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Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is an NP-hard combinatorial optimization problem in the field of modern logistics, with high computational complexity. This paper proposes an improved genetic algorithm by incorporating a fusion tabu search strategy to address this problem. The algorithm employs a three-dimensional loading mathematical model and utilizes a wall-building method under residual space constraints for stacking goods. Furthermore, adaptation of fitness variation strategy, chromosome adjustment, and tabu search algorithm are introduced to balance the algorithm's global and local search capabilities, as well as to enhance population diversity and convergence speed. Through testing on benchmark cases such as Bischoff and Ratcliff, the improved algorithm demonstrates an average increase of over 3% in packing space utilization compared to traditional genetic algorithms and other heuristic algorithms, validating its feasibility and effectiveness. The proposed improved genetic algorithm provides new insights for solving three-dimensional packing problems and optimizing logistics loading schedules, offering promising prospects for various applications. [ABSTRACT FROM AUTHOR]

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system's evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata. [ABSTRACT FROM AUTHOR]

This paper explores the problem of formalizing the development of autonomous artificial intelligence systems (AAISs) whose mathematical models may be complex or non-identifiable. Using the value-iterations method for Q-functions of rewards, a methodology for constructing ε-optimal strategies with a given accuracy was developed. The results allow us to outline classes (including dual-use), for which it is possible to rigorously justify the construction of optimal and ε-optimal strategies even in cases where the models are identifiable, but the computational complexity of standard dynamic programming algorithms may not be strictly polynomial. [ABSTRACT FROM AUTHOR]

Undetected infections fuel the dissemination of many infectious agents. However, identification of unobserved infectious individuals remains challenging due to limited observations of infections and imperfect knowledge of key transmission parameters. Here, we use an ensemble Bayesian inference method to infer unobserved infections using partial observations. The ensemble inference method can represent uncertainty in model parameters and update model states using all ensemble members collectively. We perform extensive experiments in both model-generated and real-world networks in which individuals have differential but unknown transmission rates. The ensemble method outperforms several alternative approaches for a variety of network structures and observation rates, despite that the model is mis-specified. Additionally, the computational complexity of this algorithm scales almost linearly with the number of nodes in the network and the number of observations, respectively, exhibiting the potential to apply to large-scale networks. The inference method may support decision-making under uncertainty and be adapted for use for other dynamical models in networks. Author summary: Mathematical models in networks can be used to infer unobserved infections and support decision-making in outbreak control and management. However, a major challenge in the operational use of these models is model misspecification–whether models can reliably represent the real-world disease transmission process. As we can only observe part of the transmission process, mathematical models are inherently misspecified due to the uncertainty in the model structure and parameters. A reliable modeling method, therefore, should be robust to such uncertainty and imperfect knowledge of the transmission dynamics to support real-time decision-making. In this study, we used an ensemble inference method to infer unobserved infections using partial observations. We considered the condition where individuals have differential but unknown transmission rates as an example of model uncertainty mirroring the situation encountered in real-world settings. We found the ensemble inference can robustly infer unobserved infections using partial observations with uncertainty in model parameters, although the distribution of parameters is mis-specified. The ensemble inference algorithm presents a general framework for inference of spreading dynamics in networks and may contribute to the toolbox supporting operational epidemic control in the face of model uncertainty and limited observation. [ABSTRACT FROM AUTHOR]

Fast and accurate power-flow methods are of great importance, especially in near real-time optimal operation of power systems. This importance will be even more highlighted in the presence of more repetitions of power-flow calculations, which cause more computational complexities in optimization problems. As a solution, in this paper, a novel fast and accurate approach of linear power-flow formulation is proposed. Principles of the proposed approach are based on dividing power-flow calculations into base and variable parts. To this aim, at first, system modeling of base and variable parts are presented. For the base-part modeling, utilizing a nonlinear power-flow, an accurate base power-flow (BPF) is extracted. Afterwards, by linearizing the power system around the BPF, variable-part model which is the result of a linear fitting process, is obtained. Then, it is shown that the variable-part of the operating point is always a function of the obtained base-part and variable-part models. In this paper, by focusing on the stochastic application of the proposed approach, different uncertainties in a distribution system are considered. Finally, numerical results carried out in the Matlab environment, for a IEEE 34-bus standard distribution system and then a 1486-bus case study, verify the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence of tests the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods. [ABSTRACT FROM AUTHOR]

In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code’s length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders. [ABSTRACT FROM AUTHOR]

