, the as-fabricated [110]-oriented GGS M@SiOC metamaterials exhibit outstanding wide-temperature-range multispectral camouflage: (i) ultrabroadband microwave absorption exceeding 80% in the X-Ku band from room temperature (RT) to 500 °C with absorption above 86.0% (91.4% on average) at 500 °C; (ii) excellent long-wavelength infrared camouflage for object temperatures from RT to 450 °C, reaching an infrared signal intensity of 78.5% for objects at 450 °C; and (iii) camouflage against both 1.06 μm-lidar and dark environment. Compared with traditional hierarchical metamaterials necessitating complex micro/nano-fabrication processes, this work provides a novel pathway toward the realization of structurally integrated multispectral stealth components by combining flexible metastructure design and high-fidelity additive manufacturing.

3D Hand Pose and Shape Estimation from Single RGB Image for Augmented Reality

In the realm of Human-Computer Interaction (HCI), the importance of hands cannot be overstated. Hands serve as a fundamental means of communication, expression, and interaction in the physical world. In recent years, Augmented Reality (AR) has emerged as a next-generation technology that seamlessly merges the digital and physical worlds, providing transformative experiences across various domains. In this context, accurate hand pose and shape estimation plays a crucial role in enabling natural and intuitive interactions within AR environments. Augmented Reality, with its ability to overlay digital information onto the real world, has the potential to revolutionize how we interact with technology. From gaming and education to healthcare and industrial training, AR has opened up new possibilities for enhancing user experiences. This study proposes an innovative approach for hand pose and shape estimation in AR applications. The methodology commences with the utilization of a pre-trained Single Shot Multi-Box (SSD) model for hand detection and cropping. The cropped hand image is then transformed into the HSV color model, followed by applying histogram equalization on the value band. To precisely isolate the hand, specific bounds are set for each band of the HSV color space, generating a mask. To refine the mask and diminish noise, contouring techniques are applied to the mask, and gap-filling methods are employed. The resultant refined mask is then combined with the original cropped image through logical AND operations to accurately delineate the hand boundaries. This meticulous approach ensures robust hand detection even in complex scenes. To extract pertinent features, the detected hand undergoes two concurrent processes. Firstly, the Scale-Invariant Feature Transform (SIFT) algorithm identifies distinctive keypoints on the hand's outer surface. Simultaneously, a pre-trained lightweight Convolutional Neural Network (CNN), namely MobileNet, is employed to extract 3D hand landmarks, the hand's center (middle finger metacarpophalangeal joint), and handedness information. These extracted features, encompassing hand keypoints, landmarks, center, and handedness, are aggregated and compiled into a CSV file for further analysis. A Gated Recurrent Unit (GRU) is then employed to process the features, capturing intricate dependencies between them. The GRU model successfully predicts the 3D hand pose, achieving high accuracy even in dynamic scenarios. The evaluation results for the proposed model are very promising that the Mean Per Joint Position Error in 3D (MPJPE) is 0.0596 between the predicted pose and the ground truth hand landmarks, while the Percentage of Correct Keypoints (PCK) is 95%. Upon predicting the hand pose, a mesh representation is employed to reconstruct the 3D shape of the hand. This mesh provides a tangible representation of the hand's structure and orientation, enhancing the realism and usability of the AR application. By integrating sophisticated detection, feature extraction, and predictive modeling techniques, this method contributes to creating more immersive and intuitive AR experiences, thereby fostering the seamless fusion of the digital and physical worlds.

A new approach for fault diagnosis in TCSC compensated transmission lines using FWHT and machine learning techniques

In this research a new approach is introduced for detecting and classifying faults in a Thyristor-Controlled Series Capacitor (TCSC) compensated power system. Our proposed scheme utilizes both the Fast Walsh Hadamard Transform (FWHT) and machine learning algorithms. The FWHT is employed to extract fault features from current data obtained from the TCSC compensated transmission line, while machine learning algorithms such as K-Nearest Neighbor (K-NN) and Support Vector Machine (SVM) are used to classify the extracted features for the purpose of fault detection and identification. To evaluate the performance of our proposed scheme, simulation studies were conducted on a test system under various fault conditions. The simulation results demonstrate that our approach is highly effective in accurately and quickly detecting and classifying faults, even when noise and TCSC compensation are present. This scheme has the potential to enhance the reliability and efficiency of power transmission systems.

Soft Fall Detection With a Height-Tracking Method Based on MIMO Radar System

Radar-based fall detection technology has attracted much attention for its high accuracy, robustness, and privacy preservation potential. Detection of “Soft Fall”, i.e., high-freedom fall, is the key to practical application. This paper proposes a novel height-tracking method based on a multiple-input multiple-output (MIMO) radar system to address this problem. First, the received signal was segmented into a time sequence with a sliding window along slow time. Next, Fast Fourier Transform (FFT) and Multiple Signal Classification (MUSIC) algorithms were applied to estimate the general trend of the human body’s time-varying range and pitch angle information. Then, they were fused with a geometrical relationship to describe height changes during fall motions using a height trajectory map. Two height-based features were extracted as input to Support Vector Machine (SVM) to distinguish soft fall and fall-similar motions. Finally, experiments, including four soft fall and five typical fall-similar motions, were conducted to demonstrate its feasibility and superiority.

COLLATZ CONJECTURE 3n±1 AS A NEWTON BINOMIAL PROBLEM

The power transformation of Newton's binomial forms two equal 3n±1 algorithms for transformations of numbers n belongs to N, each of which have one infinite cycle with a unit lower limit of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower limits of the corresponding cycles, and the last element goes to a multiple of three odd numbers. It was found that for infinite transformation cycles 3n-1 isolated from the main graph with minimum amplitudes of 5, 7, 17 lower limits of oscillations, additional conditions are fulfilled.