Nonlinear Projection Research Articles

Manifolds of amphiphilic bilayers: Stability up to the boundary

We consider the mass preserving L 2 -gradient flow of the strong scaling of the functionalized Cahn Hilliard gradient flow and establish the nonlinear stability of a manifold comprised of quasi-equilibrium bilayer distributions up to the manifold's boundary. In the limit of thin but non-zero interfacial width, ε ≪ 1 , the bilayer manifold is parameterized by meandering modes that describe the interfacial evolution. The normal coercivity of the manifold is limited by “pearling” modes that control the structure of the profile near the interface, these are weakly damped and can lead to the dynamic rupture of the interface. Amphiphilic interfaces may decrease energy by either lengthening or shortening, depending upon the amphiphilic mass distributed in the bulk. We introduce an implicitly defined parameterization of the interfacial shape that uncouples the length change from the parameters describing the shape and introduce a nonlinear projection onto the manifold from a surrounding neighborhood. The bilayer manifold has asymptotically large but finite dimension tuned to maximize normal coercivity while preserving the wave-number gap between the meandering and the pearling modes. Modulo a pearling stability assumption, we show that the manifold attracts nearby orbits into a tubular neighborhood about itself so long as the interfacial shape remains sufficiently smooth and far from self-intersection. In a companion paper, [8] , we identify open sets of initial data whose orbits converge to circular equilibrium after a significant transient, and derive a singularly perturbed interfacial evolution comprised of motion against curvature regularized by an asymptotically weak Willmore term.

합성곱 오토인코더 기반 메탄 제트 화염에 대한 차수축소모델 적용

In this work, the convolutional autoencoder is applied to the reduced order model for a turbulent methane jet flame. Autoencoder is a machine learning algorithm, which reduces the problem dimension by non-linear projection. It has an advantage in reconstruction of data with significant non-linearity. Additionally, with a convolutional layer the characteristics of original data can be trained with a relatively small number of hyper-parameters. To check accuracy of the reduced order model using the convolutional autoencoder, we applied it to surrogate model and sparse reconstruction problem, and compared it with other dimension reduction algorithms. For model training, five parameters are selected as the model training parameters and 20 and 40 sensor data are extracted for the sparse reconstruction problem. The proposed convolutional autoencoder shows better accuracy than the linear projection-based dimension reduction algorithm.

Uncertainty, Wages and the Business Cycle

AbstractWe show that limited wage flexibility in economic downturns generates strong and state-dependent amplification of uncertainty shocks. It also explains the cyclical behaviour of empirical measures of uncertainty. In the presence of matching frictions, an occasionally binding constraint on downward wage adjustment enhances the concavity of firms’ hiring rule, resulting in an endogenous profit risk-premium. In turn, higher uncertainty increases the profit risk-premium when the economy operates close to the wage constraint, deepening a recession. Non-linear local projections and vector autoregression estimates support the model predictions. In addition, we show that measured uncertainty rises in a recession even without uncertainty shocks.

On the transfer of damage detectors between structures: An experimental case study

Incomplete data – which fail to represent environmental effects or damage – are a significant challenge for structural health monitoring (SHM). Population-based frameworks offer one solution by considering that information might be shared, in some sense, between similar structures. In this work, the data from a group of aircraft tailplanes are considered collectively, in a shared (more consistent) latent space. As a result, the measurements from one tailplane enable damage detection in another, utilising various pair-wise comparisons within the population.Specifically, Transfer Component Analysis (TCA) is applied to match the normal condition data from different population members. The resulting nonlinear projection leads to a general representation for the normal condition across the population, which informs damage detection via measures of discordancy. The method is applied to a experimental dataset, based on vibration-based laser vibrometer measurements from three tailplanes. By considering the partial datasets together, consistent damage-sensitive features can be defined, leading to an 87% increase in the true positive rate, compared to conventional SHM.

Color-space analytics for damage detection in 3D point clouds

Recent advances have enabled the use of modern remote sensing technologies to create high-resolution 3 D point clouds that capture the in-situ geometry of infrastructure systems. However, there is a need for new methods of analyzing and leveraging these complex data types. In this paper, the authors present an approach to quantifying textural deterioration and surficial damages manifested in point cloud data, such as corrosion or spall. This is achieved through geometric analysis of a nonlinear projection of the original color-space, and results in an algorithm that is generalizable to a variety of structural defects. The behavior of this algorithm is illustrated through both laboratory and field-scale experimental analysis, in which point cloud colorimetric differentials are identified automatically via the color-space damage detection algorithm and then compared with pixel-wise ground truth measurements. Overall measurement errors were on the order of 5-10%, with most error resulting from surface staining and surface reflectivity.