The paper presents several novel residual recurrent neural network (RNN) models for digital predistortion of radio-frequency power amplifiers. Then, unstructured and structured neural network (NN) pruning algorithms are proposed to reduce the per-sample computational complexity and the required memory, without compromising their modeling performance. The mathematical equations of the complexity and the memory are derived to analyze the hardware cost and design low cost models. An experimental platform is developed to measure the modeling performance in terms of adjacent channel leakage ratio (ACLR), normalized mean square error, error vector magnitude (EVM) and bit error rate. The platform uses an envelope tracking PA excited by 80 MHz IEEE 802.11ac signals. Compared with the state-of-the-art RNN model in (Sun et al., 2019), the proposed models reduce the per-sample complexity and required memory by $94\hbox{--}99$ %, they also improve the ACLR and EVM by at least 3 dB and 1 dB at 0.45 dB and 3.15 dB gain compression, respectively. Furthermore, an observation path with time alignment is used to remove the transmit latency in the state-of-the-art approach. At 3.15 dB gain compression, the proposed models outperform the state-of-the-art feedforward and convolutional NN models by at least 1.3 dB in EVM, outperform the general memory polynomial model by at least 3.3 dB in EVM. The above evidences indicate that the proposed RNN models can be implemented with relatively low hardware cost and achieve the best EVM in high power efficiency scenario. [ABSTRACT FROM AUTHOR]

In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance. [ABSTRACT FROM AUTHOR]

While fuzzy controllers with multiple fuzzy sets and non-uniformly distributed membership functions have the potential to provide better system performance, from the literature, it appears to the authors that till now, no one has found exact mathematical models of fuzzy PI/PD controllers with non-uniformly distributed multiple fuzzy sets and Center of Area (CoA) defuzzification. To bridge this gap, in this paper, analytical structures of the general Mamdani type fuzzy PI/PD controllers are presented using unequally distributed multiple fuzzy sets, Minimum (Min) t-norm, Maximum (Max) s-norm, Larsen Product (LP) inference, and CoA defuzzification. For the purpose of comparison, analytical structures of the controllers are also obtained using Center of Sums (CoS) defuzzification. Properties of the newly obtained controllers are analyzed and compared. Since digital computers are often used for simulation, a rough estimate of the computational complexities and memory requirements are provided. To show the applicability of the newly developed controllers, a nonlinear DC series motor and a nonlinear plant with dead-time are considered. The effectiveness of the proposed controllers is finally shown through a detailed system performance comparison. [ABSTRACT FROM AUTHOR]

It is an essential technique for the moving user nodes (UNs) with clock offset and clock skew to resolve the joint localization and synchronization (JLAS) problem. Existing iterative maximum likelihood methods using sequential one-way time-of-arrival (TOA) measurements from the anchor nodes’ (AN) broadcast signals require a good initial guess and have a computational complexity that grows with the number of iterations, given the size of the problem. In this paper, we propose a new closed-form JLAS approach, namely CFJLAS, which achieves the asymptotically optimal solution in one shot without initialization when the noise is small, and has a low computational complexity. After squaring and differencing the sequential TOA measurement equations, we devise two intermediate variables to reparameterize the non-linear problem, and convert it to a simpler one of solving two simultaneous quadratic equations. We then solve the equations analytically to obtain a raw closed-form JLAS estimation. Finally, we apply a weighted least squares (WLS) step to optimize the estimation. We derive the Cramér-Rao lower bound (CRLB), analyze the estimation error, and show that the estimation accuracy of the CFJLAS reaches the CRLB under the small noise condition. The complexity of the new CFJLAS is only determined by the size of the problem, unlike the conventional iterative method, whose complexity is additionally multiplied by the number of iterations. Simulations in a 2D scene verify that the estimation accuracies of the new CFJLAS method all reach the CRLB under the small noise condition. Compared with the conventional iterative method, the proposed new CFJLAS method does not require initialization, obtains the optimal solution under the small noise condition, and has a low computational complexity. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (mMIMO) is a promising technique to realize the ever-increasing demand for high-speed data, quality of service (QoS), and energy efficiency for 5G and beyond wireless systems. However, the increased number of users in mMIMO systems significantly affects performance of the existing approximate matrix inversion based and matrix inversion less iterative symbol detection techniques. Conventional detection algorithms cannot learn the inter-relations of input-output parameters based on available data without having specific mathematical models of communication scenarios. Moreover, existing deep learning (DL) based symbol detection models lack in-network compression, resulting in large training time and high computational load while expected to be deployed in a low latency communication system. In this article, a sparse refinement architecture is proposed for symbol detection in uplink mMIMO. The proposed DL architecture requires less trainable parameters as compared to a conventional fully connected detection network and refines the estimated symbol vector in each layer. Convergence of the proposed symbol detection technique is analytically justified. An expression for the approximate upper bound on the BER is derived which is supported by simulations. The obtained results prove viability of the proposed symbol detection model as compared to the several existing state-of-art uplink mMIMO detection techniques, in terms of superior the error performance and low computational complexity. [ABSTRACT FROM AUTHOR]

Wide-area backup protection (WABP) refers to the identification of the faulted line amongst candidate lines by using sparse PMU measurements. This letter proposes a technique for reducing the computational complexity of WABP methods that employ the superimposed-circuit concept. A proposition is presented and proved to justify that the system of equations pertaining to every candidate line can be directly obtained from the bus impedance matrix of the pre-fault power system. This is in contrast with existing WABP methods requiring the establishment of as many distinct bus impedance matrices as the number of candidate lines in the power system. The applicability and effectiveness of the proposed technique are verified by conducting more than 20,000 simulations on the IEEE 39-bus test system. [ABSTRACT FROM AUTHOR]

