Search

In this article, a novel linear parallel control method is developed for output regulation problems with disturbances. The traditional feedback regulators are passive regulation methods. In order to solve this problem, the parallel controllers are presented, where the time variation of the control is constructed instead of the control value itself, to stabilize the output of the system. The main contributions of the developed method include two aspects: 1) a novel parallel regulator structure is presented, which can provide greater flexibility comparing with traditional methods and 2) the necessary and sufficient conditions for the existence of parallel regulators are analyzed. First, the structure of the linear parallel regulators is provided. Next, considering the situations that the full system information is obtained and the information of error is obtained, respectively, the properties of the parallel regulators are analyzed, and the regulator designs for the two situations are provided. Finally, numerical examples are provided to verify the correctness of the present method.

This paper considers linear panel data models with a grouped pattern of heterogeneity when the latent group membership structure and/or the values of slope coefficients change at a break point. We propose a least squares approach to jointly estimate the break point, group membership structure, and coefficients. The proposed estimators are consistent, and the asymptotic distribution of the coefficient estimators is identical to that under known break point and group structure even when the cross-sectional sample size is much larger than the length of time series. Monte Carlo simulations and an empirical example illustrate the use of the approach and associated inference.

A case study of the steel–concrete composite structure in the Pidie Jaya Regency Multipurpose Hall which experienced substantial permanent lateral deformation due to the effect of an earthquake is presented in this study. Therefore, it is important to assess the response of the structure to earthquake load and propose the strengthening strategies to make the buildings useful again. The purpose was to evaluate the causes of large deformations and the behavior of structure in resisting earthquake loads. The building structure model used in this study is a space frame with two-column base support conditions which are fixed and hinged supports after which a non-linear time history analysis was conducted. The time history analysis was conducted using five ground motion acceleration data recorded during earthquakes to determine the deformation and it was found that the large structure permanent deformation was due to the small structure stiffness in the direction of the deformation due to the use of only one column row in front of the building. Moreover, hinged support was observed to have caused a greater deformation than fixed support but was found not to be the main cause of large permanent deformation of the structure. The building structure was further strengthened by adding 4 columns while the oblique columns remained in a sloping condition. Meanwhile, the response spectrum analysis showed the strengthening structure was able to withstand earthquake loads with less deformation than the required standard.

Density-Based clustering are the main clustering algorithms because they can cluster data with different shapes and densities, but some of these algorithms have high time complexity like OPTICS (Ordering Points to Identify Clustering Structure) and DBSCAN (Density-based spatial clustering of applications with noise) where the time complexity up to O( n 2 ). In this paper, we use an approach to reduce this complexity by providing fuzzy clusters to OPTICS, which make the process of finding neighbours within an only narrow region (fuzzy group) instead of searching all the state space making the algorithm faster than the original one with keeping almost the same accuracy of the innovative algorithm. The results show that there is an improvement in execution time using some synthetic and real datasets with high dimensions.

In this paper, for each of six families of three-valued \begin{document}$ m $\end{document} -sequence correlation, we construct an infinite family of five-weight codes from trace codes over the ring \begin{document}$ R = \mathbb{F}_2+u\mathbb{F}_2 $\end{document} , where \begin{document}$ u^2 = 0. $\end{document} The trace codes have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Their support structure is determined. An application to secret sharing schemes is given. The parameters of the binary image are \begin{document}$ [2^{m+1}(2^m-1),4m,2^{m}(2^m-2^r)] $\end{document} for some explicit \begin{document}$ r. $\end{document}

