scholarly journals RELATIVELY COHERENT SETS AS A HIERARCHICAL PARTITION METHOD

2013 ◽  
Vol 23 (07) ◽  
pp. 1330026 ◽  
Author(s):  
TIAN MA ◽  
ERIK M. BOLLT
Keyword(s):  
Computational Complexity ◽  
Objective Function ◽  
Oil Spill ◽  
Empirical Data ◽  
Finite Time ◽  
Transfer Operator ◽  
Operator Method ◽  
Hierarchical Partition ◽  
Partition Method ◽  
Double Gyre

Finite time coherent sets [Froyland et al., 2010] have recently been defined by a measure-based objective function describing the degree that sets hold together, along with a Frobenius–Perron transfer operator method to produce optimally coherent sets. Here, we present an extension to generalize the concept to hierarchically define relatively coherent sets based on adjusting the finite time coherent sets to use relative measures restricted to sets which are developed iteratively and hierarchically in a tree of partitions. Several examples help clarify the meaning and expectation of the techniques, as they are the nonautonomous double gyre, the standard map, an idealized stratospheric flow, and empirical data from the Mexico Gulf during the 2010 oil spill. Also for the sake of analysis of computational complexity, we include an Appendix concerning the computational complexity of developing the Ulam–Galerkin matrix estimates of the Frobenius–Perron operator centrally used here.

scholarly journals Marine Oil Slick Detection Based on Multi-Polarimetric Features Matching Method Using Polarimetric Synthetic Aperture Radar Data

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5176
Author(s):  
Guannan Li ◽  
Ying Li ◽  
Bingxin Liu ◽  
Peng Wu ◽  
Chen Chen
Keyword(s):  
Computational Complexity ◽  
Synthetic Aperture Radar ◽  
Oil Spill ◽  
Similarity Measures ◽  
Synthetic Aperture ◽  
Matching Method ◽  
Polarimetric Synthetic Aperture Radar ◽  
Spectral Similarity ◽  
Oil Spill Detection ◽  
Aperture Radar

Polarimetric synthetic aperture radar is an important tool in the effective detection of marine oil spills. In this study, two cases of Radarsat-2 Fine mode quad-polarimetric synthetic aperture radar datasets are exploited to detect a well-known oil seep area that collected over the Gulf of Mexico using the same research area, sensor, and time. A novel oil spill detection scheme based on a multi-polarimetric features model matching method using spectral pan-similarity measure (SPM) is proposed. A multi-polarimetric features curve is generated based on optimal polarimetric features selected using Jeffreys–Matusita distance considering its ability to discriminate between thick and thin oil slicks and seawater. The SPM is used to search for and match homogeneous unlabeled pixels and assign them to a class with the highest similarity to their spectral vector size, spectral curve shape, and spectral information content. The superiority of the SPM for oil spill detection compared to traditional spectral similarity measures is demonstrated for the first time based on accuracy assessments and computational complexity analysis by comparing with four traditional spectral similarity measures, random forest (RF), support vector machine (SVM), and decision tree (DT). Experiment results indicate that the proposed method has better oil spill detection capability, with a higher average accuracy and kappa coefficient (1.5–7.9% and 1–25% higher, respectively) than the four traditional spectral similarity measures under the same computational complexity operations. Furthermore, in most cases, the proposed method produces valuable and acceptable results that are better than the RF, SVM, and DT in terms of accuracy and computational complexity.

The Exergy Efficiency and Output Acoustic Power Performance Optimization of the Thermoacoustic Engine Micro-Cycle

2013 ◽  
Vol 712-715 ◽  
pp. 1609-1613 ◽  
Author(s):  
Jie Lin ◽  
Feng Wu ◽  
Jin Hua Fei ◽  
Tuo Wang
Keyword(s):  
Heat Resistance ◽  
Objective Function ◽  
Performance Optimization ◽  
Finite Time ◽  
Acoustic Power ◽  
Exergy Efficiency ◽  
Power Performance ◽  
Thermoacoustic Engine ◽  
The Relationship ◽  
High Output