The structure of open-winding motor fed by the dual-inverter can increase the winding terminal voltage of the primary permanent-magnet linear motor (PPMLM). So, it is an effective method to improve the thrust performance of the PPMLM. Based on the detailed derivation of the mathematical model of the open-winding PPMLM and the in-depth analysis of the space voltage vector distribution characteristics of the dual-inverter, a deadbeat two-vector model predictive current control (MPCC) model is proposed in this paper. First, the optimal vector of the inverter 1 is determined by judging the position of the large sector. Second, two optimal vectors of the inverter 2 is determined by judging the position of the small sector. Finally, the duty cycle of the two optimal vectors of the inverter 2 is calculated to realize the proposed deadbeat two-vector MPCC algorithm. Compared with the traditional model predictive torque control (MPTC) and MPCC strategies, the proposed algorithm has the advantages of lower current harmonics (lower 34 % and 44 % under rated conditions, respectively) and better thrust performance (higher 77 % and 61 % under rated conditions, respectively) as well as lower computational complexity. Simulation and experimental results show that the proposed two-vector MPCC has good steady-state and dynamic performances, which can reduce the current harmonics and thrust ripple, and thus improve the motor drive performance compared with the traditional method. [ABSTRACT FROM AUTHOR]

This article discusses the properties of the practical application results of the Coulomb and the “tree-cotree” gauge conditions for problems based on massive finite element 3-D-meshes (up to 12 million tetrahedrons) and with the ${A}$ – ${V}$ formulation of the magnetic potential. The influence of the sort of gauging of the magnetic vector potential on the accuracy of the calculated solution of systems of linear algebraic equations (SLAEs) is shown by the example of magnetostatics and quasi-static (frequency domain) benchmark problems. The study was carried out for the cases of solving problems by iterative methods of the Krylov subspace and by direct methods. Iterative methods have shown the complexity of achieving the required solution accuracy with an increase in the number of finite elements and deterioration of the properties of the SLAE. The analysis of the dependence of the iterative process convergence and the required solution accuracy on the number of elements in the mesh and the type of gauging applied is accomplished. For direct methods for solving SLAEs, an a posteriori estimate of the dependence of the value of the relative forward error on the presence and type of the gauge condition is performed. The possibility and efficiency of using block low-rank (BLR) factorization for solving SLAEs in the presence and absence of gauge conditions are considered. The conditions for using the gauging of the magnetic vector potential are shown, which are suitable for simplifying the process of preparing and solving numerical problems and increasing the accuracy of the calculated values of the magnetic vector potential in the frequency domain. [ABSTRACT FROM AUTHOR]

This article presents an optimization-based control framework for the autonomous forced landing of a fixed-wing unmanned aircraft (UA). A two-level model-predictive control (MPC) scheme is proposed to realize this framework, where an economic model-predictive control (EMPC) in a long piecewise constant fashion is proposed at the high level, while a short fixed-horizon linear time-varying MPC at the low level responds to fast dynamics of UA and tracks the optimal path provided by the high-level controller, alleviating computational burden compared to the high-frequency single-layer MPC scheme. Compared with a single EMPC setup with high sampling frequency, this hierarchical EMPC controller can significantly reduce the computational complexity and make it feasible to be implemented in real time. In addition, it also responds to disturbances (e.g., wind) and aircraft fast dynamics in a timely manner. The recursive feasibility and stability of the high- and low-level MPC schemes are established. The performance of the proposed EMPC forced landing function is illustrated by simulation case studies on both Aerosonde and Skywalker X8, compared favorably with competing schemes. [ABSTRACT FROM AUTHOR]

The search procedure, as a part of the Modified Ambiguity Function Approach (MAFA), is conducted in the coordinate space. The main advantage of searching for a fixed solution in the coordinate domain, instead of in the ambiguity domain, is the constant search space dimension, which amounts to three. In contrast, an ambiguity space dimension can presently achieve over twenty when the positioning is based on multi-system data. Thus, in the MAFA method, the computational complexity is independent of the number of satellites. We propose a new method of estimating the length of the search step. In this method, the actual satellite configuration determines the size of the search step. Therefore, the data-driven search step is always optimal, regardless of the current satellite configuration. The mathematical model of the new approach is provided together with a detailed algorithm. The numerical experiment follows the description of the search procedure. [ABSTRACT FROM AUTHOR]

