Ultrafast dynamics of femtosecond laser-induced high spatial frequency periodic structures on silicon surfaces

Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.

Spatial correlations in time and frequency domains between chlorophyll-a concentration and environmental factors in the Bohai Sea

Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol optical thickness(AOT),and wind speed(WS)in the Bohai Sea were analyzed from the perspective of time domain and frequency domain.Results indicate that the frequency domain analysis was more conducive to revealing the correlations between Chl a and environmental factors.The spatial pattern of time-domain correlations was similar to the isobaths of the Bohai Sea,which was positive in shallow waters and negative in deep waters for SST,PAR,and AOT,and was reversed for WS.Frequency-domain correlations were obtained by performing Fourier Transform and were higher than correlations in time domain.The spatial distributions indicated that the effects of SST and PAR on Chl a were greater than AOT and WS in the Bohai Sea.Additionally,cross-spectrum analysis was applied to explore the response relationships.A depth-dependent pattern was shown in correlations and time lags,indicating that the influential mechanism of environmental factors on Chl-a concentration is related to seawater depth.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

Spatial structural characteristics of the Deda ancient landslide in the eastern Tibetan Plateau:Insights from Audio-frequency Magnetotellurics and the Microtremor Survey Method

It is of crucial importance to investigate the spatial structures of ancient landslides in the eastern Tibetan Plateau’s alpine canyons as they could provide valuable insights into the evolutionary history of the landslides and indicate the potential for future reactivation.This study examines the Deda ancient landslide,situated in the Chalong-ranbu fault zone,where creep deformation suggests a complex underground structure.By integrating remote sensing,field surveys,Audio-frequency Magnetotellurics(AMT),and Microtremor Survey Method(MSM)techniques,along with engineering geological drilling for validation,to uncover the landslide’s spatial feature s.The research indicates that a fault is developed in the upper part of the Deda ancient landslide,and the gully divides it into Deda landslide accumulation zoneⅠand Deda landslide accumulation zoneⅡin space.The distinctive geological characteristics detectable by MSM in the shallow subsurface and by AMT in deeper layers.The findings include the identification of two sliding zones in the Deda I landslide,the shallow sliding zone(DD-I-S1)depth is approximately 20 m,and the deep sliding zone(DD-I-S2)depth is 36.2-49.9 m.The sliding zone(DD-Ⅱ-S1)depth of the DedaⅡlandslide is 37.6-43.1 m.A novel MSM-based method for sliding zone identification is proposed,achieving less than 5%discrepancy in depth determination when compared with drilling data.These results provide a valuable reference for the spatial structural analysis of large-deepseated landslides in geologically complex regions like the eastern Tibetan Plateau.

Numerical Simulation of Super-Resolution Structured Illumination Microscopy (SIM) Using Heintzmann-Cremer Algorithm with Non-Continuous Spatial Frequency Support

We report a comprehensive numerical study of super resolution (SR) structured illumination microscopy (SIM) utilizing the classic Heintzmann-Cremer SIM process and algorithm. In particular, we investigated the impact of the diffraction limit of the underlying imaging system on the optimal SIM grating frequency that can be used to obtain the highest SR enhancement with non-continuous spatial frequency support. Besides confirming the previous theoretical and experimental work that SR-SIM can achieve an enhancement close to 3 times the diffraction limit with grating pattern illuminations, we also observe and report a series of more subtle effects of SR-SIM with non-continuous spatial frequency support. Our simulations show that when the SIM grating frequency exceeds twice that of the diffraction limit, the higher SIM grating frequency can help achieve a higher SR enhancement for the underlying imaging systems whose diffraction limit is low, though this enhancement is obtained at the cost of losing resolution at some lower resolution targets. Our simulations also show that, for underlying imaging systems with high diffraction limits, however, SR-SIM grating frequencies above twice the diffraction limits tend to bring no significant extra enhancement. Furthermore, we observed that there exists a limit grating frequency above which the SR enhancement effect is lost, and the reconstructed images essentially have the same resolution as the one obtained directly from the underlying imaging system without using the SIM process.

