Projection Operator Research Articles

Randomized greedy magic point selection schemes for nonlinear model reduction

An established way to tackle model nonlinearities in projection-based model reduction is via relying on partial information. This idea is shared by the methods of gappy proper orthogonal decomposition (POD), missing point estimation (MPE), masked projection, hyper reduction, and the (discrete) empirical interpolation method (DEIM). The selected indices of the partial information components are often referred to as “magic points.” The original contribution of the work at hand is a novel randomized greedy magic point selection. It is known that the greedy method is associated with minimizing the norm of an oblique projection operator, which, in turn, is associated with solving a sequence of rank-one SVD update problems. We propose simplification measures so that the resulting greedy point selection has the following main features: (1) The inherent rank-one SVD update problem is tackled in a way, such that its dimension does not grow with the number of selected magic points. (2) The approach is online efficient in the sense that the computational costs are independent from the dimension of the full-scale model. To the best of our knowledge, this is the first greedy magic point selection that features this property. We illustrate the findings by means of numerical examples. We find that the computational cost of the proposed method is orders of magnitude lower than that of its deterministic counterpart. Nevertheless, the prediction accuracy is just as good if not better. When compared to a state-of-the-art randomized method based on leverage scores, the randomized greedy method outperforms its competitor.

PRSCS-Net: Progressive 3D/2D rigid Registration network with the guidance of Single-view Cycle Synthesis

The 3D/2D registration for 3D pre-operative images (computed tomography, CT) and 2D intra-operative images (X-ray) plays an important role in image-guided spine surgeries. Conventional iterative-based approaches suffer from time-consuming processes. Existing learning-based approaches require high computational costs and face poor performance on large misalignment because of projection-induced losses or ill-posed reconstruction. In this paper, we propose a Progressive 3D/2D rigid Registration network with the guidance of Single-view Cycle Synthesis, named PRSCS-Net. Specifically, we first introduce the differentiable backward/forward projection operator into the single-view cycle synthesis network, which reconstructs corresponding 3D geometry features from two 2D intra-operative view images (one from the input, and the other from the synthesis). In this way, the problem of limited views during reconstruction can be solved. Subsequently, we employ a self-reconstruction path to extract latent representation from pre-operative 3D CT images. The following pose estimation process will be performed in the 3D geometry feature space, which can solve the dimensional gap, greatly reduce the computational complexity, and ensure that the features extracted from pre-operative and intra-operative images are as relevant as possible to pose estimation. Furthermore, to enhance the ability of our model for handling large misalignment, we develop a progressive registration path, including two sub-registration networks, aiming to estimate the pose parameters via two-step warping volume features. Finally, our proposed method has been evaluated on a public dataset CTSpine1k and an in-house dataset C-ArmLSpine for 3D/2D registration. Results demonstrate that PRSCS-Net achieves state-of-the-art registration performance in terms of registration accuracy, robustness, and generalizability compared with existing methods. Thus, PRSCS-Net has potential for clinical spinal disease surgical planning and surgical navigation systems.

“Global challenge program” projects themed on preventing zoonosis: developing One Health core competences in medical students at SJTU

Abstract Objectives To develop One Health (OH) core competencies in medical students, Shanghai Jiao Tong University has conducted an OH practice project named the “Global Challenge Program” (GCP) for three years. This study aims to understand the outcomes and challenges of the pilot projects, thereby providing evidences to support the expansion of One Health education program on a larger scale. Methods We conducted a questionnaire survey to a purposive sample of 48 participants who were involved in GCP projects. A questionnaire was designed to assess the effect of GCP projects on improving the core competencies of OH professionals. It consists of 32 questions divided into four categories: basic information, overall assessment, communication skills, and interdisciplinary collaboration. Statistical analysis was conducted and reported based on the data collected from the survey. Results A total of 42 students (87.5 % of 48 participants) completed the follow-up survey. Among them, 64.3 % perceived a significant improvement in their understanding of the OH concept and approach after participating in the GCP projects. Benefiting from the communication opportunities offered by the GCP projects, 24.0 % and 49.0 % of the students reported significant and moderate improvement in their international communication abilities, respectively. In addition, 74 .0% of the students noted that the GCP projects greatly enhanced their capabilities in interdisciplinary cooperation and systematic thinking in addressing complex health issues. Conclusions The GCP project has served as a pilot initiative for participatory OH education, contributing to the development of OH core competencies in medical students, particularly in systems thinking, international communication, and interdisciplinary collaboration. However, generalizing the experience of the pilot project to a large-scale education program for medical students requires careful revisit of the gaps of resources and talents in curriculum building and project operation.

