Showing papers on "Matrix (mathematics) published in 2021"
TL;DR: Empirical studies on six HiDS matrices from industrial application indicate that an FNLF model outperforms an NLF model in terms of both convergence rate and prediction accuracy for missing data, and is more practical in industrial applications.
Abstract: Non-negative latent factor (NLF) models can efficiently acquire useful knowledge from high-dimensional and sparse (HiDS) matrices filled with non-negative data. Single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) is an efficient algorithm for building an NLF model on an HiDS matrix, yet it suffers slow convergence. A momentum method is frequently adopted to accelerate a learning algorithm, but it is incompatible with those implicitly adopting gradients like SLF-NMU. To build a fast NLF (FNLF) model, we propose a generalized momentum method compatible with SLF-NMU. With it, we further propose a single latent factor-dependent non-negative, multiplicative and momentum-incorporated update algorithm, thereby achieving an FNLF model. Empirical studies on six HiDS matrices from industrial application indicate that an FNLF model outperforms an NLF model in terms of both convergence rate and prediction accuracy for missing data. Hence, compared with an NLF model, an FNLF model is more practical in industrial applications.
155 citations
TL;DR: In this article, a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound.
Abstract: We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.
131 citations
TL;DR: A robust three-branch model with triplet module and matrix Fisher distribution module is proposed to address head pose estimation problems and achieves state-of-the-art performance in comparison with traditional methods.
Abstract: Head pose estimation suffers from several problems, including low pose tolerance under different disturbances and ambiguity arising from common head pose representation. In this study, a robust three-branch model with triplet module and matrix Fisher distribution module is proposed to address these problems. Based on metric learning, the triplet module employs triplet architecture and triplet loss. It is implemented to maximize the distance between embeddings with different pose pairs and minimize the distance between embeddings with same pose pairs. It can learn a highly discriminate and robust embedding related to head pose. Moreover, the rotation matrix instead of Euler angle and unit quaternion is utilized to represent head pose. An exponential probability density model based on the rotation matrix (referred to as the matrix Fisher distribution) is developed to model head rotation uncertainty. The matrix Fisher distribution can further analyze the head pose, and its maximum likelihood obtained using singular value decomposition provides enhanced accuracy. Extensive experiments executed over AFLW2000 and BIWI datasets demonstrate that the proposed model achieves state-of-the-art performance in comparison with traditional methods.
120 citations
TL;DR: In this article, a droop coefficients stability region analysis approach was proposed to assess the droop coefficient stability point, but not the stability region, in which a novel forbidden region criterion based on the return-ratio matrix was constructed, which reduced conservatism compared with normbased impedance criteria and partial forbidden region criteria.
Abstract: The droop control is an advantageous approach for stand-alone supply systems consisting of multiple batteries, allowing among various inverters without intercommunication. The droop coefficients of batteries always vary with their state-of-charge (SoC) and charge/discharge mode, resulting in small-signal instability. Nevertheless, the existing impedance-based approaches can only assess the droop coefficients stability point, but not the stability region. Therefore, this article proposes a droop coefficients stability region analysis approach. First, the charge/discharge SoC-based droop controlled battery, the P&Q controlled distributed generator and the constant power load are separately discussed. Meanwhile, the state matrix and return-ratio matrix are established, respectively. Furthermore, the novel forbidden region criterion based on the return-ratio matrix is constructed, which reduces conservatism compared with norm-based impedance criteria and partial forbidden region criteria. Such a forbidden region criterion is first switched to the Hurwitz identification problem regarding the equivalent return-ratio matrix. Combined the state matrix and the equivalent return-ratio matrix, the generalized incidence matrix is constructed to simultaneously identify subsystem stability and interactive stability. Based on the generalized incidence matrix, an adaptive step search strategy is proposed to obtain the droop coefficients coordinated stability region. Finally, the simulation and experimental results illustrate the validity of the proposed method.