Single-cell and spatial omics:exploring hypothalamic heterogeneity

Elucidating the complex dynamic cellular organization in the hypothalamus is critical for understanding its role in coordinating fundamental body functions. Over the past decade, single-cell and spatial omics technologies have significantly evolved, overcoming initial technical challenges in capturing and analyzing individual cells. These high-throughput omics technologies now offer a remarkable opportunity to comprehend the complex spatiotemporal patterns of transcriptional diversity and cell-type characteristics across the entire hypothalamus. Current single-cell and single-nucleus RNA sequencing methods comprehensively quantify gene expression by exploring distinct phenotypes across various subregions of the hypothalamus. However, single-cell/single-nucleus RNA sequencing requires isolating the cell/nuclei from the tissue, potentially resulting in the loss of spatial information concerning neuronal networks. Spatial transcriptomics methods, by bypassing the cell dissociation, can elucidate the intricate spatial organization of neural networks through their imaging and sequencing technologies. In this review, we highlight the applicative value of single-cell and spatial transcriptomics in exploring the complex molecular-genetic diversity of hypothalamic cell types, driven by recent high-throughput achievements.

Spatial transcriptomics combined with single-nucleus RNA sequencing reveals glial cell heterogeneity in the human spinal cord

Glial cells play crucial roles in regulating physiological and pathological functions,including sensation,the response to infection and acute injury,and chronic neurodegenerative disorders.Glial cells include astrocytes,microglia,and oligodendrocytes in the central nervous system,and satellite glial cells and Schwann cells in the peripheral nervous system.Despite the greater understanding of glial cell types and functional heterogeneity achieved through single-cell and single-nucleus RNA sequencing in animal models,few studies have investigated the transcriptomic profiles of glial cells in the human spinal cord.Here,we used high-throughput single-nucleus RNA sequencing and spatial transcriptomics to map the cellular and molecular heterogeneity of astrocytes,microglia,and oligodendrocytes in the human spinal cord.To explore the conservation and divergence across species,we compared these findings with those from mice.In the human spinal cord,astrocytes,microglia,and oligodendrocytes were each divided into six distinct transcriptomic subclusters.In the mouse spinal cord,astrocytes,microglia,and oligodendrocytes were divided into five,four,and five distinct transcriptomic subclusters,respectively.The comparative results revealed substantial heterogeneity in all glial cell types between humans and mice.Additionally,we detected sex differences in gene expression in human spinal cord glial cells.Specifically,in all astrocyte subtypes,the levels of NEAT1 and CHI3L1 were higher in males than in females,whereas the levels of CST3 were lower in males than in females.In all microglial subtypes,all differentially expressed genes were located on the sex chromosomes.In addition to sex-specific gene differences,the levels of MT-ND4,MT2A,MT-ATP6,MT-CO3,MT-ND2,MT-ND3,and MT-CO_(2) in all spinal cord oligodendrocyte subtypes were higher in females than in males.Collectively,the present dataset extensively characterizes glial cell heterogeneity and offers a valuable resource for exploring the cellular basis of spinal cordrelated illnesses,including chronic pain,amyotrophic lateral sclerosis,and multiple sclerosis.

An operational modal analysis method in frequency and spatial domain

A frequency and spatial domain decomposition method （FSDD） for operational modal analysis （OMA） is presented in this paper, which is an extension of the complex mode indicator function （CMIF） method for experimental modal analysis （EMA）. The theoretical background of the FSDD method is clarified, Singular value decomposition is adopted to separate the signal space from the noise space. Finally, an enhanced power spectrum density （PSD） is proposed to obtain more accurate modal parameters by curve fitting in the frequency domain. Moreover, a simulation case and an application case are used to validate this method.

Spatial and temporal distribution of forest fire frequency and forest area burnt in Jilin Province, Northeast China

Forest fires caused by natural forces or human activities are one of the major natural risks in Northeast China.The incidence and spatial distribution of these fires vary over time and across the forested areas in Jilin Province,Northeast China.In this study,the incidence and distribution of 6519 forest fires from 1969 to 2013 in the province were investigated.The results indicated that the spatiotemporal distribution of the burnt forest area and the fire frequency varied significantly by month,year,and region.Fire occurrence displayed notable temporal patterns in the years after forest fire prevention measures were strictly implemented by the provincial government.Generally,forest fires in Jilin occurred in months when stubble and straw were burned and human activities were intense during traditional Chinese festivals.Baishan city,Jilin city,and Yanbian were defined as fire-prone regions for their high fire frequency.Yanbian had the highest frequency,and the fires tended to be large with the highest burned area per fire.Yanbian should thus be listed as the key target area by the fire management agency in Jilin Province for better fire prevention.

