Calculation Of Sum Research Articles

Scan-Angle-Independent FEM Analysis of Infinite Arrays Based on Spherical Harmonic Lattice Sums and the Generalized Scattering Matrix of an Isolated Antenna

Infinite periodic arrays of antennas that can be individually described by means of spherical modes are analyzed starting from the generalized scattering matrix (GSM) of an isolated element. After computing the GSM of an isolated element with the finite-element method (FEM), a fast postprocessing can be carried out to calculate the response of the element in an infinite array environment by using addition theorems for spherical modes. For this purpose, an efficient computation of lattice sums of spherical harmonics is used. The main advantage of this method is that the antenna is analyzed only once whatever the array lattice or scan angle. In addition, fast frequency analysis can be performed since the starting point is the computation of the isolated antenna with the FEM, which is suitable for fast frequency sweep. The active reflection coefficient and the embedded radiation pattern of the infinite periodic array are calculated for several examples to show the capabilities of the proposed method.

Joint Active and Passive Beamforming in IRS-Enhanced Wireless Powered MEC Networks

This letter studies the joint active and passive beamforming in intelligent reflecting surface (IRS)-enhanced wireless powered mobile edge computing (MEC) networks, in which a hybrid access point (HAP) is deployed to charge multiple wireless devices (WDs) and assist in computation of the offloaded tasks from the WDs. An IRS is deployed to enhance the downlink wireless power transfer (WPT) and the uplink tasks offloading (TO). To maximize the systems’ sum computation rate, an optimization problem is formulated by jointly optimizing the time assignment of WPT and TO, the active beamforming at the HAP, the transmit power and computing frequency of the WDs, and the passive beamforming at the IRS. To tackle the non-convex problem, we present an efficient algorithm by utilizing the alternating optimization (AO) and semidefinite relaxation (SDR) techniques. Simulation results show that by deploying IRS in the system, a significant computation rate gain can be achieved. Especially, when the IRS is closer to the WDs or the HAP, the much higher computation rate can be reached.

Joint resource allocation, user clustering and 3-D location optimization in multi-UAV-enabled mobile edge computing

This paper studies a multi-unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) system, where UAVs are equipped with a powerful MEC server to provide computation services for ground users. Under NOMA protocol and partial offloading mode, we aim to jointly optimize the NOMA user clustering, sub-carrier assignment, transmit power of users, CPU frequency, and 3-D location of UAVs to maximize the sum computation bits of all users. Since the formulated problem is a mixed-integer non-linear optimization, we propose a three-stage algorithm to address the four sub-problems iteratively. First, two efficient NOMA user clustering algorithms are proposed to divide the users into several NOMA clusters. Second, a heuristic sub-carrier assignment algorithm is presented based on the channel gain and interfering users. Third, by adopting the successive convex approximation (SCA) technique and Lagrange dual method, the closed-form expressions of the transmit power and CPU frequency of users are derived. Forth, a convex optimization problem is obtained to optimize the 3-D location of UAVs. The numerical evaluations illustrate that the proposed system outperforms the benchmark schemes in terms of sum computation bits performance.

Binary vs partial offloading in wireless powered mobile edge computing systems with fairness guarantees

Mobile Edge Computing (MEC) has recently emerged as a new communications/computing concept that amends the limited computing of IoT devices by completely or partially offloading the computational tasks to the MEC servers at the network edge (typically co-located with the base stations). Because IoT devices are typically power limited, the potential of the MEC is further enhanced by its integration with wireless power transfer technology, especially for those IoT devices with a high duty cycle that requires frequent battery replacement. This paper develops fairness-aware resource allocation schemes for a WPT-assisted MEC system whose Energy Harvesting Users (EHUs) employ either binary or partial offloading. Specifically, the proposed schemes optimize the computational speeds and the energy harvesting and offloading durations of the EHUs with the aim to maximize the minimum of their computed bits (sum of locally and remotely processed bits of each EHU), subject to the RF energy harvested from the base station. When EHUs are concentrated closer to the base station, remote processing is preferred over local processing, as local processing consumes more energy than the Radio Frequency (RF) power for offloading data to the MEC server, but this effect diminishes for lower values of the computational effort needed for the processing of a single bit. Interestingly, in terms of the sum computation rate, the partial offloading scheme only slightly outperforms the binary offloading scheme, but only when the EHUs are moderately away from the base station.

