Computational Explosion Research Articles

A distributional perspective on the gavagai problem in early word learning

Word learning entails the mapping of an auditory word-form to its appropriate grammatical category (e.g., noun, verb, adjective), but before that mapping can occur, the naïve learner must infer which of the myriad of possible referents of that word was intended by the speaker. This creates a computational explosion of referential ambiguity referred to as the gavagai problem. In a set of corpus analyses of parent-directed speech to young infants, we describe the distributional information available to early word learners, with a focus on nouns and adjectives that refer to whole objects and object properties. And in two experiments on word-learning in adults spanning seven different distributional conditions, we document how variations in the ratio of novel labels for objects and properties affect the robustness of word learning. Our results suggest that the language input to 6- to 20-month-olds is robustly populated with high-frequency object words and high-frequency property words, but their co-occurrence is sparse. Although this distributional information slightly favors object words over property words, a more plausible account of the whole-object bias in early word learning is the inability to encode the details of an object/event during rapid naming. Our results from adults, presented with novel labels for multi-referent objects in a cross-situational statistical learning paradigm, also reveal this whole-object bias as well as the absence of property-label generalization to novel objects, even when the distribution of labels is shifted almost exclusively to property words. These results are discussed in terms of the relative ease of mapping auditory word-forms to whole objects vs. object properties, thereby limiting the combinatorics of the gavagai problem, especially in infants with immature encoding and memory representation abilities.

Adaptive cross backstepping control for a class of nonstrict feedback nonlinear systems with partial state constraints

AbstractThe tracking control problem for a class of partial state constrained nonlinear system is studied in this article. The system is divided into two semistrict feedback nonlinear subsystems, one is state constrained and the other is state free. By means of state transformation, the state constraint problem is transformed into the bounded problem of the transformed function. Compared with the barrier Lyapunov function (BLF) method, it not only solves the state constraint problem but also circumvents the feasibility check on virtual controllers. Based on the cross backstepping control, the constrained controller and unconstrained controller are designed simultaneously. It solves the coupling problem effectively in the design of cross processing control. On the other hand, dynamic surface control is used which effectively avoids “computation explosion” caused by backstepping control. The designed controllers can ensure the error signals converge to a small neighbourhood of zero and keep the asymmetric time‐varying constraints on system partial states are satisfied for all the time. Finally, simulation experiments are carried out on a hyperchaotic Rössler system to verify the efficacy of the control scheme.

Adaptive Torsional Vibration Control of the Nonlinear Rolling Mill Main Drive System with Performance Constraints and Sensor Errors

This paper studies the torsional vibration suppression control problem for the nonlinear rolling mill main drive system with performance constraint requirements and unknown measurement sensitivities. Firstly, considering the nonlinear friction between the roll gaps, a torsional vibration model of the main drive system of rolling mill is established. Then, with the asymmetric performance constraints transformation, the motor torque control law is proposed based on backstepping algorithm. By introducing an adaptive bound estimation approach, the multiple unknown parameters caused by the sensor sensitivities can be approximated with very few adaptive laws. The dynamic surface technology is introduced to simplified the control design procedure and solve the computational explosion problem. It is strictly proved that the resulting closed-loop system is stable in the sense of uniformly ultimately boundedness and both transient and steady-state performances of the load speed are preserved. Finally, the simulation is provided to show the validity and the advantages of the proposed techniques.

A novel framework based on wavelet transform and principal component for face recognition under varying illumination

One of the most primitive problems in face recognition is illumination variation, which is of significance for image processing and pattern recognition. Existing studies concentrate on the wavelet transform (WT) without elaborately considering high-frequency information and most do not efficiently tackle a computation explosion of facial dimensions in classification. Therefore, a novel framework based on wavelet transform and principal component is proposed to improve the accuracy under illumination variation in this paper. In the proposed framework, low-frequency sub-band (LFSB) and high-frequency sub-band (HFSB) images from wavelet transform are simultaneously enhanced and denoised, unlike previous studies that usually cause loss of details due to less consideration of HFSB. For LFSB image, a multiple scale Retinex-based steering kernel is designed to enhance more details, and then an adaptive strategy of gamma correction is developed to automatically expand gray-dynamic range. For HFSB image, a non-local mean filtering is established to suppress the noise and subsequently, more image details are preserved by local of mean of local variance. Moreover, the principal component technique based Fisherface and virtual auxiliary sample strategy is developed in order to overcome the computation explosion of facial dimensions, in which a sample strategy with interpolation mechanism is employed to avoid the complicated singularity and Fisherface analysis is further applied to extract features and dimensionality reduction. In addition, the particle swarm optimization-neural network (PSO-NN) is employed to perform classification in the framework. Experimental results prove that the proposed framework can effectively obtain the robust visual effect under varying illumination and significantly improve the recognition performance in comparison to existing methods.

