Orthogonal Projection Method Research Articles

Dynamic Evaluation of Carbon Emission Performance of New Energy Enterprises based on Orthogonal Projection Method

The rapid development of economic society causes people to increase the energy demand, produce more and more carbon dioxide, environmental pollution is becoming more and more serious, to solve the problem of carbon peak is imminent. Under the same and complete evaluation system, the carbon emission performance varies slightly according to different R&D directions of new energy enterprises. Therefore, it is particularly important to select evaluation indicators. In fact, each enterprise has different efforts to control carbon emissions. While studying the performance of carbon emissions, the direct and indirect impacts of carbon dioxide produced by each enterprise in the process of production on the ecological environment should be considered. In order to guarantee systematic and scientific outcomes, carbon emissions performance evaluation indicator system for new energy enterprises is constructed. With new energy enterprises as examples, based on the construction of carbon emissions performance evaluation indicator system of new energy enterprises, orthogonal projection method is used to carry out an empirical analysis of the dynamic evaluation of carbon emissions performance of thirty new energy enterprises. Through the questionnaire survey of thirty new energy enterprises, the indicator weight of carbon emission performance evaluation of new energy enterprises was determined, and the carbon emission performance of new energy enterprises was analyzed. The results will reflect the actual situation of China’s new energy enterprises, and provide the data support and references for future research on carbon emission control by the country and enterprises.

Колебания системы твёрдых тел, частично заполненных вязкими жидкостями, под действием упругодемпфирующего устройства

In this paper, we investigate the linearized two-dimensional problem on small motions of a system of rigid bodies partially filled with viscous incompressible fluids and connected in series by springs. The first and last bodies are attached by springs to two supports with a given law of motion. The trajectory of the system is perpendicular to the direction of gravity, and the damping forces acting on the hydrodynamical system are generated by the friction of bodies against a stationary horizontal support. For the described system, the law of total energy balance is formulated. Using the orthogonal projection method and a number of auxiliary boundary problems, the original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential-operator equation in the orthogonal sum of some Hilbert spaces. The properties of operator matrices, which are coefficients of the obtained differential equation, are investigated. A theorem on the unique solvability of the resulting Cauchy problem on the positive semi-axis is proved. On the basis of the proved theorem, sufficient conditions for the existence of a strong with respect to time solution of an initial-boundary value problem describing the evolution of a hydrodynamical system, are found. From a mathematical point of view, the system under consideration is a finite-dimensional perturbation of the well-known S.G. Krein’s problem on small motions of a viscous fluid in an open vessel.

An improvement of the pinned distance set problem in even dimensions

We study the pinned distance set $\Delta _x(E)=\{|x-y|:y\in E\}$ in even dimensions. We utilize the orthogonal projection method as in [X. Du et al., Math. Ann. 380 (2021)] to show that for any compact subset $E\subset \mathbb R ^d$, where $d$ is an even

Autonomic Nervous System characterization in hyperbaric environments considering respiratory component and non-linear analysis of Heart Rate Variability

Objectives: an evaluation of Principal Dynamic Mode (PDM) and Orthogonal Subspace Projection (OSP) methods to characterize the Autonomic Nervous System (ANS) response in three different hyperbaric environments was performed. Methods: ECG signals were recorded in two different stages (baseline and immersion) in three different hyperbaric environments: (a) inside a hyperbaric chamber, (b) in a controlled sea immersion, (c) in a real reservoir immersion. Time-domain parameters were extracted from the RR series of the ECG. From the Heart Rate Variability signal (HRV), classic Power Spectral Density (PSD), PDM (a non-linear analysis of HRV which is able to separate sympathetic and parasympathetic activities) and OSP (an analysis of HRV which is able to extract the respiratory component) methods were used to assess the ANS response. Results: PDM and OSP parameters follows the same trend when compared to the PSD ones for the hyperbaric chamber dataset. Comparing the three hyperbaric scenarios, significant differences were found: i) heart rate decreased and RMSSD increased in the hyperbaric chamber and the controlled dive, but they had the opposite behavior during the uncontrolled dive; ii) power in the OSP respiratory component was lower than power in the OSP residual component in cases a and c; iii) PDM and OSP methods showed a significant increase in sympathetic activity during both dives, but parasympathetic activity increased only during the uncontrolled dive. Conclusions: PDM and OSP methods could be used as an alternative measurement of ANS response instead of the PSD method. OSP results indicate that most of the variation in the heart rate variability cannot be described by changes in the respiration, so changes in ANS response can be assigned to other factors. Time-domain parameters reflect vagal activation in the hyperbaric chamber and in the controlled dive because of the effect of pressure. In the uncontrolled dive, sympathetic activity seems to be dominant, due to the effects of other factors such as physical activity, the challenging environment, and the influence of breathing through the scuba mask during immersion. In sum, a careful description of the changes in all the possible factors that could affect the ANS response between baseline and immersion stages in hyperbaric environments is needed for better interpretation of the results.

