Recursive Scheme Research Articles

On Hierarchical Construction of the State Space of an Automated Manufacturing System Modeled With Petri Nets

State space techniques are one of the main approaches deployed for the analysis of concurrent systems. However, state space construction is stalled by a common phenomenon called the state explosion problem which makes it a tough task or even impossible when the state space computation demands prohibitive cost (time and memory). We limit general resource allocation systems (RASs) to a certain class whose state space can be hierarchically constructed, yet it comprises various enough types of real-world discrete event systems, such as automated manufacturing systems. This paper focuses on a class of RASs modeled with Petri nets (PNs), where, through pure algebraic operations, a novel method to compute the state spaces is proposed, which is motivated by the superposition property. Given a PN model of a system and a target resource configuration, we first propose a special initial marking called the initial basis marking and compute the corresponding reachability graph. Then, we increase the capacity of the resource places in an incremental way and generate the reachability graphs by taking advantage of the PN structure and the previously computed reachability graph until the capacity function of resources reaches the target resource configuration. A complete enumeration of reachable states can be obtained by a recursive scheme. Experimental studies also demonstrate the efficiency of the proposed approach in terms of computational cost and its high-potential to cope with the state-explosion problem.

Recursive State Estimation for Networked Multirate Multisensor Systems With Distributed Time-Delays Under Round-Robin Protocol.

This article is concerned with the problem of recursive state estimation for a class of multirate multisensor systems with distributed time delays under the round-robin (R-R) protocol. The state updating period of the system and the sampling period of the sensors are allowed to be different so as to reflect the engineering practice. An iterative method is presented to transform the multirate system into a single-rate one, thereby facilitating the system analysis. The R-R protocol is introduced to determine the transmission sequence of sensors with the aim to alleviate undesirable data collisions. Under the R-R protocol scheduling, only one sensor can get access to transmit its measurement at each sampling time instant. The main purpose of this article is to develop a recursive state estimation scheme such that an upper bound on the estimation error covariance is guaranteed and then locally minimized through adequately designing the estimator parameter. Finally, simulation examples are provided to show the effectiveness of the proposed estimator design scheme.

A novel recursive learning identification scheme for Box–Jenkins model based on error data

In this paper, a recursive learning identification scheme is proposed to estimate the parameters of the Box–Jenkins model, which is obtained by designing a new cost function. To facilitate the establishment of the new cost function, the Box–Jenkins model is transformed into an output error model through the usage of the polynomial transformation. Then, the cost function is developed based on the system output error information and the initial parameter error information, in which the output error information is introduced to raise the robustness of the identifier, and the initial parameter error information is presented to improve the convergence rate of the estimation scheme. Under the fresh framework, a novel recursive learning adaptive law can be obtained. Compared with the frequently-used loss function, the proposed algorithm provides a better estimation performance. Furthermore, under the persistent excitation condition, the estimation error can converge to zero. Finally, numerical examples and experiment are used to verify the effectiveness and usefulness of the presented algorithm.

A modified incremental creep integral approach for meshfree analysis of viscoelastic problems

In the present work, an improved meshfree radial point interpolation method (RPIM) is developed for the analysis of homogeneous, as well as non-homogeneous viscoelastic problems. A novel strategy for implementing integral-based viscoelastic constitutive theories using the meshfree methods is presented. This strategy makes use of the integral formulation of Schapery-type constitutive theories and higher-order finite difference (FD) schemes. The Cartesian transformation method (CTM) is adopted for accurate and efficient calculation of the domain integrals in the formulation of the meshfree RPIM. The superior performance of this modified algorithm is assessed through some benchmark examples and by comparing the obtained results with the existing analytical or numerical solutions. Through these comparisons, an improvement over the conventional integral-based recursive strategies of viscoelastic materials is observed.

