This study compares an existing method with a novel approach for state estimation of Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering does not apply to this system class, despite co...
详细信息
This study compares an existing method with a novel approach for state estimation of Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering does not apply to this system class, despite computable posterior probability density function (PDF) support. Existing literature suggests a limited scalability disjunctive approach using difference-bound matrices. To overcome this, we study an alternative method recently investigated in Mufid et al. (2022) using Satisfiability Modulo Theory (SMT) techniques, which are known to be NP-hard. We propose a concise method that utilizes a pseudo-polynomial time algorithm using max-plus algebra. We evaluate its efficiency against SMT techniques through numerical experiments involving sparse matrix multiplications for enhanced computational speed.
In this work a numerical methodology to solve the steady state Population Balance Equation (PBE) is developed. Three crystallisation mechanisms are included, namely: nucleation, size-independent growth and size-depend...
详细信息
In this work a numerical methodology to solve the steady state Population Balance Equation (PBE) is developed. Three crystallisation mechanisms are included, namely: nucleation, size-independent growth and size-dependent loose agglomeration. The numerical method is based on the discretisation of the crystal size as distributed variable. In order to describe the loose agglomeration, the numerical methodology solves two PBE: one including the nucleation and growth mechanisms and one accounting for the agglomeration process. From the first PBE, liquid phase composition, supersaturation, developed crystal surface and Crystallite Size Distribution (CSD) are obtained. Similarly, the second PBE leads to the Agglomerate Size Distribution (ASD). The study of the size -dependant agglomeration kernel induces an additional numerical difficulty due to the dependency of both PBE and agglomeration kernel on the particle size. An accelerated fixed point algorithm based on the crossed secant method is adapted to overcome the difficulty and accurately solve the agglomeration PBE. The oxalic precipitation of uranium is simulated using this numerical methodology. First, the experimental results of a reference case are compared with the numerical predictions in terms of particle size distribution, mean size, mass fraction and moments. Then, the operating conditions are varied in order to test the algorithm robustness and performances. In all cases, the crossed secant method ensures the size-dependent agglomeration PBE solution and properly predicts the ASD. The developed numerical methodology predicts the mean particle size under the experimental uncertainty in a reasonable computation time and number of iterations.
We propose a method that combines fixed point algorithms with a neural network to optimize jointly discrete and continuous variables in millimeter-wave communication systems, so that the users' rates are allocated...
详细信息
ISBN:
(纸本)9781728157672
We propose a method that combines fixed point algorithms with a neural network to optimize jointly discrete and continuous variables in millimeter-wave communication systems, so that the users' rates are allocated fairly in a well-defined sense. In more detail, the discrete variables include user-access point assignments and the beam configurations, while the continuous variables refer to the power allocation. The beam configuration is predicted from user-related information using a neural network. Given the predicted beam configuration, a fixed point algorithm allocates power and assigns users to access points so that the users achieve the maximum fraction of their interference-free rates. The proposed method predicts the beam configuration in a "one-shot" manner, which significantly reduces the complexity of the beam search procedure. Moreover, even if the predicted beam configurations are not optimal, the fixed point algorithm still provides the optimal power allocation and user-access point assignments for the given beam configuration.
We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a re...
详细信息
We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regularizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixedpoint-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in practical contexts, by dealing with neuroimaging and hemodynamic data.
In this article, we focus on the extensively utilized algorithm for Fast Fourier Transform (FFT) radix-2 DecimationInTime (DIT). It proposes a variable-length FFT processor that can be reconfigured. The processor desi...
详细信息
ISBN:
(数字)9781728145143
ISBN:
(纸本)9781728145136
In this article, we focus on the extensively utilized algorithm for Fast Fourier Transform (FFT) radix-2 DecimationInTime (DIT). It proposes a variable-length FFT processor that can be reconfigured. The processor designed for different FFT / IFFT stages can perform 8, 16 and 32 point FFT / IFFT with different word length scaling modes. Furthermore, in many applications, the processor is suitable for various FFT / IFFT length requirements. Single-path delay feedback (SDF) pipeline architecture is incorporated in order to achieve higher throughput. Cadence NC Launch, RTL Compiler, Simvision Simulator and Altera DE2 FPGA EP2C35F672C6 board are used to test the design in TSMC 45 nm technology. We often worked with 2/3/5 radices and thus make a clear comparison between different radices and the efficiency associated with each of them. This work achieves better specifications for area use and delay. Meanwhile, the occupied resources are approximately same. Moreover, the performance of different FFT length is analyzed.
This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on ...