Hierarchical microstructures with high spatial frequency laser induced periodic surface structures possessing different orientations created by femtosecond laser ablation of silicon in liquids

High spatial frequency laser induced periodic surface structures(HSFLs)on silicon substrates are often developed on flat surfaces at low fluences near ablation threshold of 0.1 J/cm2,seldom on microstructures or microgrooves at relatively higher fluences above 1 J/cm^2.This work aims to enrich the variety of HSFLs-containing hierarchical microstructures,by femtosecond laser(pulse duration:457 fs,wavelength:1045 nm,and repetition rate:100 kHz)in liquids(water and acetone)at laser fluence of 1.7 J/cm^2.The period of Si-HSFLs in the range of 110–200 nm is independent of the scanning speeds(0.1,0.5,1 and 2 mm/s),line intervals(5,15 and 20μm)of scanning lines and scanning directions(perpendicular or parallel to light polarization direction).It is interestingly found that besides normal HSFLs whose orientations are perpendicular to the direction of light polarization,both clockwise or anticlockwise randomly tilted HSFLs with a maximal deviation angle of 50°as compared to those of normal HSFLSs are found on the microstructures with height gradients.Raman spectra and SEM characterization jointly clarify that surface melting and nanocapillary waves play important roles in the formation of Si-HSFLs.The fact that no HSFLs are produced by laser ablation in air indicates that moderate melting facilitated with ultrafast liquid cooling is beneficial for the formation of HSFLs by LALs.On the basis of our findings and previous reports,a synergistic formation mechanism for HSFLs at high fluence was proposed and discussed,including thermal melting with the concomitance of ultrafast cooling in liquids,transformation of the molten layers into ripples and nanotips by surface plasmon polaritons(SPP)and second-harmonic generation(SHG),and modulation of Si-HSFLs direction by both nanocapillary waves and the localized electric field coming from the excited large Si particles.

Design and Analysis of Spatial Modulation Based Orthogonal Time Frequency Space System

In this paper,we design a spatial modulation based orthogonal time frequency space(SMOTFS)system to achieve improved transmission reliability and meet the high transmission rate and highspeed demands of future mobile communications,which fully utilizes the characteristics of spatial modulation(SM)and orthogonal time frequency space(OTFS)transmission.The detailed system design and signal processing of the SM-OTFS system have been presented.The closed-form expressions of the average symbol error rate(ASER)and average bit error rate(ABER)of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function(MGF).Meanwhile,the system complexity has been evaluated.Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio(SNR)regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing(SM-OFDM)system with limited complexity increase under mobile conditions,especially in high mobility scenarios.

Fabrication and cold test of prototype of spatially periodic radio frequency quadrupole focusing linac

A 325 MHz aluminum prototype of a spatially periodic RF quadrupole focusing linac was developed at the Institute of Modern Physics,Chinese Academy of Sciences,as a promising candidate for the front end of a high-current linac.It consists of an alternating series of crossbar H-type drift tubes and RF quadrupole sections.Owing to its special geometry,cavity fabrication is a major hurdle for its engineering development and application.In this paper,we report the detailed mechanical design of this structure and describe its fabrication process,including machining,assembly,and inspection.The field distribution was measured by the bead-pull technique.The results show that the field errors of both the accelerating and focusing fields are within an acceptable range.A tuning scheme for this new structure is proposed and verified.The cold test process and results are presented in detail.The development of this prototype provides valuable guidance for the application of the spatially periodic RF quadrupole structure.

Combined spatial frequency spectroscopy analysis with visible resonance Raman for optical biopsy of human brain metastases of lung cancers

The purpose of this study is to examine optical spatial frequency spectroscopy analysis(SFSA)combined with visible resonance Raman(VRR)spectroscopic method,for thefirst time,to discriminate human brain metastases of lung cancers adenocarcinoma(ADC)and squamous cell carcinoma(SCC)from normal tissues.A total of 31 label-free micrographic images of three type of brain tissues were obtained using a confocal micro-Raman spectroscopic system.VRR spectra of the corresponding samples were synchronously collected using excitation wavelength of 532 nm from the same sites of the tissues.Using SFSA method,the difference in the randomness of spatial frequency structures in the micrograph images was analyzed using Gaussian functionfitting.The standard deviations,calculated from the spatial frequencies of the micrograph images were then analyzed using support vector machine(SVM)classifier.The key VRR biomolecularfingerprints of carotenoids,tryptophan,amide II,lipids and proteins(methylene/methyl groups)were also analyzed using SVM classifier.All three types of brain tissues were identified with high accuracy in the two approaches with high correlation.The results show that SFSA–VRR can potentially be a dual-modal method to provide new criteria for identifying the three types of human brain tissues,which are on-site,real-time and label-free and may improve the accuracy of brain biopsy.