Evaluating crop models to assess rice yield potential in Argentina

Due to the high concentration of the rice production in Asia, the study and comprehension of rice producing chains outside this continent are key to guarantee the global food security. The objectives of this study were to validate the SimulArroz and ORYZA v3 crop simulation models for rice production in Argentina, estimate the yield potential (Yp) for different sowing dates with both models, and estimate how much Argentina can increase rice production in the current agricultural area by reducing the yield gap. Two contrasting rice models (ORYZA v3 and SimulArroz) were used. Besides both are mechanistic models, Simularroz model requires fewer coefficients than ORYZA v3,. which may increase the systematic error. The coefficient of determination between simulated and measured values was at least 0.74 for grain yield and 0.97 for phenology. RMSEn values for phenology ranged from 5.7% to 9.4%. Both models simulated grain yield accurately at high yield levels (>13 ​Mg ​ha−1) with an RMSE <0.5 ​Mg ha-1. The average irrigated rice Yp for subtropical Argentina estimated by the SimulArroz model ranged from 3.8 to 15.6 ​Mg ​ha−1, and from 7.6 to 14.3 ​Mg ​ha−1 in the ORYZA v3. The differences in the Yp between the models were due to different approaches in the calculation of thermal sum and radiation use efficiency. The increase in the rice production in Argentina if the fields close the exploitable gap (80% of the Yp) would be 42% of the current total rice production or 916,091 ​Mg annually.

DRL based partial offloading for maximizing sum computation rate of FDMA-based wireless powered mobile edge computing

Since most Internet of Things (IoT) nodes are powered by small-capacity batteries and equipped with small computing units, it is difficult for them to process computing-intensive and delay-sensitive tasks. To address these two limitations, a feasible approach is to use both wireless power transmission (WPT) and mobile edge computing (MEC) technologies. Wireless edge devices (EDs) have stable energy supply by capturing radio frequency (RF) energy transmitted by the energy source and offloading computation workload to edge computing servers (ECSs) to enhance the computation rate. In this paper, an FDMA-based wireless-powered MEC network is considered, which consists of an ECS, an RF energy source and multiple EDs. The research goal is to maximize the sum computation rate (SCR) by jointly optimizing the WPT duration, energy allocation for local computation, and computation offloading, and bandwidth allocation among EDs. We first formulate this as a non-convex optimization problem that is hard to address. Then, we decompose it into a top-problem for optimizing the WPT duration and a sub-problem for optimizing the energy allocation and bandwidth allocation under a given WPT duration. An online offloading algorithm based on deep reinforcement learning (DRL) is proposed to quickly obtain the near-optimal WPT duration. For the sub-problem, we design an efficient two-stage algorithm to obtain the optimal solution. The simulation results show that the proposed algorithm can obtain the near-optimal solutions with low computation complexity.

DRL based offloading of industrial IoT applications in wireless powered mobile edge computing

Mobile edge computing is the network technology for providing computing resources of edge computing server to Internet of Things (IoT) applications. Additionally, wireless power transfer (WPT) technology can provide stable energy supplying to IIoT nodes and to overcome the limited node lifetime problem faced when using batteries. In this paper, the wireless powered mobile edge computing network is considered where the edge computing server transfers RF energy to IIoT nodes which use harvested energy to offload partial computation workload based on OFDMA and also conduct local computation. The aim is to maximise the weighted sum computation rate by jointly optimising the WPT duration and the amount of energy used for offloading at each node for each time frame. This paper proposes an offloading approach based on deep reinforcement learning which is able to quickly obtain the near-optimal offloading solutions. Specifically, the original offloading problem is decomposed into the sub-problem of optimising the energy allocated for offloading under a given WPT duration and the top-problem of optimising the WPT duration. Simulation results demonstrate that the proposed algorithm can achieve the near-optimal weighted sum computation rate with very low complexity, which is tailored for the practical dynamic-channel environment.