Variable Bandwidth Adaptive Course Keeping Control Strategy for Unmanned Surface Vehicle

This paper proposes a new and original course keeping control strategy for an unmanned surface vehicle in the presence of modeling error, external disturbance and input saturation. The trajectory linearization control method is used as the basic algorithm to design the course keeping strategy, and the radial basis function neural network and disturbance observer are used to compensate modeling error and external disturbance respectively to enhance the robustness of the control system. Moreover, a robust term is used to compensate various compensation errors to further improve the robustness of the system. In addition, hyperbolic tangent function and Nussbaum function are hired to deal with the potential input saturation problem, and the neural shunting model is adopted to avoid the computational explosion caused by the derivation of virtual control law. Taking the above facts into account will help to further realize engineering practice. Finally, the control strategy proposed in this paper is compared with the classical proportional–integral–derivative control strategy. The simulation results show that the course control results of the proposed control strategy are more robust than proportional–integral–derivative control, regardless of whether the external disturbance is weak or strong.

From hard spheres and cubes to nonequilibrium maps with thirty-some years of thermostatted molecular dynamics.

This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models that best achieve reproducibility and promote understanding. Few-body models with pair forces have led to today's "realistic" simulations with billions of atoms and molecules. Rapid advances in computer technology have led to change. Theoretical formalisms have largely been replaced by simulations incorporating ingenious algorithm development. We choose to study particularly simple, yet relevant, models directed toward understanding general principles. Simplicity remains a worthy goal, as does relevance. We discuss hard-particle virial series, melting, thermostatted oscillators with and without heat conduction, chaotic dynamics, fractals, the connection of Lyapunov spectra to thermodynamics, and finally simple linear maps. Along the way, we mention directions in which additional modeling could provide more clarity and yet more interesting developments in the future.

COMPOSITIONALITY, COMPUTABILITY, AND COMPLEXITY

AbstractThis paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (factorial complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional.

Trajectory Tracking Control for Unmanned Surface Vehicle Subject to Unmeasurable Disturbance and Input Saturation

This paper presents a trajectory tracking control controller for an unmanned surface vehicle in the presence of unmeasurable disturbance and input saturation. An adaptive trajectory tracking control strategy is developed with the aid of disturbance observer, neural shunting model, adaptive technology, and auxiliary design system. Disturbance observer is used to estimate unmeasurable disturbances in order to compensate for them. The functions of neural shunting model and adaptive technology are respectively used to deal with the “computational explosion” caused by derivation of virtual control law and to enhance the robustness of the controlled system. Besides, to avoid the potential input saturation issue, auxiliary design system is employed in the design of control strategy. By Lyapunov stability theory, it is proved that all the error signals in the trajectory tracking control system are uniform ultimate bounded. The simulation results are given to prove the correctness of the proposed control scheme.

Evidence-Based Structural Uncertainty Quantification by Dimension Reduction Decomposition and Marginal Interval Analysis

Abstract Evidence theory has the powerful feature to quantify epistemic uncertainty. However, the huge computational cost has become the main obstacle of evidence theory on engineering applications. In this paper, an efficient uncertainty quantification (UQ) method based on dimension reduction decomposition is proposed to improve the applicability of evidence theory. In evidence-based UQ, the extremum analysis is required for each joint focal element, which generally can be achieved by collocating a large number of nodes. Through dimension reduction decomposition, the response of any point can be predicted by the responses of corresponding marginal collocation nodes. Thus, a marginal collocation node method is proposed to avoid the call of original performance function at all joint collocation nodes in extremum analysis. Based on this, a marginal interval analysis method is further developed to decompose the multidimensional extremum searches for all joint focal elements into the combination of a few one-dimensional extremum searches. Because it overcomes the combinatorial explosion of computation caused by dimension, this proposed method can significantly improve the computational efficiency for evidence-based UQ, especially for the high-dimensional uncertainty problems. In each one-dimensional extremum search, as the response at each marginal collocation node is actually calculated by using the original performance function, the proposed method can provide a relatively precise result by collocating marginal nodes even for some nonlinear functions. The accuracy and efficiency of the proposed method are demonstrated by three numerical examples and two engineering applications.

Sliding mode based neural adaptive formation control of underactuated AUVs with leader-follower strategy

In this brief, the leader-follower formation control of underactuated autonomous underwater vehicles subject to uncertain dynamics and ocean disturbances is addressed. A robust sliding mode formation control strategy is presented by utilizing backstepping method, adaptive neural network and dynamic surface control technique. The stability of the formation control system is proved based on the Lyapunov's direct method where all the signals are guaranteed to be uniformly ultimately bounded. The main advantages of this control strategy are summarized as: (i) the presented controller only depends on the position measurements of the leader, which is more convenient to implement in practice. (ii) the proposed controller does not require any prior knowledge about the hydrodynamic damping and disturbances from the environment. (iii) a continuous PI function is designed to avoid the effect of inherent chattering in standard sliding mode control. (iv) the computational explosion of the standard backstepping method is avoided by the command filter based on the dynamic surface control technique. At last, the comparative simulations are provided to verify the effectiveness of the presented control strategy.

