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Flow distribution uniformity in manifolds is important in various engineering applications. In this study, the effect of manifold design on flow distribution is examined using both experimental and numerical methods. A comparison was made between a straight manifold and a gradually decreasing cross-sectional design considering two different inlet diameters. In addition, the staggered manifold case with the most homogeneous outlet was compared with the conical manifold under the same conditions. The results demonstrate that the gradually decreasing manifold design significantly improves the flow rate uniformity compared with the straight manifold. This improvement is achieved by reducing the flow rate differences between the distribution branches, leading to a more balanced fluid distribution. The gradual reduction in the cross-sectional area allows the fluid to traverse at lower velocities in regions with higher resistance, effectively minimizing flow rate discrepancies and pressure drops. In addition, the effect of varying the inlet diameter on flow rate uniformity was investigated, revealing that larger inlet diameters contribute to improved flow distribution. The outlet uniformity of the staggered manifold matches the effective performance of the conical manifold, demonstrating similar performance at a lower cost. The results highlight the importance of designing an appropriate manifold, considering factors such as inlet diameter, channel geometry, and staggered ratio, to achieve efficient and uniform fluid distribution. [ABSTRACT FROM AUTHOR]

Flow distribution uniformity in manifolds is important in various engineering applications. In this study, the effect of manifold design on flow distribution is examined using both experimental and numerical methods. A comparison was made between a straight manifold and a gradually decreasing cross-sectional design considering two different inlet diameters. In addition, the staggered manifold case with the most homogeneous outlet was compared with the conical manifold under the same conditions. The results demonstrate that the gradually decreasing manifold design significantly improves the flow rate uniformity compared with the straight manifold. This improvement is achieved by reducing the flow rate differences between the distribution branches, leading to a more balanced fluid distribution. The gradual reduction in the cross-sectional area allows the fluid to traverse at lower velocities in regions with higher resistance, effectively minimizing flow rate discrepancies and pressure drops. In addition, the effect of varying the inlet diameter on flow rate uniformity was investigated, revealing that larger inlet diameters contribute to improved flow distribution. The outlet uniformity of the staggered manifold matches the effective performance of the conical manifold, demonstrating similar performance at a lower cost. The results highlight the importance of designing an appropriate manifold, considering factors such as inlet diameter, channel geometry, and staggered ratio, to achieve efficient and uniform fluid distribution.

Background: The World Health Organization has reported that approximately 300 million individuals suffer from the mood disorder known as MDD. Noninvasive measurement techniques have been utilized to reveal the mechanism of MDD, with rsfMRI being the predominant method. The previous functional connectivity and energy landscape studies have shown the difference in the coactivation patterns between MDD and HCs. However, these studies did not consider oscillatory temporal dynamics. Methods: In this study, the dynamic mode decomposition, a method to compute a set of coherent spatial patterns associated with the oscillation frequency and temporal decay rate, was employed to investigate the alteration of the occurrence of dynamic modes between MDD and HCs. Specifically, The BOLD signals of each subject were transformed into dynamic modes representing coherent spatial patterns and discrete-time eigenvalues to capture temporal variations using dynamic mode decomposition. All the dynamic modes were disentangled into a two-dimensional manifold using t-SNE. Density estimation and density ratio estimation were applied to the two-dimensional manifolds after the two-dimensional manifold was split based on HCs and MDD. Results: The dynamic modes that uniquely emerged in the MDD were not observed. Instead, we have found some dynamic modes that have shown increased or reduced occurrence in MDD compared with HCs. The reduced dynamic modes were associated with the visual and saliency networks while the increased dynamic modes were associated with the default mode and sensorymotor networks. Conclusion: To the best of our knowledge, this study showed initial evidence of the alteration of occurrence of the dynamic modes between MDD and HCs. To deepen understanding of how the alteration of the dynamic modes emerges from the structure, it is vital to investigate the relationship between the dynamic modes, cortical thickness, and surface areas. [ABSTRACT FROM AUTHOR]

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The aim of the present paper is to study the geometry of n-dimensional differentiable manifolds endowed with F(a0, a1, ...., aan)-structure satisfying anFn +an-1Fn-1+.......+a1V F+a0I = 0 and establish its existence. Also, it is proved that for the complex numbers, the dimension of a manifold M endowed with F(a0, a1, ...., aan)-structure is even. Furthermore, we study the Nijenhuis tensor of a tensor field F of type (1,1) satisfying the general quadratic equation, which is a particular case of the F(a0, a1, ......, aan)-structure. At last, we study the integrability conditions of an F(a0, a1, ......, aan)-structure. [ABSTRACT FROM AUTHOR]