Using quantum mechanics for calculation of different infinite sums

We demonstrate that a certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the problem of a particle in a box. Twofold calculation of the mean value of energy for the polynomial wave function inside the well yields even argument p (p > 2) of Riemann zeta and related functions. This method can be applied to a wide class of exactly solvable quantum mechanical problems which may lead to different infinite sums. Besides, the analysis performed here provides deeper understanding of superposition principle and presents useful exercise for physics students.

Latency and energy aware rate maximization in MC-NOMA-based multi-access edge computing: A two-stage deep reinforcement learning approach

Future network services are emerging with an inevitable need for high wireless capacity along with strong computational capabilities, stringent latency and reduced energy consumption Two technologies are promising, showing potential to support these requirements: multi-access (or mobile) edge computing (MEC) and non-orthogonal multiple access (NOMA). While MEC allows users to access the abundant computing resources at the edge of the network, NOMA technology enables an increase in the density of a cellular network. However, integrating NOMA technology into MEC systems faces challenges in terms of joint offloading decisions (remote or local computation) and inter-user interference management. In this paper, with the objective of maximizing the system-wide sum computation rate under latency and energy consumption constraints, we propose a two-stage deep reinforcement learning algorithm to solve the joint problem in a multicarrier NOMA-based MEC system, in which the first-stage agent handles offloading decisions while the second-stage agent considers the offloading decisions to determine the resource block assignments for users. Simulation results show that compared with other benchmark algorithms, the proposed algorithm improves the sum computation rate while meeting the latency and energy consumption requirements, and it outperforms the approach in which a single agent handles both offloading decisions and resource block assignments due to faster convergence performance.

On the Efficient Computation of Large Scale Singular Sums with Applications to Long-Range Forces in Crystal Lattices

We develop a new expansion for representing singular sums in terms of integrals and vice versa. This method provides a powerful tool for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. It also offers a generalised trapezoidal rule for the precise computation of singular integrals. In both cases, the difference between sum and integral is approximated by derivatives of the non-singular factor of the summand function, where the coefficients in turn depend on the singularity. We show that for a physically meaningful set of functions, the error decays exponentially with the expansion order. For a fixed expansion order, the error decays algebraically both with the grid size, if the method is used for quadrature, or the characteristic length scale of the summand function in case the sum over a fixed grid is approximated by an integral. In absence of a singularity, the method reduces to the Euler–Maclaurin summation formula. We demonstrate the numerical performance of our new expansion by applying it to the computation of the full nonlinear long-range forces inside a domain wall in a macroscopic one-dimensional crystal with 2times 10^{10} particles. The code of our implementation in Mathematica is provided online. For particles that interact via the Coulomb repulsion, we demonstrate that finite size effects remain relevant even in the thermodynamic limit of macroscopic particle numbers. Our results show that widely-used continuum limits in condensed matter physics are not applicable for quantitative predictions in this case.

Anonymous and Verifiable Reputation System for E-Commerce Platforms Based on Blockchain

