REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

How do lateral septum projections to the ventral CA1 influence sociability?

Social dysfunction is a risk factor for several neuropsychiatric illnesses.Previous studies have shown that the lateral septum(LS)-related pathway plays a critical role in mediating social behaviors.Howeve r,the role of the connections between the LS and its downstream brain regions in social behavio rs remains unclea r.In this study,we conducted a three-chamber test using electrophysiological and chemogenetic approaches in mice to determine how LS projections to ventral CA1(vCA1)influence sociability.Our res ults showed that gamma-aminobutyric acid(GABA)-e rgic neuro ns were activated following social experience,and that social behavio rs were enhanced by chemogenetic modulation of these neurons.Moreover,LS GABAergic neurons extended their functional neural connections via vCA1 glutamatergic pyramidal neurons,and regulating LSGABA→vCA1Gluneural projections affected social behaviors,which were impeded by suppressing LSprojecting vCA1 neuronal activity or inhibiting GABAAreceptors in vCA1.These findings support the hypothesis that LS inputs to the vCA1 can control social prefe rences and social novelty behaviors.These findings provide new insights rega rding the neural circuits that regulate sociability.

Future changes in precipitation and water availability over the Tibetan Plateau projected by CMIP6 models constrained by climate sensitivity

Precipitation projections over the Tibetan Plateau(TP)show diversity among existing studies,partly due to model uncertainty.How to develop a reliable projection remains inconclusive.Here,based on the IPCC AR6–assessed likely range of equilibrium climate sensitivity(ECS)and the climatological precipitation performance,the authors constrain the CMIP6(phase 6 of the Coupled Model Intercomparison Project)model projection of summer precipitation and water availability over the TP.The best estimates of precipitation changes are 0.24,0.25,and 0.45 mm d^(−1)(5.9%,6.1%,and 11.2%)under the Shared Socioeconomic Pathway(SSP)scenarios of SSP1–2.6,SSP2–4.5,and SSP5–8.5 from 2050–2099 relative to 1965–2014,respectively.The corresponding constrained projections of water availability measured by precipitation minus evaporation(P–E)are 0.10,0.09,and 0.22 mm d^(−1)(5.7%,4.9%,and 13.2%),respectively.The increase of precipitation and P–E projected by the high-ECS models,whose ECS values are higher than the upper limit of the likely range,are about 1.7 times larger than those estimated by constrained projections.Spatially,there is a larger increase in precipitation and P–E over the eastern TP,while the western part shows a relatively weak difference in precipitation and a drier trend in P–E.The wetter TP projected by the high-ECS models resulted from both an approximately 1.2–1.4 times stronger hydrological sensitivity and additional warming of 0.6℃–1.2℃ under all three scenarios during 2050–2099.This study emphasizes that selecting climate models with climate sensitivity within the likely range is crucial to reducing the uncertainty in the projection of TP precipitation and water availability changes.

Projecting Spring Consecutive Rainfall Events in the Three Gorges Reservoir Based on Triple-Nested Dynamical Downscaling

Spring consecutive rainfall events(CREs) are key triggers of geological hazards in the Three Gorges Reservoir area(TGR), China. However, previous projections of CREs based on the direct outputs of global climate models(GCMs) are subject to considerable uncertainties, largely caused by their coarse resolution. This study applies a triple-nested WRF(Weather Research and Forecasting) model dynamical downscaling, driven by a GCM, MIROC6(Model for Interdisciplinary Research on Climate, version 6), to improve the historical simulation and reduce the uncertainties in the future projection of CREs in the TGR. Results indicate that WRF has better performances in reproducing the observed rainfall in terms of the daily probability distribution, monthly evolution and duration of rainfall events, demonstrating the ability of WRF in simulating CREs. Thus, the triple-nested WRF is applied to project the future changes of CREs under the middle-of-the-road and fossil-fueled development scenarios. It is indicated that light and moderate rainfall and the duration of continuous rainfall spells will decrease in the TGR, leading to a decrease in the frequency of CREs. Meanwhile, the duration, rainfall amount, and intensity of CREs is projected to regional increase in the central-west TGR. These results are inconsistent with the raw projection of MIROC6. Observational diagnosis implies that CREs are mainly contributed by the vertical moisture advection. Such a synoptic contribution is captured well by WRF, which is not the case in MIROC6,indicating larger uncertainties in the CREs projected by MIROC6.

Onto Orthogonal Projections in the Space of Polynomials Pn[x]

In this article, I consider projection groups on function spaces, more specifically the space of polynomials Pn[x]. I will show that a very similar construct of projection operators allows us to project into the subspaces of Pn[x] where the function h ∈Pn[x] represents the closets function to f ∈Pn[x] in the least square sense. I also demonstrate that we can generalise projections by constructing operators i.e. in Rn+1 using the metric tensor on Pn[x]. This allows one to project a polynomial function onto another by mapping it to its coefficient vector in Rn+1. This can be also achieved with the Kronecker Product as detailed in this paper.

A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets

An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions.

