scholarly journals Total variation regularization of multi-material topology optimization

2018 ◽  
Vol 52 (1) ◽  
pp. 275-303 ◽  
Author(s):  
Christian Clason ◽  
Florian Kruse ◽  
Karl Kunisch
Keyword(s):  
Diffusion Coefficient ◽  
Total Variation ◽  
Homogenization Theory ◽  
Analytic Structure ◽  
Semismooth Newton Method ◽  
Total Variation Regularization ◽  
Functions Of Bounded Variation ◽  
Distributed Data ◽  
The One ◽  
Pointwise Constraints

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.

scholarly journals On the Taut String Interpretation and Other Properties of the Rudin–Osher–Fatemi Model in One Dimension

2019 ◽  
Vol 61 (9) ◽  
pp. 1276-1300
Author(s):  
Niels Chr Overgaard
Keyword(s):  
Regularization Parameter ◽  
Total Variation Regularization ◽  
Functions Of Bounded Variation ◽  
Signal Restoration ◽  
Uniqueness Of Solutions ◽  
Taut String ◽  
Fundamental Estimate ◽  
Dimensional Version ◽  
String Algorithm ◽  
The One

Abstract We study the one-dimensional version of the Rudin–Osher–Fatemi (ROF) denoising model and some related TV-minimization problems. A new proof of the equivalence between the ROF model and the so-called taut string algorithm is presented, and a fundamental estimate on the denoised signal in terms of the corrupted signal is derived. Based on duality and the projection theorem in Hilbert space, the proof of the taut string interpretation is strictly elementary with the existence and uniqueness of solutions (in the continuous setting) to both models following as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. The taut string interpretation plays an essential role in the proof of the fundamental estimate. This estimate implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the corrupted signal as the regularization parameter vanishes. It can also be used to prove semi-group properties of the denoising model. Finally, it is indicated how the methods developed can be applied to related problems such as the fused lasso model, isotonic regression and signal restoration with higher-order total variation regularization.

Security Test by using F T M and Data Allocation Strategies on Leakage Detection

2005 ◽  
Vol 4 (2) ◽  
pp. 393-400
Author(s):  
Pallavali Radha ◽  
G. Sireesha
Keyword(s):  
Third Party ◽  
Distributed Data ◽  
Data Allocation ◽  
Security Testing ◽  
Sensitive Data ◽  
Sample Data ◽  
The One ◽  
Security Test ◽  
Data Request ◽  
Allocation Strategies

The data distributors work is to give sensitive data to a set of presumably trusted third party agents.The data i.e., sent to these third parties are available on the unauthorized places like web and or some ones systems, due to data leakage. The distributor must know the way the data was leaked from one or more agents instead of as opposed to having been independently gathered by other means. Our new proposal on data allocation strategies will improve the probability of identifying leakages along with Security attacks typically result from unintended behaviors or invalid inputs.  Due to too many invalid inputs in the real world programs is labor intensive about security testing.The most desirable thing is to automate or partially automate security-testing process. In this paper we represented Predicate/ Transition nets approach for security tests automated generationby using formal threat models to detect the agents using allocation strategies without modifying the original data.The guilty agent is the one who leaks the distributed data. To detect guilty agents more effectively the idea is to distribute the data intelligently to agents based on sample data request and explicit data request. The fake object implementation algorithms will improve the distributor chance of detecting guilty agents.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals An Improved Particle Swarm Optimization Based on Total Variation Regularization and Projection Constraint with Applications in Ground-Penetrating Radar Inversion: A Model Simulation Study

2021 ◽  
Vol 13 (13) ◽  
pp. 2514
Author(s):  
Qianwei Dai ◽  
Hao Zhang ◽  
Bin Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Total Variation ◽  
Ground Penetrating Radar ◽  
Particle Swarm ◽  
Premature Convergence ◽  
Total Variation Regularization ◽  
Interface Model ◽  
Swarm Optimization ◽  
Tv Regularization ◽  
Ground Penetrating

The chaos oscillation particle swarm optimization (COPSO) algorithm is prone to binge trapped in the local optima when dealing with certain complex models in ground-penetrating radar (GPR) data inversion, because it inherently suffers from premature convergence, high computational costs, and extremely slow convergence times, especially in the middle and later periods of iterative inversion. Considering that the bilateral connections between different particle positions can improve both the algorithmic searching efficiency and the convergence performance, we first develop a fast single-trace-based approach to construct an initial model for 2-D PSO inversion and then propose a TV-regularization-based improved PSO (TVIPSO) algorithm that employs total variation (TV) regularization as a constraint technique to adaptively update the positions of particles. B by adding the new velocity variations and optimal step size matrices, the search range of the random particles in the solution space can be significantly reduced, meaning blindness in the search process can be avoided. By introducing constraint-oriented regularization to allow the optimization search to move out of the inaccurate region, the premature convergence and blurring problems can be mitigated to further guarantee the inversion accuracy and efficiency. We report on three inversion experiments involving multilayered, fluctuated terrain models and a typical complicated inner-interface model to demonstrate the performance of the proposed algorithm. The results of the fluctuated terrain model show that compared with the COPSO algorithm, the fitness error (MAE) of the TVIPSO algorithm is reduced from 2.3715 to 1.0921, while for the complicated inner-interface model the fitness error (MARE) of the TVIPSO algorithm is reduced from 1.9539 to 1.5674.

scholarly journals Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 506
Author(s):  
Sho Nakade ◽  
Kazuki Kanki ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Constant ◽  
Mean Square Displacement ◽  
Second Law Of Thermodynamics ◽  
Molecular Chain ◽  
Chain Model ◽  
Phase Mixing ◽  
One Dimensional ◽  
The One ◽  
Negative Diffusion

An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

A new nonlinear reconstruction method based on total variation regularization of neutron penumbral imaging

2011 ◽  
Vol 82 (9) ◽  
pp. 093504 ◽  
Author(s):  
Weixin Qian ◽  
Shuangxi Qi ◽  
Wanli Wang ◽  
Jinming Cheng ◽  
Dongbing Liu
Keyword(s):  
Total Variation ◽  
Total Variation Regularization ◽  
Reconstruction Method ◽  
Penumbral Imaging
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