Chromosome conformation capture (3C) is a method of measuring chromosome topology in terms of loci interaction. The Hi-C method is a derivative of 3C that allows for genome wide quantification of chromosome interaction. From such interaction data, it is possible to infer the three-dimensional (3D) structure of the underlying chromosome. In this paper, we use a node embedding algorithm and a graph neural network to predict the 3D coordinates of each genomic loci from the corresponding Hi-C contact data. Unlike other chromosome structure prediction methods, our method can generalize a single model across Hi-C resolutions, multiple restriction enzymes, and multiple cell populations while maintaining reconstruction accuracy. We derive these results using three separate Hi-C data sets from the GM12878, GM06990, and K562 cell lines. We also compare the reconstruction accuracy of our method to four other existing methods and show that our method yields superior performance. Our algorithm outperforms the state-of-the-art methods in the accuracy of prediction and introduces a novel method for 3D structure prediction from Hi-C data.Author SummaryWe developed a novel method, HiC-GNN, for predicting the three-dimensional structures of chromosomes from Hi-C data. HiC-GNN is unique from other methods for chromosome structure prediction in that it learns in an eager setting rather than a lazy setting. Thus, the models learned by HiC-GNN can be generalized to unseen data. To the authors’ knowledge, this generalizing capability is not present in any existing methods. We show that this generalization is robust to input resolution, restriction enzyme, and contact sparsity. We also show that our method outperforms existing methods using both generalized and non-generalized models. Moreover, we also show that our method is more robust to contact variance than the compared methods.AvailabilityAll our source codes and data are available at https://github.com/OluwadareLab/HiC-GNN, and is made available as a containerized application that can be run on any platform.

An asymmetric coloring of a graph is a coloring of its vertices that is not preserved by any non-identity automorphism of the graph. The motion of a graph is the minimal degree of its automorphism group, i.e., the minimum number of elements displaced by any non-identity automorphism. In this paper we confirm Tom Tucker's "Infinite Motion Conjecture" that connected locally finite graphs with infinite motion admit an asymmetric 2-coloring. We infer this from the more general result that the inverse limit of a sequence of finite permutation groups with disjoint domains, viewed as a permutation group on the union of those domains, admits an asymmetric 2-coloring. The proof is based on the study of the interaction between epimorphisms of finite permutation groups and the structure of the setwise stabilizers of subsets of their domains., Comment: V.2 updates: Choi 1972 ref. added, Sec. 8.3 (Mathieu groups) updated, question about $M_{24}$ deleted from "Open questions." New material: New Sec. 14 added, incl. two conjectures. Minor changes made for improved clarity throughout the paper. None of the updates affects the main results or their proofs

We introduce the two-step average tree value for transferable utility games with restricted cooperation represented by undirected communication graphs or hypergraphs. The solution can be considered as an alternative for both the average tree solution for graph games and the average tree value for hypergraph games. Instead of averaging players’ marginal contributions corresponding to all admissible rooted spanning trees of the underlying (hyper)graph, which determines the average tree solution or value, we consider a two-step averaging procedure, in which first, for each player the average of players’ marginal contributions corresponding to all admissible rooted spanning trees that have this player as the root is calculated, and second, the average over all players of all the payoffs obtained in the first step is computed. In general these two approaches lead to different solution concepts. Contrary to the average tree value, the new solution satisfies component fairness and the total cooperation equal treatment property on the entire class of hypergraph games. Moreover, the two-step average tree value is axiomatized on the class of semi-cycle-free hypergraph games, which is more general than the class of cycle-free hypergraph games by allowing the underlying hypergraphs to contain certain cycles. The two-step average tree value is also core stable on the subclass of superadditive semi-cycle-free hypergraph games.

A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion.

We extend the block filtration, defined by Brown based on the work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. We construct a Lie algebra describing relations among motivic multiple zeta values modulo terms of lower block degree, proving Charlton's cyclic insertion conjecture in this structure, and showing the existence of a `block shuffle' relation, and a previously unknown dihedral symmetry and differential relation., Comment: 23 pages, based on work in the author's doctoral thesis. Typo in statement of Corollary 2.9 corrected

We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast with the static case, it is NP-hard to determine whether a given temporal graph is temporally Eulerian even if strong restrictions are placed on the structure of the underlying graph and each edge is active at only three times. However, we do obtain an FPT-algorithm with respect to a new parameter called interval-membership-width which restricts the times assigned to different edges; we believe that this parameter will be of independent interest for other temporal graph problems. Our techniques also allow us to resolve two open question of Akrida, Mertzios and Spirakis [CIAC 2019] concerning a related problem of exploring temporal stars. Furthermore, we introduce a vertex-variant of interval-membership-width (which can be arbitrarily larger than its edge-counterpart) and use it to obtain an FPT-time algorithm for a natural vertex-exploration problem that remains hard even when interval-membership-width is bounded., Extended abstract of this paper appeared in IWOCA 2021: Combinatorial Algorithms pp 107-121 (doi: https://doi.org/10.1007/978-3-030-79987-8_8 )