The relationship between exergy efficiency and output acoustic power of the thermoacoustic engine microcycle model which only was accounted for the heat resistance had been analyzed using finite time thermodynamics.And through the new objective function,we obtain the optimization that not only obtain high exergy efficiency but also high output acoustic power at the same time.Optimized imperfection that we only pursue the high exergy efficiency, we obtain low output acoustic power and vice versa.We approve this conclusion by numerical calculation.The results that we obtained will be useful to optimal the design of a actual thermoacoustic engine.

scholarly journals Markov Chain Realization of Multiple Detection Joint Integrated Probabilistic Data Association

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 112 ◽  
Author(s):  
Yuan Huang ◽  
Taek Song ◽  
Dae Cheagal
Keyword(s):  
Markov Chain ◽  
Computational Complexity ◽  
Data Association ◽  
Computational Cost ◽  
Chain Process ◽  
Random Data ◽  
Probabilistic Data ◽  
Probabilistic Data Association ◽  
Multiple Detection ◽  
Partition Method

In multiple detection target tracking environments, PDA-based algorithms such as multiple detection joint integrated probabilistic data association (MD-JIPDA) utilize the measurement partition method to generate measurement cells. Thus, one-to-many track-to-measurements associations can be realized. However, in this structure, the number of joint data association events grows exponentially with the number of measurement cells and the number of tracks. MD-JIPDA is plagued by large increases in computational complexity when targets are closely spaced or move cross each other, especially in multiple detection scenarios. Here, the multiple detection Markov chain joint integrated probabilistic data association (MD-MC-JIPDA) is proposed, in which a Markov chain is used to generate random data association sequences. These sequences are substitutes for the association events. The Markov chain process significantly reduces the computational cost since only a few association sequences are generated while keeping preferable tracking performance. Finally, MD-MC-JIPDA is experimentally validated to demonstrate its effectiveness compared with some of the existing multiple detection data association algorithms.

MEASURABLE DYNAMICS ANALYSIS OF TRANSPORT IN THE GULF OF MEXICO DURING THE OIL SPILL

2012 ◽  
Vol 22 (03) ◽  
pp. 1230012 ◽  
Author(s):  
ERIK M. BOLLT ◽  
AARON LUTTMAN ◽  
SEAN KRAMER ◽  
RANIL BASNAYAKE
Keyword(s):  
Gulf Of Mexico ◽  
Oil Spill ◽  
Marine Ecosystem ◽  
Transfer Operator ◽  
Flow Dynamics ◽  
Invariant Sets ◽  
Oil Well ◽  
Finite Time Lyapunov Exponents ◽  
Oil Flow ◽  
Oil Rig

On April 20, 2010, an oil well cap explosion below the Deepwater Horizon, an off-shore oil rig in the Gulf of Mexico, started the worst human-caused submarine oil spill ever. Though an historic tragedy for the marine ecosystem, the unprecedented monitoring of the spill in real time by satellites and increased modeling of the natural oceanic flows has provided a wealth of data, allowing analysis of the flow dynamics governing the spread of the oil. In this work, we present the results of two computational analyses describing the mixing, mass transport, and flow dynamics of the oil dispersion in the Gulf of Mexico over the first 100 days of the spill. Transfer operator methods are used to determine the spatial partitioning of regions of homogeneous dynamics into almost-invariant sets, and Finite Time Lyapunov Exponents are used to compute pseudo-barriers to the mixing of the oil between these regions. The two methods give complementary results, generating a comprehensive description of the oil flow dynamics over time.

scholarly journals An effective method for determining consensus in large collectives

2021 ◽  
pp. 62-62
Author(s):  
Dai Dang ◽  
Thanh Nguyen ◽  
Dosam Hwang
Keyword(s):  
Information Technology ◽  
Computational Complexity ◽  
Essential Role ◽  
Rapid Development ◽  
Consensus Method ◽  
Distributed Knowledge ◽  
Partition Method ◽  
Small Parts ◽  
Vertical Partition