E-commerce platforms incorporate reputation systems that allow customers to rate suppliers following financial transactions. Existing reputation systems cannot defend the centralized server against arbitrarily tampering with the supplier’s reputation. Furthermore, they do not offer reputation access across platforms. Rates are faced with privacy leakages because rating activities are correlated with privacy (e.g., identity and rating). Meanwhile, raters could be malicious and initiate multiple rating attacks and abnormal rating attacks. Determining how to address these issues have both research and practical value. In this paper, we propose a blockchain-based privacy-preserving reputation system for e-commerce platforms named RepChain; our system allows cross-platform reputation access and anonymous and private ratings. Using RepChain, all e-commerce platforms collaborate and share users’ reputations by co-constructing a consortium blockchain and modeling the rating process as a finite state machine. In particular, we facilitate one-show anonymous credentials constructed from two-move blind signatures to protect customers’ identities and resist multiple rating attacks, leverage zero-knowledge range proof to verify the correctness of ratings and defend against abnormal rating attacks, design a secure sum computation protocol among nodes to update reputations, and verify ratings via batch processing and consensus hashes. Finally, we demonstrate the security and privacy of RepChain via a formal analysis and evaluate its performance based on Ethereum test network.

Analysis of snakebite data in Volta and Oti Regions, Ghana, 2019.

Introductionglobally about 5.4 million people are affected by snakebite annually leading to 2.7 million cases of snakebite envenoming and 81,000-138,000 deaths. In sub-Saharan Africa, the burden of disease caused by snakebite is often underestimated despite its status as a category A neglected tropical disease. We reviewed snakebite data to determine the magnitude of snakebite by person, place, and time in the Volta and Oti Regions of Ghana.Methodswe conducted a descriptive secondary data analysis using snakebite data from 2014-2018 extracted from the District Health Information and Management Systems (DHIMS 2) database. Data were analyzed descriptively by person, place, and time using summary statistics and results were presented in proportions and graphs. Missed outbreaks were determined through calculation of cumulative sum (CUSUM 2).Resultsa total of 2,973 cases of snakebites were reported over the 5 years of which 1675 (56.3%) were males. Majority 867 (29.2%) of snakebite victims were between 20-34 years of age with recorded 5-year average incidence of 24 snakebite cases per 100,000. Nkwanta North District recorded the highest cases 499 (16.8%) with most of the snakebite cases 2,411 (81%) recorded in the rainy season. Overall, there was a decreasing trend of snakebites and four missed snakebite outbreaks occurred during the period. No snakebite death was recorded.Conclusiona 5-year average snakebite incidence of 24 cases per 100,000 persons was recorded and Nkwanta North District recorded the highest cases with peaks occurring in rainy and harvesting seasons. Four outbreaks were missed. There is a need to conduct periodic data analysis for effective intervention programs.

Hybrid Beamforming Design and Resource Allocation for UAV-Aided Wireless-Powered Mobile Edge Computing Networks With NOMA

Beamforming and non-orthogonal multiple access (NOMA) serve as two potential solutions for achieving spectral efficient communication in the fifth generation and beyond wireless networks. In this paper, we jointly apply a hybrid beamforming and NOMA techniques to an unmanned aerial vehicle (UAV)-carried wireless-powered mobile edge computing (MEC) system, within which the UAV is equipped with a wireless power charger and the MEC platform delivers energy and computing services to Internet of Things (IoT) devices. Our aim is to maximize the sum computation rate at all IoT devices whilst satisfying the constraint of energy harvesting and coverage. The resultant optimization problem is non-convex involving joint optimization of the UAV’s 3D placement and hybrid beamforming matrices as well as computation resource allocation in both partial and binary offloading patterns, and thus is quite difficult to tackle directly. By applying the polyhedral annexation method and the deep deterministic policy gradient (DDPG) algorithm, we develop an effective algorithm to derive the closed-form solution for the optimal 3D deployment of the UAV, and find the solution for the hybrid beamformer. Two resource allocation algorithms for partial and binary offloading patterns are thereby proposed. Simulation results verify that our designed algorithms achieve a significant computation performance enhancement as compared to the benchmark schemes.

Harmonic analysis on the positive rationals: computation of character sums

The authors carry out detailed calculations of group character sums attached to the multiplicative representation of positive rationals by pairs of sequences \(an+b\), \(An+B\), \(n = 1, 2 \dots \), with the integer coefficients a, b, A, B satisfying \(a>0\), \(A>0\), \(aB - Ab \ne 0\). Non-intuitive examples are given.

