An implicit self-tuning technique for processes with variable time-delay

Most implicit self-tuning schemes are based on least-squares k-step-ahead prediction over the system time-delay. On systems where the time-delay is variable the use of such self-tuning algorithms presents problems. For the case when there is a significant variation in the time-delay, it has been thought necessary either to determine the actual time-delay explicitly or to use explicit self-tuning schemes. Neither is in fact necessary, and it is shown in this paper how an implicit scheme may be used for such systems. In the proposed scheme, knowledge of the system time-delay is not required. A simulation example and a practical application are included which demonstrate the capability of the technique when dealing with systems having variable time delay.     

Design of stochastic discrete time linear optimal regulators Part I. Relationship between control laws based on a time series approach and a state space approach

Distinct approaches to sampled data control system design use either a state space model or a ‘ controlled autoregressive moving average ’ (CARMA) model, sometimes known as Åström's representation, One reason for the current interest in the CARMA model is that it is a useful basis for self-tuning controllers as its parameters can be readily estimated on-line. Moreover, simple transfer function controllers can be derived using κ-step-ahead prediction theory. On the other hand, these controllers can be interpreted as minimizing a single stage cost function in state space terms, and the corresponding performance can sometimes be poor. This paper explores the relationship between the κ-stop-ahead prediction approach and the state space approach, and is a generalization of the earlier work of Caines to include control weighting and time delay on the control. Two forms of state space model are used (‘ explicit ’ and ‘ implicit’ time delay models) and a new representation of the steady state Kalman filter is shown to be required in the generalization ; this filter is put into a computationally convenient form. The technical machinery created in this paper allows for a straightforward generalization to the control of systems described by CARMA models by minimizing an N-stage cost function ; this generalization will be discussed in paper II     

An experimental study on methods for the selection of basis functions in regression

A comparative study is carried out in the problem of selecting a subset of basis functions in regression tasks. The emphasis is put on practical requirements, such as the sparsity of the solution or the computational effort. A distinction is made according to the implicit or explicit nature of the selection process. In explicit selection methods the basis functions are selected from a set of candidates with a search process. In implicit methods a model with all the basis functions is considered and the model parameters are computed in such a way that several of them become zero. The former methods have the advantage that both the sparsity and the computational effort can be controlled. We build on earlier work on Bayesian interpolation to design efficient methods for explicit selection guided by model evidence, since there is strong indication that the evidence prefers simple models that generalize fairly well. Our experimental results indicate that very similar results between implicit and explicit methods can be obtained regarding generalization performance. However, they make use of different numbers of basis functions and are obtained at very different computational costs. It is also reported that the models with the highest evidence are not necessarily those with the best generalization performance.     

结合显式和隐式特征交互的深度融合模型

特征工程是影响机器学习算法性能的关键因素之一,随着互联网数据规模的扩大,传统特征工程的人力成本不断增加。为减少对特征工程的依赖,构建一种结合显式和隐式特征交互的融合模型。将稀疏结构单元与残差单元相结合以提取隐式特征,利用压缩交互网络学习显式特征,在最后一层全连接层上将两种特征进行融合。在4种不同数据集上的实验结果表明,该模型相比PNN、DCN等模型具有更好的特征提取结果。     

Finite difference method for time-space-fractional Schrödinger equation

In this paper, an implicit finite difference scheme for the nonlinear time-space-fractional Schrödinger equation is presented. It is shown that the implicit scheme is unconditionally stable with experimental convergence order of O(τ^2?α+h²), where τ and h are time and space stepsizes, respectively, and α (0<α<1) is the fractional-order in time. In order to reduce the computational cost, the explicit–implicit scheme is proposed such that the nonlinear term is easily treated. Meanwhile, the implicit finite difference scheme for the coupled time-space-fractional Schrödinger system is also presented, which is unconditionally stable too. Numerical examples are given to support the theoretical analysis.     

