This paper delves into the possibility of creating a precise mathematical equation to calculate the exact number of prime numbers below a certain threshold. By utilizing tools from function analysis, series of functions, and innovative methods, the goal is to create a comprehensive formula that can accurately determine the quantity of primes within a specified numerical range. The research explores the theoretical underpinnings of prime numbers, using advanced techniques to improve and expand upon current methodologies. Through a combination of insights from function analysis and series theory, the proposed formula seeks to offer a strong and efficient solution for computing prime counts. This effort not only adds value to the field, but it also enhances our understanding of prime number distribution.

In this paper, we investigate the joint resource allocation and trajectory design for a multiuser , multi-target unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) system, where the link capacity between a ground base station (BS) and the UAV is limited. The UAV conducts target sensing and information transmission in orthogonal time slots to prevent interference. As is common in practical systems, sensing is performed while the UAV hovers, allowing the UAV to acquire high-quality sensing data. Subsequently, the acquired sensing data is offloaded to the ground BS for further processing. We jointly optimize the UAV trajectory, UAV velocity, beamforming for the communication users, power allocated to the sensing beam, and time of hovering for sensing to minimize the power consumption of the UAV while ensuring the communication quality of service (QoS) and successful sensing. Due to the prohibitively high complexity of the resulting nonconvex mixed integer non-linear program (MINLP), we employ a series of transformations and optimization techniques, including semidefinite relaxation, big-M method, penalty approach, and successive convex approximation, to obtain a low-complexity suboptimal solution. Our simulation results reveal that 1) the proposed design achieves significant power savings compared to two baseline schemes; 2) stricter sensing requirements lead to longer sensing times, highlighting the challenge of efficiently managing both sensing accuracy and sensing time; 3) the optimized trajectory design ensures precise hovering directly above the targets during sensing, enhancing sensing quality and enabling the application of energy-focused beams; and 4) the proposed trajectory design balances the capacity of the backhaul link and the downlink rate of the communication users.

Sagittal views provide detailed and critical information about the anatomy and pathology in diagnosing and managing lumbar spine diseases. Radiologists comprehensively evaluate the spinal alignment, structural integrity, and health of bone and soft tissue elements in the sagittal view in diagnosing various spinal conditions and planning appropriate treatments. The first step in the automatic diagnosis is localizing the region of interest, typically the lumbar spine segments. To accomplish this, we present a modified U-Net (MU-Net) for the segmentation and localization of the lumbar spine from sagittal views of Magnetic Resonance Imaging (MRI) images and compare the performances with a series of state-of-the-art YOLOv implementations. We employ different techniques to augment data, address issues with limited training samples, and improve the generalization of deep models. We use the two YOLOv series for localization and MU-Net for segmentation. The MU-Net model achieves an accuracy of 98.97%, accompanied by a Mean Intersection Over Union (IoU) of 82.49%. For the localization, YOLOv8 yields a Precision, Recall, and Mean Average Precision (mAP) of 99.6%, 99.2%, and 99.4%, respectively.

In the area of affective computing, speech has been identified as a promising biomarker for assessing depression and attention deficit hyperactivity disorder (ADHD). These disorders manifest as abnormalities in speech across various frequency bands and exhibit temporal variations. Most existing work on speech features relies on the magnitude spectrogram, which discards phase spectrogram information and also does not consider the impact of different frequency bands on depression and ADHD detection. Inspired by these, we propose a novel multi-scale complex feature refinement and a dynamic attention-aware network for enhanced speech-based assessment of depression and ADHD. Our approach incorporates three key components: multi-scale complex feature refinement (MSFR), dynamic convolutional neural network (Dy-CNN), and dual-attention feature enhancement (DAFE) module. The MSFR module utilizes depth-wise convolutional networks to process both magnitude and phase information, selectively emphasizing frequency bands associated with depression and ADHD. Importantly, the Dy-CNN module employs an attention mechanism to autonomously generate multiple convolution kernels that adapt to input features and capture relevant temporal dynamics linked to depression and ADHD. Additionally, the DAFE module includes channel shuffle attention (CSA) and spatial axial attention (SAA) mechanisms to improve the feature representation ability and detection performance by leveraging inter- and intra-channel relationships to examine the time-frequency characteristics of the feature map. Extensive experiments conducted on four publicly available datasets, i.e. AVEC 2013, AVEC 2014, E-DAIC and a self-collected authentic ADHD dataset demonstrated the effectiveness of the proposed method over previous approaches and showed superior generalization capabilities across different languages for depression and ADHD assessment.