91 citations
TL;DR: An instance-frequency-weighted regularization (IR) scheme for NLFA on HiDS data specifies the regularization effects on each latent factors with its relevant instance count, i.e., instance- frequency, which clearly describes the known data distribution of an HiDS matrix.
Abstract: High-dimensional and sparse (HiDS) data with non-negativity constraints are commonly seen in industrial applications, such as recommender systems. They can be modeled into an HiDS matrix, from which non-negative latent factor analysis (NLFA) is highly effective in extracting useful features. Preforming NLFA on an HiDS matrix is ill-posed, desiring an effective regularization scheme for avoiding overfitting. Current models mostly adopt a standard ${L} _{2}$ scheme, which does not consider the imbalanced distribution of known data in an HiDS matrix. From this point of view, this paper proposes an instance-frequency-weighted regularization (IR) scheme for NLFA on HiDS data. It specifies the regularization effects on each latent factors with its relevant instance count, i.e., instance-frequency, which clearly describes the known data distribution of an HiDS matrix. By doing so, it achieves finely grained modeling of regularization effects. The experimental results on HiDS matrices from industrial applications demonstrate that compared with an ${L} _{2}$ scheme, an IR scheme enables a resultant model to achieve higher accuracy in missing data estimation of an HiDS matrix.
91 citations
TL;DR: A novel ensemble clustering approach based on fast propagation of cluster-wise similarities via random walks based on an enhanced co-association matrix, which is able to simultaneously capture the object-wise co-occurrence relationship as well as the multiscale clusters-wise relationship in ensembles.
Abstract: Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the object-level, yet often lack the ability to explore the rich information at higher levels of granularity. Second, they mostly focus on the direct connections (e.g., direct intersection or pair-wise co-occurrence) in the multiple base clusterings, but generally neglect the multiscale indirect relationship hidden in them. To address these two issues, this paper presents a novel ensemble clustering approach based on fast propagation of cluster-wise similarities via random walks. We first construct a cluster similarity graph with the base clusters treated as graph nodes and the cluster-wise Jaccard coefficient exploited to compute the initial edge weights. Upon the constructed graph, a transition probability matrix is defined, based on which the random walk process is conducted to propagate the graph structural information. Specifically, by investigating the propagating trajectories starting from different nodes, a new cluster-wise similarity matrix can be derived by considering the trajectory relationship. Then, the newly obtained cluster-wise similarity matrix is mapped from the cluster-level to the object-level to achieve an enhanced co-association matrix, which is able to simultaneously capture the object-wise co-occurrence relationship as well as the multiscale cluster-wise relationship in ensembles. Finally, two novel consensus functions are proposed to obtain the consensus clustering result. Extensive experiments on a variety of real-world datasets have demonstrated the effectiveness and efficiency of our approach.
91 citations
TL;DR: This paper proposes an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm, which proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix to address issues of intensive computational and storage complexities, over-complicated optimization and limitedly improved clustering performance.
Abstract: Incomplete multi-view clustering (IMVC) optimally combines multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel $k$ k -means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, over-complicated optimization and limitedly improved clustering performance. In this paper, we first propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. Moreover, we further improve this algorithm by incorporating prior knowledge to regularize the learned consensus clustering matrix. Two three-step iterative algorithms are carefully developed to solve the resultant optimization problems with linear computational complexity, and their convergence is theoretically proven. After that, we theoretically study the generalization bound of the proposed algorithms. Furthermore, we conduct comprehensive experiments to study the proposed algorithms in terms of clustering accuracy, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithms deliver their effectiveness by significantly and consistently outperforming some state-of-the-art ones.
90 citations
TL;DR: In this article, a new matrix S-lemma is proposed to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data, which enables control design from large data sets.
Abstract: We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.
87 citations
TL;DR: In this paper, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system, where the classical Euler-Lagrange equations are constructed by using the classical Lagrangian approach.
Abstract: In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler–Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler–Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism.