Nowadays, using the consensus of collectives for solving problems plays an essential role in our lives. The rapid development of information technology has facilitated the collection of distributed knowledge from autonomous sources to find solutions to problems. Consequently, the size of collectives has increased rapidly. Determining consensus for a large collective is very time-consuming and expensive. Thus, this study proposes a vertical partition method (VPM) to find consensus in large collectives. In the VPM, the primary collective is first vertically partitioned into small parts. Then, a consensus-based algorithm is used to determine the consensus for each smaller part. Finally, the consensus of the collective is determined based on the consensuses of the smaller parts. The study demonstrates, both theoretically and experimentally, that the computational complexity of the VPM is lower than 57.1% that of the basic consensus method. This ratio reduces quickly if the number of smaller parts reduces.

Surface and deep ocean connectivity inferred from robust extraction of coherent sets in ocean flow using models and sparse, scattered, and incomplete float data with transfer operator and dynamic Laplacian methods.

2021 ◽  
Author(s):  
Gary Froyland ◽  
Ryan Abernathey ◽  
Michael Denes ◽  
Shane Keating
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Transfer Operator ◽  
Deep Ocean ◽  
Difficult Problem ◽  
Lagrangian Coherent Structures ◽  
Diffusion Limit ◽  
Small Diffusion ◽  
Transport And Mixing ◽  
Atmospheric Vortices

<p>Transport and mixing properties of the ocean's circulation is crucial to dynamical analyses, and often have to be carried out with limited observed information. Finite-time coherent sets are regions of the ocean that minimally mix (in the presence of small diffusion) with the rest of the ocean domain over the finite period of time considered. In the purely advective setting (in the zero diffusion limit) this is equivalent to identifying regions whose boundary interfaces remain small throughout their finite-time evolution. Finite-time coherent sets thus provide a skeleton of distinct regions around which more turbulent flow occurs. Well known manifestations of finite-time coherent sets in geophysical systems include rotational objects like ocean eddies, ocean gyres, and atmospheric vortices. In real-world settings, often observational data is scattered and sparse, which makes the difficult problem of coherent set identification and tracking challenging. I will describe mesh-based numerical methods [3] to efficiently approximate the recently defined dynamic Laplace operator [1,2], and rapidly and reliably extract finite-time coherent sets from models or scattered, possibly sparse, and possibly incomplete observed data. From these results we can infer new chemical and physical ocean connectivities at global and intra-basin scales (at the surface and at depth), track series of eddies, and determine new oceanic barriers.</p><p>[1] G. Froyland. Dynamic isoperimetry and the geometry of Lagrangian coherent structures. <em>Nonlinearity</em>, 28:3587-3622, 2015</p><p>[2] G. Froyland and E. Kwok. A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds. <em>Journal of Nonlinear Science</em>, 30:1889–1971, 2020.</p><p>[3] Gary Froyland and Oliver Junge. Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories. <em>SIAM J. Applied Dynamical Systems</em>, 17:1891–1924, 2018.</p>

ON COMPUTATIONAL COMPLEXITY OF HIERARCHICAL OPTIMIZATION

2002 ◽  
Vol 13 (05) ◽  
pp. 667-670
Author(s):  
WEIJIA JIA ◽  
ZHIBIN SUN
Keyword(s):  
Nash Equilibrium ◽  
Computational Complexity ◽  
Objective Function ◽  
Optimization Problem ◽  
Linear Constraints ◽  
The Other ◽  
Hierarchical Optimization ◽  
Linear Objective Function ◽  
Decision Variables

In this work, the computational complexity of a hierarchic optimization problem involving in several players is studied. Each player is assigned with a linear objective function. The set of variables is partitioned such that each subset corresponds to one player as its decision variables. All the players jointly make a decision on the values of these variables such that a set of linear constraints should be satisfied. One special player, called the leader, makes decision on its decision variables before of all the other players. The rest, after learnt of the decision of the leader, make their choices so that their decisions form a Nash Equilibrium for them, breaking tie by maximizing the objective function of player. We show that the exact complexity of the problem is FPNP-complete.

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