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We improve the bound on Kúhnel's problem to determine the smallest n such that the k-skeleton of an n-simplex Δ n (k) does not embed into a compact PL 2k-manifold M by showing that if Δ n (k) embeds into M, then n ≤ (2 k + 1) + (k + 1) β k (M ; Z 2) . As a consequence we obtain improved Radon and Helly type results for set systems in such manifolds. Our main tool is a new description of an obstruction for embeddability of a k-complex K into a compact PL 2k-manifold M via the intersection form on M. In our approach we need that for every map f : K → M the restriction to the (k - 1) -skeleton of K is nullhomotopic. In particular, this condition is satisfied in interesting cases if K is (k - 1) -connected, for example a k-skeleton of n-simplex, or if M is (k - 1) -connected. In addition, if M is (k - 1) -connected and k ≥ 3 , the obstruction is complete, meaning that a k-complex K embeds into M if and only if the obstruction vanishes. For trivial intersection forms, our obstruction coincides with the standard van Kampen obstruction. However, if the form is non-trivial, the obstruction is not linear but rather 'quadratic' in a sense that it vanishes if and only if certain system of quadratic diophantine equations is solvable. This may potentially be useful in attacking algorithmic decidability of embeddability of k-complexes into PL 2k-manifolds. [ABSTRACT FROM AUTHOR]

We study the structure of self-homeomorphism groups of fibered manifolds. A fibered topological space is a Birman–Hilden space whenever in each isotopic pair of its fiber-preserving (taking each fiber to a fiber) self-homeomorphisms the homeomorphisms are also fiber-isotopic (isotopic through fiber-preserving homeomorphisms). We prove in particular that the Birman–Hilden class contains all compact connected locally trivial surface bundles over the circle, including nonorientable ones and those with nonempty boundary, as well as all closed orientable Haken 3-manifold bundles over the circle, including nonorientable ones. [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.

Blending hydrogen with natural gas (NG) is an efficient method for transporting hydrogen on a large scale at a low cost. The manifold at the NG initial station is an important piece of equipment that enables the blending of hydrogen with NG. However, there are differences in the components and component contents of imported NG from different countries. The components of hydrogen-blended NG can affect the safety and efficiency of transportation through pipeline systems. Therefore, numerical simulations were performed to investigate the blending process and changes in the thermodynamic properties of four imported NGs and hydrogen in the manifold. The higher the heavy hydrocarbon content in the imported NG, the longer the distance required for the gas to mix uniformly with hydrogen in the pipeline. Hydrogen blending reduces the temperature and density of NG. The gas composition is the main factor affecting the molar calorific value of a gas mixture, and hydrogen blending reduces the molar calorific value of NG. The larger the content of high-molar calorific components in the imported NG, the higher the molar calorific value of the gas after hydrogen blending. Increasing both the temperature and hydrogen mixing ratio reduces the Joule-Thomson coefficient of the hydrogen-blended NG. The results of this study provide technical references for the transport of hydrogen-blended NG. • The blending process and thermodynamic properties of hydrogen and natural gas in the manifold are investigated. • An increase in the component content of heavy hydrocarbons in natural gas increases the distance of gas mixing uniformly. • The components of natural gas affect the transportation and thermodynamic properties of hydrogen-blended natural gas. • Hydrogen injection decreases density, molar calorific value, viscosity, and Joule-Thomson coefficient of natural gas. [ABSTRACT FROM AUTHOR]

The Half-Transform Ansatz (HTA) is a proposed method to solve hyper-geometric equations in Quantum Phase Space by transforming a differential operator to an algebraic variable and including a specific exponential factor in the wave function, but the mechanism which provides this solution scheme is not known. Analysis of the HTA’s application to the Hydrogen atom suggests an underlying mechanism which the HTA is a part of. Observations of exponential factors that act on the wave function naturally suggest modeling quantum operator definitions as a point on a Riemannian manifold in the 4D Operator Space, a novel idea we call the Operator Space Manifold Theory. On this manifold, we explore the concepts of superposition, regions of unique energy eigenvalues, and translation operators. We also find the theoretical backing to derive the HTA and how Operator Space Manifold Theory can be used to describe and solve quantum systems by manipulating how a quantum state perceives position and momentum. [ABSTRACT FROM AUTHOR]

The escalating demand for heat dissipation has prompted considerable interest in the manifold micro-pin–fin heat sink (MMPFHS) as a promising solution for high heat flux cooling applications. The two-dimensional topology of this multi-layered heat sink plays a pivotal role in organizing the three-dimensional spatial flow, consequently influencing both hydraulic and thermal performance. This study proposes and comparatively analyzes the only three rhombus-based tiling topologies applicable to MMPFHS, specifically the rhombus topology (RT), triangle hexies topology (THT), and firecracker topology (FT), all of which adhere to the principles of gapless, non-overlapping, and spatially expandable tiling topology. The relations of topological geometry and the hydraulic and thermal performances are explored and compared. And figure of merit (FOM) is also introduced to assess their overall performance. The results indicate that the overall performance of THT is predominant. When DPF = 100 μm, a = 200 μm, Din = 50, Re = 64.87, the temperature non-uniformity on the heating surface of THT is only 0.022 K, the thermal resistance is 9.4 × 10–6 km2 W−1, and the FOM of THT is about 1.14 times of that of RT. RT and FT have a similar performance, and the maximum deviation of FOM for both of them within the conditions studied in this paper is only 0.04. The paper provides a reference for selecting topologies in MMPFHS design. [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]

