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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]

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]

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]

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]

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]

Three mathematical models have been used to predict the dehydration kinetics of grape pomace. To the aim, three different temperatures have been set to determine the different desorption kinetics. All the dehydration kinetic data have been fitted to verify the predictive ability of the proposed models. The fitting goodness were assessed by using four coefficients: E ‾ % , R M S E , χ 2 , and R 2. Results show that all the proposed models can adequately fit the experimental data. In particular, the Dual-Stage Type B model is the best one, whereas the Fick model is the worst. The soundness of the mathematical approach adopted was tested by assessing the dependence of the model's parameters on the testing temperature: only some parameters followed the expected trend. The computational complexity referred to each model was considered evaluating the suitability of the proposed models to describe the desorption kinetics. To sum up, the Dual-Stage Type B model is the most complex, whereas the simplest one is the Dual-Stage Type A model. Considering both suitability and complexity, the Dual-Stage Type A is the best model to predict the dehydration kinetic of grape pomace. • 3 models have been used to predict grape pomace's dehydration kinetic. • The best but most complex model is the Dual-Stage Type B model. • The Dual-Stage Type A combines good predictive capacity with simplicity. [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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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 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]

The complexity of cancer has motivated the development of different approaches to understand the dynamics of this large group of diseases. One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations. Several ODE mathematical models concerning tumor evolution and immune response have been formulated through the years, but only a few may exhibit chaotic attractors and oscillations such as stable limit cycles and periodic orbits; these dynamics are not that common among cancer systems. In this paper, we apply the Localization of Compact Invariant Sets (LCIS) method and Lyapunov stability theory to investigate the global dynamics and the main factors involved in tumor growth and immune response for a chaotic-cancer system presented by Itik and Banks in 2010. The LCIS method allows us to compute what we define as the localizing domain, which is formulated by the intersection of all lower and upper bounds of each cells population in the nonnegative octant, R+,03. Bounds of this domain are given by inequalities in terms of the system parameters. Then, we apply Lyapunov stability theory and LaSalle’s invariance principle to establish existence conditions of a global attractor. The latter implies that given any nonnegative initial condition, all trajectories will go to the largest compact invariant set (a stable equilibrium point, limit cycles, periodic orbits, or a chaotic attractor) located either inside or at the boundaries of the localizing domain. In order to complement our analysis, numerical simulations are performed throughout the paper to illustrate all mathematical results and to better explain their biological implications. [ABSTRACT FROM AUTHOR]

Researchers in many disciplines have previously used a variety of mathematical techniques for analyzing group interactions. Here we use a new metric for this purpose, called “integrated information” or “phi.” Phi was originally developed by neuroscientists as a measure of consciousness in brains, but it captures, in a single mathematical quantity, two properties that are important in many other kinds of groups as well: differentiated information and integration. Here we apply this metric to the activity of three types of groups that involve people and computers. First, we find that 4-person work groups with higher measured phi perform a wide range of tasks more effectively, as measured by their collective intelligence. Next, we find that groups of Wikipedia editors with higher measured phi create higher quality articles. Last, we find that the measured phi of the collection of people and computers communicating on the Internet increased over a recent six-year period. Together, these results suggest that integrated information can be a useful way of characterizing a certain kind of interactional complexity that, at least sometimes, predicts group performance. In this sense, phi can be viewed as a potential metric of effective group collaboration. [ABSTRACT FROM AUTHOR]