86 citations
TL;DR: This paper proves that DNNs are of local isometry on data distributions of practical interest, and establishes a new generalization error bound that is both scale- and range-sensitive to singular value spectrum of each of networks’ weight matrices.
Abstract: In this paper, we introduce the algorithms of Orthogonal Deep Neural Networks (OrthDNNs) to connect with recent interest of spectrally regularized deep learning methods. OrthDNNs are theoretically motivated by generalization analysis of modern DNNs, with the aim to find solution properties of network weights that guarantee better generalization. To this end, we first prove that DNNs are of local isometry on data distributions of practical interest; by using a new covering of the sample space and introducing the local isometry property of DNNs into generalization analysis, we establish a new generalization error bound that is both scale- and range-sensitive to singular value spectrum of each of networks’ weight matrices. We prove that the optimal bound w.r.t. the degree of isometry is attained when each weight matrix has a spectrum of equal singular values, among which orthogonal weight matrix or a non-square one with orthonormal rows or columns is the most straightforward choice, suggesting the algorithms of OrthDNNs. We present both algorithms of strict and approximate OrthDNNs, and for the later ones we propose a simple yet effective algorithm called Singular Value Bounding (SVB), which performs as well as strict OrthDNNs, but at a much lower computational cost. We also propose Bounded Batch Normalization (BBN) to make compatible use of batch normalization with OrthDNNs. We conduct extensive comparative studies by using modern architectures on benchmark image classification. Experiments show the efficacy of OrthDNNs.
85 citations
TL;DR: The definition and related proofs of double parameters fractal sorting matrix (DPFSM) are proposed and the image encryption algorithm based on DPFSM is proposed, and the security analysis demonstrates the security.
Abstract: In the field of frontier research, information security has received a lot of interest, but in the field of information security algorithm, the introduction of decimals makes it impossible to bypass the topic of calculation accuracy. This article creatively proposes the definition and related proofs of double parameters fractal sorting matrix (DPFSM). As a new matrix classification with fractal properties, DPFSM contains self-similar structures in the ordering of both elements and sub-blocks in the matrix. These two self-similar structures are determined by two different parameters. To verify the theory, this paper presents a type of 2×2 DPFSM iterative generation method, as well as the theory, steps, and examples of the iteration. DPFSM is a space position transformation matrix, which has a better periodic law than a single parameter fractal sorting matrix (FSM). The proposal of DPFSM expands the fractal theory and solves the limitation of calculation accuracy on information security. The image encryption algorithm based on DPFSM is proposed, and the security analysis demonstrates the security. DPFSM has good application value in the field of information security.
18 Jun 2021
TL;DR: Simulation experiments and performance analysis show that the algorithm based on a four-wing hyperchaotic system combined with compressed sensing and DNA coding has good performance and security.
Abstract: An image encryption scheme based on a four-wing hyperchaotic system combined with compressed sensing and DNA coding is proposed The scheme uses compressed sensing (CS) to reduce the image according to a certain scale in the encryption process The measurement matrix is constructed by combining the Kronecker product (KP) and chaotic system KP is used to extend the low-dimensional seed matrix to the high-dimensional measurement matrix The dimensional seed matrix is generated by a four-wing chaotic system At the same time, the chaotic sequence generated by the chaotic system dynamically controls the DNA coding and then performs the XOR operation Simulation experiments and performance analysis show that the algorithm has good performance and security
TL;DR: A system architecture is developed, which contains UAVs integrated with monostatic multiple-input–multiple-output (MIMO) radars to estimate the direction-of-arrival (DOA) via MIMO radar and a novel sparse reconstruction algorithm is proposed.