We aim to examine the influence of the existence of a nonzero eigenvector ζ of the de-Rham operator Γ on a k-dimensional Riemannian manifold (N k , g) . If the vector ζ annihilates the de-Rham operator, such a vector field is called a de-Rham harmonic vector field. It is shown that for each nonzero vector field ζ on (N k , g) , there are two operators T ζ and Ψ ζ associated with ζ , called the basic operator and the associated operator of ζ , respectively. We show that the existence of an eigenvector ζ of Γ on a compact manifold (N k , g) , such that the integral of Ric (ζ , ζ) admits a certain lower bound, forces (N k , g) to be isometric to a k-dimensional sphere. Moreover, we prove that the existence of a de-Rham harmonic vector field ζ on a connected and complete Riemannian space (N k , g) , having div ζ ≠ 0 and annihilating the associated operator Ψ ζ , forces (N k , g) to be isometric to the k-dimensional Euclidean space, provided that the squared length of the covariant derivative of ζ possesses a certain lower bound. [ABSTRACT FROM AUTHOR]

Adapting to a constantly changing environment requires the human brain to flexibly switch among many demanding cognitive tasks, processing both specialized and integrated information associated with the activity in functional networks over time. In this study, we investigated the nature of the temporal alternation between segregated and integrated states in the brain during rest and six cognitive tasks using functional MRI. We employed a deep autoencoder to explore the 2D latent space associated with the segregated and integrated states. Our results show that the integrated state occupies less space in the latent space manifold compared to the segregated states. Moreover, the integrated state is characterized by lower entropy of occupancy than the segregated state, suggesting that integration plays a consolidating role, while segregation may serve as cognitive expertness. Comparing rest and the tasks, we found that rest exhibits higher entropy of occupancy, indicating a more random wandering of the mind compared to the expected focus during task performance. Our study demonstrates that both transient, short‐lived integrated and segregated states are present during rest and task performance, flexibly switching between them, with integration serving as information compression and segregation related to information specialization. [ABSTRACT FROM AUTHOR]

Accurate localization of robots in unstructured environments poses challenges due to low localization accuracy and local trajectory oscillation caused by complex feature points when using Euclidean-based filtering methods. In this study, we propose a novel 3D robot localization method named LIF-M that leverages a manifold-based approach in conjunction with an unscented Kalman filter (UKF-M). Additionally, a relocalization algorithm is designed to ensure localization stability. The proposed method addresses the limitations of conventional Euclidean-based filtering methods by incorporating manifold-based techniques, providing a more comprehensive representation of the complex geometric features. We introduce the manifold concept, where the relevant definition is defined and utilized within the LIF-M framework. By combining left and right invariants, we effectively reduce noise uncertainty, resulting in improved localization accuracy. Moreover, we employ sigma points as a matrix representation of the state points' space in order to seamlessly transition between the matrix space and the vector representation of the tangent space. Experimental tests and error calculations were conducted to evaluate the performance of various algorithm frameworks, and the results demonstrated the importance of the manifold-based approach for accurate attitude estimation. Compared to the standard UKF, the manifold space equips LIF-M with better robustness and stability in unstructured environments. [ABSTRACT FROM AUTHOR]

In the EAST (Experimental Advanced Superconducting Tokamak), the manifolds play an important role in the blow-out process, which directly affects the dryness of the plasma facing components (PFCs) and the entire drying system. This will cause corrosion of PFCs and coolant leakage, which will seriously affect the safe operation of the device. Therefore, it is necessary to study the gas–liquid​ two-phase flow characteristics of the manifold during the blowout process. In this paper, the CFD (Computational Fluid Dynamics) method was used to simulate the gas–liquid blowout process of the manifold with different header-diameters, and to discuss the influence mechanism of the change of header-diameter on the blowout effect. Under the boundary condition of a gas supply with a certain pressure difference, it can be found that enlarging the header-diameter can enhance the uniformity of the flow of branches, improve the inlet gas flow rate of manifold, which conductively improve the dryness of the manifold. The research results in this paper will provide reference for improving the dryness of internal components and drying systems, and also for the construction of future fusion reactor drying systems.

Task-related information is widely distributed across the brain with different coding properties, such as persistency. We found in mice that coding persistency of action history and value was variable across areas, learning phases, and task context, with the highest persistency in the retrosplenial cortex of expert mice performing value-based decisions where history needs to be maintained across trials. Persistent coding also emerged in artificial networks trained to perform mouse-like reinforcement learning. Persistency allows temporally untangled value representations in neuronal manifolds where population activity exhibits cyclic trajectories that transition along the value axis after action outcomes, collectively forming cylindrical dynamics. Simulations indicated that untangled persistency facilitates robust value retrieval by downstream networks. Even leakage of persistently maintained value through non-specific connectivity could contribute to the brain-wide distributed value coding with different levels of persistency. These results reveal that context-dependent, untangled persistency facilitates reliable signal coding and its distribution across the brain.