A physics-based rank-revealing multilevel algorithm to more efficiently compute low-rank (LR) approximations of the method of moments matrix blocks ${\mathbf{Z}}^{\textrm {os}}$ is presented. Using surface subsets of volumetric nonuniform spherical grids (proxy grids), an LR approximation ${\mathbf{Z}}^{\textrm {os}}\approx {\mathbf{AB}}^{\dagger }$ is obtained in two stages: 1) an upward pass and a downward pass on a multilevel tree, via truncated singular value decomposition-based analyses of interactions between source subclusters and their attendant proxy grids, rapidly estimates the rank and yields a domain of ${\mathbf{Z}}^{\textrm {os}}$ , in the form of a matrix ${\mathbf{B}}$ with orthonormal columns and 2) a fast matrix–matrix multiplication step yields ${\mathbf{A}}$. The algorithm reduces the ${\mathcal{ O}}(N^{3})$ computational costs of revealing the rank to ${\mathcal{ O}}(N^{2})$ or ${\mathcal{ O}}(N^{3/2})$ operations and that of finding an LR approximation to ${\mathcal{ O}}(N^{2})$ or ${\mathcal{ O}}(N^{3/2}\log N)$ operations by adopting enclosing or belt-like proxy grids for electromagnetically large basis/testing function distributions that are either densely packed in a volume or quasi-planar, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we describe an implementation of the fast spherical harmonic transform (SHT) algorithm in the Yin–He global spectral model (YHGSM). A new analysis method is proposed to study the potential instability of interpolative decomposition and to evaluate the performance of fast SHT on the MilkyWay-2 supercomputer. The novel aspect of the proposed method is the use of the computational complexity analysis method by studying the properties of interpolative decompositions. Furthermore, three test cases are conducted to verify fast SHT in YHGSM. The results demonstrate that fast SHT is feasible and efficient for reducing the computational complexity and memory cost of SHT while still keeping enough accuracy. [ABSTRACT FROM AUTHOR]

We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type when the labeling of the tree shares the same restrictions. [ABSTRACT FROM AUTHOR]

In this paper, we study a simplified affine motion model-based coding framework to overcome the limitation of a translational motion model and maintain low-computational complexity. The proposed framework mainly has three key contributions. First, we propose to reduce the number of affine motion parameters from 6 to 4. The proposed four-parameter affine motion model can not only handle most of the complex motions in natural videos, but also save the bits for two parameters. Second, to efficiently encode the affine motion parameters, we propose two motion prediction modes, i.e., an advanced affine motion vector prediction scheme combined with a gradient-based fast affine motion estimation algorithm and an affine model merge scheme, where the latter attempts to reuse the affine motion parameters (instead of the motion vectors) of neighboring blocks. Third, we propose two fast affine motion compensation algorithms. One is the one-step sub-pixel interpolation that reduces the computations of each interpolation. The other is the interpolation-precision-based adaptive block size motion compensation that performs motion compensation at the block level rather than the pixel level to reduce the number of interpolation. Our proposed techniques have been implemented based on the state-of-the-art high-efficiency video coding standard, and the experimental results show that the proposed techniques altogether achieve, on average, 11.1% and 19.3% bits saving for random access and low-delay configurations, respectively, on typical video sequences that have rich rotation or zooming motions. Meanwhile, the computational complexity increases of both the encoder and the decoder are within an acceptable range. [ABSTRACT FROM AUTHOR]

In this paper, a procedure based on three-dimension matrices is presented: it is the generalization of multiconductor cell analysis to any transmission line where the positions of all the active and passive conductors may change with continuity along their length. A meaningful example of this is given by a three-core single lead-screened armoured cable where cores and armour wires are wound helically with different lay lengths. Therefore, this generalization is presented with reference to these cables but it can be applied to any transmission line. The proposed matrix procedures can be implemented in any standard computer by means of a mathematical software (e.g., MATLAB). The computational complexity of this novel method is shown in comparison with the finite element method commercial software FLUX 3D, which takes 70 h for meshing and solving a 3-m long model. On the contrary, the present matrix algorithms take from minute fractions to maximum 2 min (depending on subconductor number) to obtain results having negligible differences with respect to FEM FLUX 3D ones if paramagnetic materials are involved and differences up to maximum 7% with ferromagnetic ones (which imply, for submarine cable installations, a current rating computation difference lower than 3%). [ABSTRACT FROM PUBLISHER]