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore it may take a large number of iterations to converge to the optimal solution. Successive relaxation is a popular technique that can be applied to solve a fixed point equation. It has been shown in the literature that, under a special structure of the MDP, successive over-relaxation technique computes the optimal value function faster than standard value iteration. In this work, we propose a second order value iteration procedure that is obtained by applying the Newton-Raphson method to the successive relaxation value iteration scheme. We prove the global convergence of our algorithm to the optimal solution asymptotically and show the second order convergence. Through experiments, we demonstrate the effectiveness of our proposed approach., Comment: Accepted for publication at IEEE Transactions on Automatic Control

We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph are close, in terms of vertex or edge deletions, to a sparse graph class $Π$. For example, we show that learning an optimal network whose moralized graph has vertex deletion distance at most $k$ from a graph with maximum degree 1 can be computed in polynomial time when $k$ is constant. This extends previous work that gave an algorithm with such a running time for the vertex deletion distance to edgeless graphs [Korhonen & Parviainen, NIPS 2015]. We then show that further extensions or improvements are presumably impossible. For example, we show that learning optimal networks where the network or its moralized graph have maximum degree $2$ or connected components of size at most $c$, $c\ge 3$, is NP-hard. Finally, we show that learning an optimal network with at most $k$ edges in the moralized graph presumably has no $f(k)\cdot |I|^{O(1)}$-time algorithm and that, in contrast, an optimal network with at most $k$ arcs can be computed in $2^{O(k)}\cdot |I|^{O(1)}$ time where $|I|$ is the total input size., 42 pages

The double-sided tubular linear machine (DSTLM) has a more compact structure than general single-sided motors, resulting in a higher power density, typically at the cost of a higher cogging force. To reduce this aspect and make it more suitable for applications in wave energy conversion systems or elevator driver systems, a new tooth-cutting topology is proposed in this paper. The Schwarz-Christoffel (SC) mapping method is used to model and analyze the magnetic field and cogging force of the DSTLM. Based on the analytical model and the relationships between the cutting dimensions and the force performances, optimization is carried out by using a differential evolution algorithm (DEA). The optimization and the experiment results show that the proposed tooth-cutting topology can effectively reduce the cogging force at the small cost of weakening average thrust.

In recent years, grey models based on fractional-order accumulation and/or derivatives have attracted considerable research interest because they offer better performance in handling limited samples with uncertainty than integer-order grey models; however, there remains room for improvement. This paper considers a more flexible and general structure for the fractional grey model by incorporating a generalized fractional-order derivative (GFOD) that complies by memory effects, resulting in the development of a generalized fractional grey model (denoted as GFGM(1,1)). Specifically, we comprehensively analyse the modelling mechanism of the proposed GFGM(1,1) model, involving model parameter estimation and time response function derivation, and discuss the link between the proposed approach and existing special cases. Then, to further improve the efficacy of the proposed approach, four mainstream metaheuristic algorithms are employed to ascertain the orders of fractional accumulation and derivatives. Finally, we carry out a series of simulation studies and a real-world application case to demonstrate the applicability and advantage of the our approach. The numerical results show that GFGM(1,1) outperforms other benchmarks, and some significant insights are obtained from the numerical experiments.

This article addresses the trajectory consensus problem of coordinating the trajectories of vehicles at multiple future time points. The objective is the consensus of the geometry of the vehicles' planned trajectories. The geometric feature of trajectories is parameterized by a set of trajectory states defined as required lengths along the trajectory to reduce the distance to its ending point to specific values. To solve this special consensus problem involving coupled state variables, the conventional consensus model is extended by attaching it to a mapping from the state variables to the trajectory's geometry. This mapping is established using a homotopic structure that creates a compact and efficient form for the mapping. The geometry of the homotopic structure is based on the shapes of its envelopes, and the elements in the structure are derived from their deformation. Through a homotopic search in the structure, an asymptotic consensus of trajectory states is achieved. Simulation results show the proposed coupled state consensus method can achieve better performance on the consensus of multiple vehicles than the conventional isolated state consensus method.

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of limited cardinality. In the article “'Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem”, Furini, Ljubic, Malaguti, and Paronuzzi provide a new bilevel interpretation of the associated capacitated vertex separator problem and model it as a two-player Stackelberg game in which the leader interdicts (protects) the vertices, and the follower solves a combinatorial optimization problem on the resulting graph. Thanks to this bilevel interpretation, the authors derive different families of strengthening inequalities and show that they can be separated in polynomial time. The ideas exploited in their framework can also be extended to other vertex/edge deletion/insertion problems or graph partitioning problems by modeling them as two-player Stackelberg games to be solved through bilevel optimization.