House price synchronization across the US states: The role of structural oil shocks

This paper analyzes the impact of disentangled oil shocks on the synchronization in housing price movements across all the US states plus DC. Using a Bayesian dynamic factor model, the house price movements are decomposed into national, regional, and state-specific factors. We then study the impact of oil-specific supply and demand, inventory accumulation, and global demand shocks on the national factor using linear and nonlinear local projection methods. The impulse response analyses suggest that oil-specific supply and consumption demand shocks are most important in driving the national factor. Moreover, as observed from the regime-specific local projection model, these two shocks are found to have a relatively stronger impact in a bearish rather than a bullish national housing market. Our results have important policy implications.

Joint distortion rectification and super-resolution for self-driving scene perception

Fisheye lenses are widely applied in the self-driving system due to its large field of view (FOV), which also induces the strong radial distortion in captured data. Distortion rectification is a crucial preprocessing step for scene perception since the non-linear projection heavily destroys the original geometric distribution of objects. Previous methods rectify the distorted image with a plausible global distribution, but they perform poorly on the local appearance such as the detailed texture of vehicles and pedestrians, which are hard to meet the fine requirements of object detection and semantic recognition. To solve this problem, we propose a joint distortion rectification (DR) and super-resolution (SR) end-to-end framework to generate the realistic rectification result with a visually pleasing local appearance. To the best of our knowledge, this is the first parametric framework that combines the challenging techniques DR and SR in the field of computer vision, which learns the accurate mapping function from the distorted and low-resolution domain into the corrected and high-resolution domain simultaneously. Moreover, the devised network architecture using the channel attention mechanism and object-aware loss function enables better-reconstructed scenes compared with the state-of-the-art methods. Experimental results show that our approach achieves superior rectification and enhancement performance in both quantitative measure and visual qualitative appearance, contributing a comprehensive and promising vision algorithm to the perception of the self-driving scene.

A Novel Intelligent Fault Diagnosis Method for Rolling Bearings Based on Compressed Sensing and Stacked Multi-Granularity Convolution Denoising Auto-Encoder

This paper investigates the unsupervised automatic feature extraction method with a large amount of unlabeled data for the fault diagnosis of rolling bearings in automobile production line, where the fault information is hard to identify due to the low-level features of a single category and the massive fault data is difficult to process. Different from the existing methods, which only combine the compressive sensing with single category of low-level features, or extract features from raw data, a novel intelligent fault diagnosis method for rolling bearings based on the compressive sensing and a stacked multi-granularity convolution denoise auto-encoder network is proposed, which utilizes the nonlinear projection to achieve the compressed acquisition and resolves issues with character unicity by extracting a diverse category of high-level features. Moreover, a regularization method called ‘dropout’ is used to prevent overfitting during the training process. The amount of measured data that contained all the information of faults is reduced and the classification accuracy is improved by extracting more robust features based on the proposed method. Finally, the effectiveness of the proposed method is validated using data sets from rolling bearings in an automotive production line and the analysis result show that it is superior to the existing methods and is able to obtain high diagnostic accuracies.

Shape approximation by developable wrapping

We present an automatic tool to approximate curved geometries with piece-wise developable surfaces. At the center of our work is an algorithm that wraps a given 3D input surface with multiple developable patches, each modeled as a discrete orthogonal geodesic net. Our algorithm features a global optimization routine for effectively finding the placement of the developable patches. After wrapping the mesh, we use these patches and a non-linear projection step to generate a surface that approximates the original input, but is also amendable to simple and efficient fabrication techniques thanks to being piecewise developable. Our algorithm allows users to steer the trade-off between approximation power and the number of developable patches used. We demonstrate the effectiveness of our approach on a range of 3D shapes. Compared to previous approaches, our results exhibit a smaller or comparable error with fewer patches to fabricate.

Projection algorithm-based nonlinear observation of internal states in fuel delivery systems with gas diffusion

In this paper, a nonlinear observer design to estimate different gas species profiles and partial pressures in a fuel delivery system (FDS) with gas permeation is presented. Precise knowledge of critical internal states is of great importance to ensure reliable and efficient operation for FDS. First, a nonlinear isothermal dynamic model including fuel supply, hydrogen consumption, mixture recirculation and exhaust is formulated. Then a nonlinear observer based on projection algorithm is proposed, giving detailed information on internal conditions of FDS online. Without calculation of inverse matrix, the stack output voltage is treated as the only measurable observer input. The voltage estimation error is obtained from the difference between the prediction and the actual measurement, and nonlinear error injection matrix and projection term are employed as correction inputs. Finally, the proposed dynamic state observer is validated and compared with second order sliding mode (SOSM) observer on RT-LAB platform, the results indicate that the observer shows better real-time estimation performance and robustness. Furthermore, the observer demonstrates good robustness in terms of hydrogen partial pressures observation, but less robustness in nitrogen partial pressures estimation. Moreover, the sequence of key system parameters effecting the estimations are analyzed deeply and some conclusions are extracted.

