LU Method Research Articles

WenTongGanPi decoction alleviates diarrhea-predominant irritable bowel syndrome by improving intestinal barrier

Ethnopharmacological relevanceWenTongGanPi Decoction (WTGPD) is a representative medical practice of the Fuyang School of Traditional Chinese Medicine (TCM), which originated from the classical Lu's Guizhi method. WTGPD places emphasis on the balance and functionality of yang qi, and is effective in treating TCM symptoms related to liver qi stagnation and spleen yang deficiency. In TCM, diarrhea-predominant irritable bowel syndrome (IBS-D) is often diagnosed as liver depression and spleen deficiency, and the use of WTGPD has shown significant therapeutic effect. However, the underlying mechanism of WTGPD treating IBS-D remains unclear. Aim of the studyTo explore the effect and mechanism of WTGPD in the treatment of IBS-D. Materials and methodsAn IBS-D model with liver depression and spleen deficiency was constructed by chronic immobilization stress stimulation and sennae folium aqueous gavage. The impact of WTGPD on IBS-D rats was evaluated through measurements of body weight, fecal water content, and abdominal withdrawal reflex (AWR). Intestinal permeability was assessed using hematoxylin-eosin (HE), alcian blue-periodic acid schiff (AB-PAS), immunofluorescence (IF) staining, and quantitative real-time PCR (qRT-PCR). The components of WTGPD were analyzed using UPLC-Q-TOF-MS. The underlying mechanisms were investigated through network pharmacology, transcriptomics sequencing, western blot (WB), molecular docking, and 16S rRNA sequencing. ResultsWTGPD treatment effectively alleviated diarrhea and abnormal pain in IBS-D rats (P < 0.05). It enhanced the intestinal barrier function by improving colonic structure and increasing the expression of tight junction proteins (P < 0.05). A total of 155 components were identified in WTGPD. Both network pharmacology and transcriptomics sequencing analysis highlighted MAPK as the key signaling pathway in WTGPD's anti-IBS-D effect. The WB results showed a significant decrease in p-p38, p-ERK and p-JNK expression after WTGPD treatment (P < 0.0001). Guanosine, adenosine and hesperetin in WTGPD may be involved in regulating the phosphorylation of p38, ERK and JNK. Additionally, WTGPD significantly enhanced microbial diversity and increased the production of colonic valeric acid in IBS-D rats (P < 0.01). ConclusionIn conclusion, our findings suggest that WTGPD can effectively alleviate IBS-D and improve intestinal barrier likely via inhibiting MAPK signal pathway and improving micobial dysbiosis.

A modified synthetic aperture focusing algorithm used for transmission detection based on laser ultrasonics method

Compared with traditional ultrasonic nondestructive testing technology, the laser ultrasonics method (LU) has the advantages of high precision, non-contact, wide-band response, suitable for non-destructive testing (NDT) of materials having complex shapes or working in extreme environments such as the additive manufacturing (AM) process, etc. However, for a purely optical LU system, it is still limited by the poor reflection of rough/absorption surface of the material. In order to increase the signal-to-noise ratio (SNR) of the signal detected on the rough surface of a sample, and to overcome the limitation of the resolution restricted by half wavelength, a modified Synthetic Aperture Focusing Technique (SAFT) that can be used for internal defect detection of the material is proposed. The modified SAFT is based on LU centering transmission detection and it improves the resolution of the detection system by using the characteristics of ultrasonic propagation and its mode conversion. It is firstly studied in theory with a numerical model based on finite element method (FEM), and then it is applied in experiments to reconstruct the defect according to the signals detected by LU method. In our experiment, the artificial defects buried in an AM sample with diameter from 0.2 mm to 0.75 mm are successfully characterized by the SAFT imaging of ultrasonic signals. The results prove that the position of the defect in 3D and its size can be successfully obtained by the proposed SAFT.