Simultaneous wireless information and power transfer (SWIPT) enabled wireless cooperative communication system is an emerging technology for future wireless communication applications. Furthermore, the Internet of Things (IoT) serves a diverse range of purposes, some of which are mission-critical and require constantly evolving real-time data. Thus, the information received at the destination must be updated timely manner to ensure its freshness. A performance metric named age of information (AoI) has been introduced to measure the freshness of received information. This study estimates the AoI of a SWIPT assisted decode and forward two-way relay assisted status update system in which two sources attempt to exchange status updates as quickly as possible to the destination. The relay system employs short packet communication to adhere to the latency and reliability requirements of the wireless communication system. We study the average Age of Information (AAoI) at the destination in the proposed relay network and derive approximations for the weighted sum AAoI under two different types of transmission scheduling policies at the relay: transmit without waiting (TWW) and wait until charged (WUC). Furthermore, the effects of transmission power, packet size, the distance between relay and sources and block-length on the weighted sum AAoI of the proposed SWIPT assisted short packet relay network are extensively investigated. The performance differences of the considered transmission policies are compared and insights are provided. Numerical simulations using the Monte Carlo method have been employed to validate derived analytical expressions.

Radars on unmanned vehicles can be used in indoor rescue scenarios to detect missing people based on their motion. In this case, the phase of the radar signals, which provides information about sub-millimeter changes in distance, have to be evaluated. However, in order to detect or to evaluate the motion of a missing person, the motion of the unmanned vehicle itself must be known and compensated for. To estimate the ego-motion of the unmanned vehicle, the radar system measures the phase information for multiple static objects in the radar's environment. A model describing how the motion of the radar affects the phase signals is used to estimate the ego-motion by solving a system of equations. The accuracy of the estimated position, depends on how accurately the phase measurements represent the model. By analytically decomposing the errors in the measurement model, it is shown that the radar's limited angular resolution induces a significant error. To mitigate this source of error, a weighted least squares approach is derived that minimizes the influence of the angular resolution on the position error. By calculating the position error distribution with and without the weighting approach, the benefits of the proposed algorithms are stated. Furthermore, the results are validated using simulations and real world measurements, showing that the proposed algorithm achieves sub-millimeter position accuracy.

Although research on self-driving vehicles (SDV) started long ago, developing a robust perception system is still challenging for researchers in academia and industry. Object classification, object detection and tracking, road detection, semantic segmentation, and instance segmentation are all introduced as the perception problems of the autonomous driving platform. Tons of methods have already been proposed to solve these perception problems. Some methods use a single modality (image only or Lidar only), and others use multi-modality. This review paper categorizes all semantic segmentation methods used for self-driving vehicles into three categories depending on their modality. We compare these methods according to their performance and mention the datasets used for evaluation. Some of the most common datasets in this field are also discussed in this paper. We highlight the challenges and scope of future research and discuss the background of this research field so that this paper can be used as a base for a new researcher to start research on semantic segmentation. Impact Statement-Semantic segmentation is a very useful perception tool. It can be used to get per-pixel semantic labels of the scenarios captured by the sensors of autonomous vehicles, which can then be used to identify potential obstacles, based on which planning and control decisions are made. Although many works have discussed semantic segmentation models, there are not many review papers that consolidate these works from a sensory perspective. In this paper, we analyze single and multimodal model architectures and compare their performances to guide researchers in deciding which direction (Lidar or camera, Lidar and camera) may be beneficial for them. The most frequently used datasets in this arena and the main features of the data are all elaborately discussed. Furthermore, the challenges that researchers may encounter, and the scope of future research are also included. This paper could provide a one-stop source for new researchers working in this area.