Diagnosis of Ia–Ic stages of serous high-grade ovarian cancerby the lipid profile of blood serum

Background. Ovarian cancer is the first fatal malignancy of the female reproductive system. Early detection is associated with better outcomes, but is significantly difficult because of asymptomatic or low-symptomatic course.
 Aim. To study the possibility of detecting of OC in early stages (IaIc) by the lipid profile of blood serum obtained using high-performance liquid chromatography with mass spectrometric (MS) detection.
 Materials and methods. An observational "case-control" study was conducted in period November 2019 July 2020 in the Kulakov National Medical Research Center for Obstetrics, Gynecology and Perinatology. 41 patients were included: group 1 (main) 28 patients with histologically verified high grade serous ovarian cancer of IIV FIGO stage, group 2 (control) 13 conditionally healthy women. Venous blood samples were collected immediately before the operation. Extracts of serum lipids were obtained in accordance with the modified Folch method. The composition of the samples was analyzed by electrospray ionization MS. Using the method of discriminant analysis and orthogonal projections to latent structures (OPLS-DA) were building OPLS-models based on profile of significant lipids. The comparison based on the non-parametric MannWhitney test.
 Results. The presence of 128 lipids in blood serum samples makes a major contribution to the OPLS-models, that are different for patients with IIV OC stage and controls. The OPLS-model parameters are: R2=0.87 and Q2=0.80, the area under the ROC curve reached 1, sensitivity and specificity of the model 100%. The second OPLS-model was developed to assign patients to 13 blood serum samples of the control group or to 5 blood samples of patients with I-II stages of OC: 108 lipids made the main contribution to this model (R2=0.97, Q2=0.86). The third OPLS-model was constructed to distinguish patients with earlier (IaIa stages; n=5) and advanced (IIaIVa; n=23) stages: R2=0.96 and Q2=1.00, AUC=0.99. Diglycerides, triglycerides, phosphatidylcholines, ethanolamines, sphingomyelins, ceramides, phosphatidylserines, phosphoinositols and prostaglandins significantly differ in the blood serum samples of patients with IaIc stages of OC and patients with IIIV stages and controls, that indicates the diagnostic value.
 Conclusion. It is possible to distinguish a healthy person from patient with IaIc or IIIV stages of OC. Serum oncolipids profile obtained by high-performance liquid chromatography with MS detection can be used as markers of early stages of OC, that are associated with better prognosis.

Cascaded and Recursive ConvNets (CRCNN): An effective and flexible approach for image denoising

Recently, discriminative learning methods have gained substantial interest in solving inverse imaging problems due to their decent performance and fast inferencing capability. Those methods need separate models for specific noise levels, which in turn require multiple models to be trained to denoise an image. However, images exhibit spatial variant noise which limits the applicability of such methods. In addition, the discriminative learning methods introduce artifacts such as blurring, deblocking, and so forth while denoising an image. To address these issues, we propose a cascaded and recursive convolutional neural network (CRCNN) framework which can cope with spatial variant noise and blur artifacts in a single denoising framework. The CRCNN takes into account down-sampled sub-images for fast inferencing along with the noise level map. We adopt the hybrid orthogonal projection and estimation method on the convolutional layers to improve the generalization capability of the network in terms of non-uniform and spatial variant noise levels. In contrast to the existing methods, the CRCNN framework allows both denoising and deblurring of images using a single framework which preserves the fine details in a denoised image. Extensive experiments have been conducted to validate the effectiveness and flexibility of the CRCNN framework on real as well as synthetic noisy images in comparison to the state-of-the-art denoising methods. The results show that the CRCNN performs effectively on both synthetic as well as spatial variant noise-induced images, thus, proving the practicability of the framework.