Reasoning tractably about explicit belief: A model‐theoretic approach

Existing epistemic logics such as the logic of implicit and explicit belief and the logic of awareness adopt a deductive‐theoretic approach for characterizing belief. In this approach, an agent represents the state of the world with a conjunction of axioms in its knowledge base (KB) and evaluates queries by trying to prove or disprove that they follow from KB. This paper presents a multivalued epistemic logic (MEL) that allows agents to reason both deductively and model theoretically about implicit and explicit belief. By characterizing an agent's KB with a class of finite models, the set of formulas that an agent believes can be determined by checking their validity in all these models. This rests on the fact that MEL has a complete axiomatization (sentences that are true in all these models will also be provable). In this paper, the soundness, completeness, and decidability of MEL are proven. Furthermore, a polynomial time model‐checking algorithm for determining the satisfiability of a sentence at a particular state in a given model of MEL is also presented. © 2000 John Wiley & Sons, Inc.     

Multivariate weighted minimum variance self-tuning controllers†

The weighted minimum variance (WMV) controller is employed in a self-tuning control system for plants which can be multivariate and non-square. Both explicit and implicit self-tuning strategies are discussed. Existing strategies, based upon k-steps ahead cost functions, have stability problems on systems whose open-loop dynamics are both unstable and non-minimum phase. The WMV controller has the advantage that when plant parameters are known and the control weighting is zero, the optimal system is guaranteed to be stable.     

Third-order temporal discrete scheme for the non-stationary Navier–Stokes equations

In this article, we suggest a new third-order time discrete scheme for the two-dimensional non-stationary Navier–Stokes equations. After presenting the Galerkin finite element approximation for the spatial discretization, we consider an implicit/explicit time discrete scheme for the problem, which is based on the two-step Adams–Moulton scheme (implicit scheme) for the linear term and the three-step Adams–Bashforth scheme (explicit scheme) for the nonlinear term. In this method, we only need to solve a linearized discrete system at each time step, so the scheme can converge fast and the computational cost can be reduced. Moreover, under some assumptions, we deduce the stability and optimal error estimate for the velocity in L ²-norm.     

A practical approach to the design of concurrency in object-oriented systems

Object-oriented software development methods deal with concurrency according to either the implicit concurrency model or the explicit concurrency model. In the implicit model, the objects themselves have concurrent execution capabilities whereas in the explicit model, objects are encapsulated inside processes, the latter providing concurrent execution capabilities. Both models have their advantages and disadvantages. In this paper, we propose applying the implicit model only while conducting object-oriented analysis and then switching over to the explicit model in the design phase. The implicit model naturally fits the analysis phase because the resulting models of the software system will be based on objects—the important concepts of the application—not the issues of how concurrency is implemented. A switch over to the explicit model in the design phase achieves smooth integration with already existing software consisting of processes—which is the main constraint in many industrial applications. This paper presents in detail a systematic solution for the switch over between the concurrency models that applies for soft real-time systems and demonstrates it by a simplified example from a real telecommunication project. Any object-oriented method not yet dealing with concurrency issues can easily integrate the solution. ©1997 John Wiley & Sons, Ltd.     

Epistemic logic and logical omniscience: A survey

This survey brings together a collection of epistemic logics and discusses their approaches in alleviating the logical omniscience problem. Of particular note is the logic of implicit and explicit belief. Explicit belief refers to information actively held by an agent, while implicit belief refers to the logical consequence of explicit belief. Ramifications of Levesque's logic include nonstandard epistemic logic and the logics of awareness and local reasoning. Models of nonstandard epistemic logic are defined with respect to nonstandard proportional logic to weaken its semantics. In the logic of awareness, an agent can only believe a concept that it is aware of. Closely related to awareness are S-1 and S-3 epistemic operators which can be used to model skeptical and credulous agents. The logic of local reasoning provides a semantics for representing the fact that agents can have different clusters of beliefs which may contradict each other. Other variations include epistemic structures which are generalizations of the logic of local reasoning and fusion epistemic models which provide an account that agents can combine information conjunctively or disjunctively. Another closely related approach is the logic of explicit propostions which captures the insight that agents can hold beliefs independently without putting them together. © 1997 John Wiley & Sons, Inc.     