详细信息
This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity. The recent l(1)-minimization based methods do provide such guarantees but the associated algorithms recover the dictionary one column at a time. In this work, we propose a new formulation that maximizes the l(4)-norm over the orthogonal group, to learn the entire dictionary. We prove that under a random data model, with nearly minimum sample complexity, the global optima of the l(4)-norm are very close to signed permutations of the ground truth. Inspired by this observation, we give a conceptually simple and yet effective algorithm based on "matching, stretching, and projection" (MSP). The algorithm provably converges locally and cost per iteration is merely an SVD. In addition to strong theoretical guarantees, experiments show that the new algorithm is significantly more efficient and effective than existing methods, including KSVD and l(1)-based methods. Preliminary experimental results on mixed real imagery data clearly demonstrate advantages of so learned dictionary over classic PCA bases.
The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended m...
详细信息
The notion of generalized power function in the space of real symmetric matrices is used to introduce a kind of extended matrix-variate beta function. With the aid of this, we define a different versions of extended matrix-variate beta distributions. Some fundamental properties of these distributions are established. We show that using a linear transformation on the extended matrix-variate beta distributions of the first and second kind, we can generalize these distributions. We also show that the distribution of the sum of two independent inverse Riesz matrices introduced by Tounsi and Zine (J Multivar Anal 111:174-182, 2012) can be written in terms of the generalized extended matrix-variate beta function. Finally, using fixedpoint iterative method, we provide a calculable maximum a posteriori (MAP) estimator for the unknown covariance matrix of a multivariate normal distribution based on the class of the extended matrix-variate beta prior distribution. Additionally, we evaluated the Gaussian finite sample performance by calculating such evaluation criteria as Mean Square Error (MSE) and Hilbert-Schmidt distance (DHS). The obtained results confirm the performance of the proposed prior.
It is well known that Kalman Filter is good for a state estimation on a linear system. The criterion is a square error function, which is efficient and sufficient for most systems. However, the square error evaluation...
详细信息
ISBN:
(纸本)9781538663769
It is well known that Kalman Filter is good for a state estimation on a linear system. The criterion is a square error function, which is efficient and sufficient for most systems. However, the square error evaluation function is often not sufficient in the systems under non-Gaussian noise. In recent years, an entropy has been attracting attention as an evaluation function changing to the square error criterion. Beginning with entropy of Shannon, its characteristics are related to higher-order statistics. When the entropy is set as criterion, all moments or all even moments of the state estimation error can be constrained. These characteristics have been utilized for learning system, adaptive filtering, and neuro-control. In this research, we focus on a correntropy, which has expanded Renyi 's entropy more generally, and the correntropy is utilized in order to estimate states of systems. This method uses multi-step ahead predictions, and aims to better state estimation. The method of multi-step ahead predictions is effective for the case that the system has not only statistic process noise but also other disturbances. Previous methods using the correntropy as a criterion are introduced here, and compared with modified method through experimental data.
This paper is pedagogic in nature, meant to provide researchers a single reference for learning how to apply the emerging literature on differential variational inequalities to the study of dynamic traffic assignment ...
详细信息
This paper is pedagogic in nature, meant to provide researchers a single reference for learning how to apply the emerging literature on differential variational inequalities to the study of dynamic traffic assignment problems that are Cournot-like noncooperative games. The paper is presented in a style that makes it accessible to the widest possible audience. In particular, we apply the theory of differential variational inequalities (DVIs) to the dynamic user equilibrium (DUE) problem. We first show that there is a variational inequality whose necessary conditions describe a DUE. We restate the flow conservation constraint associated with each origin-destination pair as a first-order two-point boundary value problem, thereby leading to a DVI representation of DUE;then we employ Pontryagin-type necessary conditions to show that any DVI solution is a DUE. We also show that the DVI formulation leads directly to a fixed-pointalgorithm. We explain the fixed-pointalgorithm by showing the calculations intrinsic to each of its steps when applied to simple examples. (C) 2018 Elsevier Ltd. All rights reserved.
This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on ...
详细信息
This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity. The recent l1-minimization based methods do provide such guarantees but the associated algorithms recover the dictionary one column at a time. In this work, we propose a new formulation that maximizes the l4-norm over the orthogonal group, to learn the entire dictionary. We prove that under a random data model, with nearly minimum sample complexity, the global optima of the l4-norm are very close to signed permutations of the ground truth. Inspired by this observation, we give a conceptually simple and yet effective algorithm based on "matching, stretching, and projection" (MSP). The algorithm provably converges locally and cost per iteration is merely an SVD. In addition to strong theoretical guarantees, experiments show that the new algorithm is significantly more efficient and effective than existing methods, including KSVD and l1-based methods. Preliminary experimental results on mixed real imagery data clearly demonstrate advantages of so learned dictionary over classic PCA bases.
暂无评论