NEW WIND-INDUCED RESPONSES ANALYSIS METHOD OF SPATIAL STRUCTURES IN FREQUENCY DOMAIN WITH MODE COMPENSATION

Large span spatial lattice structures have many natural frequencies in a narrow frequency range, the conventional frequency domain method is difficult to contain all significant contribution modes. Through numerical examples, it is found that some high order modes are likely to be overlooked because of their higher positions of modal order, in spite of their significance to wind response. According to the contributions of modes to strain energy of system, the paper presented an efficient method to compensate the errors owing to missing out some significant high order modes. The effectiveness of the proposed method is verified through a numerical analysis of the wind responses of a spherical dome.

Compressive imaging based on multi-scale modulation and reconstruction in spatial frequency domain

Imaging quality is a critical component of compressive imaging in real applications. In this study, we propose a compressive imaging method based on multi-scale modulation and reconstruction in the spatial frequency domain. Theoretical analysis and simulation show the relation between the measurement matrix resolution and compressive sensing(CS)imaging quality. The matrix design is improved to provide multi-scale modulations, followed by individual reconstruction of images of different spatial frequencies. Compared with traditional single-scale CS imaging, the multi-scale method provides high quality imaging in both high and low frequencies, and effectively decreases the overall reconstruction error.Experimental results confirm the feasibility of this technique, especially at low sampling rate. The method may thus be helpful in promoting the implementation of compressive imaging in real applications.

A Spatial-Nonparametric Approach for Prediction of Claim Frequency in Motor Insurance

Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as Generalized linear models (GLMs) have been made available to prediction of the claim frequencies. However, due to heterogeneity nature of policies, the methods do not generate precise and accurate claim frequencies predictions;these parametric statistical methods extensively depend on limiting assumptions (linearity, normality, independence among predictor variables, and a pre-existing functional form relating the criterion variable and predictive variables). This study investigates how to derive a spatial nonparametric model estimator based on smoothing Spline for predicting claim frequencies. The simulation results showed that the proposed estimator is efficient for prediction of claim frequencies than the kernel based counterpart. The estimator derived was applied to a sample of 6500 observations obtained from Cooperative Insurance Company, Kenya for the period of 2018-2020 and the results showed that the proposed method performs better than the kernel based counterpart. It is worth noting that inclusion of the spatial effects significantly improves the estimator prediction of claim frequency.

Investigating the Existence of Second Order Spatial Autocorrelation in Crash Frequency across Adjacent Freeway Segments

This study developed spatial Poisson model to incorporate spatial autocorrelation in crash frequency across contagious freeway segments. Spatial autocorrelation is the presence of spatial pattern in crash frequency over space due to geographic proximity. Usually crash caused congestion on a freeway segment propagates upstream and creates chance of occurring secondary crashes. This phenomenon makes the crash frequency on the contiguous freeway segments correlated. This correlation makes the distributional assumption of independence of crash frequency invalid. The existence of spatial autocorrelation is investigated by using Conditional autoregressive models (CAR models). The models are set up in a Bayesian modeling framework, to include terms which help to identify and quantify residual spatial autocorrelation for neighboring observation units. Models which recognize the presence of spatial dependence help to obtain unbiased estimates of parameters quantifying safety levels since the effects of spatial autocorrelation are accounted for in the modeling process. Based on CAR models, approximately 51% of crash frequencies across contiguous freeway segments are spatially auto-correlated. The incident rate ratios revealed that wider shoulder and weaving segments decreased crash frequency by factors of 0.84 and 0.75 respectively. The marginal impacts graphs showed that an increase in longitudinal space for segments with two lanes decreased crash frequency. However, an increase of facility width above three lanes results in more crashes, which indicates an increase in traffic flows and driving behavior leading to crashes. These results call an important step of analyzing contagious freeway segments simultaneously to account for the existence of spatial autocorrelation.

Spatial analysis of the osteoarthritis microenvironment: techniques, insights, and applications