Digital Twin Smart Water Conservancy: Status, Challenges, and Prospects

Digital twin technology, a new type of digital technology emerging in recent years, realizes real-time simulation, prediction and optimization by digitally modeling the physical world, providing a new idea and method for the design, operation and management of water conservancy projects, which is of great significance for the realization of the transformation of water conservancy informatization to intelligent water conservancy. In view of this, this paper systematically discusses the concept and development history of digital twin smart water conservancy, compares its differences with traditional water conservancy models, and further proposes the digital twin smart water conservancy five-dimensional model. Based on the five-dimensional model of digital twin water conservancy, the research progress of digital twin smart water conservancy is summarized by focusing on six aspects, namely digital twin water conservancy data perception, data transmission, data analysis and processing, digital twin water conservancy model construction, digital twin water conservancy interaction and collaboration and digital twin water conservancy service application, and the challenges and problems of digital twin technology in the application of smart water conservancy. Finally, the development trend of digital twin technology and the direction of technological breakthroughs are envisioned, aiming to provide reference and guidance for the research on digital twin technology in the field of smart water conservancy and to promote the further development of the field.

Study on the regularities of flow‐sediment transport and sedimentation in the lower Yellow River

AbstractThe training effectiveness of the lower Yellow River (LYR) depends on the understanding of the regularity of flow‐sediment transport and riverbed sedimentation. The measured data of daily flow discharge and sediment transport rate at the five hydrological stations (Xiaolangdi [Xld], Huayuankou [Hyk], Gaocun [Gc], Aishan [As], and Lijin [Lj]) in the LYR during the period from 1960 to 2017 are used to investigate the regularity of flow‐sediment transport and sedimentation in the LYR. The Xld station is used as the inlet control station, and the LYR is divided into four segments using four other stations, and the whole year is divided into three periods, namely, the dry season, the flood period, and the nonflood period of the wet season. On this basis, the relationships between the sediment transport rates at the four stations (Hyk, Gc, As, and Lj) and the rates at their respective closest upstream stations are analyzed in each of the three periods. According to the incoming sediment coefficient of the Xld station, the flow and sediment processes in the three periods are classified, and the refined equations for the relationship between the sediment transport rates at the downstream station and its upstream station are established. The results show that the calculated amount and process of erosion and deposition in each period and each segment of the LYR using the equations are in good agreement with the measured values. The relationship equations established in this study can conveniently predict the amount of erosion and deposition in different periods and different segments of the LYR in the future, which is of great significance to the rapid decision of the impact of the construction and operation of hydraulic projects in the upper and middle reaches of the Yellow River on the sedimentation in the LYR.

Distributed Frank-Wolfe Solver for Stochastic Optimization With Coupled Inequality Constraints.

Distributed stochastic optimization (DSO) with local set constraints and coupled inequality constraints over a multiagent network is considered in this article. Usually, such problems are tackled by projected primal-dual methods, which require expensive projection operations when set constraints are complicated. In this context, this article focuses on the Frank-Wolfe (FW) framework, which provides computational simplicity by avoiding expensive projection operations, for solving DSO with local set and coupled inequality constraints. By combining recursive momentum and weighted averaging, this article proposes a distributed stochastic FW primal-dual algorithm (DSFWPD), which is the first stochastic FW solver for DSO problems with coupled constraints. The proposed algorithm achieves zero constraint violation on average with a sublinear decay of the optimality gap over a directed and time-varying network. The efficacy of DSFWPD is demonstrated by several numerical experiments.