Dynamicity of the cloud computing system, complexity of real-world decision-making problems, and nontransparent market imply numerous difficulties in finding the corresponding solution for cloud supplier evaluation and selection. Due to that reason, there is a need to develop a model that can contribute to increase of reliability of evaluation and reduction of subjectivity of the decision-maker. Having in mind the aforementioned, the authors proposed a new concept to model a cloud supplier evaluation based on technology perspective. Here, we developed a model that combined fuzzy techniques with implemented simulation of model parameters. The proposed method for cloud supplier evaluation is flexible with an objective evaluation and ensures more precise numerical value. Numerical examples are presented to demonstrate the effectiveness and pragmatism of the proposed approach. [ABSTRACT FROM AUTHOR]

Surrogate modeling, or metamodeling, is an efficient way of alleviating the high computational cost and complexity for iterative function evaluation in design optimization. Accuracy is significantly important because optimization algorithms rely heavily on the function response calculated by surrogate model and the optimum solution is directly affected by the quality of surrogate model. In this study, an optimized trend kriging model is proposed to improve the accuracy of the existing kriging models. Within the framework of the proposed model, regression analysis is carried out to approximate the unknown trend of the true function and to determine the order of the universal kriging model, which has a fixed form with a mean structure dependent on the order of model. In addition, the selection of an optimal basis function is conducted to separate the useful basis function terms from the full set of the basis function. The optimal subset of the basis function is selected with the global optimization algorithm; which can accurately represent the trend of true response surface. The mean structure of proposed model has been optimized to maximize the accuracy of kriging model depending on the trend of true function. Two- and three-dimensional analytic functions and a practical engineering problem are chosen to validate the proposed model. The results showed that the OTKG model yield the most accurate responses regardless of the number of initial sample points, and can conversed into well-trained model with few additional sample points. [ABSTRACT FROM AUTHOR]

Gradient descent provides a simple and flexible approach to sequence design. Simplicity is inherent in the gradient approach itself—The negative of the gradient of a given cost function gives an indication of the change to make to a sequence to find the local minimum of the cost function. Flexibility is provided by the lack of constraints on the cost function, allowing different aspects of a sequence to be optimized, e.g., autocorrelation or cross-correlation sidelobe energy, or spectral characteristics. Additional flexibility is provided by the linearity of gradients. The gradient of a linear combination of cost functions is simply an equivalent linear combination of their gradients. This allows multiple objectives to be optimized simultaneously. Gradient computational complexity has been one impediment to the use of gradient descent in sequence design in the past. In this paper, it is shown that gradients for a large variety of cost functions can be computed very efficiently. For a sequence of length $N$ , the computational complexity of computing the full gradient (the gradient with respect to all $N$ elements) is $O(N^3)$ in a “naive” implementation. In this paper, equations are derived that allow the gradients to be computed with $O(N \log N)$ operations, a substantial improvement over previous methods. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis is a tool that primarily focuses on identifying the effects of uncertain input variables on the output and has been investigated widely in chemical kinetic studies. Conventional variance-based methods, such as Sobol’ sensitivity estimation and high dimensional model representation (HDMR) methods, are computationally expensive. To accelerate global sensitivity analysis, a new framework that combines a variance-based (Wu's method) and two ANN-based sensitivity analysis methods (Weights and PaD) was proposed. In this framework, a back-propagation neural network (BPNN) methodology was applied, which was optimized by a particle swarm optimization (PSO) algorithm and trained with original samples. The Wu's method and Weights and PaD methods were employed to calculate sensitivity indices based on a well-trained PSO-BPNN. The convergence and accuracy of the new framework were compared with previous methods using a standard test case (Sobol’ g-function) and a methane reaction kinetic model. The results showed that the new framework can greatly reduce the computational cost by two orders of magnitude, as well as guaranteeing accuracy. To take maximum advantage of the new framework, a four-step process combining the advantages of each method was proposed and applied to estimate the sensitivity indices of a C 2 H 4 ignition model. The sensitivity indices of the more complex model could be implemented easily with good accuracy when the four-step process is followed [ABSTRACT FROM AUTHOR]