This study proposes a hierarchical structure-based fault-tolerant tracking control methodology for multiple 3-DOF helicopters in the presence of system nonlinearities, uncertainties and simultaneous actuator faults (partial loss of effectiveness, stuck, and saturation), and sensor faults (bias and drift). The hierarchical structure consists of the decentralized fault estimation hierarchy and distributed fault-tolerant tracking control hierarchy. The distributed constant gain-based, node-based, and edge-based adaptive fault-tolerant tracking control designs are developed to cope with bidirectional interactions and to guarantee the robust asymptotic stability and the good tracking property of multihelicopter systems, respectively. Simulation results validate the effectiveness of the proposed hierarchical structure-based tracking control algorithm.

We consider optimal control problems for continuous-time systems with time-dependent dynamics, in which the time-dependence arises from the presence of a known exogenous signal. The problem has been elegantly solved in the case of linear input-affine systems, for which it has been shown that the solution has a remarkable structure: it is given by the sum of two contributions; a state feedback, which coincides with the unperturbed optimal control law, and a purely feedforward term in charge of compensating the effect of the exogenous signal. The objective of this note is to extend the above result to nonlinear input-affine systems. It is shown that, while some of the relevant features of the linear case indeed rely heavily on linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear case.

In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization and coupling structure is studied. Conditions on the interconnection under which synchronization can be achieved for some selection of coupling strengths are established. How to strengthen those conditions so that synchronization is guaranteed for all admissible parameter values is also presented.

Decision making under uncertainty includes reassessing and reevaluating risk after initial decisions. To this end, it is essential to consider a governing value process and to track its evolution over time. The paper, “Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping,” by Pichler, Liu, and Shapiro, develops a consistent framework by consolidating risk and optimal stopping. The paper develops the notion of time consistency for the stochastic multistage optimization problem. Supermartingales and envelopes characterizing optimal decisions are given explicitly. With that, dynamic equations are derived, which gradually reveal the optimal policy. Taking risk into account requires updating optimal policies, as an explicit example on American options demonstrates.

To obtain the seismic performance of plate-shell integrated concrete liquid-storage structures (PSICLSS), a scale test model was built for shaking table testing. A combination isolation layer is proposed, and the dynamic responses of non-isolation and combination isolation PSICLSS under unidirectional and bidirectional earthquakes were tested. The results show that the combination isolation layer can change the spectral characteristics of the input acceleration, reducing the acceleration response and displacement of the structure, but it will increase the hydrodynamic pressure and liquid sloshing height. Under earthquake action, the liquid sloshing of combination isolation PSICLSS clearly appears as a nonlinear splash phenomenon. When considering the vertical earthquake, the horizontal acceleration response of PSICLSS and the liquid sloshing height change little, the peak hydrodynamic pressure changes significantly, and the peak position also changes. The maximum displacement of the isolation layer increases, but the residual displacement decreases.

A metamaterial is any material engineered with a property not discovered in naturally occurring materials. Its existence is important in the development and application of modern technology in this century. Furthermore, Its characteristics such as high sensitivity and gain can be potentially applied in antenna technology. In this research, the metamaterial implementation was used to improve low-profile microstrip antennas as ultra-wideband (UWB) applications. The proposed metamaterial consists of variations of one to four hexagonal shape split ring resonator (SRR-H) elements. This study was carried out through simulation and experiments which were operated in the frequency range 0.05–9 GHz. Based on the results, the proposed antenna with the variation of the SRR-H elements provides increased performance than the without SRR-H. The highest double-negative (DNG) metamaterial characteristic of the SRR-H four-element structure provides the highest antenna performance compared to others. The given working frequency occurs at 5.98 GHz with an increase in bandwidth of 47.49% from without SRR-H. The antenna metamaterial structure also responds by providing an ultimate gain radiation pattern of 5.97 dBi at a 45-degree angle in the Quadrant II region. Thus, the performance of the proposed antenna shows the potential for use in UWB technology.