In the 3-D density inversion calculation of gravity data, the entire subsurface space is discretized into rectangular prisms, and the density value of each prism is calculated. However, the method of dividing the entire space often results in invalid calculations. In this study, we proposed a highly efficient density inversion method using a locally adaptive unstructured mesh. In this method, the inversion scope is reduced by using the feature that the zero value of the tilt angle method corresponds to the edge of the field source. In addition, the local inversion area is divided by unstructured meshes, which can better represent irregular geological bodies and undulating terrain. In the proposed method, the size of the grid cells is changed according to the value of the tilt angle to reduce the amount of mesh, which reduces the computational complexity and improves the computational efficiency. In addition, by introducing a volume weighting function, the sensitivity of grid cells of different sizes can be balanced. Through synthetic modeling experiments, we verified that the locally adaptive unstructured mesh method can improve the efficiency and accuracy of inversion, flexibly deal with undulating terrain, and obtain the distribution features of irregular bodies. We applied this method to gravimetric data of the North Qinling region of the Shaanxi province, which clearly shows the spatial distribution information of five high-density geological bodies, and the depth range of ore bodies formed is from 240 to 1481 m according to our inversion results. [ABSTRACT FROM AUTHOR]

Let G = (V (G),E(G)) be a finite simple undirected graph with vertex set V (G), edge set E(G) and vertex subset S ⊑ V (G). S is termed open-dominating if every vertex of G has at least one neighbor in S, and open-independent, open-locating-dominating (an OLDoind-set for short) if no two vertices in G have the same set of neighbors in S, and each vertex in S is open-dominated exactly once by S. The problem of deciding whether or not G has an OLDoind-set has important applications that have been reported elsewhere. As the problem is known to be NP-complete, it appears to be notoriously difficult as we show that its complexity remains the same even for just planar bipartite graphs of maximum degree five and girth six, and also for planar subcubic graphs of girth nine. Also, we present characterizations of both P4-tidy graphs and the complementary prisms of cographs that have an OLDoind-set. [ABSTRACT FROM AUTHOR]

When a depolarizing event occurs across a cell membrane there is a remarkable change in its electrical properties. A complete depolarization event produces a considerably rapid increase in voltage that propagates longitudinally along the axon and is accompanied by changes in axial conductance. A dynamically changing magnetic field is associated with the passage of the action potential down the axon. Over 75 years of research has gone into the quantification of this phenomenon. To date, no unified model exist that resolves transmembrane polarization in a closed-form description. Here, a simple but formative description of propagated signaling phenomena in the membrane of an axon is presented in closed-form. The focus is on using both biophysics and mathematical methods for elucidating the fundamental mechanisms governing transmembrane polarization. The results presented demonstrate how to resolve electromagnetic and thermodynamic factors that govern transmembrane potential. Computational results are supported by well-established quantitative descriptions of propagated signaling phenomena in the membrane of an axon. The findings demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation function together in generating an action potential in a unified closed-form description. The work presented in this paper provides compelling evidence that three basic factors contribute to the propagated signaling in the membrane of an axon. It is anticipated this work will compel those in biophysics, physical biology, and in the computational neurosciences to probe deeper into the classical and quantum features of membrane magnetization and signaling. It is hoped that subsequent investigations of this sort will be advanced by the computational features of this model without having to resort to numerical methods of analysis. [ABSTRACT FROM AUTHOR]

XOR arbiter PUF (XOR APUF), where the outputs of multiple arbiter PUF (APUFs) are XOR-ed, has proven to be more robust to machine learning-based modeling attacks. The reported successful modeling attacks for XOR APUF either employ auxiliary side-channel or reliability information, or require enormous computational effort. This robustness is primarily due to the difficulty in learning the unknown internal delay parameter terms in the mathematical model of a XOR APUF, and the robustness increases as the number of APUFs being XOR-ed increases. In this article, we employ a novel machine learning-based modeling technique called efficient CANDECOMP/PARAFAC-tensor regression network (CP-TRN), a variant of CP-decomposition-based tensor regression network, to reduce the computational resource requirement of model building attacks on XOR APUF. We theoretically prove the reduction in computational complexity, as well as give supporting experimental results. In addition, our proposed technique does not require any auxiliary information, and is robust to noisy training data. The proposed technique allowed us to successfully model 64-bit 8-XOR APUF and 128-bit 7-XOR APUF on a single desktop workstation, with high prediction accuracy. Further, we extend the proposed modeling attack technique to XOR APUF variants, e.g., lightweight secure PUF (LSPUF), which rely on input challenge transformation. The modeling accuracy results obtained by us for the LSPUF are comparable with those obtained by applying other state-of-the-art techniques, while requiring less training data. [ABSTRACT FROM AUTHOR]

In spite of accuracy, but due to computational complexity, Center of Gravity (CoG) defuzzification remained dormant for the mathematical modeling of fuzzy controllers for a long time in the past. Recently, Arun and Mohan (ISA Trans 70:16–29, 2017) obtained the mathematical models of two simplest fuzzy PI/PD controllers using CoG defuzzification. In this study, the mathematical models of another five simplest fuzzy PI/PD controllers are obtained, and their properties and computational aspects are investigated. Sufficient conditions for Bounded-Input-Bounded-Output stability of a closed-loop system containing one of these controllers in the loop are also established using the Small-Gain theorem. To justify the theoretical developments made in this manuscript, the applicability of the controllers is shown in simulation and real-time. [ABSTRACT FROM AUTHOR]

