scholarly journals New variational and multisymplectic formulations of the Euler–Poincaré equation on the Virasoro–Bott group using the inverse map

2018 ◽  
Vol 474 (2213) ◽  
pp. 20180052 ◽  
Author(s):  
Darryl D. Holm ◽  
Tomasz M. Tyranowski
Keyword(s):  
Variational Principle ◽  
Momentum Map ◽  
Soliton Equations ◽  
Special Cases ◽  
De Vries ◽  
New Type ◽  
Conclusion Section ◽  
Future Work ◽  
Nonlinearity Dispersion

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler–Poincaré equations defined on the Virasoro–Bott group, by using the inverse map (also called ‘back-to-labels’ map). This family contains as special cases the well-known Korteweg–de Vries, Camassa–Holm and Hunter–Saxton soliton equations. In the conclusion section, we sketch opportunities for future work that would apply the new Clebsch momentum map with 2-cocycles derived here to investigate a new type of interplay among nonlinearity, dispersion and noise.

New Type of Soliton Equations

2007 ◽  
Vol 76 (2) ◽  
pp. 024005 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Ryogo Hirota
Keyword(s):  
Soliton Equations ◽  
New Type

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

2020 ◽  
Vol 34 (25) ◽  
pp. 2050226 ◽  
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He Li ◽  
Xue-Hui Zhao ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Atmospheric Science ◽  
Backlund Transformation ◽  
Atmospheric Flow ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Nonlinearity Dispersion

For a variable-coefficient Korteweg–de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Bäcklund transformation, non-isospectral Ablowitz–Kaup–Newell–Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.

Best Harmony, Unified RPCL and Automated Model Selection for Unsupervised and Supervised Learning on Gaussian Mixtures, Three-Layer Nets and ME-RBF-SVM Models

2001 ◽  
Vol 11 (01) ◽  
pp. 43-69 ◽  
Author(s):  
Lei Xu
Keyword(s):  
Model Selection ◽  
Supervised Learning ◽  
Kernel Regression ◽  
Gaussian Mixture ◽  
Parameter Learning ◽  
Special Cases ◽  
Regularization Techniques ◽  
New Type ◽  
New Criterion ◽  
Nonparametric Statistical

After introducing the fundamentals of BYY system and harmony learning, which has been developed in past several years as a unified statistical framework for parameter learning, regularization and model selection, we systematically discuss this BYY harmony learning on systems with discrete inner-representations. First, we shown that one special case leads to unsupervised learning on Gaussian mixture. We show how harmony learning not only leads us to the EM algorithm for maximum likelihood (ML) learning and the corresponding extended KMEAN algorithms for Mahalanobis clustering with criteria for selecting the number of Gaussians or clusters, but also provides us two new regularization techniques and a unified scheme that includes the previous rival penalized competitive learning (RPCL) as well as its various variants and extensions that performs model selection automatically during parameter learning. Moreover, as a by-product, we also get a new approach for determining a set of 'supporting vectors' for Parzen window density estimation. Second, we shown that other special cases lead to three typical supervised learning models with several new results. On three layer net, we get (i) a new regularized ML learning, (ii) a new criterion for selecting the number of hidden units, and (iii) a family of EM-like algorithms that combines harmony learning with new techniques of regularization. On the original and alternative models of mixture-of-expert (ME) as well as radial basis function (RBF) nets, we get not only a new type of criteria for selecting the number of experts or basis functions but also a new type of the EM-like algorithms that combines regularization techniques and RPCL learning for parameter learning with either least complexity nature on the original ME model or automated model selection on the alternative ME model and RBF nets. Moreover, all the results for the alternative ME model are also applied to other two popular nonparametric statistical approaches, namely kernel regression and supporting vector machine. Particularly, not only we get an easily implemented approach for determining the smoothing parameter in kernel regression, but also we get an alternative approach for deciding the set of supporting vectors in supporting vector machine.