人工智能背景下Materials Project数据库在计算材料学课程教学中的应用

该文探讨了在人工智能背景下,Materials Project数据库在计算材料学课程教学中的应用和影响。Materials Project数据库是一个集成了AI和大数据技术的开放获取的材料库,能为学生提供海量的材料晶体结构和物性数据,使教学内容更为丰富,让学生能通过亲自操作获取和分析数据,深入理解微观结构与物性之间的关系。这一新兴的教学模式不仅提升了学生的科研能力和创新思维能力,还有助于培养具备计算材料专业知识和多学科交叉的复合型人才。总体来说,人工智能时代下,大数据的引入为计算材料学课程带来新的活力,并对未来教育改革和实践产生了积极影响。

Transcriptional regulation in the development and dysfunction of neocortical projection neurons

Glutamatergic projection neurons generate sophisticated excitatory circuits to integrate and transmit information among different cortical areas,and between the neocortex and other regions of the brain and spinal cord.Appropriate development of cortical projection neurons is regulated by certain essential events such as neural fate determination,proliferation,specification,differentiation,migration,survival,axonogenesis,and synaptogenesis.These processes are precisely regulated in a tempo-spatial manner by intrinsic factors,extrinsic signals,and neural activities.The generation of correct subtypes and precise connections of projection neurons is imperative not only to support the basic cortical functions(such as sensory information integration,motor coordination,and cognition)but also to prevent the onset and progression of neurodevelopmental disorders(such as intellectual disability,autism spectrum disorders,anxiety,and depression).This review mainly focuses on the recent progress of transcriptional regulations on the development and diversity of neocortical projection neurons and the clinical relevance of the failure of transcriptional modulations.

Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Simulations and Projections of Winter Sea Ice in the Barents Sea by CMIP6 Climate Models

Dramatic changes in the sea ice characteristics in the Barents Sea have potential consequences for the weather and climate systems of mid-latitude continents,Arctic ecosystems,and fisheries,as well as Arctic maritime navigation.Simulations and projections of winter sea ice in the Barents Sea based on the latest 41 climate models from the Coupled Model Intercomparison Project Phase 6(CMIP6)are investigated in this study.Results show that most CMIP6 models overestimate winter sea ice in the Barents Sea and underestimate its decreasing trend.The discrepancy is mainly attributed to the simulation bias towards an overly weak ocean heat transport through the Barents Sea Opening and the underestimation of its increasing trend.The methods of observation-based model selection and emergent constraint were used to project future winter sea ice changes in the Barents Sea.Projections indicate that sea ice in the Barents Sea will continue to decline in a warming climate and that a winter ice-free Barents Sea will occur for the first time during 2042-2089 under the Shared Socioeconomic Pathway 585(SSP5-8.5).Even in the observation-based selected models,the sensitivity of winter sea ice in the Barents Sea to global warming is weaker than observed,indicating that a winter ice-free Barents Sea might occur earlier than projected by the CMIP6 simulations.

Recent Ventures in Interdisciplinary Arctic Research:The ARCPATH Project

This paper celebrates Professor Yongqi GAO's significant achievement in the field of interdisciplinary studies within the context of his final research project Arctic Climate Predictions: Pathways to Resilient Sustainable Societies-ARCPATH(https://www.svs.is/en/projects/finished-projects/arcpath). The disciplines represented in the project are related to climatology, anthropology, marine biology, economics, and the broad spectrum of social-ecological studies. Team members were drawn from the Nordic countries, Russia, China, the United States, and Canada. The project was transdisciplinary as well as interdisciplinary as it included collaboration with local knowledge holders. ARCPATH made significant contributions to Arctic research through an improved understanding of the mechanisms that drive climate variability in the Arctic. In tandem with this research, a combination of historical investigations and social, economic, and marine biological fieldwork was carried out for the project study areas of Iceland, Greenland, Norway, and the surrounding seas, with a focus on the joint use of ocean and sea-ice data as well as social-ecological drivers. ARCPATH was able to provide an improved framework for predicting the near-term variation of Arctic climate on spatial scales relevant to society, as well as evaluating possible related changes in socioeconomic realms. In summary, through the integration of information from several different disciplines and research approaches, ARCPATH served to create new and valuable knowledge on crucial issues, thus providing new pathways to action for Arctic communities.

Diagnosis of indirectly driven double shell targets with point-projection hard x-ray radiography

We present an application of short-pulse laser-generated hard x rays for the diagnosis of indirectly driven double shell targets. Coneinserted double shell targets were imploded through an indirect drive approach on the upgraded SG-II laser facility. Then, based on thepoint-projection hard x-ray radiography technique, time-resolved radiography of the double shell targets, including that of their near-peakcompression, were obtained. The backlighter source was created by the interactions of a high-intensity short pulsed laser with a metalmicrowire target. Images of the target near peak compression were obtained with an Au microwire. In addition, radiation hydrodynamicsimulations were performed, and the target evolution obtained agrees well with the experimental results. Using the radiographic images, arealdensities of the targets were evaluated.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Quantum block coherence with respect to projective measurements

Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

Progress of Taiji-2 Project

Taiji-2 project is the second step of Taiji program,which is to verify the required technology for Taiji-3 mission.The feasibility study of Taiji-2 is successfully finished,and some of the main progress is introduced here.