An efficient algorithm based on the contour integral method (CIM) is presented in this letter for the modeling of lossy multiconductor transmission lines. Different from the volume integral equation, the CIM only discretizes the contour of the cross section of each conductor, which significantly reduces the number of unknowns in the resultant system equations. The solution of the CIM is accelerated by the hierarchical-matrix ( \mathcal H-matrix) algorithm for the extraction of the per-unit-length resistance and inductance parameters of massively coupled transmission lines. The procedures for the \mathcal H-matrix-based solution are optimized to keep its optimal computational complexity. The numerical results from the proposed method agree well with those from the commercial software. The complexities of CPU time and memory cost for the construction of the \mathcal H-matrices are both $O(N\log {}N)$, and the complexity of the solution for parameter extraction is $O(N\log ^2{}N)$. [ABSTRACT FROM AUTHOR]

We present a computational framework for conceptual blending , a concept invention method that is advocated in cognitive science as a fundamental and uniquely human engine for creative thinking. Our framework treats a crucial part of the blending process, namely the generalisation of input concepts, as a search problem that is solved by means of modern answer set programming methods to find commonalities among input concepts. We also address the problem of pruning the space of possible blends by introducing metrics that capture most of the so-called optimality principles , described in the cognitive science literature as guidelines to produce meaningful and serendipitous blends. As a proof of concept, we demonstrate how our system invents novel concepts and theories in domains where creativity is crucial, namely mathematics and music. [ABSTRACT FROM AUTHOR]

In this article, we study computational uncertainties in probabilistic risk/safety assessment resulting from the computational complexity of calculations of risk indicators. We argue that the risk analyst faces the fundamental epistemic and aleatory uncertainties of risk assessment with a bounded calculation capacity, and that this bounded capacity over-determines both the design of models and the decisions that can be made from models. We sketch a taxonomy of modelling technologies and recall the main computational complexity results. Then, based on a review of state of the art assessment algorithms for fault trees and event trees, we make some methodological proposals aiming at drawing conceptual and practical consequences of bounded calculability. [ABSTRACT FROM AUTHOR]

We consider the problem of detecting an odd process among a group of Poisson point processes, all having the same rate except the odd process. The actual rates of the odd and non-odd processes are unknown to the decision maker. We consider a time-slotted sequential detection scenario where, at the beginning of each slot, the decision maker can choose which process to observe during that time slot. We are interested in policies that satisfy a given constraint on the probability of false detection. We propose a variation on a sequential policy based on the generalised likelihood ratio statistic. The policy, via suitable thresholding, can be made to satisfy the given constraint on the probability of false detection. Furthermore, we show that the proposed policy is asymptotically optimal in terms of the conditional expected stopping time among all policies that satisfy the constraint on the probability of false detection. The asymptotic is as the probability of false detection is driven to zero. We apply our results to a particular visual search experiment studied recently by neuroscientists. Our model suggests a neuronal dissimilarity index for the visual search task. The neuronal dissimilarity index, when applied to visual search data from the particular experiment, correlates strongly with the behavioural data. However, the new dissimilarity index performs worse than some previously proposed neuronal dissimilarity indices. We explain why this may be attributed to some experiment conditions. [ABSTRACT FROM AUTHOR]

The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which are mainly caused by coupling effect of connection relationships between nodes. However, the connection relationships between nodes are also one main body of a time-varying dynamic complex network, and thus they may evolve with time and maybe show certain characteristic phenomena. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. Therefore, it is important to investigate theoretically the reasons in dynamics for the occurrence. Especially, from the angle of large-scale systems, how the dynamic behaviors of nodes (such as the individuals, neurons) contribute to the connection relationships is one of worthy research directions. In this paper, according to the structural balance theory of triad proposed by F. Heider, we mainly focus on the connection relationships body, which is regarded as one of the two subsystems (another is the nodes body), and try to find the dynamic mechanism of the structural balance with the internal state behaviors of the nodes. By using the Riccati linear matrix differential equation as the dynamic model of connection relationships subsystem, it is proved under some mathematic conditions that the connection relationships subsystem is asymptotical structural balance via the effects of the coupling roles with the internal state of nodes. Finally, the simulation example is given to show the validity of the method in this paper. [ABSTRACT FROM AUTHOR]

