scholarly journals The Dantzig selector: recovery of signal via ℓ 1 − αℓ 2 minimization

2021 ◽  
Vol 38 (1) ◽  
pp. 015006
Author(s):  
Huanmin Ge ◽  
Peng Li
Keyword(s):  
Numerical Experiments ◽  
Restricted Isometry Property ◽  
Signal Recovery ◽  
Effective Algorithm ◽  
Dantzig Selector ◽  
Error Vector ◽  
Small Constant ◽  
Proposed Model ◽  
Better Than

Abstract In the paper, we proposed the Dantzig selector based on the ℓ 1 − αℓ 2 (0 < α ⩽ 1) minimization for the signal recovery. In the Dantzig selector, the constraint ‖ A ⊤ ( b − Ax )‖∞ ⩽ η for some small constant η > 0 means the columns of A has very weakly correlated with the error vector e = Ax − b . First, recovery guarantees based on the restricted isometry property are established for signals. Next, we propose the effective algorithm to solve the proposed Dantzig selector. Last, we illustrate the proposed model and algorithm by extensive numerical experiments for the recovery of signals in the cases of Gaussian, impulsive and uniform noises. And the performance of the proposed Dantzig selector is better than that of the existing methods.

An Unequal-Sized Unidirectional Loop Layout Design Problem Considering Empty Vehicle Trip

2010 ◽  
Vol 37-38 ◽  
pp. 116-121
Author(s):  
Yu Lan Li ◽  
Bo Li ◽  
Su Jun Luo
Keyword(s):  
Material Handling ◽  
Design Principle ◽  
Facility Layout ◽  
Original Model ◽  
Layout Problem ◽  
Proposed Model ◽  
Loop Layout ◽  
Material Handling Costs ◽  
Loop Layout Problem ◽  
Better Than

In the facility layout decisions, the previous general design principle is to minimize material handling costs, and the objective of these old models only considers the costs of loaded trip, without regard to empty vehicle trip costs, which do not meet the actual demand. In this paper, the unequal-sized unidirectional loop layout problem is analyzed, and the model of facility layout is improved. The objective of the new model is to minimize the total loaded and empty vehicle trip costs. To solve this model, a heuristic algorithm based on partheno-genetic algorithms is designed. Finally, an unequal-sized unidirectional loop layout problem including 12 devices is simulated. Comparison shows that the result obtained using the proposed model is 20.4% better than that obtained using the original model.

scholarly journals The coalescent process in models with selection, recombination and geographic subdivision

1991 ◽  
Vol 57 (1) ◽  
pp. 83-91 ◽  
Author(s):  
Norman Kaplan ◽  
Richard R. Hudson ◽  
Masaru Iizuka
Keyword(s):  
Genetic Variation ◽  
Population Genetic ◽  
Genetic Model ◽  
Sequence Data ◽  
Balancing Selection ◽  
Similar Model ◽  
Proposed Model ◽  
Coalescent Approach ◽  
Neutral Mutations ◽  
Better Than

SummaryA population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus of Drosophila melanogaster are found to fit the proposed model slightly better than a similar model without subdivision.

scholarly journals Both Freud and Hoffman are Right: Anxious-Aggressive and Empathic Dimensions of Guilt

2008 ◽  
Vol 11 (1) ◽  
pp. 159-171 ◽  
Author(s):  
Itziar Etxebarria ◽  
Pedro Apodaca
Keyword(s):  
Young Adults ◽  
Subjective Experience ◽  
Negative Emotions ◽  
The Other ◽  
Point Scale ◽  
Nested Models ◽  
Proposed Model ◽  
Better Than

The purpose of the study was to confirm a model which proposed two basic dimensions in the subjective experience of guilt, one anxious-aggressive and the other empathic, as well as another dimension associated but not intrinsic to it, namely, the associated negative emotions dimension. Participants were 360 adolescents, young adults and adults of both sexes. They were asked to relate one of the situations that most frequently caused them to experience feelings of guilt and to specify its intensity and that of 9 other emotions that they may have experienced, to a greater or lesser extent, at the same time on a 7-point scale. The proposed model was shown to adequately fit the data and to be better than other alternative nested models. This result supports the views of both Freud and Hoffman regarding the nature of guilt, contradictory only at a first glance.

scholarly journals Integrated Harvest and Farm-to-Door Distribution Scheduling with Postharvest Quality Deterioration for Vegetable Online Retailing

Agronomy ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 724
Author(s):  
Yiping Jiang ◽  
Bei Bian ◽  
Lingling Li
Keyword(s):  
Genetic Algorithm ◽  
Numerical Experiments ◽  
Programming Model ◽  
Time Windows ◽  
Sensitivity Analyses ◽  
Postharvest Quality ◽  
Online Retailing ◽  
Quality Deterioration ◽  
Distribution Scheduling ◽  
Proposed Model

With the rise of vegetable online retailing in recent years, the fulfillment of vegetable online orders has been receiving more and more attention. This paper addresses an integrated optimization model for harvest and farm-to-door distribution scheduling for vegetable online retailing. Firstly, we capture the perishable property of vegetables, and model it as a quadratic postharvest quality deterioration function. Then, we incorporate the postharvest quality deterioration function into the integrated harvest and farm-to-door distribution scheduling and formulate it as a quadratic vehicle routing programming model with time windows. Next, we propose a genetic algorithm with adaptive operators (GAAO) to solve the model. Finally, we carry out numerical experiments to verify the performance of the proposed model and algorithm, and report the results of numerical experiments and sensitivity analyses.