The human hand is unique in the animal kingdom for unparalleled dexterity, ranging from complex prehension to fine finger individuation. How does the brain represent such a diverse repertoire of movements? We evaluated mesoscale neural dynamics across the human "grasp network," using electrocorticography and dimensionality reduction methods, for a repertoire of hand movements. Strikingly, we found that the grasp network represented both finger and grasping movements alike. Specifically, the manifold characterizing the multi-areal neural covariance structure was preserved during all movements across this distributed network. In contrast, latent neural dynamics within this manifold were surprisingly specific to movement type. Aligning latent activity to kinematics further uncovered distinct submanifolds despite similarities in synergistic coupling of joints between movements. We thus find that despite preserved neural covariance at the distributed network level, mesoscale dynamics are compartmentalized into movement-specific submanifolds; this mesoscale organization may allow flexible switching between a repertoire of hand movements.

The water-cooled lead lithium (WCLL) and the dual-cooled lead lithium (DCLL) are two of the breeding blanket (BB) concepts that the EUROfusion consortium is pursuing in the framework of the development of the fusion reactor industrial demonstrator DEMO. Both involve the use of a liquid metal (LM) as working fluid, the lead-lithium eutectic alloy (PbLi), due to its excellent thermal properties and the possibility to serve as both the blanket coolant and tritium breeder and carrier. Unfortunately, due to the high electrical conductivity of LMs, their motion is influenced by the magnetic field used in the reactor to confine the plasma, generating a complex phenomenology which is studied by magnetohydrodynamics (MHD). In this work, a representative prototypical manifold of a BB bottom feeder is investigated for different configurations with the custom phiFoam solver, capable of simulating unsteady, incompressible and isothermal MHD flow. The aim of this study is to investigate which configuration minimizes the flow imbalance in the manifold for the WCLL or in the poloidal breeding zone channels for the DCLL. The distribution of the flow rate among the channels is strongly influenced by the position of the feeding pipe (FP) and by the development of the MHD internal layer near the expansion, which generates important jets close to the lower plate and the upper one, where the channels are attached. The channel aligned with the FP is the one carrying most of the flow, from 55% to 82%, while in the more distant one the flow is almost stagnant, carrying from 17% to 6% of the total flow rate. The total pressure loss is also estimated and its functional dependence on the manifold configuration is discussed. [ABSTRACT FROM AUTHOR]

Vision Transformers are very popular nowadays due to their state-of-the-art performance in several computer vision tasks, such as image classification and action recognition. Although their performance has been greatly enhanced through highly descriptive patch embeddings and hierarchical structures, there is still limited research on utilizing additional data representations so as to refine the self-attention map of a Transformer. To address this problem, a novel attention mechanism, called multi-manifold multi-head attention, is proposed in this work to substitute the vanilla self-attention of a Transformer. The proposed mechanism models the input space in three distinct manifolds, namely Euclidean, Symmetric Positive Definite and Grassmann, thus leveraging different statistical and geometrical properties of the input for the computation of a highly descriptive attention map. In this way, the proposed attention mechanism can guide a Vision Transformer to become more attentive towards important appearance, color and texture features of an image, leading to improved classification and segmentation results, as shown by the experimental results on well-known datasets.

Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main tasks of modern signal processing, namely, at analog-to-digital (A/D) conversion in connection with a simple manifold model — the circle. We will focus on Sigma-Delta modulation which is a popular method for A/D conversion of bandlimited signals that employs coarse quantization coupled with oversampling. Classical Sigma-Delta schemes provide mismatches and large errors at the initialization point if the signal to be converted is defined on the circle. In this paper, our goal is to get around these problems for Sigma-Delta schemes. Our results show how to design an update for the first and the second order schemes based on the reconstruction error analysis such that for the updated scheme the reconstruction error is improved. [ABSTRACT FROM AUTHOR]

This article investigates fluid distribution in multichannel microfluidic devices with U-shaped manifolds. The parameters investigated include Reynolds number, microchannel width, microchannel spacing width, and microchannel length. The study is carried out using a microfluidic device having 50 microchannels employing water as the working fluid. The flow distribution in the microfluidic device is investigated for microchannel widths between 100 µm to 500 µm and for Reynolds number ranging between 0.04 to 100. The effect of channel spacing width on flow distribution is investigated for microchannel spacing widths between 100 µm to 500 µm. The increase in Reynolds number affects the flow distribution by increasing the non-uniformity of the flow. It is found that increasing the microchannel width causes more non-uniformity in the flow. It is also found that increasing the microchannel spacing width decreased the non-uniformity of the flow distribution. It is found that increasing the channel width from 100 µm to 300 µm increased the flow maldistribution by 83%, and increasing the microchannel spacing width from 100 µm to 300 µm decreased the flow maldistribution by 42%. It is observed that the microchannel width has a stronger influence on the flow distribution compared with microchannel spacing width. The study is useful for examining the flow maldistribution in microfluidic devices as their performance is dependent on flow rate.

