Efficient continuous skyline computation

In a number of emerging streaming applications, the data values that are produced have an associated time interval for which they are valid. A useful computation over such streaming data is to produce a continuous and valid skyline summary. Previous work on skyline algorithms have only focused on evaluating skylines over static data sets, and there are no known algorithms for skyline computation in the continuous setting. In this paper, we introduce the continuous time-interval skyline operator, which continuously computes the current skyline over a data stream. We present a new algorithm called LookOut for evaluating such queries efficiently, and empirically demonstrate the scalability of this algorithm. In addition, we also examine the effect of the underlying spatial index structure when evaluating skylines. Whereas previous work on skyline computations have only considered using the R^∗-tree index structure, we show that for skyline computations using an underlying quadtree has significant performance benefits over an R^∗-tree index.     

Computing with continuous attractors: stability and online aspects

Two issues concerning the application of continuous attractors in neural systems are investigated: the computational robustness of continuous attractors with respect to input noises and the implementation of Bayesian online decoding. In a perfect mathematical model for continuous attractors, decoding results for stimuli are highly sensitive to input noises, and this sensitivity is the inevitable consequence of the system's neutral stability. To overcome this shortcoming, we modify the conventional network model by including extra dynamical interactions between neurons. These interactions vary according to the biologically plausible Hebbian learning rule and have the computational role of memorizing and propagating stimulus information accumulated with time. As a result, the new network model responds to the history of external inputs over a period of time, and hence becomes insensitive to short-term fluctuations. Also, since dynamical interactions provide a mechanism to convey the prior knowledge of stimulus, that is, the information of the stimulus presented previously, the network effectively implements online Bayesian inference. This study also reveals some interesting behavior in neural population coding, such as the trade-off between decoding stability and the speed of tracking time-varying stimuli, and the relationship between neural tuning width and the tracking speed.     

A survey on evolutionary computation for complex continuous optimization

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

     

Parallel computation of continuous Petri nets based on hypergraph partitioning

Continuous Petri net can be used for performance analysis or static analysis. The analysis is based on solving the associated ordinary differential equations. This paper presents a method to parallel compute these differential equations. We first map the Petri net to a hypergraph, and then partition the hypergraph to minimize interprocessor communication while maintaining a good load balance; Based on the partition result, we divide the differential equations into several blocks; Finally, we design a parallel computing algorithm to compute these equations. Software hMETIS is used to partition the hypergraph, and software SUNDIALS is used to support the parallel computing of differential equations. Gas station problem and dining philosopher problem have been used to demonstrate the feasibility, accuracy, and scalability of our method.     

Analog computation for phase-based disparity estimation: continuous and discrete models

The analog implementation of a phase-based technique for disparity estimation is discussed. This technique is based on the convolution of images with Gabor filters. The article shows that by replacing the Gaussian envelope with other envelopes, the convolution operation is equivalent to the solution of a system of differential equations, whose order is related to the smoothness of the kernel. A detailed comparison between the disparity estimates obtained using these kernels and those obtained using the standard filter is presented. The discretization of the model leads to lattice networks in which the number of connections per node required to perform convolution is limited to the first few nearest neighbors. The short connection length makes these filter suitable for analog VLSI implementation, for which the number of connection per node is a crucial factor. Experimental measures on a prototype CMOS 17-node chip validated the approach. Received: 27 October 1997 / Accepted: 18 June 1998     

Dynamics of frameworks by continuous mass method

The continuous mass matrix method has been extended to include the forced vibration in the dynamic analysis of plane and space frameworks. The forcing forces may be continuous of discontinuous functions of time but all the forcing forces acting simultaneously on a framework must have the same time variation in order that the modal analysis can be applied. The damping has been neglected. The concept of code numbers in the case of static loading has been extended to the dynamics of structures. The validity of the two orthogonality conditions of the modal shapes has been proved for the continuous mass matrix method so that the modal analysis could be applied easily. The set of simultaneous equations of motion has been converted to equivalent one-degree-of-freedom systems. In the case where the forcing forces have different time variation functions a numerical analysis can be performed. Illustrative sample problems have been solved and the results are given in tabular form.     

Nowhere-differentiable attractors

The notion of nowhere-differentiable attractors is illustrated with four prototype equations, that is, maps of invertible type. Four classes of nowhere-differentiable attractors can be distinguished so far: the (nongeneric) continuous-nonchaotic-nonfractal type; the (nongeneric) continuous-fractal type; the (generic) singular-continuous-fractal type; and the (generic) continuous-fractal-in-a-projection type. the history of all four classes is linked with the name of J. A. Yorke in different ways. Even though continuous fractal nowhere-differentiable attractors do not exist genetically, the hypothesis that the fractal geometry of nature may be a consequence of the fact that nature is a differentiable dynamical system is strengthened. Attractors with nowhere-differentiable generic projections can mimic the whole richness of fractal pictures. © 1995 John Wiley & Sons, Inc.     

Analysis of spike statistics in neuronal systems with continuous attractors or multiple, discrete attractor States

Attractor networks are likely to underlie working memory and integrator circuits in the brain. It is unknown whether continuous quantities are stored in an analog manner or discretized and stored in a set of discrete attractors. In order to investigate the important issue of how to differentiate the two systems, here we compare the neuronal spiking activity that arises from a continuous (line) attractor with that from a series of discrete attractors. Stochastic fluctuations cause the position of the system along its continuous attractor to vary as a random walk, whereas in a discrete attractor, noise causes spontaneous transitions to occur between discrete states at random intervals. We calculate the statistics of spike trains of neurons firing as a Poisson process with rates that vary according to the underlying attractor network. Since individual neurons fire spikes probabilistically and since the state of the network as a whole drifts randomly, the spike trains of individual neurons follow a doubly stochastic (Poisson) point process. We compare the series of spike trains from the two systems using the autocorrelation function, Fano factor, and interspike interval (ISI) distribution. Although the variation in rate can be dramatically different, especially for short time intervals, surprisingly both the autocorrelation functions and Fano factors are identical, given appropriate scaling of the noise terms. Since the range of firing rates is limited in neurons, we also investigate systems for which the variation in rate is bounded by either rigid limits or because of leak to a single attractor state, such as the Ornstein-Uhlenbeck process. In these cases, the time dependence of the variance in rate can be different between discrete and continuous systems, so that in principle, these processes can be distinguished using second-order spike statistics.     