Time-Dependent Multireference Coupled-Cluster Method (TDMRCCM) for the Bath-Dynamics in System-Bath Approach to Nonadiabatic Dynamics.

The time-dependent multireference coupled-cluster method (TDMRCCM) fits well in the scheme of the system-bath separation used to study the nonadiabatic dynamics. In TDMRCCM, a projection operator is defined as one that projects the full Hilbert space onto the space spanned by the collection of system degrees of freedom, called the model space. The inverse of this projection operator is a wave operator that acts on the model space and takes its projection back to the full wave function. This wave operator is defined as an exponential of the excitation terms and, hence, can be expanded into a Taylor series, which we have truncated in this work at the second-order of excitations. The attraction of using TDMRCCM for describing the bath dynamics is due to the exponential nature of the ansatz used in the method, which makes it possible for the higher-order excitations to be absorbed by the lower-order terms, even upon truncating the series. This improves the accuracy of the numerical calculations using TDMRCCM as an approximation for the bath-mode dynamics in the system-bath framework for nonadiabatic dynamics. We present the theoretical details of TDMRCCM and the numerical results for implementing this method to study the dynamics in the butatriene cation.

The Water Hammer Characteristics of Long-Distance Water Pipelines under Different Water Supply Modes

The pressure characteristics of long-distance water pipelines during hydraulic transient processes are crucial for ensuring the safe, stable, and long-term operation of water transfer projects. This paper establishes a one-dimensional mathematical model based on sections of the Yinjiangjihuai long-distance water diversion project in China. The water supply requirements of the pipelines are categorized into two replenishment modes as follows: gravity supply and pump-pressurized water supply. The opening and closing strategies of the water pipelines under different flow conditions are simulated and analyzed to explore the hydraulic transient processes under various water supply modes. The transient variations of key hydraulic parameters during valve closure are clarified. Simulation results indicate that the water pipeline design is reasonable, meeting the water supply demands at relatively low Manning values and that it has the capability for long-term supply. Due to the excessive head provided by the pumps, pump-pressurized water supply and gravity supply modes cannot operate simultaneously. Under gravity supply mode, the minimum pressure in the downstream pipeline is relatively higher overall, while the maximum pressure in the upstream pipeline is relatively lower overall. In the pump-pressurized water supply mode, the safety and stability of the water supply can be ensured by adjusting the closing time of individual pumps and the interval time between adjacent pumps. The research findings provide technical guidance and scientific basis for the construction of national water networks and water transfer projects.

Massless spin 2 field in 50-component approach: exact solutions with cylindrical symmetry, eliminating the guage degrees of freedom

We begin with some known results of the 50-component theory for a spin-2 field described in cylindrical coordinates. This theory is based on the use of a 2nd-rank symmetric tensor and a 3rd-rank tensor symmetric in two indices. In the massive case, this theory describes a spin-2 particle with an anomalous magnetic moment. According to the Fedorov – Gronskiy method, which is based on projective operators, all 50 functions involved in the description of the spin-2 field for the case of the free particle can be expressed in terms of only 7 different functions constructed from Bessel functions. This leads to a homogeneous system of linear algebraic equations for 50 numerical parameters. We have found 6 independent solutions to these equations. Additionally, we have obtained explicit expressions for 4 guage solutions defined in accordance with the Pauli – Fierz approach. These solutions are exact and correspond to non-physical states that do not affect observable quantities, such as the energy-momentum tensor. Finally, we have constructed two classes of solutions that represent physically observable states.

