scholarly journals Dual-density-based reweighted $$\ell _{1}$$-algorithms for a class of $$\ell _{0}$$-minimization problems

2021 ◽  
Author(s):  
Jialiang Xu ◽  
Yun-Bin Zhao
Keyword(s):  
Statistical Learning ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Convex Relaxations ◽  
Science And Engineering ◽  
Strict Complementarity ◽  
Minimization Problems ◽  
Wide Range ◽  
Made In

AbstractThe optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted $$\ell _{1}$$ ℓ 1 -algorithms for a class of $$\ell _{0}$$ ℓ 0 -minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying $$\ell _{0}$$ ℓ 0 -minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying $$\ell _{0}$$ ℓ 0 -minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted $$\ell _1$$ ℓ 1 -algorithms has also been made in this paper.

Anticipatory Optimization of Traffic Control

2000 ◽  
Vol 1725 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Henk J. van Zuylen ◽  
Henk Taale
Keyword(s):  
Traffic Control ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Simulation Studies ◽  
Traffic Flows ◽  
System Optimum ◽  
Time Model ◽  
Traffic Conditions ◽  
Made In ◽  
Small Disturbances

Traffic control and travelers’ behavior are two mutually influential processes with different objectives. Decisions made in traffic control influence travelers’ possibilities in choosing their preferred mode, route, and time of departure; and the choices made by travelers influence the optimization possibilities for traffic control. This research presents the results of simulation studies and a mathematical analysis of this bilevel optimization problem. Under certain conditions, multiple stable situations are possible, but some of these situations are sensitive to small disturbances by which the system moves away from the original equilibrium state. There appears to be a nonlinear relationship between system parameters and the character and location of the equilibrium situations. The details of the travel time model appear to have a large influence. If road authorities want to optimize traffic control, they have to anticipate the reaction of travelers. This makes the optimization process much more complicated. Iterative optimization, where traffic control is adjusted as soon as traffic conditions change, generally does not lead to a system optimum. Methods are therefore necessary that allow for the optimization of traffic control while taking into account that traffic flows will change as a result of traffic control.

A Comprehensive Review on C-3 Functionalization of β-Lactams

2019 ◽  
Vol 16 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Reshma Nagpal ◽  
Jitender Bhalla ◽  
Shamsher S. Bari
Keyword(s):  
Scientific Community ◽  
Organometallic Reagent ◽  
Reaction Conditions ◽  
Biological Potential ◽  
Wide Range ◽  
Economic Strategies ◽  
Synthetic Utility ◽  
Recent Advancement ◽  
Equivalent Method ◽  
Made In

Background:A lot of advancement has been made in the area of β-lactams in recent times. Most of the research is targeted towards the synthesis of novel β-lactams, their functionalization and exploring their biological potential. The C-3 functionalization of β-lactams has continued to attract considerable interest of the scientific community due to their utility as versatile intermediates in organic synthesis and their therapeutic applications. This has led to the significant increase in efforts towards developing efficient and economic strategies for C-3 functionalized β-lactams.Objective:The present review aims to highlight recent advancement made in C-3 functionalization of β-lactams.Conclusion:To summarize, functionalization of β-lactams at C-3 is an essential aspect of β-lactam chemistry in order to improve/modify its synthetic utility as well as biological potential. The C-3 carbocation equivalent method has emerged as an important and convenient strategy for C-3 functionalization of β-lactam heterocycles which provides a wide range of β-lactams viz. 3-alkylated β-lactams, 3-aryl/heteroarylated β-lactams, 3- alkoxylated β-lactams. On the other hand, base mediated functionalization of β-lactams via carbanion intermediate is another useful approach but their scope is limited by the requirement of stringent reaction conditions. In addition to this, organometallic reagent mediated α-alkylation of 3-halo/3-keto-β-lactams also emerged as interesting methods for the synthesis of functionalized β-lactams having good yields and diastereoselectivities.

Qualitative simulation and related approaches for the analysis of dynamic systems

2004 ◽  
Vol 19 (2) ◽  
pp. 93-132 ◽  
Author(s):  
HIDDE DE JONG
Keyword(s):  
Qualitative Analysis ◽  
Dynamic Systems ◽  
Quantitative Information ◽  
Simulation Methods ◽  
Science And Engineering ◽  
Computational Framework ◽  
Combinatorial Explosion ◽  
Qualitative Simulation ◽  
Qualitative Phase ◽  
Made In

Methods for qualitative simulation allow predictions on the dynamics of a system to be made in the absence of quantitative information, by inferring the range of possible qualitative behaviors compatible with the structure of the system. This article reviews QSIM and other qualitative simulation methods. It discusses two problems that have seriously compromised the application of these methods to realistic problems in science and engineering: the occurrence of spurious behavior predictions and the combinatorial explosion of the number of behavior predictions. In response to these problems, related approaches for the qualitative analysis of dynamic systems have emerged: qualitative phase-space analysis and semi-quantitative simulation. The article argues for a synthesis of these approaches in order to obtain a computational framework for the qualitative analysis of dynamic systems. This should provide a solid basis for further upscaling and for the development of model-based reasoning applications of a wider scope.

scholarly journals Multiplexed Genetic Analysis Using an Expanded Genetic Alphabet