Abstract: As an indispensable part of Internet of Vehicles (IoV), unmanned aerial vehicles (UAVs) can be deployed for target positioning and navigation in space-air-ground integrated networks (SAGIN) environment Maritime target positioning is very important for the safe navigation of ships, hydrographic surveys, and marine resource exploration Traditional methods typically exploit satellites to locate marine targets in SAGIN environment, and the location accuracy does not satisfy the requirements of modern ocean observation missions In order to localize marine target, we develop a system architecture in this paper, which contains UAVs integrated with monostatic multiple-input multiple-output (MIMO) radars The main thrust is to estimate direction-of-arrival (DOA) via MIMO radar Herein, we consider a general scenario that unknown mutual coupling exist, and a novel sparse reconstruction algorithm is proposed The mutual coupling matrix (MCM) is adopted with the help of its special structure, we formulate the data model as a sparse representation form Then two novel matrices, a weighted matrix and a reduced-dimensional matrix are constructed to reduce the computational complexity and enhance the sparsity, respectively Thereafter, a sparse constraint model is constructed using the concept of optimal weighted subspace fitting (WSF) Finally, DOA estimation of maritime targets can be achieved by reconstructing the support of a block sparse matrix Based on the DOA estimation results, multiple UAVs are used to cross-locate marine targets multiple times, and an accurate marine target position is achieved in SAGIN environment Numerical results are carried out, which demonstrates the effectiveness of the proposed DOA estimator, and the multi-UAV cooperative localization system can realize accurate target localization
TL;DR: In this article, a total Bregman divergence-based matrix information geometry (TBD-MIG) detector was proposed to detect targets emerged into nonhomogeneous clutter, where each sample data is assumed to be modeled as a Hermitian positive-definite (HPD) matrix and the clutter covariance matrix is estimated by the TBD mean of a set of secondary HPD matrices.
Abstract: Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally different performances in many practical applications. In this paper, we propose a total Bregman divergence-based matrix information geometry (TBD-MIG) detector and apply it to detect targets emerged into nonhomogeneous clutter. In particular, each sample data is assumed to be modeled as a Hermitian positive-definite (HPD) matrix and the clutter covariance matrix is estimated by the TBD mean of a set of secondary HPD matrices. We then reformulate the problem of signal detection as discriminating two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as the total square loss, the total log-determinant and the total von Neumann MIG detectors, are proposed, and they can achieve great performances due to their power of discrimination and robustness to interferences. Simulations show the advantage of the proposed TBD-MIG detectors in comparison with the geometric detector using an affine invariant Riemannian metric as well as the adaptive matched filter in nonhomogeneous clutter.
TL;DR: Both delay-independent and delay-dependent criteria to guarantee the existence, uniqueness and global stability of equilibrium point for the considered FOQVNNs are derived in the form of linear matrix inequality (LMI).
TL;DR: In this paper, a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of a control outcome matrix, corresponding to treated units and periods, was proposed.
Abstract: In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix, corresponding to treated units/periods. This leads to a matrix that well-approximates the original (incomplete) matrix, but has lower complexity according to the nuclear norm for matrices. We generalize results from the matrix completion literature by allowing the patterns of missing data to have a time series dependency structure that is common in social science applications. We present novel insights concerning the connections between the matrix completion literature, the literature on interactive fixed effects models and the literatures on program evaluation under unconfoundedness and synthetic control methods. We show that all these estimators can be viewed as focusing on the same objective function. They differ solely in the way they deal with identification, in some cases solely through regularization (our proposed nuclear norm matrix completion estimator) and in other cases primarily through imposing hard restrictions (the unconfoundedness and synthetic control approaches). The proposed method outperforms unconfoundedness-based or synthetic control estimators in simulations based on real data.
TL;DR: This paper investigates secrecy-energy efficient hybrid beamforming schemes for a satellite-terrestrial integrated network, wherein a multibeam satellite system shares the millimeter wave spectrum with a cellular system and proposes two robust BF schemes to obtain approximate solutions with low complexity.