With integer linear programming problems (ILPPs) being formulated and solved, the existing approaches design optimal Petri-net supervisors via nonpure net structures, including self-loops and data inhibitor arcs. Nonpure net structures are powerful for control of Petri-net-modeled discrete-event systems. However, in the existing work, the formulated ILPPs contain a large number of constraints, which is computationally inefficient. In this article, we propose approaches that formulate ILPPs with fewer constraints such that the computational efficiency is significantly improved. To do so, in formulating ILPPs for optimal Petri-net controllers by using self-loops and data inhibitor arcs, we remove the reachability conditions for legal markings. By doing so, an obtained solution may result in some legal markings unreachable. To solve this problem, a novel technique is developed to design an optimal controller by modifying the initial marking and structure of the obtained supervisor. It is shown that, by the reduced ILPPs, one can find the same feasible solutions as that obtained by the existing work. Finally, the proposed approaches are demonstrated by examples.

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R 0 ≈ 6.6361 . Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.

Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among inequality measures, apart from multidistances we pay special attention to dispersions, and study their main features. Classical concepts will be generalized to this abstract setting. Multidistances are then revisited, and some new methods to generate them are implemented. A wide spectrum of interdisciplinary applications is outlined in the final section. This work is partially supported by the research projects ECO2015-65031-R , MTM2015-63608-P , TIN2016-77356-P , TIN2017-87600-P (MINECO/AEI-FEDER, UE) and PID2019-108392GB-I00 (AEI/10.13039/501100011033)

For achieving the desired configuration of spacecraft at the desired fixed time, a sub-optimal fixed-finite-horizon configuration control method on the Lie group SE(3) is developed based on the Model Predictive Static Programming (MPSP). The MPSP technique has been widely used to solve finite-horizon optimal control problems and is known for its high computational efficiency thanks to the closed-form solution, but it cannot be directly applied to systems on SE(3). The methodological innovation in this paper enables that the MPSP technique is extended to the geometric control on SE(3), using the variational principle, the left-invariant properties of Lie groups, and the topology structure of Lie algebra space. Moreover, the energy consumption, which is crucial for spacecraft operations, is considered as the objective function to be optimized in the optimal control formulation. The effectiveness of the designed sub-optimal control method is demonstrated through an online simulation under disturbances and state measurement errors.

This work focuses on image anomaly detection by leveraging only normal images in the training phase. Most previous methods tackle anomaly detection by reconstructing the input images with an autoencoder (AE)-based model, and an underlying assumption is that the reconstruction errors for the normal images are small, and those for the abnormal images are large. However, these AE-based methods, sometimes, even reconstruct the anomalies well; consequently, they are less sensitive to anomalies. To conquer this issue, we propose to reconstruct the image by leveraging the structure-texture correspondence. Specifically, we observe that, usually, for normal images, the texture can be inferred from its corresponding structure (e.g., the blood vessels in the fundus image and the structured anatomy in optical coherence tomography image), while it is hard to infer the texture from a destroyed structure for the abnormal images. Therefore, a structure-texture correspondence memory (STCM) module is proposed to reconstruct image texture from its structure, where a memory mechanism is used to characterize the mapping from the normal structure to its corresponding normal texture. As the correspondence between destroyed structure and texture cannot be characterized by the memory, the abnormal images would have a larger reconstruction error, facilitating anomaly detection. In this work, we utilize two kinds of complementary structures (i.e., the semantic structure with human-labeled category information and the low-level structure with abundant details), which are extracted by two structure extractors. The reconstructions from the two kinds of structures are fused together by a learned attention weight to get the final reconstructed image. We further feed the reconstructed image into the two aforementioned structure extractors to extract structures. On the one hand, constraining the consistency between the structures extracted from the original input and that from the reconstructed image would regularize the network training; on the other hand, the error between the structures extracted from the original input and that from the reconstructed image can also be used as a supplement measurement to identify the anomaly. Extensive experiments validate the effectiveness of our method for image anomaly detection on both industrial inspection images and medical images.

