Concept Of Manifold Research Articles

Order reduction of nonlinear quasi-periodic systems subjected to external excitations

This paper presents order reduction techniques for nonlinear quasi-periodic systems subjected to external excitations. The order reduction techniques presented here are based on the Lyapunov–Perron (L–P) Transformation. For a class of non-resonant quasi-periodic systems, the L-P Transformation can convert a linear quasi-periodic system into a linear time-invariant one. This Linear Time-Invariant (LTI) system retains the dynamics of the original quasi-periodic system. Once this LTI system is obtained, the tools and techniques available for analysis of LTI systems can be used, and the results could be obtained for the original quasi-periodic system via the L–P Transformation. This approach is similar to the Lyapunov–Floquet (L–F) transformation to convert a linear time-periodic system into an LTI system and perform analysis and control.Order reduction is a systematic way of constructing dynamical system models with relatively smaller states that accurately retain large-scale systems’ essential dynamics. This work presents reduced-order modeling techniques for nonlinear quasi-periodic systems subjected to external excitations. The methods proposed here use the L–P Transformation that makes the linear part of transformed equations time-invariant. In this work, two order reduction techniques are suggested. The first method is simply an application of the well-known Guyan like reduction method to nonlinear systems. The second technique is based on the concept of an invariant manifold for quasi-periodic systems.The ‘quasi-periodic invariant manifold’ based technique yields ‘reducibility conditions’. These conditions (referred to in the perturbation literature as resonance conditions) help us understand the system’s various types of resonant interactions. These resonances indicate energy interactions between the system states, nonlinearity, and external excitation. To retain the essential dynamical characteristics, one must preserve all these ‘resonant’ states in the reduced-order model. Thus, if the ‘reducibility conditions’ are satisfied then only, a nonlinear order reduction based on the quasi-periodic invariant manifold approach is possible. It is found that the invariant manifold approach yields good results. These methodologies are general and can be used for parametric study, sensitivity analysis, and controller design.

Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentations.

Self-supervision is recently surging at its new frontier of graph learning. It facilitates graph representations beneficial to downstream tasks; but its success could hinge on domain knowledge for handcraft or the often expensive trials and errors. Even its state-of-the-art representative, graph contrastive learning (GraphCL), is not completely free of those needs as GraphCL uses a prefabricated prior reflected by the ad-hoc manual selection of graph data augmentations. Our work aims at advancing GraphCL by answering the following questions: How to represent the space of graph augmented views? What principle can be relied upon to learn a prior in that space? And what framework can be constructed to learn the prior in tandem with contrastive learning? Accordingly, we have extended the prefabricated discrete prior in the augmentation set, to a learnable continuous prior in the parameter space of graph generators, assuming that graph priors per se, similar to the concept of image manifolds, can be learned by data generation. Furthermore, to form contrastive views without collapsing to trivial solutions due to the prior learnability, we have leveraged both principles of information minimization (InfoMin) and information bottleneck (InfoBN) to regularize the learned priors. Eventually, contrastive learning, InfoMin, and InfoBN are incorporated organically into one framework of bi-level optimization. Our principled and automated approach has proven to be competitive against the state-of-the-art graph self-supervision methods, including GraphCL, on benchmarks of small graphs; and shown even better generalizability on large-scale graphs, without resorting to human expertise or downstream validation. Our code is publicly released at https://github.com/Shen-Lab/GraphCL_Automated.

Computational Modeling: Human Dynamic Model.