ECCENTRIC DISTANCE SUM OF SUBSTITUTION TREE NETWORKS

In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance generalizes the result of [T. Li, K. Jiang and L. Xi, Average distance of self-similar fractal trees, Fractals 26(1) (2018) 1850016.] from symmetric case to asymmetric case. To derive formulas, we investigate the corresponding integrals on self-similar measure and use the self-similarity of distance and measure. For simplicity, we introduce some systematic symbolic assignments and make some assumptions on the graph. We verify that our formulas are correct using the numerical calculation results.

On efficient computation of sums of characters on the basis of A. G. Postnikov methods

An efficient p-adic method and the structure of an algorithm for computing the sums of characters of finite abelian groups are presented. The method and algorithm are based on the A.G. Postnikov summation method of characters modulo a prime power and its developments. A brief survey of the theory of characters of finite abelian groups, p-adic arithmetic and analysis is presented. Questions of the efficiency of p-adic methods are discussed. Moreover, we present results of computation of other types of sums of characters (Kloosterman sums), which are connecting with Artin-Schreier coverings over prime finite fields. The corresponding method and algorithm are based on the development of another method by A.G. Postnikov. Examples of computation of sums of characters are given.

Joint allocation of wireless resource and computing capability in MEC-enabled vehicular network

In MEC-enabled vehicular network with limited wireless resource and computation resource, stringent delay and high reliability requirements are challenging issues. In order to reduce the total delay in the network as well as ensure the reliability of Vehicular UE (VUE), a Joint Allocation of Wireless resource and MEC Computing resource (JAWC) algorithm is proposed. The JAWC algorithm includes two steps: V2X links clustering and MEC computation resource scheduling. In the V2X links clustering, a Spectral Radius based Interference Cancellation scheme (SR-IC) is proposed to obtain the optimal resource allocation matrix. By converting the calculation of SINR into the calculation of matrix maximum row sum, the accumulated interference of VUE can be constrained and the the SINR calculation complexity can be effectively reduced. In the MEC computation resource scheduling, by transforming the original optimization problem into a convex problem, the optimal task offloading proportion of VUE and MEC computation resource allocation can be obtained. The simulation further demonstrates that the JAWC algorithm can significantly reduce the total delay as well as ensure the communication reliability of VUE in the MEC-enabled vehicular network.

Backscatter-Assisted Data Offloading in OFDMA-Based Wireless-Powered Mobile Edge Computing for IoT Networks

Mobile-edge computing (MEC) has emerged as a prominent technology to overcome sudden demands on computation-intensive applications of the Internet of Things (IoT) with finite processing capabilities. Nevertheless, the limited energy resources also seriously hinder IoT devices from offloading tasks that consume high power in active RF communications. Despite the development of energy harvesting (EH) techniques, the harvested energy from surrounding environments could be inadequate for power-hungry tasks. Fortunately, backscatter communications (Backcom) is an intriguing technology to narrow the gap between the power needed for communication and harvested power. Motivated by these considerations, this article investigates a backscatter-assisted data offloading in OFDMA-based wireless-powered (WP) MEC for IoT systems. Specifically, we aim at maximizing the sum computation rate by jointly optimizing the transmit power at the gateway (GW), backscatter coefficient, time-splitting (TS) ratio, and binary decision-making matrices. This problem is challenging to solve due to its nonconvexity. To find solutions, we first simplify the problem by determining the optimal values of transmit power of the GW and backscatter coefficient. Then, the original problem is decomposed into two subproblems, namely, TS ratio optimization with given offloading decision matrices and offloading decision optimization with given TS ratio. Especially, a closed-form expression for the TS ratio is obtained which greatly enhances the CPU execution time. Based on the solutions of the two subproblems, an efficient algorithm, termed the fast-efficient algorithm (FEA), is proposed by leveraging the block coordinate descent method. Then, it is compared with exhaustive search (ES), the bisection-based algorithm (BA), edge computing (EC), and local computing (LC) used as reference methods. As a result, the FEA is the best solution which results in a near-globally-optimal solution at a much lower complexity as compared to benchmark schemes. For instance, the CPU execution time of FEA is about 0.029 s in a 50-user network, which is tailored for ultralow latency applications of IoT networks.