The Exploration of Skilled and Less-Skilled EFL Graduate Students' on L1 and L2 Writing Strategies

This study aims to analyze the similarities, differences, and transferability of students' writing strategies in L1 (Indonesian) and L2 (English). Data were obtained from four participants majoring in English Education, two males and two females, which were categorized into skilled and less-skilled writers. The data were collected for four months using various methods, namely think-aloud protocols (TAPs), retrospective and semi-structured interviews, observations, and written drafts. The result showed that students employed similar personal strategies while writing in Indonesian (L1) and English (L2). This means that they transferred L1 strategies to L2 with some variances and similarities. The skilled writers viewed writing as a cyclical process of planning, writing, reading/rereading, rehearsing, and revising their texts. Meanwhile, less-skilled writers tended to employ linear and less recursive strategies. Furthermore, subsequent studies need to be conducted using these research findings and suggestions.

Research on Formation Keeping of Multi-rotor UAVs Based on Improved Virtual Structure Method

Multi-UAV cooperative formation flight (CFF) can greatly improve the damage resistance and mission completion efficiency of single UAV, so it has become a research hotspot in recent years. The entire process of multi-UAV formation flight can be decomposed into target tracking, formation keeping, obstacle avoidance and collision avoidance. The research of formation keeping mainly uses the leader-follower or virtual structure method. The former has the problem of single point of failure, and the formation error will be amplified step by step. The latter is difficult to select virtual leader, and is hard to adjust the formation adaptively with limited communication conditions. Based on the virtual structure and multicast method, this paper proposes a recursive fusion strategy which reduces the requirement of communication frequency between UAVs, increases the adaptability of formation to single point of failure, and improves the accuracy and adaptability of formation keeping to a certain extent. On this basis, the cascade PID model is used to design the formation controller. Finally, the effectiveness of the strategy is verified by using MATLAB.

Robust Reconstruction of Block Sparse Signals from Adaptively One‐Bit Measurements

Though various theoretical results and algorithms have been proposed in one-bit Compressed sensing (1-bit CS), there are few studies on more structured signals, such as block sparse signals. We address the problem of recovering block sparse signals from one-bit measurements. We first propose two recovery schemes, one based on second-order cone programming and the other based on hard thresholding, for common non-adaptively thresholded one-bit measurements. Note that the worst-case error in recovering sparse signals from non-adaptively thresholded one-bit measurements is bounded below by a polynomial of oversampling factor. To break the limit, we introduce a recursive strategy that allows the thresholds in quantization to be adaptive to previous measurements at each iteration. Using the scheme, we propose two iterative algorithms and show that corresponding recovery errors are both exponential functions of the oversampling factor. Several simulations are conducted to reveal the superiority of our methods to existing approaches.

Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics

Abstract In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic Calogero–Moser type. We focused on the 1st steps of the scheme in Part I and on the cases $N=2$ and $N=3$ in Part II. In this paper, we determine the dominant asymptotics of a similarity-transformed function $\textrm{E}_N(b;x,y)$ for $y_j-y_{j+1}\to \infty $, $j=1,\ldots , N-1$ and thereby confirm the long-standing conjecture that the particles in the hyperbolic relativistic Calogero–Moser system exhibit soliton scattering. This result generalizes a main result in Part II to all particle numbers $N>3$.

Approximation‐free design for distributed consensus tracking of networked uncertain non‐linear multi‐agent systems with heterogenous high powers

This study investigates a distributed approximation-free design problem for guaranteed consensus tracking quality of networked uncertain heterogenous power-chained multi-agent systems with completely unknown non-linearities. Compared with the existing studies in the presence of power-chained state variables, the main contribution of this study is to provide a distributed low-complexity consensus tracker design strategy using only the relative output information among agents, without the use of adaptive neural or fuzzy function approximators for estimating unknown non-linear functions. A novel recursive design strategy independent of the feedback domination technique is established to deal with power-chained state variables under directed networks. Using the Lyapunov stability theorem, it is shown that the preselected performance of the consensus tracking error is ensured.