Detecting Transient Uplift at the Active Volcano Ol Doinyo Lengai in Tanzania With the TZVOLCANO Network

AbstractOver the last 7 years, geodetic data have detected periods of uplift and subsidence of the active volcano Ol Doinyo Lengai in Tanzania. Although numerous eruptions of the volcano have occurred historically, a systematic investigation of transient deformation using continuous Global Navigation Satellite System (GNSS) data has not been undertaken. We use the Targeted Projection Operator (TPO) to assess 7 years of continuous GNSS data from the TZVOLCANO network for transient signals and find rapid uplift spanning March 2022–December 2022 and then steady‐state uplift through August 2023. We conduct a nonlinear inversion of the GNSS velocities associated with the transient signal using dMODELS and find consistency with an inflating spheroidal source located 2.3 ± 0.6 km beneath the crater. Prior to March 2022, geodetic data indicated quiescence just below Ol Doinyo Lengai, thus detecting transient deformation with TPO allows for tracking changes in the magmatic system over time in the Natron Rift.

Evolution of regional rainstorm events in China's South-to-North Water Diversion Area, 1960–2022

The objective of this paper is to elucidate the patterns of evolution of regional rainstorm events (RREs) in a large-scale water resources allocation area. This is crucial for the safe operation of water transfer projects and water resources management. The Objective Identification Technique for Regional Extreme Events (OITREE) method is employed to identify all RREs in the South-to-North Water Diversion Area (SNWDA) between the years 1960 and 2022. The results indicate that among the 1397 RREs identified, the extreme RREs are significantly more severe than other classes of rainstorm events. While the extreme intensity (Im) of RREs exhibits a decreasing trend, their frequency, comprehensive index (Z), maximum area (Am), summed area (As), and summed intensity (Is) all demonstrate increasing trends. Some of these indices (Z, Am, As, and Is) exhibit a strong periodicity of approximately 20 years, while the shortening of the decline period will result in more frequent rising periods of RREs. In the second year following the water transfer operation (2015), all RRE indices exhibit abrupt changes. Furthermore, the rainy season lengthens, with more frequent and extreme RREs occurring in July, which may have implications for the Middle Route of year-round water transfers. Spatially, the occurrence frequency of regional rainstorm days (RRDs) increases by 35.9% since the 21st century, while regional rainstorm intensity (RRI) increases by 11.8%. The high-frequency zones (HFZs) of RRDs are primarily located in the southeast, with intensity increases of at least 30%. While their location remains stable, there is a clear trend of northward spread. Following the water transfer, the frequency of RREs is higher in the Eastern Route, and the high-intensity zones (HIZs) appear for the first time in the Beijing area of the Middle Route. These findings provide a scientific understanding of regional rainstorms and serve as a reference for rainstorm disaster response and optimal allocation of water resources in water transfer projects.

Second-order spectral line shift comparisons

The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. The results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.

Unconditional optimal [formula omitted]-norm error estimate and superconvergence analysis of a linearized nonconforming finite element variable-time-step BDF2 method for the nonlinear complex Ginzburg–Landau equation

In this paper, a linearized fully discrete scheme combining the variable-time-step two-step backward differentiation formula (VSBDF2) in time and the nonconforming finite element methods (FEMs) in space is constructed and analyzed for the nonlinear complex Ginzburg–Landau equation. A novel convergence analysis approach is proposed, which shows that the H1-norm error of this scheme can reach optimal order in space and sharp second-order convergence in time. The key ingredients of our analysis are temporal–spatial error splitting approach, a new positive definiteness property of discrete orthogonal convolution (DOC) kernels with respect to complex sequences, an energy projection operator and a discrete Laplace operator Δh related to the nonconforming element space, and a relationship between Δh and classical L2 projection operator in complex space. Furthermore, through a specific treatment of the error equation and the combination technique of interpolating operator and projection operator, we prove that the proposed scheme has the global superconvergence result of order O(τ2+h2) in H1-norm for the first time, which further improves the efficiency of numerical computation. Here τ and h are the maximum time and spatial step sizes, respectively. It should be pointed out that all these error results are rigorously established under mild assumptions of the time step, and get rid of the usual grid ratio constraints between temporal and spatial step sizes in linearized scheme. At last, numerical experiments are provided to verify the theoretical analysis.