Hybrid and intermittent characteristics of the distributed energy resources (DERs) bring great challenges to the security control and economic dispatch (ED) of the microgrids. To bypass these hurdles, this article proposes a multiagent system-based integrated design of security control and ED to guarantee the effective and economical operation of the interconnected microgrids. First, a hierarchical control scheme is constructed by two-level unit agents, in which the switching control and dynamic regulation are fully implemented with the corresponding hybrid behaviors based on the differential hybrid Petri-net (DHPN) model. Based on the DHPN model, a novel dynamic ED integrated with security control is proposed to overcome the issues that cannot be solved in conventional models. Furthermore, to reduce the computational complexity and unified the mathematical model of the DERs, the inverter-based power control strategy is converted to a predictive control model which can be decomposed into several subsystems. In the optimization process, all the subsystems are implemented in a fully distributed, communication free, and rolling optimization manner based on the distributed model predictive control (DMPC). The validity of the proposed design is demonstrated according to the simulation results in case studies. [ABSTRACT FROM AUTHOR]

Pachinko is a Japanese mechanical gambling game similar to pinball. Recently, several mathematical models of Pachinko have been proposed. A number of pins are spiked in a field. A ball drops from the top of the playfield and the ball falls down. In the 50-50 model, if the ball hits a pin, it moves to the left or right passage of the pin with an equal probability. An arrangement of pins generates a distribution of the drop probability for all of the columns. This problem was considered by generating uniform distributions. Previous studies have demonstrated that the (1 / 2 a) -uniform distribution is possible for a ∈ { 0 , 1 , 2 , 3 , 4 } and is conjectured so that it is possible for any positive integer a. This study describes the constructive proof for this conjecture. This study also formalizes a natural decision problem yielded by this model while investigating its computational complexity. More precisely, given any drop-probability distribution A and any partial drop-probability distribution B , this study uses non-deterministic polynomial-time (NP) hardness to determine if there exists a pin arrangement that transforms A into B. [ABSTRACT FROM AUTHOR]

A method to find the minimized state machine cover of live and safe Petri nets (PNs) is proposed in this paper. It is required that a cover be obtained in some implementation methods of PN-based control algorithms and other applications such as data mining. Most of the known methods of its computation have at least exponential time and space complexity; this is true not only for the methods which guarantee a minimal cover is obtained but also for some methods of finding approximate solutions. The proposed algorithm is an approximation algorithm and has polynomial computational complexity. The experimental verification shows a very high efficiency of the presented technique. The proposed method is especially valuable in the case of large systems where a solution is obtained hundreds of times quicker than by other methods. [ABSTRACT FROM AUTHOR]

A closed-loop supply chain structure organises material and information flows from origin points to consumption points, including production, recycling, disposal, and other reverse logistic activities. Some integration problems arise with this structure including production, inventory, location, routing, distribution, collection, recycling, and routing. The integration problems that are facing scientific researchers include inventory routing, location routing, and location inventory. This study considers the integration problem of a closed-loop supply chain for the production, distribution, collection, and recycling quantities, along with the distribution and collection routes for each time period of a finite planning horizon. We refer to this problem as the "Closed-Loop Supply Chain Integrated Production-Inventory-Distribution-Routing Problem" (CLSC-PRP). A mathematical model is proposed that is the first to determine both quantities and routes for the CLSC-PRP simultaneously. As the problem is known to be NP-hard in terms of computational complexity, a simulated annealing-based decomposition heuristic is developed for solving large-scale CLSC-PRP instances. The results of the proposed mathematical model for the CLSC-PRP are compared with the results of the developed heuristic and two separate models that manage forward and backward production routing problems. An extensive comparative study indicated the following: (i) the proposed model was able to reduce the cost required for operating the total supply chain by an average of 12%, along with providing a positive impact on the environment and (ii) the proposed heuristic is able to generate solutions that are close to optimal in most cases. [ABSTRACT FROM AUTHOR]

Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint functions of a variable optimization problem can be derived, standard numerical algorithms can be applied for finding the optimal solution, which however incurs high computational cost when the dimension of the variable is high. To reduce the on-line computational complexity, learning the optimal solution as a function of the environment's status by deep neural networks (DNNs) is an effective approach. DNNs can be trained under the supervision of optimal solutions, which however, is not applicable to the scenarios without models or for functional optimization where the optimal solutions are hard to obtain. If the objective and constraint functions are unavailable, reinforcement learning can be applied to find the solution of a functional optimization problem, which is however not tailored to optimization problems in wireless networks. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems without the supervision of the optimal solutions. When the mathematical model of the environment is completely known and the distribution of the environment's status is known or unknown, we can invoke an unsupervised learning algorithm. When the mathematical model of the environment is incomplete, we introduce reinforced- unsupervised learning algorithms that learn the model by interacting with the environment. Our simulation results confirm the applicability of these learning frameworks by taking a user association problem as an example. [ABSTRACT FROM AUTHOR]