Distributed set-membership filtering for discrete-time systems subject to denial-of-service attacks and fading measurements: A zonotopic approach

A distributed set-membership filter is designed for a kind of systems with unknown but bounded (UBB) noises over wireless sensor networks. The Denial-of-Service (DoS) attacks and the fading effects on the sensor measurements are taken into account simultaneously. To reveal the fluctuations of network environment, the coefficients of the fading channels are described by uncertain variables which take values over an interval. The objective of this paper is to estimate the desired sets involving actual states of the plant by implementing the consistency tests among the state sets, the measured outputs and the neighbor information. A recursive scheme on zonotopes involving the real system state is established in light of the zonotopic method, where an outer approximation of the exact uncertain set is performed. Moreover, based on the proposed outer approximation minimization criterion, an optimization issue is proposed to seek the parameters of the intersection zonotope. Finally, two illustrative simulations are utilised to state the feasibility of the proposed filter.

Diagrammatic Monte Carlo method for impurity models with general interactions and hybridizations

We present a diagrammatic Monte Carlo method for quantum impurity problems with general interactions and general hybridization functions. Our method uses a recursive determinant scheme to sample diagrams for the scattering amplitude. Unlike in other methods for general impurity problems, an approximation of the continuous hybridization function by a finite number of bath states is not needed, and accessing low temperature does not incur an exponential cost. We test the method for the example of molecular systems, where we systematically vary temperature, interatomic distance, and basis set size. We further apply the method to an impurity problem generated by a self-energy embedding calculation of correlated antiferromagnetic NiO. We find that the method is ideal for quantum impurity problems with a large number of orbitals but only moderate correlations.

On the Expressive Power of Higher-Order Pushdown Systems

We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists a tree generated by a second order collapsible pushdown system (equivalently, by a recursion scheme of second order) that is not generated by any deterministic higher-order pushdown system (without collapse) of any order (equivalently, by any safe recursion scheme of any order). As a side effect, we present a pumping lemma for deterministic higher-order pushdown automata, which potentially can be useful for other applications.

Adaptive Global Optimization Based on a Block-Recursive Dimensionality Reduction Scheme

Multidimensional multiextremal optimization problems and numerical methods for solving them are studied. The objective function is supposed to satisfy the Lipschitz condition with an a priori unknown constant, which is the only general assumption imposed on it. Problems of this type often arise in applications. Two dimensionality reduction approaches to multidimensional optimization problems, i.e., the use of Peano curves (evolvents) and a recursive multistep scheme, are considered. A generalized scheme combining both approaches is proposed. In the new scheme, an original multidimensional problem is reduced to a family of lower-dimensional problems, which are solved using evolvents. An adaptive algorithm with the simultaneous solution of all resulting subproblems is implemented. Computational experiments on several hundred test problems are performed. In accordance with experimental evidence, the new dimensional reduction scheme is effective.

Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function

In this work, a novel learning-based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state-of-the-art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter-column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real-world data confirm the superiority of the proposed approach to the less recent methods.

Effectively learning spatial indices

Machine learning, especially deep learning, is used increasingly to enable better solutions for data management tasks previously solved by other means, including database indexing. A recent study shows that a neural network can not only learn to predict the disk address of the data value associated with a one-dimensional search key but also outperform B-tree-based indexing, thus promises to speed up a broad range of database queries that rely on B-trees for efficient data access. We consider the problem of learning an index for two-dimensional spatial data. A direct application of a neural network is unattractive because there is no obvious ordering of spatial point data. Instead, we introduce a rank space based ordering technique to establish an ordering of point data and group the points into blocks for index learning. To enable scalability, we propose a recursive strategy that partitions a large point set and learns indices for each partition. Experiments on real and synthetic data sets with more than 100 million points show that our learned indices are highly effective and efficient. Query processing using our indices is more than an order of magnitude faster than the use of R-trees or a recently proposed learned index.