Spectral features of the empirical moment matrix constitute a resourcefultool for unveiling properties of a cloud of points, among which, density,support and latent structures. It is already well known that the empiricalmoment matrix encodes a great deal of subtle attributes of the underlyingmeasure. Starting from this object as base of observations we combine ideasfrom statistics, real algebraic geometry, orthogonal polynomials andapproximation theory for opening new insights relevant for Machine Learning(ML) problems with data supported on singular sets. Refined concepts andresults from real algebraic geometry and approximation theory are empowering asimple tool (the empirical moment matrix) for the task of solving non-trivialquestions in data analysis. We provide (1) theoretical support, (2) numericalexperiments and, (3) connections to real world data as a validation of thestamina of the empirical moment matrix approach.

In this paper, an Optimized Synergetic Nonlinear Controller (OSNC) is proposed to efficiently determine the maximum power point of a Photovoltaic Generator matched to the load through a DC–DC boost converter. The dynamic equation of the conventional synergetic controller is modified to adjust the Manifold in such a way that the optimum maximum power point (MPP) is reached. This new approach is implemented in the Matlab/Simulink software and shows increased convergence in steady and transient states. Consequently, this new approach exhibits better performance than the conventional nonlinear synergetic controller (SNC) in standard test conditions and weather varying conditions.

Abstract Representation of one-dimensional (1D) signals as surfaces and higher-dimensional manifolds reveals geometric structures that can enhance assessment of signal similarity and classification of large sets of signals. Motivated by this observation, we propose a novel robust algorithm for extraction of geometric features, by mapping the obtained geometric objects into a reference domain. This yields a set of highly descriptive features that are instrumental in feature engineering and in analysis of 1D signals. Two examples illustrate applications of our approach to well-structured audio signals: Lung sounds were chosen because of the interest in respiratory pathologies caused by the coronavirus and environmental conditions; accent detection was selected as a challenging speech analysis problem. Our approach outperformed baseline models under all measured metrics. It can be further extended by considering higher-dimensional distortion measures. We provide access to the code for those who are interested in other applications and different setups (Code: https://github.com/jeremy-levy/Classification-of-audio-signals-using-spectrogram-surfaces-and-extrinsic-distortion-measures ).

Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate gradient descent, and demonstrate their superiority over the promising baseline with the ratio of at least 24 % . [ABSTRACT FROM AUTHOR]

Generation of random fields (GRF) for image segmentation represents partitioning an image into different regions that are homogeneous or have similar facets of the image. It is one of the most challenging tasks in image processing and a very important pre-processing step in the fields of computer vision, image analysis, medical image processing, pattern recognition, remote sensing, and geographical information system. Many researchers have presented numerous image segmentation approaches, but still, there are challenges like segmentation of low contrast images, removal of shadow in the images, reduction of high dimensional images, and computational complexity of segmentation techniques. In this review paper, the authors address these issues. The experiments are conducted and tested on the Berkely dataset (BSD500), Semantic dataset, and our own dataset, and the results are shown in the form of tables and graphs. [ABSTRACT FROM AUTHOR]

A scaled-down test section representative of an Outboard Segment manifold of the Water-Cooled Lithium Lead Breeding Blanket for the European DEMO has been designed for installation and test in a high- mass flow branch of the W-HYDRA facility, under construction at the premises of ENEA Brasimone Research Center. The test section should confirm the flow repartition recently computed in the different breeding units on the full-scale manifold, validating at the same time the computational tools used for the design and analysis. The detailed objectives and requirements of the test section, as well as the scaling rationale and procedure adopted for its design, are presented in the paper. The final design of the test section is discussed. The preliminary analyses of the developed design are also presented and show that it is compliant with the initial objectives. [ABSTRACT FROM AUTHOR]

Topological spaces can be induced by various algebraic ordering relations such as, linear, partial and the inclusion-ordering of open sets forming chains and chain complexes. In general, the classifications of covering spaces are made by using fundamental groups and lifting. However, the Riesz ordered n-spaces and Urysohn interpretations of real-valued continuous functions as ordered chains provide new perspectives. This paper proposes the formulation of covering spaces of n-space charts of a foliated n-manifold containing linearly ordered chains, where the chains do not form topologically separated components within a covering section. The chained subspaces within covering spaces are subjected to algebraic split–join operations under a bijective function within chain-subspaces to form simply directed chains and twisted chains. The resulting sets of chains form simply directed chain-paths and oriented chain-paths under the homotopy path-products involving the bijective function. It is shown that the resulting embedding of any chain in a leaf of foliated n-manifold is homogeneous and unique. The finite measures of topological subspaces containing homotopies of chain-paths in covering spaces generate multiplicative and cyclic group varieties of different orders depending upon the types of measures. As a distinction, the proposed homotopies of chain-paths in covering spaces and the homogeneous chain embedding in a foliated n-manifold do not consider the formation of circular nerves and the Nachbin topological preordering, thereby avoiding symmetry/asymmetry conditions. [ABSTRACT FROM AUTHOR]