This paper involves developing new mathematical expressions to find reorder point and order quantity for inventory management policies that explicitly consider storage space capacity. Both continuous and periodic reviews, as well as backlogged and lost demand during stockout, are considered. With storage space capacity, when on-hand inventory exceeds the capacity, the over-ordering cost of storage at an external warehouse is charged on a per-unit-period basis. The objective is to minimize the total cost, consisting of ordering, shortage, holding, and over-ordering costs. Demand and lead time are stochastic and discrete in nature. Demand during varying lead time is modeled using an empirical distribution so that the findings are not subject to assumptions of demand and lead time probability distributions. Due to the complexity of the developed mathematical expressions, the problems are solved using an iterative method. The method is tested with problem instances that use real data from industry. Optimal solutions of the problem instance are determined by performing exhaustive search. The proposed method can effectively find optimal solutions for continuous review policies and near optimal solutions for periodic review policies. Fundamental insights about the inventory policies are reported from a comparison between continuous review and periodic review solutions, as well as a comparison between backlog and lost sales cases. [ABSTRACT FROM AUTHOR]

This paper is concerned with the qualitative analysis of a financial system. We focus our interest on the stability and cyclicity of the equilibria. Based on some previous results, some notes are given for a class of systems concerning focus quantities, center manifolds and Hopf bifurcations. The analysis of Hopf bifurcations on the center manifolds is carried out based on the computation of focus quantities and other analytical techniques. For each equilibrium, the structure of the bifurcation set is explored in depth. It is proved through the study of Bautin bifurcations that the system can have at most four small limit cycles (on the center manifolds) in two nests and this bound is sharp. [ABSTRACT FROM AUTHOR]

A generalized solution scheme was utilized to specialize a recently-developed 3D multi-mechanism SMA model, thus making it suitable for the kinematical/statical constraints needed for modeling two-dimensional continua, shell analysis, as well as planar and spatial beam assemblages. The accuracy and computational efficiency of the scheme were assessed in the context of two specific geometries of 55NiTi SMA actuators; i.e., multi-coil helical spring and honeycomb panel, operating under one-way or two-way shape memory conditions. The emphasis is placed on the thermomechanical response of these SMA actuators, varying in geometrical complexity, under multiple thermal cycles. In all cases investigated, the beam modeling was found to be very efficient in comparison to the shell and 3D solid elements, and this was achieved without any loss of accuracy. [ABSTRACT FROM AUTHOR]

The nonlinear complexity of a periodic sequence s is the length of the shortest feedback shift register that can generate s, and its value is upper bounded by the least period of s minus 1. In this paper, a recursive approach that generates all periodic sequences with maximum nonlinear complexity is presented, and the total number of such sequences is determined. The randomness properties of these sequences are also examined. [ABSTRACT FROM PUBLISHER]

Fracture intensity, the degree of fracturing in rock masses, is one of the fundamental parameters used in characterizing rock mass as a fracture network. Among fracture intensity measures, volumetric fracture intensity (P 32 ) is the most useful, since it directly reflects the degree of rock mass fracturing, independent of fracture orientation and size distribution. P 32 represents the total area of fractures per cubic meter, and it can simultaneously reflect the spacing and size component of fractures. Because P 32 cannot be directly measured in the field, previous works have developed various inference methods based on available 1D and 2D measures collected from field surveys. At present, discrete fracture network (DFN) models are deemed to be a suitable method for the characterization of fractured rock mass. Hence, calculating P 32 from a DFN model is also a widely accepted approach. However, the geometry-based method cannot effectively address the irregular simulation space, and the methods employed are ill-suited if polygonal fractures appear in the DFN model. To solve these deficiencies, a computational framework based on the Delaunay triangulation of 3D uniformly distributed random points is introduced, and a detailed description is presented. The proposed computational framework is suitable for various types of DFN models, such as Baecher disk models, elliptical disk models and Dershowitz polygon models. A simulated example was generated to verify the proposed computational framework. Finally, a DFN model is built based on fracture data acquired from the Songta hydropower station, and the proposed computational framework was used to calculate P 32 for the DFN model. [ABSTRACT FROM AUTHOR]