Extra-pseudocapsular Transnasal Transsphenoidal Resection of Pituitary Macroadenoma: Technique Note and Evaluation of Endocrine Function

In this study, we investigated the surgical technique and endocrine assessment of pituitary function of patients with macroadenoma treated by extra-pseudocapsular transnasal transsphenoidal surgery (ETTS). Clinical data of 144 patients with pituitary macroadenomas in the same surgical group at the Department of Neurosurgery, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology were retrospectively analyzed from January 2019 to June 2021. Based on the results of the endocrinological evaluation and MRI examinations before and after surgery, the fluctuation of pituitary function and the extent of resection were analyzed. Multiple Logistic regression analysis was used to determine the predictors affecting postoperative tumor residual. Among the 144 patients with pituitary macroadenomas, 72 (50.0%) were female and 72 (50.0%) were male, the median age was 50 years, 26 (18.1%) had invasiveness grade 0, 46 (31.9%) had grade I, 57 (39.6%) had grade II, and 15 (10.4%) had grade III according to Lu's classification method. Based on observation during surgery, 37 cases (25.7%) had no pseudocapsule, 54 cases (37.5%) had incomplete pseudocapsule, and 53 cases (36.8%) had intact pseudocapsule. In addition, 91 (63.2%) patients had total resection, 39 (27.1%) had subtotal resection, and 14 (9.7%) had partial resection. As for anterior pituitary function, 13 of 19 hypothyroid patients had recovery after surgery, with a remission rate of 68.4%. Eighteen of the 26 decreased cortisol patients got back to normal, with a remission rate of 69.2%. A total of 27 of 51 patients with hypogonadism improved, with a remission rate of 52.9%. Univariate and multivariate analyses indicated that gender, tumor size, and invasiveness were predictors of postoperative residual in patients (P<0.05). The results showed that ETTS is an effective treatment modality for restoring the function of pituitary gland of the patients with macroadenomas. Tumor size and invasiveness are predictors of the extent of surgical resection and postoperative residual of macroadenomas.

In situ measurement of neutron temperature for the extended k0 NAA at FRM II

The neutron temperature at different irradiation positions in the research reactor FRM II was measured using thermometer labels together with lutetium standards. This was the first time to measure the local temperature at the irradiation positions with this combination. The simplified Westcott formalism was used to calculate the neutron temperature using Lu and g(Tn) factors from different data sources. The results showed agreement between neutron temperature according to the Lu method and the temperature showed on the labels. They can be used as a reliable alternative to determine the neutron temperature instead of using Lu standards in the extended k0 NAA.

Deep Learning Approaches to Human Gait Pattern Classification Based On MEMS Sensors

Body motion is essential to our daily lives, and partly reflects our health. With the ubiquitous spread of mobile and wearable devices having built-in micro-electro-mechanical system (MEMS) sensors, acquisition of linear acceleration and angular velocity of personal gait is much easier today. These data can reveal different types of human movement as well as possible abnormalities. This study introduces an approach to collecting and processing human gait data, transforming these data into images and leveraging deep learning technique for the classification task. Features of three-dimensional linear acceleration are re-orientated and decomposed into various frequency components and characteristic waveforms by Zao and Lu method. Then, the summary of these characteristic waveforms produces a feature data set with four classes of human gait motion: walking, jogging, climbing upstairs, and going downstairs. We show promising results with the use of a convolutional neural network and a traditional neural network on the refined feature data. From this study, applications such as tele-monitoring, tele-rehabilitation, and assessing sedentary habits can be implemented to diagnose and intervene in human behavior.

New optimized Schwarz algorithms for one dimensional Schrödinger equation with general potential

The aim of this paper is to develop new optimized Schwarz algorithms for the one dimensional Schrödinger equation with linear and nonlinear potential. The classical algorithm is an iterative process. In case of time-independent linear potential, we construct explicitly the interface problem and use direct LU method on the interface problem. The algorithm therefore turns to be a direct process. Thus, the algorithm is independent of transmission condition and the numerical computation is smaller. To our knowledge, this is the first time that the Schwarz algorithm is constructed as direct process. Concerning the case of time-dependent linear potential or nonlinear potential, we propose to use a pre-processed linear operator as preconditioner which leads to a preconditioned algorithm. Numerically, the convergence is also independent of the transmission condition. In addition, both of these new algorithms implemented in parallel cluster are robust, scalable up to 256 sub domains (MPI process) and take much less computation time than the classical one, especially for the nonlinear case.