Koch curves as attractors and repellers

Two methods are presented for generating Koch curves, analogous to the commonly used iterative methods for producing images of Julia sets. The attractive method is based on a characterization of Koch curves as the smallest nonempty sets closed with respect to a union of similarities on the plane. The repelling method is in principle dual to the attractive one but involves a nontrivial problem of selecting the appropriate transformation to be applied at each iteration step. Both methods are illustrated with a number of computer-generated images. The mathematical presentation emphasizes the relationship between Koch construction and formal languages theory     

Invariability,orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality.     

Helping by unambiguous computation and probabilistic computation

Schöning [S] introduced a notion of helping and suggested the study of the class P_help(C) of languages that can be helped by oracles in a given classC. He showed that P_help(BPP) is included in ZPP. Later, Ko [K] introduced a weaker notion of helping, called one-sided helping, and proved that P_1-help(BPP) is included in R and that UP is included in P_1-help(UP). The three inverse inclusions are open problems (see [Hem]). Caiet al. [CHV] constructed a relativized world in which the third open inclusion fails. We show relativized worlds in which all three open inclusions fail in a strong way. In particular, we strengthen the result of Caiet al., showing that P_help(UP) is not included in Few. This is obtained as a corollary of a general result that gives sufficient conditions, on a relativizable complexity classC, to ensure the relativized separation of P_help(UP) fromC. Further separations are also derived. The other two open inclusions are showed to fail strongly by the relativized separation of ZPP from P_1-help(AM ∩ co-AM).     

Singleton and 2-periodic attractors of sign-definite Boolean networks

Although it is in general NP-hard to find a singleton attractor of a sign-definite network, if the network is strongly connected and has no directed negative cycle then it has at least two singleton attractors that can be found in polynomial time, as proved by Aracena. We describe an algorithm for finding a singleton attractor of a sign-definite network which does not have a directed negative cycle but is not necessarily strongly connected. The algorithm is not only much simpler than the algorithm of Goles and Salinas for the same problem, but also, unlike their algorithm, runs in polynomial time. It was proven by Just that the problem of finding a 2-periodic attractor is in a sense harder yet, because it remains NP-hard for a positive network. We prove, however, that if the positive network has a source strongly connected component devoid of odd cycles, then it is possible to find a 2-periodic attractor in polynomial-time, and we present an algorithm for doing so.     

Training multiple-layer perceptrons to recognize attractors

Determining the long-term behavior in dynamical systems is an area of intense research interest. In this paper, a multilayer perceptron is used to perform this task. The network is trained using an evolution strategy. A comparison against backpropagation-trained networks was performed, and the results indicate evolution strategies produce better performing networks     

Characterization of uniform attractors for control systems

This paper is devoted to the characterisation of uniform attractors for control systems by means of Lyapunov functions. We consider a uniform attractor that is compact and positively invariant by the system. We present the relationship between the concept of uniform attractor and the Conley concept of attractor.     

Learning chaotic attractors by neural networks

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series. During training, the algorithm learns to short-term predict the time series. At the same time a criterion, developed by Diks, van Zwet, Takens, and de Goede (1996) is monitored that tests the hypothesis that the reconstructed attractors of model-generated and measured data are the same. Training is stopped when the prediction error is low and the model passes this test. Two other features of the algorithm are (1) the way the state of the system, consisting of delays from the time series, has its dimension reduced by weighted principal component analysis data reduction, and (2) the user-adjustable prediction horizon obtained by "error propagation"-partially propagating prediction errors to the next time step. The algorithm is first applied to data from an experimental-driven chaotic pendulum, of which two of the three state variables are known. This is a comprehensive example that shows how well the Diks test can distinguish between slightly different attractors. Second, the algorithm is applied to the same problem, but now one of the two known state variables is ignored. Finally, we present a model for the laser data from the Santa Fe time-series competition (set A). It is the first model for these data that is not only useful for short-term predictions but also generates time series with similar chaotic characteristics as the measured data.     

Continuous attractors of discrete-time recurrent neural networks

This paper studies the continuous attractors of discrete-time recurrent neural networks. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. Continuous attractors of neural networks have been used to store and manipulate continuous stimuli for animals. A continuous attractor is defined as a connected set of stable equilibrium points. It forms a lower dimensional manifold in the original state space. Under some conditions, the complete analytical expressions for the continuous attractors of discrete-time linear recurrent neural networks as well as discrete-time linear-threshold recurrent neural networks are derived. Examples are employed to illustrate the theory.     

Newton-Leipnik系统的多种吸引子及其形成机制

研究了Newton-Leipnik混沌系统的各种动力学行为,从中发现了新的双体双核混沌吸引子,发现了混沌吸引子与小周期吸引子、大周期吸引子并存于同一相空间的各种情况,发现了趋于周期吸引子的暂态混沌运动。这些特性是由五个平衡点的属性所确定的。每个平衡点邻域的状态轨线沿某方向发散而沿某方向收敛,这导致了系统复杂的动力学行为发生。