Abstract: In this paper, we investigate secrecy-energy efficient hybrid beamforming (BF) schemes for a satellite-terrestrial integrated network, wherein a multibeam satellite system shares the millimeter wave spectrum with a cellular system. Under the assumption of imperfect angles of departure for the wiretap channels, the hybrid beamformer at the base station and digital beamformers at the satellite are jointly designed to maximize the achievable secrecy-energy efficiency, while satisfying signal-to-interference-plus-noise ratio constraints of both the earth stations (ESs) and cellular users. Since the formulated optimization problem is nonconvex and mathematically intractable, we propose two robust BF schemes to obtain approximate solutions with low complexity. Specifically, for the case of a single ES, we integrate the Charnes-Cooper approach with an iterative search algorithm to convert the original nonconvex problem into a solvable one and obtain the BF weight vectors. In the case of multiple ESs, by exploiting the sequential convex approximation method, we convert the original problem into a linear one with multiple matrix inequalities and second-order cone constraints, for which we obtain a solution with satisfactory performance. The effectiveness and superiority of the proposed robust BF design schemes are validated via simulations using realistic satellite and terrestrial downlink channel models.
26 May 2021
TL;DR: In this article, the T-Jordan canonical form and its properties are investigated for tensor similarity and the concepts of Tminimal polynomial and T-characteristic polynomials are proposed.
Abstract: In this paper, we investigate the tensor similarity and propose the T-Jordan canonical form and its properties. The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed. As a special case, we present properties when two tensors commute based on the tensor T-product. We prove that the Cayley–Hamilton theorem also holds for tensor cases. Then, we focus on the tensor decompositions: T-polar, T-LU, T-QR and T-Schur decompositions of tensors are obtained. When an F-square tensor is not invertible with the T-product, we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases. The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form. The polynomial form of the T-Drazin inverse is also proposed. In the last part, we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.
TL;DR: In this paper, a delay-compensation-based state estimation (DCBSE) method is given for a class of discrete time-varying complex networks (DTVCNs) subject to network-induced incomplete observations (NIIOs) and dynamical bias.
Abstract: In this article, a delay-compensation-based state estimation (DCBSE) method is given for a class of discrete time-varying complex networks (DTVCNs) subject to network-induced incomplete observations (NIIOs) and dynamical bias. The NIIOs include the communication delays and fading observations, where the fading observations are modeled by a set of mutually independent random variables. Moreover, the possible bias is taken into account, which is depicted by a dynamical equation. A predictive scheme is proposed to compensate for the influences induced by the communication delays, where the predictive-based estimation mechanism is adopted to replace the delayed estimation transmissions. This article focuses on the problems of estimation method design and performance discussions for addressed DTVCNs with NIIOs and dynamical bias. In particular, a new distributed state estimation approach is presented, where a locally minimized upper bound is obtained for the estimation error covariance matrix and a recursive way is designed to determine the estimator gain matrix. Furthermore, the performance evaluation criteria regarding the monotonicity are proposed from the analytic perspective. Finally, some experimental comparisons are proposed to show the validity and advantages of the new DCBSE approach.
TL;DR: The proposed chaotic system has good chaotic characteristics, and it can be shown that the chaotic system is suitable for image encryption through a variety of simulation experiments.
TL;DR: A tri-factorization-based NMF model with an embedding matrix tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative, leading to higher clustering performance.
Abstract: Multiview data processing has attracted sustained attention as it can provide more information for clustering. To integrate this information, one often utilizes the non-negative matrix factorization (NMF) scheme which can reduce the data from different views into the subspace with the same dimension. Motivated by the clustering performance being affected by the distribution of the data in the learned subspace, a tri-factorization-based NMF model with an embedding matrix is proposed in this article. This model tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative. As a result, the obtained consensus matrix can be a better representative of the multiview data in the subspace, leading to higher clustering performance. Also, a new lemma is proposed to provide the formulas about the partial derivation of the trace function with respect to an inner matrix, together with its theoretical proof. Based on this lemma, a gradient-based algorithm is developed to solve the proposed model, and its convergence and computational complexity are analyzed. Experiments on six real-world datasets are performed to show the advantages of the proposed algorithm, with comparison to the existing baseline methods.