Impact of temperature and SO42- on electrostatic controls over carbonate wettability

The use of modified salinity and modified composition brines (MSMC), referred to as smart water, to alter carbonate surface wettability at different temperatures has gained enormous popularity. However, an effective way to quantify the geochemical, thermodynamic and electrostatic factors responsible for wettability alteration have still not been fully developed. In this work, a surface complexation model (SCM) based on geochemical and thermodynamic interactions at calcite and oil surfaces was used to investigate the effect of temperature, pH, and sulfate on electrostatic interactions. SCM’s for calcite and oil surfaces were validated against zeta potential data at high temperatures and used to interpret improved oil recovery data from spontaneous imbibition experiments. The SCM was correlated to calcite wettability through the calculation of the bond product sum (BPS); a measure of the strength of the electrostatic bond linkages between calcite and oil surfaces. Increasing temperature increased the zeta potential towards more positive values for positive polarities and towards more negative values for negative polarity at both the calcite and oil surfaces. BPS decreased with increasing temperature due to the weakening of [>CO 3 – ][‒NH + ] electrostatic bonds, indicating an increase in water-wetness, consistent with the existing literature. Increasing the sulfate ion concentration in seawater brine reduced the BPS, indicating an increase in water wetness. This was attributed to the reduction in [>CaOH 2 + ][‒COO – ] associated bonds as sulfate concentration increased. Spontaneous imbibition experiments confirmed the BPS analysis, whereby oil recovery increased as sulfate concentration and temperature increased. • A surface complexation model was developed which describes high temperature calcite-brine-oil interfaces. • Increasing temperature decreased oil-calcite electrostatic bonding and increased water wetness in calcite rocks. • Increasing temperature enhanced brine imbibition into limestone, as predicted by the surface complexation model. • Sulfate concentration and brine pH also influenced calcite wettability.

Calculation of indoor air temperature using dimensionless parameters for integrated climate control systems

Introduction. It is noted that the improvement of the technology for calculating the thermal regime of premises in the conditions of automation of climate systems is still relevant. The aim of the work is to find a universal dependence of the air temperature in the building premises on time in conditions of a jump in heat access or heat loss for the integral law of regulating the compensatory heat flow from microclimate systems. In the form of a scientific hypothesis, we consider the statement about the power nature of such a dependence with the presence of a maximum and an asymptotic tendency to zero.&#x0D; Materials and methods. The study involves the use of basic equations that relate the most significant components of heat flows in rooms serviced by microclimate systems equipped with integrated controllers under conditions of abrupt changes in thermal disturbances. The method of dimension analysis is used to identify dimensionless complexes that are essential for obtaining engineering dependencies, as well as software calculation of sums of infinite series with a given accuracy, numerical solution of nonlinear equations, and the method of power series economization.&#x0D; Results. An analytical expression is found for changes in room temperature under integrated control of climate equipment under conditions of a jump in heat availability, which has the form of an infinite series in degrees of a dimensionless parameter that characterizes the properties of the room and the automation system. A simplified expression for the deviation of air temperature is obtained and a formula for the required control time is derived, as well as its estimation is given on the example of one residential building in the climatic conditions of Moscow.&#x0D; Conclusions. It is shown that the dependence of the air temperature in a room serviced by microclimate systems with integrated controllers on time is represented in a universal dimensionless form, suitable for any objects regardless of their specific characteristics. The previously discovered relationships for the moment of maximum deviation and the value of the dynamic control error depending on the air exchange of the room, the transmission coefficient of the controller and the room’s own heat stability are confirmed and refined.