The nonlinearity of vectorial functions and of their restrictions to manifolds are defined as the Hamming distance to the set of affine mappings and of their restrictions to the manifold, respectively. Relations between the parameters of the nonlinearity of a vectorial function and their analogues for its coordinate functions and its restrictions to manifolds are established. An analogue of the Parseval identity for such parameters of vectorial functions is proved, which implies the upper bound (qk − 1)qn−k − qn/2−k for the nonlinearity of a mapping over a q-element field of n variables with k coordinates. Attainability conditions for this estimate are found, and a class of Boolean vectorial functions with high value of nonlinearity is constructed. Estimates characterizing the distribution of the nonlinearity of a vectorial function and of its restrictions to manifolds are obtained. [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. [ABSTRACT FROM AUTHOR]

The hybrid manifold micro-pin-fin (MMPF) heat sink combined nozzle jets is an option for large-scale integrated circuits (LSI). The demond for uniform and ultra-high heat flux removal by MMPF heat sink has not been adequately investigated. This work aims to solve the problem of fluid organization. The proposed basic tiling topologies, including square, regular hexagon, 30° rhombus, and 60° rhombus topologies, provide different organized fluid flows and heat transfer patterns. The present study focuses on comparing these topologies according to independent porous medium parameters, such as nozzle pore size DZ, flow pore size DX,Y, and porosity ε. The results show that the square topology achieves the smallest total thermal resistance Rtot value of 0.0975 × 10−4 K m2/W, while the hexagon topology achieved the highest value of COP/ΔT, which was 2033.9 K−1. According to the sensitivity analysis results, the optimal total thermal resistance can be obtained by balancing the influences of nozzle pore size, flow pore size, and porosity. The optimal pressure drop can be obtained by maximizing the porosity. [ABSTRACT FROM AUTHOR]

BackgroundThe World Health Organization has reported that approximately 300 million individuals suffer from the mood disorder known as MDD. Non-invasive 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.MethodsIn 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.ResultsThe 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 sensory-motor networks.ConclusionTo 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.

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.

In this paper, we introduce a certain topology on the group DiffF (M) of all Cr-diffeomorphisms of the foliated manifold (M; F), where r ≥ 0. This topology depends on the foliation and is called the F-compact-open topology. It coincides with the compact-open topology when F is an n-dimensional foliation. If the codimension of the foliation is n, then the convergence in this topology coincides with the pointwise convergence, where n = dim M. We prove that some subgroups of the group DiffF (M) are topological groups with the F-compact-open topology. Throughout this paper, we use smoothness of the class C∞. [ABSTRACT FROM AUTHOR]

When the underlying density exhibits multiple modes with different scales and orientations, density estimators with locally adaptive smoothing parameters show substantial gains over those with fixed bandwidths. However, it is a concern that the local smoothing matrices may not be well parameterized, and the corresponding optimization problems will be difficult. In this paper, we build a more promising and practical algorithm. The local bandwidth factors are chosen through clustering, and the global smoothing parameter is achieved by optimizing the Asymptotic Mean Integrated Squared Error. Most importantly, our locally adaptive estimator involves optimizing a scalar rather than solving a costly multivariate optimization problem. Our method, which can also be applied to manifold density estimation, is an improvement and generalization of the binned version estimator of Sain. [ABSTRACT FROM AUTHOR]

For Brentano, an act of consciousness features a presentation of an object joined with an inner presentation – an 'inner consciousness' or inner awareness – of that object-presentation. On Mark Textor's articulation of Brentano's model, the act has the structure of a single experience directed upon a plurality, viz.: the object and the experience itself. I consider an alternative development of this Brentanian model. Drawing on Husserl's part-whole ontology, I submit, the act itself has the structure of a whole formed from two co-dependent parts, viz., the object-presentation and inner awareness of that presentation. Looking to Husserl's analysis of inner time-consciousness, Textor proposes an enhancement of Brentano's model of inner consciousness. On Textor's model, inner awareness is such that one may be aware of one's experience, in the stream of one's consciousness, 'without grasping any adumbrations [of the experience], but temporal ones'. I dig into Husserl's doctrine of 'abumbration' (as where a tree is given visually with adumbrations of its shape on the back side, of its color in gradations, etc.). On my reconstruction, inner awareness of an experience presents the experience within a manifold of 'adumbrated' temporal retentions and protentions that place the experience in its stream of consciousness. [ABSTRACT FROM AUTHOR]

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 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 study the following version of Hardy-type inequality on a domain Ω in a Riemannian manifold ( M , g ) : ∫ Ω | ∇ u | g p ρ α d V g ≥ ( | p − 1 + β | p ) p ∫ Ω | u | p | ∇ ρ | g p | ρ | p ρ α d V g + ∫ Ω V | u | p ρ α d V g , ∀ u ∈ C c ∞ ( Ω ) . We provide sufficient conditions on p , α , β , ρ and V for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, R N with p<N, R N ∖ { 0 } with p ≥ N , H N , etc. [ABSTRACT FROM AUTHOR]

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of type (1, 1). The fourth power of the additional structure is minus the identity and its components form a skew-circulant matrix in some local coordinate system. The both structures are compatible and they determine an associated indefinite metric on the manifold. [ABSTRACT FROM AUTHOR]

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]

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]

We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic normalization condition in the neighborhood of infinity. Under some conditions on dilatations of inverse mappings, we have established the existence of such solutions in the class of continuous Sobolev mappings. We have also obtained results on the locally uniform limit of a sequence of such solutions. [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.

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]

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]

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (M , g) of dimension N ≥ 3 , without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when M = R 3 , our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported. [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]