The α-normal labelling method for computing the p-spectral radii of uniform hypergraphs

ABSTRACT Let G be an r-uniform hypergraph of order n. For each , the p-spectral radius is defined as The p-spectral radius was introduced by Keevash-Lenz-Mubayi, and subsequently studied by Nikiforov in 2014. The most extensively studied case is when p = r, and is called the spectral radius of G. The α-normal labelling method, which was introduced by Lu and Man in 2014, is effective method for computing the spectral radii of uniform hypergraphs. It labels each corner of an edge by a positive number so that the sum of the corner labels at any vertex is 1 while the product of all corner labels at any edge is α. Since then, this method has been used by many researchers in studying . In this paper, we extend Lu and Man's α-normal labelling method to the p-spectral radii of uniform hypergraphs for ; and find some applications.

Multiple attribute decision making based on q-rung orthopair fuzzy generalized Maclaurin symmetic mean operators

In the article, we establish two multiple attribute decision making (MADM) approaches using the developed weighted generalized Maclaurin symmetric mean (q-ROFWGMSM) and weighted generalized geometric Maclaurin symmetric mean (q-ROFWGGMSM) operator concerning q-rung orthopair fuzzy numbers (q-ROFNs). Firstly, inspired by the generalized Maclaurin symmetric mean (G-MSM) and geometric Maclaurin symmetric mean (Geo-MSM) operators, we establish the q-rung orthopair fuzzy G-MSM (q-ROFGMSM) and q-rung orthopair fuzzy Geo-MSM (q-ROFGGMSM) operators, which assumes the grades of membership and non-membership to evaluate information can take any values in interval [0,1] respectively and the attributes are relevant to other multiple attributes. Then, we present its characteristics and some special cases. Moreover, we propose the weighted forms of the q-ROFGMSM and q-ROFGGMSM operator, which is called the q-ROFWGMSM and q-ROFWGGMSM operators, respectively. Then, we present their some characteristics and special examples. Finally, we put forward two new MADM approaches founded on the developed q-ROFWGMSM and q-ROFWGGMSM operators. The developed approaches are more general and more practicable than Liu and Wang's MADM approach (2018), Wei and Lu's MADM method (2017), Qin and Liu's MADM method (2014) and Shen et al.’s MADM approach (2018).

Anisotropic Behavior of Different Three-Dimensional Structures Materials under Thermal Stress Effect

This work concerns the numerical modeling of stationary conduction heat transfer in a 3D three-dimensional anisotropic material subjected to an internal heat source, based on the finite element method MEF and using the Galerkin method. The field of study is a cube representing the seven crystalline systems subjected to an internal heat source and convective boundaries. The obtained equation system is solved by the LU method. The automatic mesh is managed for all the domain nodes via the program which we have written in FORTRAN language. This program allowed temperature field calculation and was applied for different crystalline systems: monoclinic, triclinic, orthorhombic, trigonal, cubic that are identified by their thermal conductivity tensors [kij]. The obtained temperature profiles obtained are in accordance with heat transfer theory and clearly illustrate the crystalline structure symmetry; this calculation permits to predict the possible thermal deformations in an anisotropic solid.

Treatments of the singularity in the level set method for unstructured meshes

Straightforward computation of normal vectors and curvature of interface is a main advantage of the level set method. However, the level set method may have discontinuities (kinks) in its derivatives that may lead to erroneous estimation of the normal vector and curvature during topological changes. In this study, we extended two existing methods of singularity treatment for the level set method on structured mesh, i.e., the Salac and Lu method (SLM) and local level set extraction method (LOLEX), to those with unstructured mesh in the framework of finite element formulation. An iterative treatment for the dependent nodes that belong to two elements cut by different interfaces was newly proposed for the LOLEX approach on unstructured mesh. Three static simulations showed that the present SLM or LOLEX for unstructured mesh accurately computed the normal vector and the curvature in the regions with singularity. Two dynamic cases were further simulated to investigate the effect of singularity-treatment on the mass conservation as well as the merging mechanism of droplets. While SLM and LOLEX provided results consistent with existing experimental results, it was confirmed that LOLEX provided a better mass conservation and more accurate curvature fields than SLM after coalescence.