An Implicit Transition Matrix Approach to Stability Analysis of Flexible Multi-Body Systems

The stability of linear systems defined by ordinarydifferential equations with constant or periodic coefficients can beassessed from the spectral radius of their transition matrix. Inclassical applications of this theory, the transition matrix isexplicitly computed first, then its eigenvalues are evaluated; if thelargest eigenvalue is larger than unity, the system is unstable. Theproposed implicit transition matrix approach extracts the dominanteigenvalues of the transition matrix using the Arnoldi algorithm,without the explicit computation of this matrix. As a result, theproposed implicit method yields stability information at a far lowercomputational cost than that of the classical approach, and is ideallysuited for stability computations of systems involving a large number ofdegrees of freedom. Examples of application of the proposed methodologyto flexible multi-body systems are presented that demonstrate itsaccuracy and computational efficiency.     

Stability and convergence analysis of implicit–explicit one-leg methods for stiff delay differential equations

The purpose of this paper is devoted to studying the implicit–explicit (IMEX) one-leg methods for stiff delay differential equations (DDEs) which can be split into the stiff and nonstiff parts. IMEX one-leg methods are composed of implicit one-leg methods for the stiff part and explicit one-leg methods for the nonstiff part. We prove that if the IMEX one-leg methods is consistent of order 2 for the ordinary differential equations, and the implicit one-leg method is A-stable, then the IMEX one-leg methods for stiff DDEs are stable and convergent with order 2. Some numerical examples are given to verify the validity of the obtained theoretical results and the effectiveness of the presented methods.     

融合显隐式反馈的协同过滤推荐模型

融合显式和隐式反馈已被应用于提升推荐模型的性能,但是,现有的此类推荐模型未能保留显式反馈中反映用户偏好程度的信息,且现有研究认为拥有显式反馈的数据和仅拥有隐式反馈的数据对于模型具有同等影响,未能充分发挥显式反馈的优势.针对这些问题,提出一种新的融合显式和隐式反馈的协同过滤推荐模型(CEICF).首先,所提出模型提取显式反馈中的特征得到用户/物品的全局偏好向量;然后,从隐式反馈中提取用户/物品的潜在向量,进而将两种向量进行融合得到用户/物品的偏好向量;最后,使用神经网络预测用户与物品交互的可能性.在训练模型时,定义一种加权的二进制交叉熵损失函数,加强显式反馈对模型的影响来增强模型捕获用户偏好的能力.为了验证所提出模型的有效性,在覆盖不同领域的现实数据集上进行实验,实验结果表明,CEICF可有效地融合显式和隐式反馈,且推荐效果相对于基线模型有显著提升.     

Nonstandard finite-difference methods for predator–prey models with general functional response

Predator–prey systems with linear and logistic intrinsic growth rate of the prey are analyzed. The models incorporate the mutual interference between predators into the functional response which stabilizes predator–prey interactions in the system. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous predator–prey models, are formulated and analyzed. The proposed numerical techniques are based on a nonlocal modeling of the growth-rate function and a nonstandard discretization of the time derivative. This discretization approach leads to significant qualitative improvements in the behavior of the numerical solution. In addition, it allows for the use of an essentially implicit method for the cost of an explicit method. Applications of the PESN methods to specific predator–prey systems are also presented.     

一种无指导的隐式篇章关系推理方法研究

该文提出一种基于信息检索的无指导方法,用于推理隐式篇章片段之间的语义连接关系,如因果关系、转折关系等。该文基于Google搜索引擎,抽取在句子结构以及语义层面上均与原隐式片段相似的显式片段,通过分析和识别相关显式关系来间接推理隐式关系。主要包括以下三个模块 构建高质量查询关键词并抽取候选显式关系;结合三种隐式关系推理模型(相似度、置信度、关联度),综合考察查询关键词以及候选关系的质量;基于排序学习的方法,统计高质量候选关系中的类别分布以实现最终隐式关系的推理。该文采用Penn Discourse TreeBank 2.0篇章语料库,最终方法精确率达到54.3%,与有指导的方法相比,提高了约14.3%。     

Stability analysis of the extended ADI-FDTD technique including lumped models

The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, capacitor, and inductor, and three different formulations for each model are analyzed： the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.     