Rapid safety assessment and mitigation of radiofrequency induced implant heating using small root mean square sensors and the sensor matrix Qs.

Rapid detection and mitigation of radiofrequency (RF)-induced implant heating during MRI based on small and low-cost embedded sensors. A diode and a thermistor are embedded at the tip of an elongated mock implant. RF-induced voltages or temperature change measured by these root mean square (RMS) sensors are used to construct the sensor Q-Matrix (QS ). Hazard prediction, monitoring and parallel transmit (pTx)-based mitigation using these sensors is demonstrated in benchtop measurements at 300 MHz and within a 3T MRI. QS acquisition and mitigation can be performed in <20 ms demonstrating real-time capability. The acquisitions can be performed using safe low powers (<3 W) due to the high reading precision of the diode (126 µV) and thermistor (26 µK). The orthogonal projection method used for pTx mitigation was able to reduce the induced signals and temperatures in all 155 investigated locations. Using the QS approach in a pTx capable 3T MRI with either a two-channel body coil or an eight-channel head coil, RF-induced heating was successfully assessed, monitored and mitigated while the image quality outside the implant region was preserved. Small (<1.5 mm3 ) and low-cost (<1 €) RMS sensors embedded in an implant can provide all relevant information to predict, monitor and mitigate RF-induced heating in implants, while preserving image quality. The proposed pTx-based QS approach is independent of simulations or in vitro testing and therefore complements these existing safety assessments.

The application of ion mobility time of flight mass spectrometry to elucidate neo-formed compounds derived from polyurethane adhesives used in champagne cork stoppers

Polyurethane adhesives are used to bond agglomerated cork and natural disk cork to produce cork stoppers that are used in champagne bottles. These adhesives are manufactured by reacting polyols with an excess of diisocyanates. Isocyanates are highly reactive compounds that have a propensity to form non-intentionally added substances (NIAS) in the end product. In this work, ion mobility-time of flight-mass spectrometry was used to elucidate such NIAS, through the comparison of accurate mass spectra with the fragmentation patterns of proposed candidates. Twelve neo-formed compounds, including amines, amides and urethanes, resulting from the reaction of isocyanates with acetic acid and ethanol used as food simulants, were identified. Additionally, markers from champagne vs. champagne after its exposure to the adhesive were investigated using the supervised multivariate analysis method of Orthogonal Projection to Latent Structures – Discriminant Analysis. Four neo-formed compounds, resulting from the reaction of diisocyanates with malic acid or tartaric acid contained in the champagne, were identified for the first time in this work. All of the compounds identified were subsequently quantified using ultra-high pressure liquid chromatography coupled to a triple quadrupole mass spectrometer. Limits of detection were below 5 μg/kg in the food simulants and below 30 μg/kg in champagne samples. Migration levels ranged from 70 to 721 μg/kg, with most of them exceeding the specific migration limit established for Cramer class III compound (90 μg/kg).

Synthetic construction of the Hopf fibration in a double orthogonal projection of 4-space

Abstract The Hopf fibration mapping circles on a 3-sphere to points on a 2-sphere is well known to topologists. While the 2-sphere is embedded in 3-space, four-dimensional Euclidean space is needed to visualize the 3-sphere. Visualizing objects in 4-space using computer graphics based on their analytical representations has become popular in recent decades. For purely synthetic constructions, we apply the recently introduced method of visualization of 4-space by its double orthogonal projection onto two mutually perpendicular 3-spaces to investigate the Hopf fibration as a four-dimensional relation without analogy in lower dimensions. In this paper, the method of double orthogonal projection is used for a direct synthetic construction of the fibers of a 3-sphere from the corresponding points on a 2-sphere. The fibers of great circles on the 2-sphere create nested tori visualized in a stereographic projection onto the modeling 3-space. The step-by-step construction is supplemented by dynamic three-dimensional models showing simultaneously the 3-sphere, 2-sphere, and stereographic images of the fibers and mutual interrelations. Each step of the synthetic construction is supported by its analytical representation to highlight connections between the two interpretations.