The bifurcation structure of the oscillations of ultrasound contrast agents (UCAs) was studied as a function of the driving pressure for excitation frequencies that were determined using the UCAs pressure-dependent resonances $$(f_\mathrm{s})$$ . It was shown that when excited by the $$(f_\mathrm{s})$$ , the UCA can undergo a saddle-node bifurcation (SNB) to higher amplitude oscillations. The driving pressure at which the SNB occurs is controllable and depends on the $$(f_\mathrm{s})$$ magnitude. Utilizing the appropriate $$(f_\mathrm{s})$$ , the scattering cross section of the UCAs can significantly be enhanced (e.g., $$\sim $$ ninefold) while at the same time avoiding potential UCA destruction (by limiting the radial expansion ratio $$

A baby stroller allows the transportation of a child over long or short distances. The materials used to produce the stroller make it heavy for users, which creates difficulties when lifting the stroller. The goal of this project was to design and fabricate a three-dimensional (3D) fabric structure that can be used as part of a stroller seat to improve its mechanical and physical properties. The idea of implementing a woven 3D system allows the development of an egg-shaped or shell-like structure as part of a stroller seat. The combination of double-woven material and honeycomb polypropylene (as the reinforcing material) was used to create a 3D composite structure. Single and double layers of polypropylene honeycomb sandwiched within layers of linen flax fabric were used to prepare the composite samples. Subsequently, tests on mechanical and physical properties, such as density, flexural strength, and tensile strength, were carried out. Analysis of the results showed that the composite with one layer of honeycomb has half the density of polyvinyl chloride.

Training neural networks with the Moore-Penrose (MP) inverse has recently gained attention in view of its noniterative training nature. However, a significant drawback of learning based on the MP inverse is that the computational memory consumption grows along with the size of a dataset. In this article, based on the partitioning of the MP inverse, we propose a blockwise recursive MP inverse formulation (BRMP) for network learning with low-memory property while preserving its training effectiveness. The BRMP is an equivalent formulation to its batchwise counterpart since neither approximation nor assumption is made in the derivation process. Our further exploration of this recursive method leads to a switching structure among three different scenarios. This structure also reveals that the well-known recursive least squares method is a special case of our proposed technique. Subsequently, we apply BRMP to the training of radial basis function networks as well as multilayer perceptrons. The experimental validation covers both regression and classification tasks.

This study investigates a parameterization of all output-rectifying retrofit controllers for distributed design of a structured controller. It has been discovered that all retrofit controllers can be characterized as a constrained Youla parameterization, which is difficult to solve analytically. For synthesis, a tractable and insightful class of retrofit controllers, referred to as output-rectifying retrofit controllers, has been introduced. An unconstrained parameterization of all output-rectifying retrofit controllers can be derived under a technical assumption on measurability of particular signals. The aim of this note is to reveal the structure of all output-rectifying retrofit controllers in the general output-feedback case. It is found out that the existing developments can be generalized based on the notions of state projection and an inverse system. The result leads to the conclusion that output-rectifying retrofit controllers can readily be designed even in the general case., to be published at IEEE Transactions on Automatic Control

Hosoya introduced the concept of graph terminologies in chemistry and provide a modeling for molecules. This modeling leads to predict the chemical properties of molecules, easy classification of chemical compounds, computer simulations and computer-assisted design of new chemical compounds. In this article, we determine the non-commuting graph associated with the dihedral group by using three Hosoya parameters (Hosoya polynomial, reciprocal Hosoya polynomial and Hosoya index). These Hosoya parameters contain a pile of information about distance structure as well as the edge independent structure of the above-mentioned graph.

This work presents a derivative-free trust-region algorithm for probability maximization problems. We assume that the probability function is continuously differentiable with Lipschitz continuous gradient, but no derivatives are available. The algorithm explores the particular structure of the probability objective function through models based on copulae. Under reasonable assumptions, the global convergence of the algorithm is analyzed: we prove that all accumulation points of the sequence generated by the algorithm are stationary. The proposed approach is validated by encouraging numerical results on academic and industrial problems.

In order to solve the problems of uneven gap distribution and flow pattern in complex parts with multi-stage internal cone holes in electrochemical machining, a method of computer simulation assisted cathode design was proposed. The electric field and flow field models of machining gaps were established respectively, and the simulation of different cathode profiles was carried out. When the cathode cone angle is 2°, the electric field distribution between the cathode and the workpiece is reasonable, and the electrolyte distribution in the machining gap is uniform. With the conditions of processing voltage 10 V, electrolyte inlet pressure 1.5 MPa, electrolyte temperature 28 ℃ and cathode feed speed 5mm/min, the ECM processing of multi-stage internal cone hole was carried out by using the optimized cathode. The results show that the surface of the workpiece has no flow pattern, the dimensional forming accuracy is better than 0.1mm, and the surface roughness reaches Ra0.697µm. Research shows that the optimization of cathode structure with computer simulation can shorten the cathode development cycle and reduce the cost of cathode design effectively in ECM, which provides an efficient and feasible method for the optimization of complex cathode structure.