Word-serial unified and scalable semi-systolic processor for field multiplication and squaring

This paper exhibits a word-serial unified and scalable semi-systolic processor core for concurrently executing both multiplication and squaring operations over GF(2k). The processor is extracted by applying a chosen non-linear scheduling and projection functions to the dependency graph of the adopted bipartite multiplication-squaring algorithm. It has the advantage of sharing the data-path resources between the two operations leading to considerable savings in both space and power resources. Also, the processor’s scalability nature provides the designer with higher flexibility to manage the processor size as well as its execution time. The acquired ASIC synthesis results of the explored word-serial multiplier-squarer architecture and the reported competing word-serial multiplier architectures indicate that the developed design significantly outperforms the competing ones in terms of area and consumed energy at the word-size of 32-bits. Therefore, the explored architecture is more suited for realizing cryptographic primitives in all resource-constrained embedded applications operating at this word-size.

Improving VIP viewer gaze estimation and engagement using adaptive dynamic anamorphosis

Anamorphosis for 2D displays can provide viewer centric perspective viewing, enabling 3D appearance, eye contact and engagement, by adapting dynamically in real time to a single moving viewer’s viewpoint, but at the cost of distorted viewing for other viewers. We present a method for constructing non-linear projections as a combination of anamorphic rendering of selective objects whilst reverting to normal perspective rendering of the rest of the scene. Our study defines a scene consisting of five characters, with one of these characters selectively rendered in anamorphic perspective. We conducted an evaluation experiment and demonstrate that the tracked viewer centric imagery for the selected character results in an improved gaze and engagement estimation. Critically, this is performed without sacrificing the other viewers’ viewing experience. In addition, we present findings on the perception of gaze direction for regularly viewed characters located off-center to the origin, where perceived gaze shifts from being aligned to misalignment increasingly as the distance between viewer and character increases. Finally, we discuss different viewpoints and the spatial relationship between objects.

Zero-Shot Learning for EEG Classification in Motor Imagery-Based BCI System.

A brain-computer interface (BCI) based on motor imagery (MI) translates human intentions into computer commands by recognizing the electroencephalogram (EEG) patterns of different imagination tasks. However, due to the scarcity of MI commands and the long calibration time, using the MI-based BCI system in practice is still challenging. Zero-shot learning (ZSL), which can recognize objects whose instances may not have been seen during training, has the potential to substantially reduce the calibration time. Thus, in this context, we first try to use a new type of motor imagery task, which is a combination of traditional tasks and propose a novel zero-shot learning model that can recognize both known and unknown categories of EEG signals. This is achieved by first learning a non-linear projection from EEG features to the target space and then applying a novelty detection method to differentiate unknown classes from known classes. Applications to a dataset collected from nine subjects confirm the possibility of identifying a new type of motor imagery only using already obtained motor imagery data. Results indicate that the classification accuracy of our zero-shot based method accounts for 91.81% of the traditional method which uses all categories of data.

Multiagent Containment Control With Nonconvex States Constraints, Nonuniform Time Delays, and Switching Directed Networks.

This brief studies the constrained containment control problem of continuous-time multiagent systems with nonconvex states constraints, nonuniform time delays, and switching directed networks. A distributed containment control algorithm consisting of nonlinear projection, nonlinear constraints, and communication delays is proposed. Based on the model transformation technique, convex analysis method, and the Lyapunov function, we prove that all agents finally converge into the convex hull formed by the given stationary points with arbitrarily bounded communication delays and arbitrarily switching networks as long as each agent jointly has at least one path from the given points to itself. Finally, a numerical example is included to show the effectiveness of theoretical results.

An Image Reconstruction Model under Poisson Noise Using multiscale Compressed Sensing

For the influence of poisson noise images, in order to get rid of poisson noise, this paper put forward image reconstruction method by using multiscale compressed sensing. the algorithm can approximate the optimal sparse representation of the image edge details such as the characteristics of theShearlet domain based multi-scale compressed sensing method. The image is decomposed into the high-frequency subbands byShearlet, and the compressed sensing is applied into each subband to reconstruct the image. In this paper, A total variation of RL iterative algorithm constructed by nonlinear projection algorithm based on closed convex set is explored as the reconstruction method, which use derivation of the nonlinear projection instead of total variation. In mathematics, Shearlet has been proved to be a better tool for edge characterization than traditional wavelet. By using the nonlinear projection scheme to constrain the residual coefficients in the Shearlet domain, a better estimation can be obtained from the Shearlet representation. Numerical examples show that the denoising effect of these methods is very good, which is better than the correlation method based on Curvelet transform. In addition, the number of iterations required by our scheme is far less than that of our competitors.