Adaptive Finite-Time Consensus Tracking for Nonstrict Feedback Nonlinear Multi-Agent Systems With Unknown Control Directions

This paper investigates the finite-time consensus tracking problem for nonstrict feedback nonlinear multi-agent systems with unknown dynamics and control directions. Firstly, the backstepping scheme based on command filter and fractional power control law is proposed, which can not only solve the problem of computational explosion, but also ensure that the state of each agent can follow the leader's output within a finite time. Then, the error compensation signals are designed to compensate the error caused by filtering. The unknown nonlinear dynamics are approximated by the fuzzy logic system. The state variables problem in the non-strict feedback system is well solved through the scaling of inequalities. By introducing the Nussbaum function, the intermediate input signal and control input signal based on adaptive control law are designed respectively, and the problem of unknown control directions is solved. Simulations are given to show the effectiveness of the presented method.

The Problem of Context for Similarity: An Insight from Analogical Cognition

Similarity is central for the definition of concepts in several theories in cognitive psychology. However, similarity encounters several problems which were emphasized by Goodman in 1972. At the end of his article, Goodman banishes similarity from any serious philosophical or scientific investigations. If Goodman is right, theories of concepts based on similarity encounter a huge problem and should be revised entirely. In this paper, we would like to analyze the notion of similarity with some insight from psychological works on analogical cognition. Analogical cognition compares two situations or objects in order to find similarities between them. In doing so, the analogical process sorts the different features of the two situations or objects and determines the most important ones. The analogical process is also highly sensitive to context. Context-sensitivity is desirable at some level, but it is also problematic as it leads to a computational explosion. To answer this problem, we would like to consider salience as a possible heuristic in the analogical process. We will distinguish three forms of salience: Sensory, categorical, and operational. By taking salience into account, we can introduce a shortcut into the computation of similarity and circumvent computational explosion.

Computational explosion in the frequency estimation of sinusoidal data

This paper highlights the computational explosion issues in the autoregressive moving average approach of frequency estimation of sinusoidal data with a large sample size. A new algorithm is proposed to circumvent the computational explosion difficulty in the conditional least-square estimation method. Notice that sinusoidal pattern can be generated by a non-invertible non-stationary autoregressive moving average (ARMA) model. The computational explosion is shown to be closely related to the non-invertibility of the equivalent ARMA model. Simulation studies illustrate the computational explosion phenomenon and show that the proposed algorithm can efficiently overcome computational explosion difficulty. Real data example of sunspot number is provided to illustrate the application of the proposed algorithm to the time series data exhibiting sinusoidal pattern.

Adaptive actuator failure compensation for uncertain nonlinear fractional order strict feedback form systems

In this paper, adaptive fractional control design is established for uncertain nonlinear fractional order strict feedback form systems with unknown actuator failures. The fractional actuator failure compensation problem is considered in the sense of two actuation shapes, and output matching conditions for these shapes are employed. By means of a fractional backstepping control method, two fractional adaptive state feedback control laws are designed to accomplish output tracking and to guarantee closed-loop stability in the presence of unknown actuator failures and unknown system parameters. A fractional order filter is proposed to avoid the problem of computational explosion of the backstepping design. The stability is proved via fractional order analysis method for the whole closed-loop system. Finally, simulation results for the control of fractional Chua’s circuit and fractional Genesio–Tesi systems demonstrate the effectiveness of the proposed actuator failure compensation method and output tracking property along with fast convergence of unknown parameters estimations.

Research and analysis of video image target tracking algorithm based on significance

A target tracking algorithm based on joint probabilistic data association encounters the problems of target loss and combinatorial explosion in cluttered and target-intensive tracking environments. In order to address these challenges, this paper proposes a video target tracking algorithm based on significance joint probabilistic data association. This algorithm detects the moving target in a video sequence through significance calculation. The detection results are classified, and the returned classes are then used as valid echoes for data association. Meanwhile, the validation matrix and joint probability in the joint probabilistic data association algorithm are redefined based on the significance information and a validation matrix and association probability based on significance is proposed. The association results are compensated and corrected using the colour association probability. Experiments in real scenes demonstrate that the proposed algorithm can suppress clutter in the background, simplify interconnected events, and solve the problem of computational combinatorial explosion.