Improvements in quantitative measurements of human physical activity are proving extraordinarily useful for studying the underlying musculoskeletal system. Dynamic models of human movement support clinical efforts to analyze, rehabilitate injuries. They are also used in biomechanics to understand and diagnose motor pathologies, find new motor strategies that decrease the risk of injury, and predict potential problems from a particular procedure. In addition, they provide valuable constraints for understanding neural circuits. This paper describes a physics-based movement analysis method for analyzing and simulating bipedal humanoid movements. The model includes the major body segments and joints to report human movements' energetic components. Its 48 degrees of freedom strike a balance between very detailed models that include muscle models and straightforward two-dimensional models. It has sufficient accuracy to analyze and synthesize movements captured in real-time interactive applications, such as psychophysics experiments using virtual reality or human-in-the-loop teleoperation of a simulated robotic system. The dynamic model is fast and robust while still providing results sufficiently accurate to be used to animate a humanoid character. It can also estimate internal joint forces used during a movement to create effort-contingent stimuli and support controlled experiments to measure the dynamics generating human behaviors systematically. The paper describes the innovative features that allow the model to integrate its dynamic equations accurately and illustrates its performance and accuracy with demonstrations. The model has a two-foot stance ability, capable of generating results comparable with an experiment done with subjects, and illustrates the uncontrolled manifold concept. Additionally, the model's facility to capture large energetic databases opens new possibilities for theorizing as to human movement function. The model is freely available.

Planning in cold-war Italy

ABSTRACT Planning ideas and practices were established and spread quickly in different situations in post-war Europe. No matter the definition of this obscure and manifold concept, the utopia of rationality inherent in the planning was founded on the conviction that the economy could be anticipated and guided according to collective interest and economic development. The cold war, therefore, was a time of a broad affirmation of planning which, disseminated internationally by a class of experts and technicians, was the key instrument agreed on, both scientifically and politically, to promote growth in backward areas and underdeveloped countries. The Italian case, having been thoroughly studied and discussed at a domestic level but not always sufficiently appraised in international studies, may be able to contribute a useful element to the overall picture, precisely due to the key role played by this country, and southern Europe, in the Atlantic and Mediterranean balances.

Unsupervised Detection of Anomalies in Fetal Heart Rate Tracings using Phase Space Reconstruction.

Detection of anomalies in time series is still a challenging problem. In this paper, we provide a new approach to unsupervised detection of anomalies in time series based on the concept of phase space reconstruction and manifolds. We propose a rotation-insensitive metric for quantifying the similarity of manifolds and a method that uses it for estimating the probability of an outlier. The proposed method does not rely on any features and can be used for signals with variable lengths. We tested it on both synthetic signals and real fetal heart rate tracings. The method has promising performance and can be used for interpreting the severity of fetal asphyxia.

Design and Vibrational Characteristic Analysis of Exhaust Manifold with Experimental Validation Using FFT Analyzer

The vibrations observed in internal combustion engines transfer to the Tail pipe via exhaust manifold. Such Vibrations cause failure of exhaust system. Two types of vibration can affect the exhaust manifold: the sonic pressure waves coming from the exhaust ports, and the vibration of the engine itself. Pressure wave vibrations are usually transparent, travelling through the exhaust system to either absorb into or cancel out in the muffler. These waves are harmonic, like the vibration of a speaker, but they are usually too minute to cause noise through component movement. Engine vibrations, on the other hand, can easily shake your complete exhaust system. Such cyclic loading of waves can cause component rattling or failure. This vibration failure occurs due to resonant frequencies occurring in defined frequency range. The ‘frequency match’ could lead to a response detrimental to the life of the structure.FEA techniques are proposed in this work to avoid resonance. Physical experimentation is proposed using FFT Analyzer. This work deals with the damping of such later mentioned vibration problems with a concept of CAE (Computer Aided Engineering). In this project we are analyzing the exhaust system under various conditions for modal (natural vibrations). Static and modal analysis of exhaust manifold has been performed using ANSYS 19 software along with experimental validation of manifold using FFT and impact hammer test. Different types of methods for reducing vibration of manifold are studied. After studying these methods and procedures for reducing a vibration, we conclude that, exhaust manifold concept 02 is more efficient by changing the geometry or adding proper stiffener for reducing vertical vibration which further increases the frequency response of component..