This paper presents a novel methodology for characterizing and creating a digital twin of turbid media without the need for reference beams, employing a unique architecture for the physics-informed neural network. Unlike previous approaches utilizing various deep neural network architectures that often function as black boxes, our method prioritizes interpretability, offering a clearer understanding of the underlying processes of light propagation through turbid media. Additionally, unlike classical solutions relying on reference beams, our approach eliminates the dependence on beam quality and associated issues prevalent in both internal and external reference-based methods. The possibility and use case of gradient calculation through this presented digital twin are showcased by solving the reverse problem to retrieve the initial wavefront shape of the light that passed through this medium, known as image transmission. Surprisingly, the results surpassed the accuracy of models directly optimized for this task, underscoring the precision of the proposed digital twin. This capability represents a pivotal advancement for future developments in neuromorphic and deep learning computation and training using such a photonic and optical systems.

Line waves (LWs) are exceptional electromagnetic (EM) modes found at the junctions of impedance surfaces, satisfying either electromagnetic duality or the parity-time symmetry. To date, the implementation of LWs has been limited primarily to employing electric impedance surfaces. In our study, we unveil that a planar junction between an electric impedance surfaces, and a magnetic media sustains the LW exhibiting backscattering-immune transportation. The entirely magnetic media (ϵ = 1, and μ ≠ 1) supports TE-polarized surface magnon polaritons while we tailor the electric surface impedance to support TM-polarized surface waves. Remarkably, the envisioned line-wave waveguide emerges as a pseudospin-filtered channel, facilitating a uni-dimensional wave generated through the synergistic interplay of two surface waves possessing perpendicular polarizations. Our theoretical findings, corroborated by simulations, unveil a new type of polaritonic wave characterized by remarkably confined properties. This discovery holds promise for manipulating light on the nanoscale, opening avenues for the implementation of magneto-electric pseudospin-polarized waveguide.

In this paper, we study a new round of novel coronavirus disease 2019 (COVID-19) infection scenarios due to a mutated strain in the middle of the epidemic. By considering the characteristics of the presence or absence of symptoms, the severity of symptoms, and vaccination, we develop an extended compartmental model containing 11 compartments and describe its compartmental transformation process from both discrete and continuous perspectives by probabilistic cellular automata and a system of ordinary differential equations. Further, we analyze the relevance of the endemic equilibrium points as well as the trajectory types corresponding to the ordinary differential equations. Based on the model, we simulate the reoccurrence of an outbreak in the United States in the winter of 2021, and the results fit well with the actual data and show the consistency between the two forms of Probabilistic Cellular automata and the system of Ordinary Differential Equations. The effects of contact network and vaccination are investigated by applying the model to different scenarios. The results show that premature relaxation of social isolation campaigns may lead to subsequent waves of infection and that widespread vaccination is effective in reducing the number of severe illnesses and deaths. The significance of this paper is to provide a model of infectious diseases for mid-epidemic and to assist in epidemic prevention policy-making through Probabilistic Cellular Automata.

In order to correct different numbers of erasures in distributed storage systems, the design of locally repairable codes with hierarchical locality (H-LRCs) is crucial. In this paper, we study h-level H-LRCs where h is not limited to 2. We present four constructions of cyclic h-level H-LRCs with length ln1 such that gcd(l, q) = 1 and n1|(q−1). These four classes of cyclic h-level H-LRCs are optimal with respect to the generalized Singleton-like bound. The minimum Hamming distances of them are d = δ1, δ1+1, δ1+2, δ1+δh respectively. Furthermore, these four classes of cyclic h-level H-LRCs have new and flexible parameters which are not covered in the literature. By setting the parameter l appropriately for the third construction, one can construct optimal cyclic h-level H-LRCs with length n|(q−1) and distance d = δ1+σ where σ is not limited to 0, 1, 2, δh.