Introduction Let G be a Lie group with a differentiable action on a differentiable manifold M. Consider the orbit space M/G with the quotient topology. Dimension of M/G is called the cohomogeneity of the action of G on M. Study of the orbit spaces has many important applications in invariant function theory and G-invariant variational problems associated to M. Many G-invariant objects associated to M can be related to similar objects associated to the orbit space. Therefore, if the dimension of the orbit space is small enough (the cohomgeneity of the action of G on M is small) we can effectively reduce many problems about G-invariant objects of M to generally easier problems on M/G . Because of this motivation, many mathematicians studied topological properties of the orbit spaces of Lie group actions on manifolds. A pioneer theorem in this area is a theorem proved by P. Mostert in 1957: If M is a differentiable manifold which is of cohomogeneity one under the action of G a compact connected Lie group, then the orbit space is homeomorphic to one of the spaces [0,1], (0,1], S¹ or R. This theorem has been generalized to noncompact Lie groups with proper actions on manifolds. Moreover, If M is endowed with a Riemannian metric, and G is a closed and connected subgroup of the isometries of M, which acts by cohomogeneity one on M, there are more interesting results about the orbit space and orbits. It is proved that if M is a Riemannian manifold of negative curvature and G is a connected and closed subgroup of the isometries of M, acting on M with cohomogeneity one, then the orbit space is not homeomorphic to [0,1], so by (generalized) Mostert's theorem, it would be homeomorphic to [0,1) or S¹ or R, and if in addition, M is simply connected then the orbit space is homeomorphic to [0,1) or R. This result, has been generalized to flat Riemannian manifolds, and recently it is proved for Riemannian manifolds of non-positive curvature. To extend Mostert's theorem, it is natural to ask, what may be the orbit space, when M is a cohomogeneity two G-manifold. There is no classification for orbit spaces of cohomogeneity two G-manifolds in general. Cohomogeneity two actions of compact Lie groups on Euclidean spaces are polar an all such actions are classified. It is clear in this case that the orbit space is homeomorphic to plane or half-plane. Also, It is proved that if G is a connected (compact or non-compact) group of the isometries which acts by cohomogeneity two on Rn, then the orbit space is homeomorphic to plane or half-plane. Classification of orbit spaces of cohomogeneity two actions on the standard sphere Sn has been described in a series of papers . Also, the orbit space of cohomogeneity two actions on simply connected spaces of constant curvature (hyperbolic spaces) has been classified before. To extend this classification to all Riemannian manifolds of constant positive curvature, we prove the following theorem: Theorem. If M is a coghomogeneity two Riemannian G-manifold of constant negative curvature, then the orbit space M/G is homeomorphic to one of the following spaces: R × S¹, R², R× [0, ∞). [ABSTRACT FROM AUTHOR]

Abstract Background Electronic medical records (EMR) contain detailed information about patient health. Developing an effective representation model is of great significance for the downstream applications of EMR. However, processing data directly is difficult because EMR data has such characteristics as incompleteness, unstructure and redundancy. Therefore, preprocess of the original data is the key step of EMR data mining. The classic distributed word representations ignore the geometric feature of the word vectors for the representation of EMR data, which often underestimate the similarities between similar words and overestimate the similarities between distant words. This results in word similarity obtained from embedding models being inconsistent with human judgment and much valuable medical information being lost. Results In this study, we propose a biomedical word embedding framework based on manifold subspace. Our proposed model first obtains the word vector representations of the EMR data, and then re-embeds the word vector in the manifold subspace. We develop an efficient optimization algorithm with neighborhood preserving embedding based on manifold optimization. To verify the algorithm presented in this study, we perform experiments on intrinsic evaluation and external classification tasks, and the experimental results demonstrate its advantages over other baseline methods. Conclusions Manifold learning subspace embedding can enhance the representation of distributed word representations in electronic medical record texts. Reduce the difficulty for researchers to process unstructured electronic medical record text data, which has certain biomedical research value.

In this paper, a numerical study was performed to investigate the flow distribution in a 52-cell proton exchange membrane (PEM) fuel cell stack. The non-uniformity factor and standard deviation parameters were used to determine the flow distribution uniformity. Flow channels of each bipolar plate were replaced with straight parallel channels filled with porous media to reduce computational costs. The effect of external and integrated humidifiers on the gas distribution among the channels was investigated. Using integrated humidifiers improved the non-uniformity factor and standard deviation by 35% and 19%, respectively. Two methods were employed to improve the flow distribution: gradual reduction of the manifold height, and installing a bump at the bottom wall of the inlet manifold. Reducing the height of the inlet manifold in the stack with integrated and external humidifiers decreased the non-uniformity factor by 62% and 44%, respectively. The installation of the bump on the manifold wall enhanced flow distribution in the stack with the external humidifier. The results show that by using an integrated humidifier in this method, the flow distribution became more non-uniform. The best flow distribution in the stack was obtained with an integrated humidifier and a 90% reduction in manifold height. In this case, the flow rate passing through each channel was more than 99% of the average mass flow rate passing through the entire channel. [ABSTRACT FROM AUTHOR]