Evaluation and projection of marine heatwaves in the South China Sea: insights from CMIP6 multi-model ensemble

This study evaluates the performance of 16 models sourced from the coupled model intercomparison project phase 6(CMIP6)in simulating marine heatwaves(MHWs)in the South China Sea(SCS)during the historical period(1982−2014),and also investigates future changes in SCS MHWs based on simulations from three shared socioeconomic pathway(SSP)scenarios(SSP126,SSP245,and SSP585)using CMIP6 models.Results demonstrate that the CMIP6 models perform well in simulating the spatial-temporal distribution and intensity of SCS MHWs,with their multi-model ensemble(MME)results showing the best performance.The reasonable agreement between the observations and CMIP6 MME reveals that the increasing trends of SCS MHWs are attributed to the warming sea surface temperature trend.Under various SSP scenarios,the year 2040 emerges as pivotal juncture for future shifts in SCS MHWs,marked by distinct variations in changing rate and amplitudes.This is characterized by an accelerated decrease in MHWs frequency and a notably heightened increase in mean intensity,duration,and total days after 2040.Furthermore,the projection results for SCS MHWs suggest that the spatial pattern of MHWs remains consistent across future periods.However,the intensity shows higher consistency only during the near-term period(2021−2050),while notable inconsistencies are observed during the medium-term(2041−2070)and long-term(2071−2100)periods under the three SSP scenarios.During the nearterm period,the SCS MHWs are characterized by moderate and strong events with high frequencies and relatively shorter durations.In contrast,during the medium-term period,MHWs are also characterized by moderate and strong events,but with longer-lasting and more intense events under the SSP245 and SSP585 scenarios.However,in the long-term period,extreme MHWs become the dominant feature under the SSP585 scenario,indicating a substantial intensification of SCS MHWs,effectively establishing a near-permanent state.

Polar-coordinate line-projection light-curing continuous 3D printing for tubular structures

3D printing techniques offer an effective method in fabricating complex radially multi-material structures.However,it is challenging for complex and delicate radially multi-material model geometries without supporting structures,such as tissue vessels and tubular graft,among others.In this work,we tackle these challenges by developing a polar digital light processing technique which uses a rod as the printing platform.The 3D model fabrication is accomplished through line projection.The rotation and translation of the rod are synchronized to project and illuminate the photosensitive material volume.By controlling the distance between the rod and the printing window,we achieved the printing of tubular structures with a minimum wall thickness as thin as 50 micrometers.By controlling the width of fine slits at the printing window,we achieved the printing of structures with a minimum feature size of 10 micrometers.Our process accomplished the fabrication of thin-walled tubular graft structure with a thickness of only 100 micrometers and lengths of several centimeters within a timeframe of just 100 s.Additionally,it enables the printing of axial multi-material structures,thereby achieving adjustable mechanical strength.This method is conducive to rapid customization of tubular grafts and the manufacturing of tubular components in fields such as dentistry,aerospace,and more.

Construction and Research Progress of the Chinese Meridian Project in 2022–2023

The Chinese Meridian Project(CMP)is a major national science and technology infrastructure constructed in two steps.The first phase of the CMP has been operating for more than a solar cycle.From 2022 to 2023,utilizing the monitoring data collected by the CMP,scientists made major breakthroughs in fields of ionosphere,middle and upper atmosphere,and coupling between layers.The construction of the second phase of the CMP is nearly finished,and the project is expected to operate as a whole in 2025 after national acceptance of the second phase.The whole project was built in an architecture of so-called“One Chain,Three Networks and Four Focuses”.It is promising to make a three-dimensional observation of the whole solar-terrestrial space.The science community is looking forward to the great contribution of the CMP to space weather and space physics research.

Two Monte Carlo-based simulators for imaging-system modeling and projection simulation of flat-panel X-ray source

The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and resolving overlapping projection issues in FPXS.The conventional analytical ray-tracing approach is limited by the number of patterns and is not applicable to FPXS-projection calculations.However,the computation time of Monte Carlo(MC)simulation is independent of the size of the patterned arrays in FPXS.This study proposes two high-efficiency MC projection simulators for FPXS:a graphics processing unit(GPU)-based phase-space sampling MC(gPSMC)simulator and GPU-based fluence sampling MC(gFSMC)simulator.The two simulators comprise three components:imaging-system modeling,photon initialization,and physical-interaction simulations in the phantom.Imaging-system modeling was performed by modeling the FPXS,imaging geometry,and detector.The gPSMC simulator samples the initial photons from the phase space,whereas the gFSMC simulator performs photon initialization from the calculated energy spectrum and fluence map.The entire process of photon interaction with the geometry and arrival at the detector was simulated in parallel using multiple GPU kernels,and projections based on the two simulators were calculated.The accuracies of the two simulators were evaluated by comparing them with the conventional analytical ray-tracing approach and acquired projections,and the efficiencies were evaluated by comparing the computation time.The results of simulated and realistic experiments illustrate the accuracy and efficiency of the proposed gPSMC and gFSMC simulators in the projection calculation of various phantoms.