Automated fetal heart rate analysis for baseline determination and acceleration/deceleration detection: A comparison of 11 methods versus expert consensus

The fetal heart rate (FHR) serves as a guide to fetal well-being during the first stage of delivery. The visual morphological analysis of the FHR during labor is subject to inter- and intra-observer variability – particularly when the FHR is abnormal. It has been suggested that automatic analysis of the FHR can reduce this variability. To compare 11 morphological FHR analyses (baseline computation, and detection of FHR decelerations and accelerations) produced by automatic analysis methods (AAMs) with an expert consensus. Eleven AAMs were reprogrammed (using the description published in the literature) and applied to 90 FHR recordings collected during the early phase of labor. Furthermore, the recordings were divided into three tertiles, according to the difficulty of analysis. The results of the morphological FHR analyses produced by the AAMs were compared with a consensus morphological analysis performed by four experts. In addition to standard discriminant criteria, a new morphological analysis discriminant index (MADI) was introduced; it provides an overall evaluation that collates all the individual criteria. The AAM developed by Lu and Wei's gave better results than the other AAMs for baseline computation. Regarding this method's detection of FHR decelerations and accelerations, the F-measure [95% confidence interval] was respectively 0.73 [0.67; 0.76] and 0.70 [0.64; 0.76]. The MADI indicated that Lu and Wei's AAM agreed best with the expert consensus (discordance: 7.3% [6.10; 8.60]). Our study demonstrated the superiority of Lu and Wei's method for baseline computation and deceleration/acceleration detection, although there was still a significant degree of discordance versus expert consensus. The MADI appears to be a good overall index for evaluating AAMs with regard to the quality of baseline computation and acceleration/deceleration detection. The application of precise criteria and the methodology and software tools developed here should facilitate the evaluation of new AAMs and their comparison with other methods.

LU-Decomposition Computerized Method to Solve Linear Programming Problems

The purpose of this work is to solve Linear Programming (LP) problems using LU factorization. LU method is based on the fact that a square matrix can be factorized into the product of unit lower triangular matrix (L) and upper triangular matrix (U), and the direct solution was obtained without iterations. Three different problem cases were considered and solved using step-by-step calculations as well as using MATLAB. Results show this method is superior than the traditional simplex method with cases of cycling.

Testing for Unobserved Heterogeneous Treatment Effects

Unobserved heterogeneous treatment effects have been emphasized in recent policy evaluation literature. In this paper, we extend Lu and White (2014)'s testing method for unobserved heterogeneous treatment effects by developing nonparametric tests under the standard exogenous instrumental variable assumption and allowing for endogenous treatment. Specifically, we propose Kolmogorov--Smirnov--type statistics that are consistent and simple to implement. To illustrate, we apply the proposed test method with two empirical applications: treatment effects of job training program on earnings as well as the impact of fertility on family income. The null hypotheses, i.e., lack of unobserved heterogeneous treatment effects, cannot be rejected at a 10% significance level in the former case, but should be rejected at all usual significance levels in the latter.

Controlling the long-range corrections in atomistic Monte Carlo simulations of two-phase systems.