A 2-DIMENSIONAL ALGORITHM RELATED TO THE FAREY–BROCOT SEQUENCE

2012 ◽  
Vol 08 (01) ◽  
pp. 149-160
Author(s):  
F. SCHWEIGER
Keyword(s):  
Continued Fractions ◽  
Dual Algorithm ◽  
Ergodic Properties ◽  
Minkowski Function ◽  
Special Cases ◽  
Multidimensional Continued Fractions ◽  
New Type ◽  
Interesting Generalization

Moshchevitin and Vielhaber gave an interesting generalization of the Farey–Brocot sequence for dimension d ≥ 2 (see [N. Moshchevitin and M. Vielhaber, Moments for generalized Farey–Brocot partitions, Funct. Approx. Comment. Math.38 (2008), part 2, 131–157]). For dimension d = 2 they investigate two special cases called algorithm [Formula: see text] and algorithm [Formula: see text]. Algorithm [Formula: see text] is related to a proposal of Mönkemeyer and to Selmer algorithm (see [G. Panti, Multidimensional continued fractions and a Minkowski function, Monatsh. Math.154 (2008) 247–264]). However, algorithm [Formula: see text] seems to be related to a new type of 2-dimensional continued fractions. The content of this paper is first to describe such an algorithm and to give some of its ergodic properties. In the second part the dual algorithm is considered which behaves similar to the Parry–Daniels map.

Framework and Key Enabling Technologies for Social Manufacturing

2013 ◽  
Vol 312 ◽  
pp. 498-501 ◽  
Author(s):  
Jie Wu Leng ◽  
Ping Yu Jiang ◽  
Fu Qiang Zhang ◽  
Wei Cao
Keyword(s):  
Value Chain ◽  
Large Scale ◽  
Enabling Technologies ◽  
Industry Value Chain ◽  
Machining System ◽  
New Type ◽  
Key Enabling Technologies ◽  
Manufacturing Network ◽  
Future Work ◽  
Manufacturing Mode

The role of manufacturing has changed from a producer of products and services to one that integrates the whole industry value chain. In this situation, this paper proposed a new-type networked manufacturing mode which is called outsourcing-driven social manufacturing (od-SM) to solve complex manufacturing problems and perform large-scale collaborative manufacturing. First, the framework of od-SM is proposed. Then, some key enabling technologies such as modeling and community structure of outsourcing-driven social manufacturing network (od-SMN) and generation of outsourcing-driven transient machining system (od-TMS) are talked about in detail. Finally, the conclusions and future work are put forward.

scholarly journals Safety Evaluation of Flower Roundabout Considering Autonomous Vehicles Operation

2021 ◽  
Vol 13 (18) ◽  
pp. 10120
Author(s):  
Alessandro Severino ◽  
Giuseppina Pappalardo ◽  
Salvatore Curto ◽  
Salvatore Trubia ◽  
Isaac Oyeyemi Olayode
Keyword(s):  
Autonomous Vehicles ◽  
Safety Evaluation ◽  
Tail Length ◽  
Entry And Exit ◽  
Special Cases ◽  
Technological Growth ◽  
Micro Simulation ◽  
Safety Interventions ◽  
Dynamic Performances ◽  
Conclusion Section

With the significant technological growth that affected autonomous vehicles in the last decade, several consequences occurred as: human factor exclusion, entry and exit manoeuvres precision from roundabouts, and headway reduction. In this paper, it was carried out a microsimulation approach study that aims to evaluate benefits in terms of safety obtained with flower roundabouts in a scenario where traffic is characterized by conventional vehicles “CVs” and Connected Autonomous Vehicles “CAVs”. This study focused on the evaluation of CAVs and CVs operation with the presence of the so called “weak users” or rather, pedestrians and bikes. Then, simulated scenarios were characterized by the presence of zebra-crossings in main roads, positioned at 20 m from circulatory carriageway edges. Micro simulation choice is due to the absence of survey data collection because the presence of CAVs in ordinary traffic is still minimal. The micro simulation was carried out through VISSIM, so it was operated with a specific methodological path, consisting, in the application, of O–D matrix based on real cases, in order to achieve an assessment of potential conflicts in relation with the increase in CAVs. Simulation results showed that higher safety levels were achieved for special cases of O–D distribution and with CAVs present. Finally, considering crash absence in results related to CAVs presence, safety interventions of such roundabout types have to be thorough. There were 10 O/D matrices analysed through VISSIM considering parameters as: average tail length, maximum tail length, average speed, vehicles, and number of stops quantity. As reported in the conclusion section, O/D matrices that showed minimum conflicts and maximum dynamic performances were identified.

scholarly journals Variational formulations for soliton equations arising in water transport in porous soils

2013 ◽  
Vol 17 (5) ◽  
pp. 1483-1485 ◽  
Author(s):  
Zheng-Biao Li ◽  
Jun Liu
Keyword(s):  
Water Transport ◽  
Inverse Method ◽  
Variational Principles ◽  
Soliton Equations ◽  
De Vries ◽  
Porous Soils ◽  
Variational Formulations

The semi-inverse method is adopted to establish variational principles for Korteweg De-Vries-like equations arising in water transport in porous soils.