An Almost Deterministic Cooling by Measurements

AbstractNondeterministic measurement‐based techniques are efficient in reshaping the population distribution of a quantum system but suffer from a limited success probability of holding the system in the target state. To save the experimental cost, a two‐step protocol is proposed to cool a resonator down to the ground state with a near‐unit probability by exploiting the state‐engineering mechanisms of both conditional and unconditional measurements on an ancillary qubit. In the first step, the unconditional measurements on the ancillary qubit are applied to reshape the target resonator from a thermal state to a reserved Fock state. The measurement sequence can be efficiently optimized by reinforcement learning for maximum fidelity. In the second step, the population on the reserved state can be faithfully transferred in a stepwise way to the resonator's ground state with a near‐unit fidelity by the conditional measurements on the qubit. Properly designing the projection operator and the measurement interval enables the Kraus operator to act as a lowering operator for neighboring Fock states. Through dozens of measurements in all, the initial thermal average population of the resonator can be reduced by five orders in magnitude with a success probability of over 95%.

Environmental implication identification on water quality variation and human health risk assessment in the middle and lower reaches of the Hanjiang River, China

As the longest tributary of the Yangtze River, the Hanjiang River has been a “lifeline” for the “Yangtze River Economic Belt of China”. The water quality of the middle and lower reaches of the Hanjiang River (MLHR) has received considerable attention due to environmental degradation, increasing population, and water diversion project operations during the past decade. In this study, 16 water quality parameters from 14 national water quality monitoring stations along the MLHR were collected monthly from January 2021 to December 2022. Water quality index (WQI) methods coupling multivariate statistical techniques, e.g., seasonal Mann-Kendall test (SKT) and Mantel’s test, were applied to analyze and evaluate the spatiotemporal variations of water quality under different environmental and hydrological conditions. The Hazard Quotients (HQs) were used to assess the non-carcinogenic and carcinogenic risk for adults and children via ingestion and dermal pathways. The results showed that the overall water quality in the MLHR was classified as “excellent”, with the average WQI higher than “91”, and each single water quality indicator met Class I or Class II surface water quality standards of China. Ammonia (NH3-N), Total phosphorus (TP), Permanganate (CODMn), pH, and Arsenic (As) were significantly correlated with water level variations. CODMn and TP were decisive in explaining the WQI variations of the MLHR. NH3-N, water temperature, pH, and dissolved oxygen were key parameters for explaining WQI variations in most regions of the MLHR. As, Cadmium (Cd), and Chromium (Cr) presented potential health risks in the MLHR and should warrant close monitoring due to their significant health implications. Due to the continuous construction and operation of cascade hydro-projects, the synchronous monitoring of water quality and hydrological data of the MLHR should be conducted in the future. This study provides a scientific reference for managing water quality in the MLHR and similar natural riverine water bodies.

Projected data assimilation using sliding window proper orthogonal decomposition

Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model. Data Assimilation (DA) techniques improve state estimates by combining model simulations with real-time data. Few DA techniques can simultaneously handle nonlinear evolution, non-Gaussian uncertainty, and the high dimension of the state. We recently proposed addressing these challenges using a POD technique that projects the physical and data models into a reduced-dimensional subspace. Proper Orthogonal Decomposition (POD) is a tool to extract spatiotemporal patterns (modes) that dominate the observed data. We combined the POD-based projection operator, computed in an offline fashion, with a DA scheme that models non-Gaussian uncertainty in lower dimensional subspace. If the model parameters change significantly during time evolution, the offline computation of the projection operators ceases to be useful. We address this challenge using a Sliding Window POD (SW-POD), which recomputes the projection operator based on a sliding subset of snapshots from the entire evolution. The physical model projection is updated dynamically in terms of modes and number of modes, and the data model projection is also chosen to promote a sparse approximation. We test the efficacy of this technique on a modified Lorenz'96 model (L96) with a time-varying forcing and compare it with the time-invariant offline projected algorithm. In particular, dynamically determined physical and data model projections decrease the Root Mean Squared Error (RMSE) and the resampling rate.