We consider significantly enhancing the angular resolution of a single-chip multiple-input multiple-output (MIMO) radar sensor equipped with only 3 transmit and 4 receive antennas for radar imaging. We adopt the slow-time code-division multiplexing (ST-CDM) transmission scheme, which is a low-cost viable option to attain a large virtual array without reducing the unambiguous Doppler range. Moreover, to significantly improve the angular resolution without increasing antenna numbers, we introduce a practical 3 × 4 sparse linear array (SLA) design. We extend the iterative adaptive approach (IAA) to the slow-time IAA (ST-IAA) algorithm, aiming to mitigate the impact of waveform separation residuals and the high angular sidelobes on ST-CDM MIMO radar imaging equipped with SLAs. Furthermore, we construct a single-chip ST-CDM MIMO radar prototype with the 3 × 4 SLA design for experimental validations. The numerical and experimental results are provided to demonstrate the enhanced imaging performance of the radar prototype when used with the ST-IAA algorithm.

To solve real-world expensive constrained multi-objective optimization problems (ECMOPs), surrogate/approximation models are commonly incorporated in evolutionary algorithms to pre-select promising candidate solutions for evaluation. However, the performance of existing approaches are highly dependent on the relative position of unconstrained and constrained Pareto fronts (UPF and CPF, respectively). In addition, the uncertainty information of surrogate models is often ignored, which can misguide the search. To mitigate these key issues (among others), an efficient probabilistic selection based constrained multi-objective EA is proposed, referred to as PSCMOEA. It comprises novel elements such as (a) an adaptive search bound identification scheme based on the feasibility and convergence status of evaluated solutions (b) a probabilistic selection method backed by theoretical formulations of model mean and uncertainties to conduct search in the predicted space to identify promising solutions (c) an efficient single infill sampling approach to balance feasibility, convergence and diversity across different stages of the search and (d) an adaptive switch to unconstrained search based on certain search conditions. Numerical experiments are conducted on an extensive range of challenging constrained problems using low evaluation budgets to simulate ECMOPs. The performance of PSCMOEA is benchmarked against five competitive state-of-the-art algorithms, to demonstrate its competitive and consistent performance.

Deep Neural Networks (DNNs) have gained considerable traction in recent years due to the unparalleled results they gathered. However, the cost behind training such sophisticated models is resource intensive, resulting in many to consider DNNs to be intellectual property (IP) to model owners. In this era of cloud computing, high-performance DNNs are often deployed all over the internet so that people can access them publicly. As such, DNN watermarking schemes, especially backdoor-based watermarks, have been actively developed in recent years to preserve proprietary rights. (Add that no backdoor watermark guarantee). Nonetheless, there lies much uncertainty on the robustness of existing backdoor watermark schemes, towards both adversarial attacks and unintended means such as fine-tuning neural network models. In this paper, we extensively evaluate the persistence of recent backdoor-based watermarks within neural networks in the scenario of fine-tuning, we propose/develop a novel data-driven idea to restore watermark after fine-tuning without exposing the trigger set. Our empirical results show that by solely introducing training data after fine-tuning, the watermark can be restored if model parameters do not shift dramatically during fine-tuning. Depending on the types of trigger samples used, trigger accuracy can be reinstated to up to 100%. Our study further explores how the restoration process works using loss landscape visualization, as well as the idea of introducing training data in fine-tuning stage to alleviate watermark vanishing.