Point clouds have attracted attention as a representation of an object’s surface. Deep generative models have typically used a continuous map from a dense set in a latent space to express their variations. However, a continuous map cannot adequately express the varying numbers of holes. That is, previous approaches disregarded the topological structure of point clouds. Furthermore, a point cloud comprises several subparts, making it difficult to express it using a continuous map. This paper proposes ChartPointFlow, a flow-based deep generative model that forms a map conditioned on a label. Similar to a manifold chart, a map conditioned on a label is assigned to a continuous subset of a point cloud. Thus, ChartPointFlow is able to maintain the topological structure with clear boundaries and holes, whereas previous approaches generated blurry point clouds with fuzzy holes. The experimental results show that ChartPointFlow achieves state-of-the-art performance in various tasks, including generation, reconstruction, upsampling, and segmentation. [ABSTRACT FROM AUTHOR]

Representation of one-dimensional (1D) signals as surfaces and higher-dimensional manifolds reveals geometric structures that can enhance assessment of signal similarity and classification of large sets of signals. Motivated by this observation, we propose a novel robust algorithm for extraction of geometric features, by mapping the obtained geometric objects into a reference domain. This yields a set of highly descriptive features that are instrumental in feature engineering and in analysis of 1D signals. Two examples illustrate applications of our approach to well-structured audio signals: Lung sounds were chosen because of the interest in respiratory pathologies caused by the coronavirus and environmental conditions; accent detection was selected as a challenging speech analysis problem. Our approach outperformed baseline models under all measured metrics. It can be further extended by considering higher-dimensional distortion measures. We provide access to the code for those who are interested in other applications and different setups (Code: https://github.com/jeremy-levy/Classification-of-audio-signals-using-spectrogram-surfaces-and-extrinsic-distortion-measures). [ABSTRACT FROM AUTHOR]

This article (correspondence) develops a composite adaptive control system for the attitude trajectory tracking of a spacecraft in elliptic orbit around a uniformly rotating asteroid. It is assumed that the spacecraft’s moment of inertia and the asteroid’s gravitational parameters are unknown. The adaptation law designed here includes a positive semidefinite regressor-dependent matrix integral. For its synthesis, the tracking error as well as two model prediction errors are used. This enhances parameter excitation and causes faster decay of the parameter error. By the Lyapunov analysis, local convergence of the tracking error is established. In addition, it is shown that the trajectories of the system converge to two manifolds. Simulation results for a spacecraft on prograde elliptic orbit around asteroid 433 Eros are presented. These results show nadir-pointing attitude regulation. Interestingly, six out of nine unknown parameters are estimated accurately for certain proportional perturbations in the model parameters. [ABSTRACT FROM AUTHOR]

This paper studied the oxygen flow distribution in a PEM fuel cell stack numerically. At first, the flow in the stack was simulated as a single phase, and the effect of gradual reduction of manifold height (tapered manifold) on improving the flow distribution between fuel cells was investigated. Standard deviation and non-uniformity coefficient have been used to measure the flow maldistribution. Gradual reduction of manifold height up to 70% in the tapered manifold improved standard deviation and non-uniformity coefficient by 6.9% and 8.4%, respectively. The results of the two-phase simulation showed that the condensation of water vapor in the saturated oxygen could cause the accumulation of liquid water at the end of the manifold. As the smaller droplets merged, the droplet radius formed at the end of the manifold increased until it detached from the manifold wall and entered the last cells. Less liquid water entered the last cell at shorter intervals in the tapered manifold. It was suggested that by creating a water chamber at the end of the manifold, condensed water be collected from the manifold and discharged from the stack. Increasing the mass flow at the manifold inlet and discharging the excess gas through the water collection chamber can push the liquid water into the chamber without causing significant changes in pressure drop. [ABSTRACT FROM AUTHOR]

Manifold representations of rotational/translational motion and conformational space of a ligand were previously shown to be effective for local energy optimization. In this paper we report the development of the Monte-Carlo energy minimization approach (MCM), which uses the same manifold representation. The approach was integrated into the docking pipeline developed for the current round of D3R experiment, and according to D3R assessment produced high accuracy poses for Cathepsin S ligands. Additionally, we have shown that (MD) refinement further improves docking quality. The code of the Monte-Carlo minimization is freely available at https://bitbucket.org/abc-group/mcm-demo .

Deep learning based on neural network has achieved excellent results in a large number of fields,but it is difficult to deal with similar or untrained tasks,and it is difficult to learn and adapt to new tasks.Moreover,it requires a high scale of trai-ning samples,resulting in its poor generalization and expansion.Meta learning is a new learning framework,which aims to solve the problem that traditional learning methods can't solve fast learning and adapt to new tasks.Aiming at the meta learning problem of image classification,a novel fiber bundle meta learning algorithm based on Bayesian theory is proposed.Firstly,the convolution neural network is used to extract the image information supporting the dataset,and the image representation is obtained.Then the manifold structure of data features and the fiber bundle of data features are constructed.The input query set selects the manifold section of the current new task to obtain the fiber suitable for the new task,so as to get the correct label of the image.Experimental results show that the model based on the proposed algorithm (FBBML) achieves the best accuracy performance compared with the standard four-layer convolutional neural network model on the common data set (mini-ImageNet).At the same time,the fiber bundle theory is introduced into meta learning,which makes the algorithm more interpretable.