Osteoarthritis(OA)is a debilitating degenerative disease affecting multiple joint tissues,including cartilage,bone,synovium,and adipose tissues.OA presents diverse clinical phenotypes and distinct molecular endotypes,including inflammatory,metabolic,mechanical,genetic,and synovial variants.Consequently,innovative technologies are needed to support the development of effective diagnostic and precision therapeutic approaches.Traditional analysis of bulk OA tissue extracts has limitations due to technical constraints,causing challenges in the differentiation between various physiological and pathological phenotypes in joint tissues.This issue has led to standardization difficulties and hindered the success of clinical trials.Gaining insights into the spatial variations of the cellular and molecular structures in OA tissues,encompassing DNA,RNA,metabolites,and proteins,as well as their chemical properties,elemental composition,and mechanical attributes,can contribute to a more comprehensive understanding of the disease subtypes.Spatially resolved biology enables biologists to investigate cells within the context of their tissue microenvironment,providing a more holistic view of cellular function.Recent advances in innovative spatial biology techniques now allow intact tissue sections to be examined using various-omics lenses,such as genomics,transcriptomics,proteomics,and metabolomics,with spatial data.This fusion of approaches provides researchers with critical insights into the molecular composition and functions of the cells and tissues at precise spatial coordinates.Furthermore,advanced imaging techniques,including high-resolution microscopy,hyperspectral imaging,and mass spectrometry imaging,enable the visualization and analysis of the spatial distribution of biomolecules,cells,and tissues.Linking these molecular imaging outputs to conventional tissue histology can facilitate a more comprehensive characterization of disease phenotypes.This review summarizes the recent advancements in the molecular imaging modalities and methodologies for in-depth spatial analysis.It explores their applications,challenges,and potential opportunities in the field of OA.Additionally,this review provides a perspective on the potential research directions for these contemporary approaches that can meet the requirements of clinical diagnoses and the establishment of therapeutic targets for OA.

Spatial distribution of shallow landslides caused by Typhoon Lekima in 2019 in Zhejiang Province, China

In recent years, the coastal region of Southeast China has witnessed a significant increase in the frequency and intensity of extreme rainfall events associated with landfalling typhoons. The hilly and mountainous terrain of this area, combined with rapid rainfall accumulation, has led to a surge in flash floods and severe geological hazards. On August 10, 2019, Typhoon Lekima made landfall in Zhejiang Province, China, and its torrential rainfall triggered extensive landslides, resulting in substantial damage and economic losses. Utilizing high-resolution satellite images, we compiled a landslide inventory of the affected area, which comprises a total of 2,774 rainfallinduced landslides over an area of 2965 km2. The majority of these landslides were small to mediumsized and exhibited elongated, clustered patterns. Some landslides displayed characteristics of high-level initiation, obstructing or partially blocking rivers, leading to the formation of debris dams. We used the inventory to analyze the distribution pattern of the landslides and their relationship with topographical, geological, and hydrological factors. The results showed that landslide abundance was closely related to elevation, slope angle, faults, and road density. The landslides were predominantly located in hilly and low mountainous areas, with elevations ranging from 150 to 300 m, slopes of 20 to 30 degrees, and a NE-SE aspect. Notably, we observed the highest Landslide Number Density(LND) and Landslide Area Percentage(LAP) in the rhyolite region. Landslides were concentrated within approximately 4 km on either side of fault zones, with their size and frequency negatively correlated with distances to faults, roads, and river systems. Furthermore, under the influence of typhoons, regions with denser vegetation cover exhibited higher landslide density, reaching maximum values in shrubland areas. In areas experiencing significantly increased concentrated rainfall, landslide density also showed a corresponding rise. In terms of spatial distribution, the rainfall-triggered landslides primarily occurred in the northeastern part of the study area, particularly in regions characterized by complex topography such as Shanzao Village in Yantan Town, Xixia Township, and Shangzhang Township. The research findings offer crucial data on the rainfallinduced landslides triggered by Typhoon Lekima, shedding light on their spatial distribution patterns. These findings provide valuable references for mitigating risks and planning reconstruction in typhoon-affected area.

FPGA-based position reconstruction method for neutron beam flux spatial distribution measurement in BNCT

A new measurement method for the spatial distribution of neutron beam flux in boron neutron capture therapy(BNCT)is being developed based on the two-dimensional Micromegas detector.To address the issue of long processing times in traditional offline position reconstruction methods,this paper proposes a field programmable gate array based online position reconstruction method utilizing the micro-time projection chamber principle.This method encapsulates key technical aspects:a self-adaptive serial link technique built upon the dynamical adjustment of the delay chain length,fast sorting,a coordinate-matching technique based on the mapping between signal timestamps and random access memory(RAM)addresses,and a precise start point-merging technique utilizing a circular combined RAM.The performance test of the selfadaptive serial link shows that the bit error rate of the link is better than 10-12 at a confidence level of 99%,ensuring reliable data transmission.The experiment utilizing the readout electronics and Micromegas detector shows a spatial resolution of approximately 1.4 mm,surpassing the current method’s resolution level of 5 mm.The beam experiment confirms that the readout electronics system can obtain the flux spatial distribution of neutron beams online,thus validating the feasibility of the position reconstruction method.The online position reconstruction method avoids traditional methods,such as bubble sorting and traversal searching,simplifies the design of the logic firmware,and reduces the time complexity from O(n2)to O(n).This study contributes to the advancement in measuring neutron beam flux for BNCT.