Almost α -Cosymplectic Pseudo Metric Manifolds

The main purpose of this paper is to study almost α -cosymplectic pseudo metric manifold satisfying certain η -parallel tensor fields. We first focus on the concept of almost α -cosymplectic pseudo metric manifold and its curvature properties. Then, we obtain some results related to the η -parallelity of h , φ h , and τ . Moreover, the deformation of almost α -Kenmotsu pseudo metric structure is given. We conclude the paper with an illustrative example of almost α -cosymplectic pseudo metric manifold.

Tracking and vibration control of a free-floating space manipulator system with flexible links and joints

The problem of modeling and controlling of a free-floating space manipulator with flexures in both links and joints is addressed in this study. A mathematical model of the system is developed by combining Lagrange’s equations and momentum conservation. The finite element method is introduced to discretize multi-links with complex cross-sections. In order to reduce the dimensions and maintain the precision of a rigid-flexible coupled system, an iterated improved reduction system method is adopted. Then, a novel composite control scheme for the reduced system is presented that uses the concept of integral manifolds and singular perturbation theory. Finally, an augmented computed torque controller is applied to the under-actuated slow subsystem to realize trajectory tracking in joint space, while a linear-quadratic controller is designed to damp out the vibration of joints and links. Numerical simulation results verified that the proposed hybrid controller can successfully suppress vibration and track trajectory at the same time.

Active Manifold and Model-Order Reduction to Accelerate Multidisciplinary Analysis and Optimization

A computational framework is proposed for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in a relatively high-dimensional design parameter space. It relies on projection-based reduced-order models (PROMs) and a new concept of an active manifold (AM) to mitigate the curse of dimensionality during the training of the PROMs. The AM is discovered using a deep convolutional autoencoder for dimensionality reduction: it is proposed as a superior alternative to the concept of active subspace whose capabilities are limited by the associated affine approximation. The computational framework also blends the concept of a global PROM as a surrogate model of a nonlinear partial differential equation (PDE)-based behavior function with that of a database of local, linear PROMs for approximating a linear PDE-based behavior function. It is demonstrated for the solution of a flexible instance of NASA’s Common Research Model for transport aircraft, where the objective function pertains to aerodynamics, the constraint relates to flutter, and the design space contains 58 structural and shape parameters. The obtained results illustrate the potential of the AM concept for mitigating the aforementioned curse of dimensionality. They also demonstrate the feasibility of the proposed computational framework for realistic MDAO problems and its ability to reduce solution time.

Global invariant manifolds delineating transition and escape dynamics in dissipative systems: an application to snap-through buckling

Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between potential wells is governed by the invariant manifolds of a periodic orbit around the saddle. In two-degree-of-freedom systems, such invariant manifolds appear as cylindrical conduits which are referred to as transition tubes. In this study, we apply the concept of invariant manifolds to study the transition between potential wells in not only conservative systems, but more realistic dissipative systems, by solving respective proper boundary value problems. The example system considered is a two-mode model of the snap-through buckling of a shallow arch. We define the transition region, $$\mathcal {T}_h$$ , as a set of initial conditions of a given initial Hamiltonian energy h with which the trajectories can escape from one potential well to another, which in the example system corresponds to snap-through buckling of a structure. The numerical results reveal that in the conservative system, the boundary of the transition region, $$\partial \mathcal {T}_h$$ , is a cylinder, while in the dissipative system, $$\partial \mathcal {T}_h$$ is an ellipsoid. The algorithms developed in the current research from the perspective of invariant manifold provide a robust theoretical–computational framework to study escape and transition dynamics.

Manifold Learning-Inspired Mating Restriction for Evolutionary Multiobjective Optimization With Complicated Pareto Sets.