We present a pilot application of the recently proposed quasi-variational coupled cluster method to the energies, polarizabilities, and second hyperpolarizabilities of model hydrogen chains. Relative to other single-reference methods of equivalent computational complexity, we demonstrate this method to be highly robust and especially useful when traditional coupled cluster theory fails to perform adequately. In particular, our results indicate it to be a suitable method for the black-box treatment of multiradicals, making it of widespread general interest and applicability. [ABSTRACT FROM AUTHOR]

Summary A state of health (SOH) estimation method that can be achieved online and only requires battery management system (BMS) detection data is proposed in this article. In the State of Health mathematical model proposed in this article, the using time of power battery is treated as an independent variable and SOH is treated as a hidden variable. And the mathematical model just used online process data from BMS. So it would make the SOH estimation method more suitable for actual engineering. Then, the article proposes an interleaved time model parameter update framework to reduce the computational complexity of the algorithm in a single sampling period. In this framework, we propose a fast model parameter identification algorithm that uses nonlinear least squares to initialize a genetic algorithm searched range. Finally, the whole method is verified by using the NASA database. The results prove that the proposed online SOH estimation method has higher SOH estimation accuracy and is more suitable for engineering applications in the field of electric vehicles than the existing SOH estimation methods. [ABSTRACT FROM AUTHOR]

Aiming at the dynamic and nonlinear characteristics of batch process, a multiway dynamic nonlinear global neighborhood preserving embedding algorithm is proposed. For the nonlinear batch process monitoring, kernel mapping is widely used to eliminate nonlinearity by projecting the data into high-dimensional space, but the nonlinear relationships between batch process variables are limited by many physical constraints, and the infinite-order mapping is inefficient and redundant. Compared with the basic kernel mapping method which provides an infinite-order nonlinear mapping, the proposed method considers the dynamic and nonlinear characteristics with many physical constraints and preserves the global and local structures concurrently. First, the time-lagged window is used to remove the auto-correlation in time series of process variables. Second, a nonlinear method named constructive polynomial mapping is used to avoid unnecessary redundancy and reduce computational complexity. Third, the global neighborhood preserving embedding method is used to extract structures fully after the dynamic and nonlinear characteristics are processed. Finally, the effects of the proposed algorithm are demonstrated by a mathematical model and the penicillin fermentation process. [ABSTRACT FROM AUTHOR]

In order to give a comprehensive understanding of SLAM, this paper first gave an overview of the progress of visual SLAM community has made over the last 30 years in this survey. Then it presented the non-linearity of the mathematical model and computational complexity in visual SLAM algorithms. This paper mostly focused on the latest achievements and approached improving the accuracy of pose estimation, building a globally consistency representation of the environment and promoting computation efficiency. It also surveyed the failure modes of current visual SLAM algorithms for large scale, full life cycle implementation and the different ways to address that. Finally, it discussed the potential connections between deep learning architectures and visual SLAM state estimations. [ABSTRACT FROM AUTHOR]

In network-centric warfare, the interconnections among various combat resources enable an advanced operational pattern of cooperative engagement. The operational effectiveness and outcome strongly depends on the reasonable utilization of available sensors and weapons. In this paper, a mathematical model for the coallocation of sensors and weapons is built, taking into account the interdependencies between weapons and sensors, the resource constraints, the capability constraints, as well as the strategy constraints. A marginal-return-based constructive heuristic (MRBCH) is proposed to solve the formulated sensor–weapon–target assignment (S-WTA) problem. MRBCH exploits the marginal return of each sensor–weapon–target triplet and dynamically updates the threat value of all targets. It relies only on simple lookup operations to choose each assignment triplet, thus resulting in very low computational complexity. For performance evaluation, we build a general Monte Carlo simulation-based S-WTA framework. Furthermore, we employ a random sampling method and an extension of the state-of-the-art algorithm Swt_opt as competitors. The computational results show that MRBCH consistently performs very well in solving S-WTA instances of different scales, and it can generate assignment schemes much more efficiently than its competitors. [ABSTRACT FROM AUTHOR]

This paper aims to develop a recovery planning approach in a three-tier manufacturing supply chain, which has a single supplier, manufacturer, and retailer under an imperfect production environment, in which we consider three types of sudden disturbances: demand fluctuation, and disruptions to production and raw material supply, which are not known in advance. Firstly, a mathematical model is developed for generating an ideal plan under imperfect production for a finite planning horizon while maximizing total profit, and then we re-formulate the model to generate the recovery plan after happening of each sudden disturbance. Considering the high commercial cost and computational intensity and complexity of this problem, we propose an efficient heuristic, to obtain a recovery plan, for each disturbance type, for a finite future period, after the occurrence of a disturbance. The heuristic solutions are compared with a standard solution technique for a considerable number of random test instances, which demonstrates the trustworthy performance of the developed heuristics. We also develop another heuristic for managing the combined effects of multiple sudden disturbances in a period. Finally, a simulation approach is proposed to investigate the effects of different types of disturbance events generated randomly. We present several numerical examples and random experiments to explicate the benefits of our developed approaches. Results reveal that in the event of sudden disturbances, the proposed mathematical and heuristic approaches are capable of generating recovery plans accurately and consistently. [ABSTRACT FROM AUTHOR]