We propose the first data augmentation method based on optimal transport theory, with the generated data being guaranteed to belong to the original data manifold. The proposed algorithm randomly samples a clique in the nearest-neighbors graph representing the data knowledge and computes the Wasserstein barycenter between the neighbours with random uniform weights. Being extremely natural-looking, many such barycenters are then produced iteratively to overpopulate the original dataset. We apply this approach to the problem of landmarks detection in unsupervised and semi-supervised scenarios in the popular tasks of face keypoints extraction, pose detection, and the segmentation of anatomical contours in medical imaging. The barycentric oversampling approach is shown to outperform state-of-the-art data augmentation methods. The code is available at https://github.com/cviaai/LAMBO/.

It is a challenge for manifold discovery from the data in the high-dimensional space, since the data in the high-dimensional space is sparsely distributed, which hardly provides rich information for manifold discovery so as to be possible to obtain deformed manifolds. To address this issue, this paper designed a deep model based on Brenier theorem for manifold discovery. Since Brenier theorem can find the optimal transportation mass distance between the reconstructed data distribution and the original data distribution, the manifold discovered from in the reconstructed data distribution can be as close to the original manifold as possible. Results not only show that the proposed method wins over competing methods both the precision of manifold discovery and resistance to data sparsity, but also show those non-linear architectures with deep paradigms outperform those architectures without deep paradigms in terms of manifold discovery. We find that the loss function derived by Brenier theorem can help that models minimize the error between the reconstructed manifold and the original manifold. Moreover, the manner constraining neurons with norm-2 is better than that of with norm-1 in both easing data sparsity and improving the precision of for manifold discovery.

Sub-assy-manifold is one of the most significant components inside Vent-i (Indonesian ventilator). The production of sub-assy-manifold consists of two main processes that are assembly process and machining process. The assembly process of sub-assy-manifold is the longest one that takes 23.4 minutes in total compared to other components. The assembly process takes 1.4 minutes/pcs, and the body manifold machining process takes 22 minutes/pcs. Therefore, it is too hard to produce 1000 units of Vent-i per month. Making 1000 units/month can be achieved if the assembly process and the component machining process are at 10.43 minutes maximum in total. The purpose of this research is to reduce the assembly process time and machining process time of sub-assy-manifold. It’s begun with analyzing the current design of sub-assy-manifold using DFMA (Design for Manufacturing Assembly) to reduce the assembly processes time. The two-level full-factorial design experiment is used to find the optimum machining process time. The variables used in this experiment are the type of machine tools, hole toolpath strategy, and surface toolpath strategy. The result shows that assembly process time decreases to 43%, and the machining process time decreases to 63%, and it only takes 9.9 minutes to make sub-assy-manifold in total. With this result, it is possible to produce 1000 units/month Vent-i.

Millimeter Wave (mmWave) massive multiple-input multiple-output (MIMO) systems with hybrid analog-digital architectures can greatly increase system capacity and communicate with multiple users at the same time. Accurate channel estimation is crucial for multi-user communications, but its accuracy is limited as the number of antennas and users increases. In the matrix high-dimensional operation for multi-user channel estimation, not only is it computationally intensive, but also the estimation accuracy is low. It makes our work turn to channel estimation of the user group within a certain region to improve the accuracy of estimation. In this paper, we propose a tensor dictionary manifold learning method for channel estimation and interference elimination of the multi-user mmWave massive MIMO system. A multi-user digital-analog mixed received signal model is presented. The tensor dictionary manifold learning scheme is proposed to model the received signal as a third-order low-rank tensor to handle the high-dimensional user, antenna, and channel. After segmentation, clustering and manifold learning, multiple tensor dictionary manifold models containing a group of user signals are fitted. Tensor dictionary manifold learning can take advantage of the inherent multi-domain properties of signals in the frequency, time, code and spatial domains to maintain inter-user correlation within a user group while reducing the high-dimensional channels of the user group. Using the convex relaxation property of the tensor alternating direction method, we propose a strategy to eliminate interference from other groups. And with the help of the multi-signal classification method, the channel parameters of user groups are obtained to improve the accuracy of multi-user channel estimation. This method can perform channel estimation for multiple users with only a few pilots, and improve the performance of the system. Numerical results confirm the good performance of this method.