Under certain smoothness assumptions, the Pareto set of a continuous multiobjective optimization problem is a piecewise continuous manifold in the decision space, which can be derived from the Karush-Kuhn-Tucker condition. Despite that a number of multiobjective evolutionary algorithms (MOEAs) have been proposed, their performance on multiobjective optimization problems with complicated Pareto sets (MOP-cPS) is still unsatisfying. In this article, we adopt the concept of manifold and propose a manifold learning-inspired mating strategy to enhance the diversity maintenance in MOEAs for solving MOP-cPS efficiently. In the proposed strategy, all of the individuals are first clustered into different manifolds according to their distribution in the objective space, and then the mating reproduction is restricted among individuals in the same manifold. Moreover, we embed the proposed mating strategy in three representative MOEAs and compare the embedded MOEAs with their original versions using the assortative genetic operators on a variety of MOP-cPS. The experimental results demonstrate the significant performance improvements benefitting from the proposed mating restriction strategy.

Mapping Ground Water Access in Two Rural Communes of Burkina Faso

Granting safe water access worldwide is a major objective of the Sustainable Development Goals. Water access is a manifold concept that encompasses collection time, distance from the household, water quality, affordability, and reliability of water sources, among other factors. GIS-based methods can be particularly useful in improving water access estimates, particularly in rural areas of developing countries. Based on an extensive water point database (n = 770), this paper explores the main challenges involved in mapping water access in two rural communes of Burkina Faso. Water access is estimated in terms of coverage per surface area. Coverage is filtered into four distinct categories of improved water sources, namely existing infrastructures, operational infrastructures, permanent infrastructures, and permanent infrastructures that provide safe water. The outcomes suggest that the study area is better endowed with water access than rural Burkina Faso and the remainder of the African continent, although there are important questions regarding groundwater quality. The outcomes highlight the conceptual differences between coverage and access, as well as some of the practical difficulties involved in estimating water access beyond standard ratios. The shortcomings include the absence of continuous monitoring of infrastructure functionality and water quality, as well as water affordability, among others. Enhancing national borehole databases with items aligned with the United Nations’ definition of water access is recommended.

On the stability of invariant almost complex structures on flag manifolds

By analyzing the Ricci star tensor Ric*, we study the harmonic almost complex structure in maximal flag manifolds. We show that flag manifolds have diagonal Ric* tensor. Using the concept of ⁎Einstein manifolds, we study the stability of the invariant almost complex structure and show examples of stables parabolic almost complex structures on maximal flag manifolds.

The dually flat structure for singular models

The dually flat structure introduced by Amari-Nagaoka is highlighted in information geometry and related fields. In practical applications, however, the underlying pseudo-Riemannian metric may often be degenerate, and such an excellent geometric structure is rarely defined on the entire space. To fix this trouble, in the present paper, we propose a novel generalization of the dually flat structure for a certain class of singular models from the viewpoint of Lagrange and Legendre singularity theory - we introduce a quasi-Hessian manifold endowed with a possibly degenerate metric and a particular symmetric cubic tensor, which exceeds the concept of statistical manifolds and is adapted to the theory of (weak) contrast functions. In particular, we establish Amari-Nagaoka's extended Pythagorean theorem and projection theorem in this general setup, and consequently, most of applications of these theorems are suitably justified even for such singular cases. This work is motivated by various interests with different backgrounds from Frobenius structure in mathematical physics to Deep Learning in data science.

The motion response and hydrodynamic performance comparisons of the new subsea suspended manifold with two mooring scenarios

The subsea manifold as the hub oil and gas transportation equipment is a critical part for the layout optimization of subsea production system and reducing the number of pipelines. The traditional subsea manifold is fixed on seabed by its foundation, so traditional manifold system is hard to be discarded and recovered although it has many advantages and is applied widely in the deep water development scenario. In this paper, a new subsea suspended manifold concept is proposed to discuss its feasibility by the hydrodynamic performance state in vertical tension and catenary mooring methods. A mathematical model is established to solve the chain tension distribution and displacement of the subsea suspended manifold. Meanwhile, the motion response of the subsea suspended manifold under different influence factors, tension distribution of the mooring chains and the flexible jumpers in two mooring schemes are simulated, respectively, through OrcaFlex software. The research results will provide an important reference for the optimization of the preliminary scenario design of the subsea suspended manifold mooring system.