Drought mitigation operation of water conservancy projects under severe droughts

ABSTRACT Severe droughts typically last for extended periods and result in substantial water shortages, posing challenges for water conservancy projects. This study proposed a framework for coordinating drought mitigation operations across projects of various scales. First, the regulation and drought mitigation capacities of each project were analyzed, and thus critical reservoirs was identified. Subsequently, a joint regulation model for water supply, prioritizing projects based on their regulatory capacity from weak to strong, was established. An optimization model is then developed to determine the drought-limited levels for critical reservoirs, aiming to minimize water shortages. This model facilitates temporal coordination of water resources to prevent severe water shortages with frequent mild water shortages. Results in the Chuxionglucheng District of Chuxiong, Yunnan Province, during the severe drought period from 2009 to 2013 demonstrate significant reductions in water shortage. Specifically, the maximum shortage ratio decreased from 59 to 45% for agriculture and from 52 to 8% for industry. Moreover, emergency measures for drought mitigation were compared and recommended for regions with weak projects regulation. Overall, this framework offers a systematic approach to enhancing drought resilience across diverse water conservancy projects in severe drought conditions.

Cost-benefit analysis of an irrigation unit with treated wastewater in Chihuahua, Mexico

The reuse of water in agriculture is an alternative to guarantee food security in Mexico and efficient management of this resource. The objective was to conduct an economic evaluation by benefit-cost analysis in an irrigation district of treated wastewater (TWW) in Tabalaopa-Aldama, Chihuahua, Mexico. The cost-benefit methodology was used to estimate the economic assessment of public projects. The results indicated that the project operation would obtain a net social value of $1,054.4 million, a social return intern fee of 31.19 %, and a cost-benefit relation of 2.48. Even if the costs and benefits increase by up to 30 %, the project would still be economically viable and provide social benefits. The start-up of a TWW irrigation district will generate economic benefits for society and promote the reduction of environmental impact on the agricultural land in Tabalaopa, Aldama, Chihuahua, Mexico.

A MODEL FOR ASSESSING SHIPPING SAFETY WITHIN PROJECT-ORIENTATED RISK MANAGEMENT BASED ON HUMAN ELEMENT

Safety risk management in shipping projects is an extremely important aspect aimed at ensuring the success of the project and the safety of all participants in the maritime transportation process. This paper presents an approach to assessing safety risks that considers multiple factors including equipment condition, external circumstances, and human factors. The risk assessment utilizes the probability of accidents and their consequences, as well as the weighting factors of each factor. The results of the assessment are interpreted using a scale that defines the hazard level. The proposed methodology can effectively identify, analyse and manage safety risks, which can contribute to the success and safety of shipping projects. The study also discusses the importance of dividing the crew into functional groups based on the operations performed, which helps to better identify the safety risk for each group. Safety risk assessment is conducted for each operation individually as well as for the entire project or multiple operations to provide a comprehensive safety assessment. The results of the study have shown the feasibility of the proposed method for assessing the safety risks of shipping projects and its suitability to the initial data “safety” taking into account its separate sides, features, as well as the constituent aspects of the concept, systematization of the ship's safety structure in order to develop solutions to improve integral safety and optimize decision-making in emergency situations. Achievement of the general purpose of shipping safety thus means realization of ways of reduction of influence of the human factor on the number of accidents, and an estimation of the degree of influence of a set of factors on a ship during operation.

Role of Pacific Ocean climate in regulating runoff in the source areas of water transfer projects on the Pacific Rim

Over the past two decades, more frequent and intense climate events have seriously threatened the operation of water transfer projects in the Pacific Rim region. However, the role of climatic change in driving runoff variations in the water source areas of these projects is unclear. We used tree-ring data to reconstruct changes in the runoff of the Hanjiang River since 1580 CE representing an important water source area for China’s south-north water transfer project. Comparisons with hydroclimatic reconstructions for the southwestern United States and central Chile indicated that the Pacific Rim region has experienced multiple coinciding droughts related to ENSO activity. Climate simulations indicate an increased likelihood of drought occurrence in the Pacific Rim region in the coming decades. The combination of warming-induced drought stresses with dynamic El Niño (warming ENSO) patterns is a thread to urban agglomerations and agricultural regions that rely on water transfer projects along the Pacific Rim.