A three-dimensional computational model for the dynamical sensing response of Galfenol magnetostrictive devices based on the rate equations is developed. The sensing model calculates the fraction of magnetic moments oriented along each of the energetically preferred directions of the crystal as a function of time, which can then be used to determine the time evolution of the total magnetization. Results from this 3D sensing model are compared to quasistatic loading experiments for the validation and extraction of phenomenological parameters. Using these extracted parameters, calculations are made for the dynamical sensing response. Thermodynamic effects are also incorporated into the model by a Boltzmann distribution of the magnetic moments in the crystal. Good quantitative agreement between the model and experiment at low magnetic bias fields and qualitative agreement at higher magnetic bias fields is obtained. [ABSTRACT FROM AUTHOR]

Based on cylindrical algebraic decomposition (CAD) technique, an algorithm for solving the stable parameter region of factional-order systems with structured perturbations (FOSSP) is presented. The algorithm is nonconservative and universal for fractional order systems with order 0 < α < 2. And the computational complexity of the algorithm is less than existing methods. Two examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The modular multilevel converter (MMC) has become a promising topology for high-voltage direct current (HVDC) transmission systems. To control a MMC system properly, the ac-side current, circulating current and submodule (SM) capacitor voltage are taken into consideration. This paper proposes a low-computation indirect model predictive control (IMPC) strategy that takes advantages of the conventional MPC and has no weighting factors. The cost function and duty cycle are introduced to minimize the tracking error of the ac-side current and to eliminate the circulating current. An optimized merge sort (OMS) algorithm is applied to keep the SM capacitor voltages balanced. The proposed IMPC strategy effectively reduces the controller complexity and computational burden. In this paper, a discrete-time mathematical model of a MMC system is developed and the duty ratio of switching state is designed. In addition, a simulation of an eleven-level MMC system based on MATLAB/Simulink and a five-level experimental setup are built to evaluate the feasibility and performance of the proposed low-computation IMPC strategy. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the Approximate Agreement problem in the Mobile Byzantine Fault model. Our contribution is three-fold. First, we refine the problem specification to adapt it to the Mobile Byzantine Fault environment. Then, we propose the first mapping from the existing variants of Mobile Byzantine models to the Mixed-mode Fault model. This mapping further help us to prove the correctness of MSR (Mean-Subsequence-Reduce) algorithms class in our context and it is of independent interest. We also prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine fault models. [ABSTRACT FROM AUTHOR]

In this paper, we present a qualitative study in which we analyse the videorecordings of four groups of students solving Fermi Problems. Previous studies show that Secondary School students solve this type of problems using complex problem solving processes and developing mathematical models. In order to analyse the students' problem solving processes, so-called Modelling Activity Diagrams were used. The results of the present study demonstrate that solving Fermi problems is a complex matter, and that some of the theoretical tools used in the field of Mathematical Education fail to adequately reflect this level of complexity. In addition, Modelling Activity Diagrams are presented as a more detailed analysis tool to characterise student choices and actions, as well as to make the structure of the Fermi problem addressed more visible. [ABSTRACT FROM AUTHOR]

In quality control applications, the control chart is a powerful tool but its performance is adversely affected by the contamination from either the inspector or the measuring device leading to measurement errors. In this paper, we investigate the performance of the AEWMA median chart with measurement errors, and a methodology is proposed to obtain the optimal parameters by considering a linearly covariate error model. Several figures and tables show that, with the existence of measurement errors, the efficiency of the AEWMA median chart can be strongly affected, but this negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the Shewhart and the classical EWMA schemes confirm the superiority of the AEWMA scheme for detecting a wide range of shifts in the case of precise and imprecise data. An example is provided to illustrate the use of the AEWMA median chart with measurement errors. [ABSTRACT FROM AUTHOR]

Abstract Motivated by the study of genomes evolving by reversals, we consider pseudograph transformations known as "pressing sequences". In particular, we address the question of when a graph has precisely one pressing sequence resulting in the empty graph, thus answering an question from Cooper and Davis (2015) [13]. We characterize such "uniquely pressable" graphs, count the number of them on a given number of vertices, and provide a polynomial-time recognition algorithm. We conclude with several open questions. [ABSTRACT FROM AUTHOR]