2004 ◽  
Vol 50 (11) ◽  
pp. 2019-2027 ◽  
Author(s):  
Scott C Johnson ◽  
David J Marshall ◽  
Gerda Harms ◽  
Christie M Miller ◽  
Christopher B Sherrill ◽  
...  
Keyword(s):  
Newborn Screening ◽  
Cftr Gene ◽  
Transmembrane Conductance Regulator ◽  
Transmembrane Conductance ◽  
Genetic Tests ◽  
Wide Range ◽  
Additional Base ◽  
A Prospective Study ◽  
Cystic Fibrosis Transmembrane ◽  
Made In

Abstract Background: All states require some kind of testing for newborns, but the policies are far from standardized. In some states, newborn screening may include genetic tests for a wide range of targets, but the costs and complexities of the newer genetic tests inhibit expansion of newborn screening. We describe the development and technical evaluation of a multiplex platform that may foster increased newborn genetic screening. Methods: MultiCode® PLx involves three major steps: PCR, target-specific extension, and liquid chip decoding. Each step is performed in the same reaction vessel, and the test is completed in ∼3 h. For site-specific labeling and room-temperature decoding, we use an additional base pair constructed from isoguanosine and isocytidine. We used the method to test for mutations within the cystic fibrosis transmembrane conductance regulator (CFTR) gene. The developed test was performed manually and by automated liquid handling. Initially, 225 samples with a range of genotypes were tested retrospectively with the method. A prospective study used samples from >400 newborns. Results: In the retrospective study, 99.1% of samples were correctly genotyped with no incorrect calls made. In the perspective study, 95% of the samples were correctly genotyped for all targets, and there were no incorrect calls. Conclusions: The unique genetic multiplexing platform was successfully able to test for 31 targets within the CFTR gene and provides accurate genotype assignments in a clinical setting.

scholarly journals Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Idris Kharroubi ◽  
Thomas Lim ◽  
Xavier Warin
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Learning Approach ◽  
The Neural Network ◽  
Machine Learning Approach ◽  
Mesh Grid

AbstractWe study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

scholarly journals A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues

2021 ◽  
Author(s):  
Sven-Erik Ekström ◽  
Paris Vassalos
Keyword(s):  
Distribution Function ◽  
Asymptotic Distribution ◽  
Numerical Experiments ◽  
Toeplitz Matrices ◽  
Future Research ◽  
Research Directions ◽  
Numerical Examples ◽  
Working Hypothesis ◽  
Wide Range ◽  
Future Research Directions

AbstractIt is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$ f , appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$ f is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$ f . The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$ f is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$ f . Future research directions are outlined at the end of the paper.

scholarly journals Dust Explosion Prevention and Mitigation, Status and Developments in Basic Knowledge and in Practical Application

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Rolf K. Eckhoff
Keyword(s):  
Process Design ◽  
Basic Knowledge ◽  
Industrial Plant ◽  
Practical Application ◽  
Process Industries ◽  
Wide Range ◽  
Firm Knowledge ◽  
Systematic Education ◽  
Training Of Personnel ◽  
Made In

Right from the early days of the process industries, continuous efforts have been made to develop and improve measures for prevention and mitigation of dust explosions in these industries. Nevertheless this hazard continues to threaten industries that manufacture, use and/or handle powders and dusts of a wide range of combustible materials. To improve methods for predicting explosion development in real industrial plant has been one major challenge. Hence, during the last years comprehensive numerical simulation codes, for addressing this problem, have been developed. Progress has also been made in other areas, for example, ignition source prevention. The importance of adopting inherently safer process design, by building on firm knowledge in powder science and technology, and of systematic education/training of personnel, is also emphasized.

Experimental Investigations on Aluminium Ultrasonic Welding Parameters

2014 ◽  
Vol 657 ◽  
pp. 306-310
Author(s):  
Lăcrămioara Apetrei ◽  
Vasile Rață ◽  
Ruxandra Rață ◽  
Elena Raluca Bulai
Keyword(s):  
Microstructural Analysis ◽  
Base Material ◽  
Welding Process ◽  
Ultrasonic Welding ◽  
Experimental Investigations ◽  
Welding Parameters ◽  
Material Structure ◽  
Welding Temperature ◽  
Wide Range ◽  
Made In

Research evolution timely tendencies, in the nonconventional technologies field, are: manufacture conditions optimization and complex equipments design. The increasing of ultrasonic machining use, in various technologies is due to the expanding need of a wide range materials and high quality manufacture standards in many activity fields. This paper present a experimental study made in order to analyze the welded zone material structure and welding quality. The effects of aluminium ultrasonic welding parameters such as relative energy, machining time, amplitude and working force were compared through traction tests values and microstructural analysis. Microhardness tests were, also, made in five different points, two in the base material and three in the welded zone, on each welded aluminium sample. The aluminum welding experiments were made at the National Research and Development Institute for Welding and Material Testing (ISIM) Timişoara. The ultrasonic welding temperature is lower than the aluminium melting temperature, that's so our experiments reveal that the aluminium ultrasonic welding process doesn't determine the appearance of moulding structure. In the joint we have only crystalline grains deformation, phase transformation and aluminium diffusion.

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