scholarly journals Order-Dependent Event Models for Agent Interactions

2020 ◽  
Author(s):  
Debarun Bhattacharjya ◽  
Tian Gao ◽  
Dharmashankar Subramanian
Keyword(s):  
Arrival Rate ◽  
Event Data ◽  
Political Event ◽  
Instantaneous Rate ◽  
Agent Interactions ◽  
Occurrence Data ◽  
Proposed Model ◽  
Event Models ◽  
Better Than ◽  
Event Occurrence

In multivariate event data, the instantaneous rate of an event's occurrence may be sensitive to the temporal sequence in which other influencing events have occurred in the history. For example, an agent’s actions are typically driven by preceding actions taken by the agent as well as those of other relevant agents in some order. We introduce a novel statistical/causal model for capturing such an order-sensitive historical dependence, where an event’s arrival rate is determined by the order in which its underlying causal events have occurred in the recent past. We propose an algorithm to discover these causal events and learn the most influential orders using time-stamped event occurrence data. We show that the proposed model fits various event datasets involving single as well as multiple agents better than baseline models. We also illustrate potentially useful insights from our proposed model for an analyst during the discovery process through analysis on a real-world political event dataset.

scholarly journals Improvements on Learning Kernel Extended Dictionary for Face Recognition

2020 ◽  
Vol 34 (4) ◽  
pp. 387-394
Author(s):  
Soodabeh Amanzadeh ◽  
Yahya Forghani ◽  
Javad Mahdavi Chabok
Keyword(s):  
Sparse Representation ◽  
Face Image ◽  
Collaborative Representation ◽  
Training Images ◽  
Input Face ◽  
Proposed Model ◽  
Eigen Values ◽  
New Type ◽  
The Mean ◽  
Better Than

Kernel extended dictionary learning model (KED) is a new type of Sparse Representation for Classification (SRC), which represents the input face image as a linear combination of dictionary set and extended dictionary set to determine the input face image class label. Extended dictionary is created based on the differences between the occluded images and non-occluded training images. There are four defaults to make about KED: (1) Similar weights are assigned to the principle components of occlusion variations in KED model, while the principle components of the occlusion variations have different weights, which are proportional to the principle components Eigen-values. (2) Reconstruction of an occluded image is not possible by combining only non-occluded images and the principle components (or the directions) of occlusion variations, but it requires the mean of occlusion variations. (3) The importance and capability of main dictionary and extended dictionary in reconstructing the input face image is not the same, necessarily. (4) KED Runtime is high. To address these problems or challenges, a novel mathematical model is proposed in this paper. In the proposed model, different weights are assigned to the principle components of occlusion variations; different weights are assigned to the main dictionary and extended dictionary; an occluded image is reconstructed by non-occluded images and the principle components of occlusion variations, and also the mean of occlusion variations; and collaborative representation is used instead of sparse representation to enhance the runtime. Experimental results on CAS-PEAL subsets showed that the runtime and accuracy of the proposed model is about 1% better than that of KED.

A Novel Neural Model with Lateral Interaction for Learning Tasks

2020 ◽  
pp. 1-24
Author(s):  
Dequan Jin ◽  
Ziyan Qin ◽  
Murong Yang ◽  
Penghe Chen
Keyword(s):  
Numerical Experiments ◽  
State Of The Art ◽  
Neural Model ◽  
Parameter Tuning ◽  
Small Sample ◽  
Lateral Interaction ◽  
Learning Tasks ◽  
Proposed Model ◽  
High Level ◽  
Elementary Field

We propose a novel neural model with lateral interaction for learning tasks. The model consists of two functional fields: an elementary field to extract features and a high-level field to store and recognize patterns. Each field is composed of some neurons with lateral interaction, and the neurons in different fields are connected by the rules of synaptic plasticity. The model is established on the current research of cognition and neuroscience, making it more transparent and biologically explainable. Our proposed model is applied to data classification and clustering. The corresponding algorithms share similar processes without requiring any parameter tuning and optimization processes. Numerical experiments validate that the proposed model is feasible in different learning tasks and superior to some state-of-the-art methods, especially in small sample learning, one-shot learning, and clustering.

scholarly journals Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 708 ◽  
Author(s):  
Suthep Suantai ◽  
Suparat Kesornprom ◽  
Prasit Cholamjiak
Keyword(s):  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Signal Recovery ◽  
Proximal Algorithms ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Lipschitz Constants ◽  
Theoretical Results

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

scholarly journals On the Multiwavelets Galerkin Solution of the Volterra–Fredholm Integral Equations by an Efficient Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
H. Bin Jebreen
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Fredholm Operators ◽  
Linear Type ◽  
Galerkin Solution ◽  
Better Than

We develop the multiwavelet Galerkin method to solve the Volterra–Fredholm integral equations. To this end, we represent the Volterra and Fredholm operators in multiwavelet bases. Then, we reduce the problem to a linear or nonlinear system of algebraic equations. The interesting results arise in the linear type where thresholding is employed to decrease the nonzero entries of the coefficient matrix, and thus, this leads to reduction in computational efforts. The convergence analysis is investigated, and numerical experiments guarantee it. To show the applicability of the method, we compare it with other methods and it can be shown that our results are better than others.

scholarly journals A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 271 ◽  
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Mathematical Modeling ◽  
Banach Space ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Real Life ◽  
System Of Nonlinear Equations ◽  
Life Problems ◽  
Lipschitz Constants ◽  
Better Than

Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes.

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