Twin-width I: Tractable FO Model Checking

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of d -contractions , witness that the twin-width is at most d . We show that FO model checking, that is deciding if a given first-order formula ϕ evaluates to true for a given binary structure G on a domain D , is FPT in |ϕ| on classes of bounded twin-width, provided the witness is given. More precisely, being given a d -contraction sequence for G , our algorithm runs in time f ( d ,|ϕ |) · |D| where f is a computable but non-elementary function. We also prove that bounded twin-width is preserved under FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS’15].

Fault diagnosis of rolling bearings based on improved direct fast iterative filtering and spectral amplitude modulation

As the transient impulse components in early fault signals are weak and easily buried by strong background noise, the fault features of rolling bearings are difficult to be extracted effectively. Focusing on this issue, a novel method based on improved direct fast iterative filtering and spectral amplitude modulation (IDFIF-SAM) is presented for detecting the early fault of rolling bearings. First, the ratio of the average crest factor of autocorrelation envelope spectrum to the average envelope entropy is taken as the fitness function to search the optimal parameters of direct fast iterative filtering (DFIF) adaptively via particle swarm optimization (PSO). Then, the efficient kurtosis entropy (EKE) index is being employed to choose the suitable components to reconstruct the signal. Finally, the reconstructed signal is subjected to spectral amplitude modulation (SAM) to strengthen the impulse features. The superiority of improved direct fast iterative filtering (IDFIF) over fixed-parameter DFIF, fast iterative filtering (FIF), and hard thresholding fast iterative filtering (HTFIF) is clarified through the simulated signal. Moreover, the comparative experimental analysis shows that the proposed IDFIF-SAM method can identify the early fault feature of rolling bearings more effectively.

Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Nonlinear dynamics of magnetorheological whole-satellite with variable parameters under small amplitude and medium-high frequency vibration

Whole-satellite vibration isolation system with magneto-rheological (MR) damper is a new idea to solve the problem of small amplitude and medium-high frequency vibration. However, it also brings challenges to MR technology, wherein the super hysteresis and variable stiffness properties of MR damper are lack of research. Considering the particularity of MR damper under small amplitude and medium-high frequency conditions, the MR damper is identified by employing an improved Bingham model, then dynamic characteristics of the whole-satellite system are analyzed by nonlinear bifurcation theory, and then the nonlinear analysis method of MR whole-satellite system with variable parameters is proposed. To verify the effectiveness of the nonlinear analysis method of MR whole-satellite system with variable parameters, the influence of bifurcation parameters on the system parameters is analyzed qualitatively and quantitatively, then time histories and phase diagrams of fixed-parameter and parameter-varying MR whole-satellite system are compared. The analysis suggests that the improved Bingham model adequately characterizes the strong nonlinear hysteretic and variable stiffness behavior of the MR damper. Moreover, the comparison results illustrate that the time histories and phase portraits of the parameter-varying system are in good agreement with those of different fixed-parameter system, and the parameter-varying system has good adaptability in the selected range of bifurcation parameters. This study provides a basis for the design of structural parameters and the optimization of control strategy for MR whole-satellite system.

The Accurate Measurement of Students’ Learning in E-Learning Environments

The ultimate goal of E-learning environments is to improve students’ learning. To achieve that goal, it is crucial to accurately measure students’ learning. In the field of educational measurement, it is well known that the key issue in the measurement of learning is to place test scores on a common metric. Despite the crucial role of a common metric in the measurement of learning, however, less attention has been paid to this important issue in E-learning studies. In this study, we propose to use fixed-parameter calibration (FPC) in an item response theory (IRT) framework to set up a common metric in E-learning environments. To demonstrate FPC, we used the data from the MOOC “Introduction to Psychology as a Science” offered through Coursera collaboratively by Georgia Institute of Technology (GIT) and Carnegie Mellon University (CMU) in 2013. Our analysis showed that the students’ learning gains were substantially different with and without FPC.

Multiplicative Parameterization Above a Guarantee

Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k + g(I) . Here, g(I) is usually a lower bound on the minimum size of a solution. Since its introduction in 1999 for M AX SAT and M AX C UT (with g(I) being half the number of clauses and half the number of edges, respectively, in the input), analysis of parameterization above a guarantee has become a very active and fruitful topic of research. We highlight a multiplicative form of parameterization above (or, rather, times) a guarantee: Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k · g(I) . In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, which is the most natural guarantee for this problem, and provide a fixed-parameter algorithm. Apart from being of independent interest, this exemplifies how parameterization above a multiplicative guarantee can arise naturally. We also show that, for any fixed constant ε > 0, multiplicative parameterization above g(I) 1+ε of Long Cycle yields para-NP-hardness, thus our parameterization is tight in this sense. We complement our main result with the design (or refutation of the existence) of fixed-parameter algorithms as well as kernelization algorithms for additional problems parameterized multiplicatively above girth.

Incorporating Instantaneous Reaction Delay in Car-Following Models: A Hybrid Approach

Car-following is considered as one of the most prevalent fundamental driving behaviors that substantially influences traffic performance as well as road safety and capacity. Drivers’ car-following behavior is affected by numerous factors. However, in practice, very few of these factors have been scrutinized, because of their latent essence and unavailability of appropriate data. Owing to its importance, drivers’ reaction time has attracted the attention of many researchers; nevertheless, it is considered as a fixed parameter in car-following models, which is far from reality. To take the variability of drivers’ reaction time into account, a flexible hybrid approach has been suggested in the present study. In the proposed structure, in the first step, the desirable acceleration of the driver is estimated by applying an equation-based car-following model. In the next step, the driver’s reaction delay in applying the calculated acceleration is estimated by an artificial neural network. The corresponding parameters are jointly estimated by applying an estimated distribution algorithm. Statistical tests indicate better performance of the hybrid model, which considers the variations of the driver’s reaction time, compared with a traditional model with fixed reaction time. Furthermore, the cross-validation results indicate better generalizability and transferability of the proposed model in action.

Identification of active modules in interaction networks using node2vec network embedding

The identification of condition-specific gene sets from transcriptomic experiments is important to reveal regulatory and signaling mechanisms associated with a given cellular response. Statistical approaches using only expression data allow the identification of genes whose expression is most altered between different conditions. However, a phenotype is rarely a direct consequence of the activity of a single gene, but rather reflects the interplay of several genes to carry out certain molecular processes. Many methods have been proposed to analyze the activity of genes in light of our knowledge of their molecular interactions. However, existing methods have many limitations that make them of limited use to biologists: they detect modules that are too large, too small, or they require the users to specify a priori the size of the modules they are looking for. We propose AMINE (Active Module Identification through Network Embedding), an efficient method for the identification of active modules. Experiments carried out on artificial data sets show that the results obtained are more reliable than many available methods. Moreover, the size of the modules to be identified is not a fixed parameter of the method and does not need to be specified; rather, it adjusts according to the size of the modules to be found. The applications carried out on real datasets show that the method enables to find important genes already highlighted by approaches solely based on gene variations, but also to identify new groups of genes of high interest. In addition, AMINE method can be used as a web service on your own data (http://amine.i3s.unice.fr).