Multi-nonlinear multi-view locality-preserving projection with similarity learning for random cross-view gait recognition

View variation is one of the greatest challenges in the field of gait recognition. Subspace learning approaches are designed to solve this issue by projecting cross-view features into a common subspace before recognition. However, similarity measures are data-dependent, which results in low accuracy when cross-view gait samples are randomly arranged. Inspired by the recent developments of data-driven similarity learning and multi-nonlinear projection, we propose a new unsupervised projection approach, called multi-nonlinear multi-view locality-preserving projections with similarity learning (M2LPP-SL). The similarity information among cross-view samples can be learned adaptively in our M2LPP-SL. Besides, the complex nonlinear structure of original data can be well preserved through multiple explicit nonlinear projection functions. Nevertheless, its performance is largely affected by the choice of nonlinear projection functions. Considering the excellent ability of kernel trick for capturing nonlinear structure information, we further extend M2LPP-SL into kernel space, and propose its multiple kernel version MKMLPP-SL. As a result, our approaches can capture linear and nonlinear structure more precisely, and also learn similarity information hidden in the multi-view gait dataset. The proposed models can be solved efficiently by alternating direction optimization method. Extensive experimental results over various view combinations on the multi-view gait database CASIA-B have demonstrated the superiority of the proposed algorithms.

DIGITALIZATION PROBLEM ANALYSIS OF THE SPHERE OF TECHNICAL REGULATION IN CONSTRUCTION

The main aim of the work is to substantiate the feasibility of implementing models of semantic analysis in the system of technical regulation in construction. To do this, an analysis of the problem of digitalisation of the normative base in construction and the definition of contradictory building codes and regulations, which has manifested in the integration of Ukraine into the international regulatory space. Procedure of interaction of geographic information systems as sources of initial data for design and further management of indicators of life cycle of objects of construction, and information model of object as a tool of reception, accumulation and storage of information on object in the course of its creation and operation has investigated in this paper. A study of artificial neural networks that can has used to search for web documents in the electronic database of regulations in the field of construction and building materials. It has proposed to use deeply structured semantic models to search for documents by their content. Deep structured semantic models perform a nonlinear projection to map the query into the common semantic space. After such a reflection of the relevance of each document found on the record, it has excluded for the cosines of the angles between the vector record model and the vector document model. In addition, the Deep Structured Semantic Models architecture uses hidden layers designed to resize input vectors. This allows the model to manipulate vectors of different sizes. Further research has planned to focus on the implementation of a deeply structured semantic model in the infocommunication system of using the information resource of the regulatory framework in construction to solve the search problem.

Co-teaching in non-linear projects: A contextualised model of co-teaching to support educational change

Co-teaching is regularly paired with school improvements and educational reforms, yet research does not clearly separate the challenges of co-teaching for teacher professional development, course improvement and for wider reforms. We explored how co-teaching emerged and what barriers teachers experienced as meaningful for their co-teaching after a national core curriculum reform. Two cross-sectional data sets were collected. Three qualitatively different co-teaching profiles emerged: highly collaborative, collaborative, and imbalanced co-operative co-teaching. However, teachers’ experiences of the meaningful barriers varied. Finally, we propose a model of contextualised co-teaching that supports implementing and researching co-teaching as a part of second-order educational changes.

High-dimensional Bayesian optimization using low-dimensional feature spaces

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10–20 parameters. To scale BO to high dimensions, we usually make structural assumptions on the decomposition of the objective and/or exploit the intrinsic lower dimensionality of the problem, e.g. by using linear projections. We could achieve a higher compression rate with nonlinear projections, but learning these nonlinear embeddings typically requires much data. This contradicts the BO objective of a relatively small evaluation budget. To address this challenge, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Our approach allows for optimization of BO’s acquisition function in the lower-dimensional subspace, which significantly simplifies the optimization problem. We reconstruct the original parameter space from the lower-dimensional subspace for evaluating the black-box function. For meaningful exploration, we solve a constrained optimization problem.

On the Use of a Rotatable ECT Sensor to Investigate Dense Phase Flow: A Feasibility Study.

This paper presents the feasibility study of dynamic flow measurements using the concept of a rotatable electrical capacitance tomography (ECT) sensor. The experiment considered horizontal flow in a pneumatic conveying flow loop in the case of dense phase flow. Slugs and settled layers were imaged and a comparison was made between no rotation or rotation of the sensor for two image reconstruction schemas: linear back projection (LBP) and non-linear iterative back projection. Data were evaluated both qualitatively and quantitatively by estimating the solids concentration level for different hue levels.