Why did Bernhard Riemann (1826–1866), arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving at. Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the "poetry of hypothesis". He believed that human thought was fundamentally the dynamics of "mind-masses" and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner's law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness—drawing on Riemann's mind-masses and the similar "psychons" proposed by Eccles—is put forward. [ABSTRACT FROM AUTHOR]

As per the objective of the present experimental investigation, influence of various configurations of manifolds for optimum flow distribution in concentric glass tube solar air collector (CGTSAC) has been analyzed for transient conditions. Based on the previous studies it was found that the performance of solar air collector is robustly dependent on the flow distribution and decreases with non-uniform flow distribution. For evaluating four different flow distribution arrangements, the experimental setup of CGTSAC is installed at N.I.T., Kurukshetra (29°58′ (latitude) North and 76°53′ (longitude) East), India, and tested with various configurations of manifolds at different operating conditions. The experimental data have been recorded and found that the maximum exit air temperature is 53.1 and 52.9 °C, and the average values of COPt are 0.2731 and 0.2943 at air mass flow rate of 26.6 and 34.2 kg/h respectively with series flow arrangement. Also, the circular fin is introduced in CGTSAC to enhance the performance of the series flow arrangement by increasing the heat transfer. [ABSTRACT FROM AUTHOR]

Anhydrous ammonia is the most used raw material in chemical fertilizer production. In the fertilizer production process, during the transportation of anhydrous ammonia, pressure and temperature have to be kept under control. Transport and storage of anhydrous ammonia requires resistance to cryogenic conditions. Therefore, materials that are resistant to cryogenic conditions are preferred for the transport of ammonia. In this study, the kinetic energy of anhydrous ammonia transported under cryogenic conditions (−33 °C) was analysed and solutions proposed to minimize the problems such as cracking and corrosion occurring in the materials that form the structure of transportation and storage systems due to cryogenic conditions were discussed.

In this paper, we create a new type of fundamental group called the neutrosophic fundamental group. We obtain some kinds of conditional foldings that are confined to the elements of the neutrosophic fundamental groups. Also, we deduce the limit foldings of a neutrosophic fundamental group. We present the variant and invariant of the neutrosophic fundamental group under the folding of the neutrosophic manifold into itself. We show that the neutrosophic fundamental group at the ending limits of neutrosophic foldings on the n-dimensional neutrosophic manifold into itself is the neutrosophic identity group.

Background: Electronic medical records (EMR) contain detailed information about patient health. Developing an effective representation model is of great significance for the downstream applications of EMR. However, processing data directly is difficult because EMR data has such characteristics as incompleteness, unstructure and redundancy. Therefore, preprocess of the original data is the key step of EMR data mining. The classic distributed word representations ignore the geometric feature of the word vectors for the representation of EMR data, which often underestimate the similarities between similar words and overestimate the similarities between distant words. This results in word similarity obtained from embedding models being inconsistent with human judgment and much valuable medical information being lost. Results: In this study, we propose a biomedical word embedding framework based on manifold subspace. Our proposed model first obtains the word vector representations of the EMR data, and then re-embeds the word vector in the manifold subspace. We develop an efficient optimization algorithm with neighborhood preserving embedding based on manifold optimization. To verify the algorithm presented in this study, we perform experiments on intrinsic evaluation and external classification tasks, and the experimental results demonstrate its advantages over other baseline methods. Conclusions: Manifold learning subspace embedding can enhance the representation of distributed word representations in electronic medical record texts. Reduce the difficulty for researchers to process unstructured electronic medical record text data, which has certain biomedical research value. [ABSTRACT FROM AUTHOR]

The regulation and supply of oxygen as one of the medical gases in the hospital is important to ensure the availability of these gases for the survival of patients. The regulation of oxygen gas in hospitals usually uses a piping system with manifolds. The manifold will monitor the oxygen gas pressure on each tube. Manifold systems that are widely used in general can only monitor pressure but cannot perform an automatic exchange on gas cylinders if the pressure is under the permissible conditions. The manifold system design developed is equipped with pressure monitoring for automatic exchange of oxygen gas cylinders using pressure sensors and microprocessors. The test results of the system using regulator and barometer comparisons showed the percentage value of sensor pressure accuracy of 96.92 percent and 97.16 percent. At pressure below the limit of 285 KPa manifold can perform the exchange of active gas cylinders automatically. These results show the manifold design built can work quite well.

A scaled-down test section representative of an Outboard Segment manifold of the Water-Cooled Lithium Lead Breeding Blanket for the European DEMO has been designed for installation and test in a high- mass flow branch of the W-HYDRA facility, under construction at the premises of ENEA Brasimone Research Center. The test section should confirm the flow repartition recently computed in the different breeding units on the full-scale manifold, validating at the same time the computational tools used for the design and analysis. The detailed objectives and requirements of the test section, as well as the scaling rationale and procedure adopted for its design, are presented in the paper. The final design of the test section is discussed. The preliminary analyses of the developed design are also presented and show that it is compliant with the initial objectives.

Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate gradient descent, and demonstrate their superiority over the promising baseline with the ratio of at least 24%.