On lightlike geometry of indefinite Sasakian statistical manifolds

<abstract><p>In the present study, the concept of Sasakian statistical manifold has been generalized to indefinite Sasakian statistical manifolds. We also introduce lightlike hypersurfaces of an indefinite Sasakian statistical manifold and establish relations between induced geometrical objects with respect to dual connections. Finally, invariant lightlike submanifold of indefinite Sasakian statistical manifold is proved to be an indefinite Sasakian statistical manifold.</p></abstract>

Estimation of Consecutively Missed Samples in Fetal Heart Rate Recordings.

During labor, fetal heart rate (FHR) is monitored externally using Doppler ultrasound. This is done continuously, but for various reasons (e.g., fetal or maternal movements) the system does not record any samples for varying periods of time. In many settings, it would be quite beneficial to estimate the missing samples. In this paper, we propose a (deep) Gaussian process-based approach for estimation of consecutively missing samples in FHR recordings. The method relies on similarities in the state space and on exploiting the concept of attractor manifolds. The proposed approach was tested on a short segment of real FHR recordings. The experimental results indicate that the proposed approach is able to provide more reliable results in comparison to several interpolation methods that are commonly applied for processing of FHR signals.

An existence theorem for generalized quasi-variational inequalities involving the Grassmannian manifold with an application

We present an existence theorem for a class of generalized quasi-variational problem involving Grassmannian manifolds. This class is directly inspired by a general equilibrium problem with time, uncertainty and incomplete financial market with real assets. The problem of the existence of this equilibrium cannot be analyzed using standard techniques employed in similar models. Then, we show how the concept of equilibrium is strictly related to the concept of Grassmannian manifolds. Finally, we present a variational inequality problem, whose solutions are equilibria of the proposed model.

$C^infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^infty$ $LG$-fuzzy mappings of them

In this paper, we generalize all of the fuzzy structures which we have discussed in cite{MM} to $L$-fuzzy set theory, where $L= $ denotes a complete distributive lattice with at least two elements. We define the concept of an $LG$-fuzzy topological space $(X, mathfrak{T} )$ which $X$ is itself an $L$-fuzzy subset of a crisp set M and $mathfrak{T}$ is an $L$-gradation of openness of $L$-fuzzy subsets of $M$ which are less than or equal to $ X $. Then we define $C^infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^infty$ $LG$-fuzzy mappings of them such as $LG$-fuzzy immersions and $LG$-fuzzy imbeddings. We fuzzify the concept of the product manifolds with $L$-gradation of openness and define $LG$-fuzzy quotient manifolds when we have an equivalence relation on $M$ and investigate the conditions of the existence of the quotient manifolds. We also introduce $LG$-fuzzy immersed, imbedded and regular submanifolds.

Modeling the collapse of the edge when two transition routes compete.

The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in, e.g., boundary layer flows. The dynamical systems concept of an edge manifold has been suggested in the subcritical case to explain the partition of the state space of the system. This investigation is devoted to the evolution of the edge manifold when linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows. In particular, the fate of the edge state as a mediator of transition is unclear. A deterministic three-dimensional model is suggested, parametrized by the linear instability growth rate. The edge manifold evolves topologically, via a global saddle-loop bifurcation of the underlying invariant sets, from the separatrix between two attraction basins to the mediator between two transition routes. For larger instability rates, the stable manifold of the saddle point increases in codimension from 1 to 2 after an additional local pitchfork node bifurcation, causing the collapse of the edge manifold. As the growth rate is increased, three different regimes of this model are identified, each one associated with a flow case from the recent hydrodynamic literature. A simple nonautonomous generalization of the model is also suggested in order to capture the complexity of spatially developing flows.