Time Stepping Via One-Dimensional Padé Approximation

The numerical solution of time-dependent ordinary and partial differential equations presents a number of well known difficulties—including, possibly, severe restrictions on time-step sizes for stability in explicit procedures, as well as need for solution of challenging, generally nonlinear systems of equations in implicit schemes. In this note we introduce a novel class of explicit methods based on use of one-dimensional Padé approximation. These schemes, which are as simple and inexpensive per time-step as other explicit algorithms, possess, in many cases, properties of stability similar to those offered by implicit approaches. We demonstrate the character of our schemes through application to notoriously stiff systems of ODEs and PDEs. In a number of important cases, use of these algorithms has resulted in orders-of-magnitude reductions in computing times over those required by leading approaches.     

Narrow band region-based active contours and surfaces for 2D and 3D segmentation

We describe a narrow band region approach for deformable curves and surfaces in the perspective of 2D and 3D image segmentation. Basically, we develop a region energy involving a fixed-width band around the curve or surface. Classical region-based methods, like the Chan–Vese model, often make strong assumptions on the intensity distributions of the searched object and background. In order to be less restrictive, our energy achieves a trade-off between local features of gradient-like terms and global region features. Relying on the theory of parallel curves and surfaces, we perform a mathematical derivation to express the region energy in a curvature-based form allowing efficient computation on explicit models. We introduce two different region terms, each one being dedicated to a particular configuration of the target object. Evolution of deformable models is performed by means of energy minimization using gradient descent. We provide both explicit and implicit implementations. The explicit models are a parametric snake in 2D and a triangular mesh in 3D, whereas the implicit models are based on the level set framework, regardless of the dimension. Experiments are carried out on MRI and CT medical images, in 2D and 3D, as well as 2D color photographs.     

Euler-like discrete models of the logistic differential equation

To understand the behavior of difference schemes on nonlinear differential equations, it seems desirable to extend the standard linear stability theory into a nonlinear theory. As a step in that direction, we investigate the stability properties of Euler-related integration algorithms by checking how they preserve and violate the dynamical structure of the logistic differential equation.Among the schemes considered are two linearly implicit nonstandard schemes which are adjoint to each other. We find that these schemes are superior to explicit schemes when they are stable and the blow-up time has not passed: for these λh-values they are dynamically faithful. When these schemes ‘turn unstable’, however, they have much less desirable properties than explicit or fully implicit schemes: they become simultaneously superstable and unstable. This is explained by the fact that these schemes are not self-adjoint: the linearly implicit self-adjoint scheme is dynamically faithful in an Euler-typical range of step sizes and gives correct stability for all step sizes.     

An Explicit Implicit Scheme for Cut Cells in Embedded Boundary Meshes

We present a new mixed explicit implicit time stepping scheme for solving the linear advection equation on a Cartesian cut cell mesh. We use a standard second-order explicit scheme on Cartesian cells away from the embedded boundary. On cut cells, we use an implicit scheme for stability. This approach overcomes the small cell problem—that standard schemes are not stable on the arbitrarily small cut cells—while keeping the cost fairly low. We examine several approaches for coupling the schemes in one dimension. For one of them, which we refer to as flux bounding, we can show a TVD result for using a first-order implicit scheme. We also describe a mixed scheme using a second-order implicit scheme and combine both mixed schemes by an FCT approach to retain monotonicity. In the second part of this paper, extensions of the second-order mixed scheme to two and three dimensions are discussed and the corresponding numerical results are presented. These indicate that this mixed scheme is second-order accurate in \(L^1\) and between first- and second-order accurate along the embedded boundary in two and three dimensions.