In conventional energy systems, the synchronization of power generation and consumption is largely handled by thermal power plants. The increasing share of volatile renewable energy generation which does not follow the demand, makes it necessary to shift the synchronization tasks to the system and demand level. The intended demand side consumption management is usually incentivized via financial mechanisms. However, the optimum design of related incentives is still unclear. It is usually discussed under the term "system friendliness" which in turn still lacks a broadly accepted definition. In this article we introduce a new technical definition of "system friendliness" and develop comprehensive and holistic related indicators. Our findings demonstrate that today's regulatory environments that usually support residential self-consumption maximization are counterproductive. Instead, we show that dynamic end-user prices coupled with dynamic feed in tariffs are able to incentivize an almost 100% system friendly behavior of distributed prosumers.

Non-Orthogonal Multiple Access (NOMA) received significant attention in the field of wireless communications during the last ten years, particularly focusing on Power-Domain NOMA (PD-NOMA) that uses a successive interference cancellation (SIC) receiver. This review paper reexamines PD-NOMA from a pragmatic angle and sheds light on its virtues and limitations in uplink and downlink scenarios. We observe that the concept of PD-NOMA in the downlink can be seen as a pure signal constellation design and that a simple threshold detector is sufficient at the receiver end. For the uplink, we first address the fairness concerns arising from the mismatch between the users' data rates that can be achieved by the SIC receiver and the fair rates suggested by the power distribution among users. Furthermore, we discuss findings from a recent analysis comparing PD-NOMA to MultiUser MIMO under a common system framework. This study reveals that assigning the same power levels to users, thereby aligning PD-NOMA with MultiUser MIMO, optimizes performance in terms of average bit error rate. These insights raise questions about the fundamental utility of PD-NOMA and suggest that its best application is hierarchical multiple access, where devices with different power capabilities are paired together.

The Einstein's theory of special relativity is based on his two postulates. The first is that the laws of physics are the same in all inertial reference frames. The second is that the velocity of light in the vacuum is the same in all inertial frames. The theory of special relativity is considered to be supported by a large number of experiments. This paper revisits the two postulates according to the new interpretations to the exact solutions of moving sources in the laboratory frame. The exact solutions are obtained using the classic Maxwell's theory, which clearly show that the propagation velocity of the electromagnetic waves of moving sources in the vacuum is not isotropic; the propagation velocity of the electromagnetic waves and the moving velocity of the sources cannot be added like vectors; the transverse Doppler effect is intrinsically included in the fields of the moving sources. The electromagnetic sources are subject to the Newtonian mechanics, while the electromagnetic fields are subject to the Maxwell's theory. We argue that since their behaviors are quite different, it is not a best choice to try to bind them together and force them to undergo the same coordinate transformations as a whole, like that in the Lorentz transformations. Furthermore, the Maxwell's theory does not impose any limitations on the velocity of the electromagnetic waves. To assume that all objects cannot move faster than the light in the vacuum need more examinations. We have carefully checked the main experiment results that were considered as supporting the special relativity. Unfortunately, we found that the experimental results may have been misinterpreted. We here propose a Galilean-Newtonian-Maxwellian relativity, which can give the same or even better explanations to those experimental results.

In the context of the Internet of Things (IoT), reliable and energy-efficient provision of IoT applications has become critical. Equipping IoT systems with tools that enable a flexible, well-performing, and automated way of monitoring and managing IoT edge devices is an essential prerequisite. In current IoT systems, low-power edge appliances have been utilized in a way that can not be controlled and reconfigured in a timely manner. Hence, conducting a tradeoff solution between manageability, performance and design requirements are demanded. This paper introduces a novel approach for fine-grained monitoring and managing individual micro-services within low-power edge devices, which improves system reliability and energy efficiency. The proposed method enables operational flexibility for IoT edge devices by leveraging a modularization technique. Following a review of existing solutions for remote-managed IoT services, a detailed description of the suggested approach is presented. Also, to explore the essential design principles that must be considered in this approach, the suggested architecture is elaborated in detail. Finally, the advantages of the proposed solution to deal with disruptions are demonstrated in the proof of concept-based experiments.