In this article, we studied the fractional dynamics of the most dangerous deathly disease which outbreaks have been recorded all over the world, called 2019-nCOV or COVID-19. We used the numerical values of the given parameters based on the real data of the 2019-nCOV cases in Spain for the time duration of 25 February to 9 October 2020. We performed our observations with the help of the Atangana-Baleanu (AB) non-integer order derivative. We analysed the optimal control problem in a fractional sense for giving the information on all necessary health care issues. We applied the Predictor-Corrector method to do the important graphical simulations. Also, we provided the analysis related to the existence of a unique solution and the stability of the proposed scheme. The aim and the main contribution of this research is to analyse the structure of novel coronavirus in Spain at different transmission rate and to indicate the danger of this deathly disease for future with the introduction of some optimal controls and health care measures.

In an intersection join, we are given t sets R 1 , . . . , R t of axis-parallel rectangles in R d , where d ≥ 1 and t ≥ 2 are constants, and a join topology which is a connected undirected graph G on vertices 1 , . . . , t . The result consists of tuples ( r 1 , . . . , r t ) ∈ R 1 × . . . × R t where r i ∩ r j ≠ ∅ for all i , j connected in G. A structure is feasible if it stores O ˜ ( n ) words, supports an update in O ˜ ( 1 ) amortized time, and can enumerate the join result with an O ˜ ( 1 ) delay, where n = ∑ i | R i | and O ˜ ( . ) hides a polylog n factor. We provide a dichotomy as to when feasible structures exist: they do when t = 2 or d = 1 ; subject to the OMv-conjecture, they do not exist when t ≥ 3 and d ≥ 2 , regardless of the join topology.

Numerical analysis of collision is an important aspect of bridge seismic research. This paper introduces precise integration to the numerical analysis of seismic collision. Firstly, the collision forces of four contact element models were expressed in a unified form, including linear spring model, Kelvin-Voigt model, Hertz model, and Jan-Hertz-Damp model, and then the precision integration formula was derived for solving the collision force. Next, a collision time search method was proposed under the linear acceleration hypothesis, and the seismic collision was divided into a collision phase and a non-collision phase. Different time steps were adopted for the two phases. This strategy was verified by comparing simulation results with the data of theoretical analysis and shaking table test. The results show that precision integration ensures the accuracy of numerical calculation for bridge structure collision under seismic action, and achieves a high calculation efficiency; the contact element model and model parameters should be selected reasonably to analyze seismic collision of bridges; the Jan-Hertz-Damp model of contact elements boasts the highest simulation accuracy among the commonly used models.

Sinusoidal reference tracking is required in important practical applications. Resonant controllers are suitable for that task. However, stable implementation of these controllers in a digital processor is difficult to achieve. On the other hand, quasi-resonant controllers are easier to implement, but they do not guarantee asymptotic reference tracking. This paper proposes a new resonant controller based on Generalized Predictive Control (GPC) and Internal Model Principle (IMP). The first-order and second-order difference operators are applied to create a GPC system whose structure embeds the Z-transform of the sinusoidal reference. Thus, according to IMP, the proposed controller, named Resonant Generalized Predictive Control (RGPC), asymptotically tracks sinusoidal references. Besides, the proposed RGPC has the advantages of GPC, such as fast response and easy implementation in digital processors. Experimental tests prove that the proposed RGPC has better performance than other controllers for sinusoidal reference tracking.