Radiative–conductive transfer equation in spherical geometry: arithmetic stability for decomposition using the condition number criterion

The radiative–conductive transfer equation in the $$S_N$$ approximation for spherical geometry is solved using a modified decomposition method. The focus of this work is to show how to distribute the source terms in the recursive equation system in order to guarantee arithmetic stability and thus numerical convergence of the obtained solution, guided by a condition number criterion. Some examples are compared with results from literature and parameter combinations are analyzed, for which the condition number analysis indicates convergence of the solutions obtained by the recursive scheme.

Heat Kernel Approximation on Kendall Shape Space

The heat kernel on Kendall shape subspaces is approximated by an expansion. The Kendall space is useful for representing the shapes associated to collections of landmarks’positions. The Minakshisundaram-Pleijel recursion formulas are used in order to calculate the closed-form approximations of the first and second coefficients of the heat kernel expansion. Prior to the exploitation of the recursion scheme, the expression of the Laplace-Beltrami operator is adapted to the targeted space using geodesic spherical and angular coordinates.

A Type System Describing Unboundedness

We consider nondeterministic higher-order recursion schemes as recognizers of languages of finite words or finite trees. We propose a type system that allows to solve the simultaneous-unboundedness problem (SUP) for schemes, which asks, given a set of letters A and a scheme G, whether it is the case that for every number n the scheme accepts a word (a tree) in which every letter from A appears at least n times. Using this type system we prove that SUP is (m-1)-EXPTIME-complete for word-recognizing schemes of order m, and m-EXPTIME-complete for tree-recognizing schemes of order m. Moreover, we establish the reflection property for SUP: out of an input scheme G one can create its enhanced version that recognizes the same language but is aware of the answer to SUP.

New Transceiver Designs for Interleaved Frequency-Division Multiple Access

This paper puts forth a class of new transceiver designs for interleaved frequency division multiple access (IFDMA) systems. These transceivers are significantly less complex than conventional IFDMA transceivers. The simple new designs are founded on a key observation that multiplexing and demultiplexing of IFDMA data streams of different sizes are coincident with the IFFTs and FFTs of different sizes embedded within the Cooley-Tukey recursive FFT decomposition scheme. For flexible resource allocation, this paper puts forth a new IFDMA resource allocation framework called Multi-IFDMA, in which a user can be allocated multiple IFDMA streams. Our new transceivers are unified designs in that they can be used in conventional IFDMA as well as multi-IFDMA systems. Two other well-known multiple-access schemes are localized FDMA (LFDMA) and orthogonal FDMA (OFDMA). In terms of flexibility in resource allocation, Multi-IFDMA, LFDMA, and OFDMA are on an equal footing. With our new transceiver designs, however, IFDMA has the following advantages (besides other known advantages not due to our new transceiver designs): 1) IFDMA/Multi-IFDMA transceivers are significantly less complex than LFDMA transceivers; in addition, IFDMA/Multi-IFDMA has better Peak-to-Average Power Ratio (PAPR) than LFDMA; 2) IFDMA/Multi-IFDMA transceivers and OFDMA transceivers are comparable in complexity; but IFDMA/Multi-IFDMA has significantly better PAPR than OFDMA.

Recursive cointegration analytics for adaptive monitoring of nonstationary industrial processes with both static and dynamic variations

Conventional adaptive monitoring strategies detect anomalies in time-varying process by frequently updating models, which requires high computation complexity and may falsely include abnormal samples. Cointegration analysis (CA) based monitoring strategies can be implemented with less model updating since they are developed based on the extracted long-term equilibrium relationship. However, once the cointegration relationship changes, the previous CA model cannot accurately reflect the operation status of future nonstationary process. In this study, an adaptive monitoring scheme based on recursive CA is proposed to address the aforementioned issues for nonstationary processes. First, a recursive strategy is developed for CA to effectively update the monitoring model. After that, three monitoring statistics are developed to reflect the operation status of the industrial process with representation of both static deviation and dynamic fluctuation. Finally, an adaptive monitoring strategy is constructed based on the proposed recursive CA using the aforementioned monitoring statistics. Experimental results of two real industrial processes show that the adaptive monitoring strategy based on recursive CA can effectively adapt to normal process changes without frequent model updating.