Quasi-pseudo-MV algebras (quasi-pMV algebras, for short) arising from quantum computational logics are the generalizations of both quasi-MV algebras and pseudo-MV algebras. In this paper, we introduce the notions of states, state-morphisms, state operators and state-morphism operators to quasi-pMV algebras. First, we present the related properties of states on quasi-pMV algebras and show that states and Bosbach states coincide on any quasi-pMV algebra. And then we investigate the relationship between state-morphisms and the normal and maximal ideals of quasi-pMV algebras. We prove state-morphisms and extremal states are equivalent. The existence of states on quasi-pMV algebras is also discussed. Finally, state operators and state-morphism operators are introduced to quasi-pMV algebras, and the corresponding structures are called state quasi-pMV algebras and state-morphism quasi-pMV algebras, respectively. We investigate the related properties of ideals under state operators and state-morphism operators. Meanwhile, we show that there is a bijective correspondence between normal σ-ideals and ideal congruences on state quasi-pMV algebras. [ABSTRACT FROM AUTHOR]

Chemical reaction network has been a model of interest to both theoretical and applied computer scientists, and there has been concern about its physical-realisticity which calls for study on the atomic property of chemical reaction networks. Informally, a chemical reaction network is “atomic” if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Primitive atomic, which requires each reaction to preserve the total number of atoms, is shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving (Mayr and Weihmann, in: International conference on applications and theory of petri nets and concurrency, Springer, New York, 2014), the equivalence we show gives an efficient algorithm to decide primitive atomicity. Subset atomic further requires all atoms be species, so intuitively this type of network is endowed with a “better” property than primitive atomic (i.e. mass conserving) ones in the sense that the atoms are not just abstract indivisible units, but also actual participants of reactions. We show that deciding if a network is subset atomic is in NP, and “whether a network is subset atomic with respect to a given atom set” is strongly NP-complete. Reachably atomic, studied by Adleman et al. (On the mathematics of the law of mass action, Springer, Dordrecht, 2014. 10.1007/978-94-017-9041-3_1), and Gopalkrishnan (2016), further requires that each species has a sequence of reactions splitting it into its constituent atoms. Using a combinatorial argument, we show that there is a polynomial-time algorithm to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is decidable. We show that the reachability problem for reachably atomic networks is PSPACE-complete. Finally, we demonstrate equivalence relationships between our definitions and some cases of an existing definition of atomicity due to Gnacadja (J Math Chem 49(10):2137, 2011). [ABSTRACT FROM AUTHOR]

Abstract Making a trade-off between the control accuracy and computational reduction is a problem frequently encountered in the system control design. This is especially difficult when one designs adaptive fuzzy (or neural network) controls for nonlinear systems, in which fuzzy controls have to consume many computational resources to tune a sufficiently large number of adaptive parameters, meanwhile nonlinear uncertainties block the high demanding control accuracy. Current works usually face a dilemma that, either the computation is reduced but the control accuracy is degraded due to the use of the norm estimation, or the asymptotic control is resulted but the computation is increased due to the extra compensation controls. To address such dilemma, we propose an asymptotic adaptive fuzzy tracking control algorithm, whose main feature is that only two adaptive laws are needed throughout the control scheme. In particular, we allocate one adaptive law to achieve adaptive fuzzy backstepping control for nonlinear systems with a focus on stabilizing the closed-loop system. We then allocate the other adaptive law not only to asymptotically drive the stabilization error to the zero, but also to achieve the elimination of overparametrization in a Nussbaum-like design, which is inspired by the tuning function-based approach. [ABSTRACT FROM AUTHOR]

In learning theory, the VC dimension of a concept class C is the most common way to measure its "richness." A fundamental result says that the number of examples needed to learn an unknown target concept c ϵ C under an unknown distribution D, is tightly determined by the VC dimension d of the concept class C . Specifically, in the PAC model ϴ(d/ε+log(1/948;)/ε) examples are necessary and sufficient for a learner to output, with probability 1- δ, a hypothesis h that is ε-close to the target concept c (measured under D). In the related agnostic model, where the samples need not come from a c ϵ C, we know that ϴ(d/ε2+log(1/δ)/ε2) examples are necessary and sufficient to output an hypothesis h ϵ C whose error is at most " worse than the error of the best concept in C . Here we analyze quantum sample complexity, where each example is a coherent quantum state. This model was introduced by Bshouty and Jackson (1999), who showed that quantum examples are more powerful than classical examples in some fixed-distribution settings. However, Atici and Servedio (2005), improved by Zhang (2010), showed that in the PAC setting (where the learner has to succeed for every distribution), quantum examples cannot be much more powerful: the required number of quantum examples is Ω(d1-n/ε+d+log(1/δ)/ε) for arbitrarily small constant n > . Our main result is that quantum and classical sample complexity are in fact equal up to constant factors in both the PAC and agnostic models. We give two proof approaches. The first is a fairly simple information-theoretic argument that yields the above two classical bounds and yields the same bounds for quantum sample complexity up to a log(d/ε) factor. We then give a second approach that avoids the log-factor loss, based on analyzing the behavior of the "Pretty Good Measurement" on the quantum state-identification problems that correspond to learning. This shows classical and quantum sample complexity are equal up to constant factors for every concept class C . [ABSTRACT FROM AUTHOR]