Automated crack severity level detection and classification for ballastless track slab using deep convolutional neural network

The classification and treatment of cracks with different severity levels based on the width measurement is a critical consideration in maintenance of ballastless track slab. Existing deep learning methods cannot directly quantify cracks, which must rely on image processing technologies to post-process the initial results by deep learning, inevitably leading to multiple steps and low efficiency. This paper proposes a novel quantitative classification method for cracks with different severity levels based on deep convolutional neural networks, using orthogonal projection method to preprocess training data and define the severity level, which is validated and evaluated from four aspects: network structures, crack data, classification methods, and environmental conditions. Results show that the Inception-ResNet-v2 network can classify crack images into three severity levels without pixel segmentation or post-processing, achieving the accuracy, precision, recall and F1 score all exceeding 93%, with good robustness and adaptability to noise and light intensity.

Factor dimension determination for panel interactive effects models: an orthogonal projection approach

We consider a computationally simple orthogonal projection method to implement the (Bai and Ng in Econometrica 70:191–221, 2002) information criterion to select the factor dimension for panel interactive effects models that bypasses issues arising from the joint estimation of the slope coefficients and factor structure. Our simulations show that it performs well in cases the method can be implemented.

Numerical method for pricing discretely monitored double barrier option by orthogonal projection method

<abstract> In this paper, we consider discretely monitored double barrier option based on the Black-Scholes partial differential equation. In this scenario, the option price can be computed recursively upon the heat equation solution. Thus we propose a numerical solution by projection method. We implement this method by considering the Chebyshev polynomials of the second kind. Finally, numerical examples are carried out to show accuracy of the presented method and demonstrate acceptable accordance of our method with other benchmark methods. </abstract>

Application of the Method of Orthogonal Projection for Identification of Objects without Specified Shape in Multispectral Analysis

An approach for identification of objects without specified shape using multispectral satellite data is developed. The approach is based on the orthogonalization procedure in extended multidimensional spectral space in which filters that are orthogonal to the hypotheses of desired and similar objects are calculated and, then, scalarly multiplied by the spectra under study. It is shown that normalized rather than original spectra must be used, which leads to a significant decrease in variability of spectra that results in worse recognition of objects and specific calibration must be employed for suppression of atmospheric distortions. It is shown that such a method provides significantly higher recognizability in comparison with the least-squares method that is used in most recognition techniques.

Short-Range Clutter Suppression for Airborne Radar Using Sparse Recovery and Orthogonal Projection

For nonside-looking airborne radar (NSLAR), the range-dependent near-range clutter degrades the performance of space–time adaptive processing (STAP), especially in the high-pulse-repetition-frequency mode. To solve this problem, a novel algorithm using sparse recovery (SR) and orthogonal projection (OP) is proposed in this letter. First, the elevation angle of short-range clutter is estimated by the off-grid SR method. Second, the near-range clutter is suppressed in the elevation domain by the OP method. Finally, the azimuth–Doppler STAP is carried out to suppress the residual range-independent far-range clutter. The proposed algorithm can obtain the elevation angle of short-range clutter more precisely with only one training snapshot and it is robust since no prior knowledge is needed. The simulation results validate the effectiveness of the proposed algorithm.

Parallel transmission medical implant safety testbed: Real-time mitigation of RF induced tip heating using time-domain E-field sensors.