There is an embedding of affine vertex algebras $V^k(\mathfrak{gl}_n) \hookrightarrow V^k(\mathfrak{sl}_{n+1})$, and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n), V^k(\mathfrak{sl}_{n+1}))$ is a natural generalization of the parafermion algebra of $\mathfrak{sl}_2$. It was called the algebra of generalized parafermions by the third author and was shown to arise as a one-parameter quotient of the universal two-parameter $\mathcal{W}_{\infty}$-algebra of type $\mathcal{W}(2,3,\dots)$. In this paper, we consider an analogous structure of orthogonal type, namely $\mathcal{D}^k(n) = \text{Com}(V^k(\mathfrak{so}_{2n}), V^k(\mathfrak{so}_{2n+1}))^{\mathbb{Z}_2}$. We realize this algebra as a one-parameter quotient of the two-parameter even spin $\mathcal{W}_{\infty}$-algebra of type $\mathcal{W}(2,4,\dots)$, and we classify all coincidences between its simple quotient $\mathcal{D}_k(n)$ and the algebras $\mathcal{W}_{\ell}(\mathfrak{so}_{2m+1})$ and $\mathcal{W}_{\ell}(\mathfrak{so}_{2m})^{\mathbb{Z}_2}$. As a corollary, we show that for the admissible levels $k = -(2n-2) + \frac{1}{2} (2 n + 2 m -1)$ for $\widehat{\mathfrak{so}}_{2n}$ the simple affine algebra $L_k(\mathfrak{so}_{2n})$ embeds in $L_k(\mathfrak{so}_{2n+1})$, and the coset is strongly rational. As a consequence, the category of ordinary modules of $L_k(\mathfrak{so}_{2n+1})$ at such a level is a braided fusion category., Comment: Minor corrections, final version to appear in J. Algebra

In this paper, a new switched capacitor-based structure is presented for a single-phase multilevel inverter. The proposed structure is capable of boosting the input voltage and producing fifteen voltage levels at the output utilizing two separated DC voltage sources along with a switched capacitor unit. The proposed structure also has self-charging capability and can automatically adjust the capacitor voltage without any sensor. A quantitative comparison with similar structures has been performed to confirm the proposed structure. Furthermore, loss and thermal simulations have been performed for the proposed structure. The functionality of the proposed structure is examined by the simulation results. Finally, a laboratory prototype is implemented to verify the effectiveness and accuracy of the proposed structure and its control method.

In many statistical learning problems, it is desired that the optimal solution conform to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires nonsmooth penalty functions that exploit group overlapping. Our study focuses on evaluating the proximal operator of the latent overlapping group lasso developed by Jacob et al. in 2009 . We implemented an alternating direction method of multiplier with a sharing scheme to solve large-scale instances of the underlying optimization problem efficiently. In the absence of strong convexity, global linear convergence of the algorithm is established using the error bound theory. More specifically, the paper contributes to establishing primal and dual error bounds when the nonsmooth component in the objective function does not have a polyhedral epigraph. We also investigate the effect of the graph structure on the speed of convergence of the algorithm. Detailed numerical simulation studies over different graph structures supporting the proposed algorithm and two applications in learning are provided. Summary of Contribution: The paper proposes a computationally efficient optimization algorithm to evaluate the proximal operator of a nonsmooth hierarchical sparsity-inducing regularizer and establishes its convergence properties. The computationally intensive subproblem of the proposed algorithm can be fully parallelized, which allows solving large-scale instances of the underlying problem. Comprehensive numerical simulation studies benchmarking the proposed algorithm against five other methods on the speed of convergence to optimality are provided. Furthermore, performance of the algorithm is demonstrated on two statistical learning applications related to topic modeling and breast cancer classification. The code along with the simulation studies and benchmarks are available on the corresponding author’s GitHub website for evaluation and future use.

We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertical sector. By generalizing an argument of Bravyi and K\"onig, we find that transversal gates for these codes must be restricted to the Clifford group.

In the sensorless control system of an induction machine, the rotor speed value is not measured but reconstructed by an observer structure. The rotor speed value can be reconstructed by the classical adaptive law with the integrator. The second approach, which is the main contribution of this paper, is the non-adaptive structure without an integrator. The proposed method of the rotor speed reconstruction is based on an algebraic relationship – the rank of the mathematical model of the observer system is not increased. However, the problem with the stabilization of the observer structure does exist. For near to zero rotor speed or in the regenerating mode of an induction machine, the speed observer structure can be unstable. Therefore, in this paper, the new stabilization functions are proposed. The stability is provided by the Lyapunov theorem and the practical stability theorems in which the uncertainty of parameters is considered. In the proposed solution, the newly introduced stabilization functions guarantee observer stability during both the motoring and regenerating conditions at the chosen low rotor speed ranges and for different load torque values. All the theoretical considerations were confirmed by simulation and experimental tests during the chosen working modes and uncertainties of nominal parameters of the induction machine.