Fixed‐time backstepping control design for high‐order strict‐feedback non‐linear systems via terminal sliding mode

In this study, the state feedback fixed-time control problem is addressed for a class of high-order strict-feedback non-linear systems (SFNSs) with mismatching system uncertainties. Based on the fixed-time control technique and uniform exact difference method, a new fixed-time tracking control algorithm via the backstepping method in conjunction with a novel second-order sliding mode super-twisting-like structure adaptive fixed-time disturbance observer is proposed. Compared with many existing finite-time control results in which the convergence time grows unboundedly when the system initial conditions grow, the fixed-time control provides faster convergence rate by using high-degree terms and the settling time function derived only with controller parameters, is allowed to be adjusted independently of the system initial conditions. Moreover, to avoid the computation explosion, the singularity problem and to relax the assumption on the mismatching system uncertainties, the dynamics surface control method is employed based on a novel non-linear non-smooth first-order filter. Then the semi-globally uniformly fixed-time convergent performance of the high-order SFNSs is achieved. Finally, theoretical results are supported by simulation and experimental results.

基于指令滤波反步法的再入飞行器姿态控制

针对再入飞行器，提出一类新型的简洁的指令滤波反步法，设计动态的状态反馈姿态控制器。所设计的指令滤波反步控制器中，构建积分滑模滤波器逼近虚拟控制输入及其导数，避免传统反步法中复杂的解析推导过程，解决传统反步法中“计算爆炸”问题。在闭环系统中，采用输入状态稳定性和非线性小增益定理分析并保证闭环系统的稳定性和状态信号的有界性。最后，在仿真中验证了所提出姿态控制方法的有效性。 A command filtered back-stepping technology is exploited and analyzed to design a dynamic state- feedback attitude controller for a generic reentry vehicle in the technical notes. In the underlying command filtered back-stepping controller, sliding-mode-based integral filters are introduced to estimate the virtual control terms and their derivatives, obviating the complex analytical compu-tation process, subsequently solving the problem of “explosion of computation” in traditional back-stepping approach. The stability analysis of the closed-loop system and the convergence of the aerodynamic angles are verified based on the input-to-state stability and small-gain theorem. Numerical simulations are included to demonstrate the effectiveness of the proposed control scheme.

Mini-symposium on automatic differentiation and its applications in the financial industry

Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes, this approach is based on software solutions applying mechanically the chain rule to obtain an exact value for the desired derivative. It has a cost in memory and cpu consumption. For participants of financial markets (banks, insurances, financial intermediaries, etc), computing derivatives is needed to obtain the sensitivity of its exposure to well-defined potential market moves. It is a way to understand variations of their balance sheets in specific cases. Since the 2008 crisis, regulation demand to compute this kind of exposure to many different case, to be sure market participants are aware and ready to face a wide spectrum of configurations. This paper shows how automatic differentiation provides a partial answer to this recent explosion of computation to perform. One part of the answer is a straightforward application of Adjoint Algorithmic Differentiation (AAD), but it is not enough. Since financial sensitivities involves specific functions and mix differentiation with Monte-Carlo simulations, dedicated tools and associated theoretical results are needed. We give here short introductions to typical cases arising when one use AAD on financial markets.

Adaptive neural synchronization control of chaotic systems with unknown control directions under input saturation

In this paper, we investigate the synchronization problem of chaotic systems with unknown control direction under input saturation nonlinearity. By utilizing backstepping technique, an adaptive neural synchronization control scheme is developed via neural approximation technique and Nussbaum-type function method. To deal with the problem of sharp corner of saturation, a tangent function based smooth function is used to approximate input saturation. To facilitate controller design, an auxiliary signal is constructed to augment the plant. Two Nussbaum functions are respectively used to deal with unknown control direction and compensate for the time-varying gain arising from the partial differentiation of the smooth function of input saturation. Tracking-differentiator is introduced to handle the problem of “explosion of computation” in the backstepping design. Adaptive robust effects are designed to deal with the “disturbance-like” term and tracking-differentiator estimation error. Lyapunov based analysis gives the transient performance and convergence of synchronization errors. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

A Discourse-Based Approach for Arabic Question Answering

The treatment of complex questions with explanatory answers involves searching for arguments in texts. Because of the prominent role that discourse relations play in reflecting text producers’ intentions, capturing the underlying structure of text constitutes a good instructor in this issue. From our extensive review, a system for automatic discourse analysis that creates full rhetorical structures in large-scale Arabic texts is currently unavailable. This is due to the high computational complexity involved in processing a large number of hypothesized relations associated with large texts. Therefore, more practical approaches should be investigated. This article presents a new Arabic Text Parser oriented for question-answering systems dealing with لماذا “why” and كيف “how to” questions. The Text Parser presented here considers the sentence as the basic unit of text and incorporates a set of heuristics to avoid computational explosion. With this approach, the developed question-answering system reached a significant improvement over the baseline with a Recall of 68% and MRR of 0.62.