A Numerical Investigation of Mixing Processes in a Novel Combustor Application

2005 ◽  
Vol 127 (12) ◽  
pp. 1334-1343 ◽  
Author(s):  
Yeshayahou Levy ◽  
Hui-Yuan Fan ◽  
Valery Sherbaum
Keyword(s):  
Support Vector ◽  
Pareto Optimum ◽  
Simulation Data ◽  
Mixing Processes ◽  
Mixing Performance ◽  
Special Cases ◽  
Conflicting Objectives ◽  
New Type ◽  
Learning Machine ◽  
Self Learning

A mixing process in a staggered toothed-indented shaped channel was investigated. It was studied in two steps: (1) numerical simulations for different sizes of the boundary-contour were performed by using a CFD code; (2) these results were used for simulation-data modeling for prediction of mixing performances across the whole field of changing geometric and the aerodynamic stream parameters. Support vector machine (SVM) technique, known as a new type of self learning machine, was selected to carry out this stage. The suitability of this application method was demonstrated in comparison with a neural network (NN) method. The established modeling system was then applied to some further studies of the prototype mixer, including observations of the mixing performance in three special cases and performing optimizations of the mixing processes for two conflicting objectives and hereby obtaining the Pareto optimum sets.

scholarly journals DIRECT QUANTIZATION OF EQUATIONS OF MOTION: FROM CLASSICAL DYNAMICS TO TRANSITION AMPLITUDES VIA STRINGS

2010 ◽  
Vol 07 (08) ◽  
pp. 1385-1405
Author(s):  
DENIS KOCHAN
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Equations Of Motion ◽  
Functional Integral ◽  
Classical Dynamics ◽  
World Sheet ◽  
Lagrange Equations ◽  
Standard Quantum ◽  
New Type ◽  
Fundamental Physical

New method of quantization is presented. It is based on classical Newton–Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is shown that classical dynamics is governed by canonical two-form Ω, which embodies kinetic energy and forces acting within the system. New type of variational principle employing differential two-form Ω and "umbilical strings" is introduced. The Feynman path integral over histories of the system is then rearranged to "umbilical world-sheet" functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, world-sheet approach reduces to the standard quantum mechanics. As an example Quantum Mechanics with friction is analyzed in detail.

Voice User Interface: Literature review, challenges and future directions

2021 ◽  
Vol 1 (2) ◽  
pp. 65-89
Author(s):  
Francis Rakotomalala ◽  
Hasindraibe Niriarijaona Randriatsarafara ◽  
Aimé Richard Hajalalaina ◽  
Ndaohialy Manda Vy Ravonimanantsoa
Keyword(s):  
User Interfaces ◽  
Human Interaction ◽  
Component Level ◽  
Natural User Interfaces ◽  
Voice User ◽  
Assistant Systems ◽  
Level 3 ◽  
New Type ◽  
The Subject ◽  
Future Work

Natural user interfaces are increasingly popular these days. One of the most common of these user interfaces today are voice-activated interfaces, in particular intelligent voice assistants such as Google Assistant, Alexa, Cortana and Siri. However, the results show that although there are many services available, there is still a lot to be done to improve the usability of these systems. Speech recognition, contextual understanding and human interaction are the issues that are not yet solved in this field. In this context, this research paper focuses on the state of the art and knowledge of work on intelligent voice interfaces, challenges and issues related to this field, in particular on interaction quality, usability, security and usability. As such, the study also examines voice assistant architecture components following the expansion of the use of technologies such as wearable computing in order to improve the user experience. Moreover, the presentation of new emerging technologies in this field will be the subject of a section in this work. The main contributions of this paper are therefore: (1) overview of existing research, (2) analysis and exploration of the field of intelligent voice assistant systems, with details at the component level, (3) identification of areas that require further research and development, with the aim of increasing its use, (4) various proposals for research directions and orientations for future work, and finally, (5) study of the feasibility of designing a new type of voice assistant and general presentation of the latter, whose realisation will be the subject of a thesis.

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