To implement a modular, flexible, open-source hardware configuration for parallel transmission (pTx) experiments on medical implant safety and to demonstrate real-time mitigation strategies for radio frequency (RF) induced implant heating based on sensor measurements. The hardware comprises a home-built 8-channel pTx system (scalable to 32-channels), wideband power amplifiers and a positioning system with submillimeter precision. The orthogonal projection (OP) method is used to mitigate RF induced tip heating and to maintain sufficient for imaging. Experiments are performed at 297MHz and inside a clinical 3T MRI using 8-channel pTx RF coils, a guidewire substitute inside a phantom with attached thermistor and time-domain E-field probes. Repeatability and precision are ~3% for E-field measurements including guidewire repositioning, ~3% for temperature slopes and an ~6% root-mean-square deviation between measurements and simulations. Real-time pTx mitigation with the OP mode reduces the E-fields everywhere within the investigated area with a maximum reduction factor of 26 compared to the circularly polarized mode. Tip heating was measured with ~100μK resolution and ~14Hz sampling frequency and showed substantial reduction for the OP vs CP mode. The pTx medical implant safety testbed presents a much-needed flexible and modular hardware configuration for the in-vitro assessment of implant safety, covering all field strengths from 0.5-7T. Sensor based real-time mitigation strategies utilizing pTx and the OP method allow to substantially reduce RF induced implant heating while maintaining sufficient image quality without the need for a priori knowledge based on simulations or in-vitro testing.

Maximal Free-Space Concentration of Electromagnetic Waves

We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the possibility for orders-of-magnitude intensity enhancements compared to existing demonstrations, and we use inverse design to discover metasurfaces operating near these new limits. We also demonstrate that our bounds may surprisingly describe maximum concentration defined by a wide variety of metrics. Our bounds require no assumptions about symmetry, scalar waves, or weak scattering, instead relying primarily on the transformation of a quadratic program via orthogonal-projection methods. The bounds and inverse-designed structures presented here can be useful for applications from imaging to 3D printing.

Modified method of orthogonal projection for object recognition in multispectral analysis

A method for recognition of objects with undefined shapes is proposed for use in multispectral analysis. The method involves an orthogonalization procedure in an extended multidimensional spectral range along with separate utilization of information on object brightness. An optimization procedure is performed to reduce the numbers of two types of recognition errors. This method demonstrated a substantial advantage in terms of precision of recognition over the least square method, on which most recognition methods are based.

Orthogonal Projection-Based Channel Estimation for Multi-Panel Millimeter Wave MIMO

Multi-panel MIMO is a promising technology in millimeter wave communications. Due to its partially hybrid structure and non-uniform antenna array, existing channel estimation cannot be directly applied to multi-panel MIMO. In this paper, we study channel estimation for multi-panel mmWave MIMO. We firstly model channel estimation of multi-panel MIMO as a block-sparse signal recovery problem. Then, according to maximum likelihood criterion, we propose an orthogonal projection method to firstly detect the support of the sparse channel response vector and then perform least square estimation, based on which we also propose a low-complexity greedy support detection in order to reduce computational complexity. Finally, through analyzing pairwise error probability of support detection, we verify the performance gain of joint multi-panel channel estimation over single panel channel estimation, and we further find that joint multi-panel channel estimation with independently generated random combining matrices outperforms that with identically generated combining matrices. Numerical results verify the superiority of our proposed joint multi-panel orthogonal projection based channel estimation over existing schemes.

Advanced Sea Surface Target Detection System for Shipborne VHF Radar in Log Periodic Dipole Array Antenna

While navigating in sea target detection is an important problem in modern era communication. In the ocean to detect moving targets and to analyze active variables such as wind, waves and current we can make use of Very High Frequency Ground Wave Radar (VHFGWR). In shipborne VHFGWR the brag spectra widened by Doppler Effect of the ship motion, due to this vessel echo easily merged.An orthogonal projection method to suppress the extended Brag spectra using a log periodic dipole array is proposed in this paper. The advanced technique majorly covers two stages: 1) by utilizing sea echo parameters calculate the approximation of sea clutter in spatial domain and 2) design multi frequency classification Doppler bins method to suppress the extended Brag spectra. After echo suppression, for target detection we can use different algorithms. Simulation result gives a proof that signal- to- clutter noise ratio (SCR) is developed and sea clutter got removed. This method gives very good target detection for shipborne VHF radar.

Oscillations of a Stratified Liquid Partially Covered with Ice (General Case)

We study the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and a region of crumbled ice. The elastic ice is modeled by an elastic plate. The crumbled ice is understood as weighty particles of some matter floating on the free surface. Using the method of orthogonal projection of boundary conditions on a moving surface and the introduction of auxiliary problems, we reduce the original initial boundary value problem to an equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions under which there exists a strong (with respect to time) solution of the initial boundary value problem describing the evolution of the hydrodynamic system under consideration.