TL;DR: A quantum algorithm for RR is presented, where the technique of parallel Hamiltonian simulation to simulate a number of Hermitian matrices in parallel is proposed and used to develop a quantum version of inline-formula LaTeX, which can efficiently handle non-sparse data matrices.
Abstract: Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ α to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present a quantum algorithm for RR, where the technique of parallel Hamiltonian simulation to simulate a number of Hermitian matrices in parallel is proposed and used to develop a quantum version of $K$ K -fold cross-validation approach, which can efficiently estimate the predictive performance of RR. Our algorithm consists of two phases: (1) using quantum $K$ K -fold cross-validation to efficiently determine a good $\alpha$ α with which RR can achieve good predictive performance, and then (2) generating a quantum state encoding the optimal fitting parameters of RR with such $\alpha$ α , which can be further utilized to predict new data. Since indefinite dense Hamiltonian simulation has been adopted as a key subroutine, our algorithm can efficiently handle non-sparse data matrices. It is shown that our algorithm can achieve exponential speedup over the classical counterpart for (low-rank) data matrices with low condition numbers. But when the condition numbers of data matrices are large to be amenable to full or approximately full ranks of data matrices, only polynomial speedup can be achieved.
TL;DR: A symp eclectic weighted sparse SMM (SWSSMM) model is proposed, which automatically extracts the symplectic weighted coefficient matrix (SWCM) as the fault feature representation and derives an effective solver for SWSSMM with fast convergence.
TL;DR: In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate by resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques.
Abstract: In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter’s modes do not synchronize with the system’s modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input–output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.
TL;DR: In this paper, it was shown that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end, which can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.
Abstract: It was proven recently that JT gravity can be defined as an ensemble of L × L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1 ≪ N ≪ L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.
TL;DR: This article focuses on the exponential synchronization problem of T–S fuzzy reaction–diffusion neural networks (RDNNs) with additive time-varying delays (ATVDs) and proposes two control strategies, namely, fuzzy time sampled-data control and fuzzy time–space sampled- data control.
Abstract: This article focuses on the exponential synchronization problem of T–S fuzzy reaction–diffusion neural networks (RDNNs) with additive time-varying delays (ATVDs). Two control strategies, namely, fuzzy time sampled-data control and fuzzy time–space sampled-data control are newly proposed. Compared with some existing control schemes, the two fuzzy sampled-data control schemes cannot only tolerate some uncertainties but also save the limited communication resources for the considered systems. A new fuzzy-dependent adjustable matrix inequality technique is proposed. According to different fuzzy plant and controller rules, different adjustable matrices are introduced. In comparison with some traditional estimation techniques with a determined constant matrix, the fuzzy-dependent adjustable matrix approach is more flexible. Then, by constructing a suitable Lyapunov–Krasovskii functional (LKF) and using the fuzzy-dependent adjustable matrix approach, new exponential synchronization criteria are derived for T–S fuzzy RDNNs with ATVDs. Meanwhile, the desired fuzzy time and time–space sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). In the end, some simulations are presented to verify the effectiveness and superiority of the obtained theoretical results.
TL;DR: A quantum solver of contracted eigenvalue equations is introduced, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states and achieves an exponential speed-up over its classical counterpart.
Abstract: The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
TL;DR: This work presents an optimization based method that can accurately compute the phase factors using standard double precision arithmetic operations and demonstrates the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and the quantum linear system problems.
Abstract: Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than $10\phantom{\rule{0.16em}{0ex}}000$ with errors below ${10}^{\ensuremath{-}12}$.
TL;DR: In this paper, a family of two-dimensional JT supergravites is studied and a non-perturbative formulation for the supergravity that is well defined and stable is presented.
Abstract: The author studies a family of two-dimensional Jackiw--Teitelboim (JT) supergravites, and, by using string theory techniques, he gives them a complete definition to all orders in the topological expansion. This construction provides a non--perturbative formulation for the JT supergravity that is well--defined and stable. Furthermore, by using a combination of analytical and numerical methods, the author shows explicitly how non--perturbative physics can be extracted for JT gravity within this framework.