The long-range correction to the surface tension can amount to up to 55% of the calculated value of the surface tension for cutoffs in the range of 2.1-6.4 σ. The calculation of the long-range corrections to the surface tension and to the configurational energy in two-phase systems remains an active area of research. In this work, we compare the long-range corrections methods proposed by Guo and Lu ( J. Chem. Phys. 1997 , 106 , 3688 - 3695 ) and Janeček ( J. Phys. Chem. B 2006 , 110 , 6264 - 6269 ) for the calculation of the surface tension and of the coexisting densities in Monte Carlo simulations of the truncated Lennard-Jones potential and the truncated and shifted Lennard-Jones potential models. These methods require an estimate of the long-range correction at each step in the Monte Carlo simulation. We apply the full version of the Guo and Lu method, which involves the calculation of a double integral that contains a series of density differences, and we compare these results with the simplified version of the method which is routinely used in two-phase simulations. We conclude that the cutoff dependencies of the surface tension and coexisting densities are identical for the full versions of Guo and Lu and Janeček methods. We show that it is possible to avoid applying the long-range correction at every step by using the truncated Lennard-Jones potential with a cutoff rc ≥ 5 σ. The long-range correction can then be applied at the end of the simulation. The limiting factor in the accurate calculation of this final correction is an accurate estimate of the coexisting densities. Link-cell simulations performed using a cutoff rc = 5.5 σ require twice as much computing time as those with a more typical cutoff of rc = 3.0 σ. The application of the Janeček correction increases the running time of the simulation by less than 10%, and it can be profitably applied with the shorter cutoff.

Incorporating Assortativity and Degree Dependence into Scalable Network Models

Due to the recent availability of large complex networks, considerable analysis has focused on understanding and characterizing the properties of these networks. Scalable generative graph models focus on modeling distributions of graphs that match real world network properties and scale to large datasets. Much work has focused on modeling networks with a power law degree distribution, clustering, and small diameter. In network analysis, the assortativity statistic is defined as the correlation between the degrees of linked nodes in the network. The assortativity measure can distinguish between types of networks---social networks commonly exhibit positive assortativity, in contrast to biological or technological networks that are typically disassortative. Despite this, little work has focused on scalable graph models that capture assortativity in networks. The contributions of our work are twofold. First, we prove that an unbounded number of pairs of networks exist with the same degree distribution and assortativity, yet different joint degree distributions. Thus, assortativity as a network measure cannot distinguish between graphs with complex (non-linear) dependence in their joint degree distributions. Motivated by this finding, we introduce a generative graph model that explicitly estimates and models the joint degree distribution. Our Binned Chung Lu method accurately captures both the joint degree distribution and assortativity, while still matching characteristics such as the degree distribution and clustering coefficients. Further, our method has subquadratic learning and sampling methods that enable scaling to large, real world networks. We evaluate performance compared to other scalable graph models on six real world networks, including a citation network with over 14 million edges.

MODIFIED CHOLESKY DECOMPOSITION FOR SOLVING THE MOMENT MATRIX IN THE RADIAL POINT INTERPOLATION METHOD

The radial point interpolation method is frequently employed in numerical computations. It can be used to interpolate scattered data, as shape functions in meshless methods and mesh deformation scheme, etc. The main problem in calculating the radial point interpolation is solving the moment matrix of the interpolation scheme, which is usually done with LU decomposition. A new decomposition technique based on the Cholesky decomposition is introduced in this paper. A comparison of the error, the consumed time and the results between the new decomposition technique and the LU method is presented for two different numerical methods.

Numerical investigation of a high order hybridizable discontinuous Galerkin method for 2d time‐harmonic Maxwell's equations

PurposeThis work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.Design/methodology/approachThe proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.FindingsThe approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L2 norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.Originality/valueThe work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.

Direct estimation of cause-specific mortality fractions from verbal autopsies: multisite validation study using clinical diagnostic gold standards

BackgroundVerbal autopsy (VA) is used to estimate the causes of death in areas with incomplete vital registration systems. The King and Lu method (KL) for direct estimation of cause-specific mortality fractions (CSMFs) from VA studies is an analysis technique that estimates CSMFs in a population without predicting individual-level cause of death as an intermediate step. In previous studies, KL has shown promise as an alternative to physician-certified verbal autopsy (PCVA). However, it has previously been impossible to validate KL with a large dataset of VAs for which the underlying cause of death is known to meet rigorous clinical diagnostic criteria.MethodsWe applied the KL method to adult, child, and neonatal VA datasets from the Population Health Metrics Research Consortium gold standard verbal autopsy validation study, a multisite sample of 12,542 VAs where gold standard cause of death was established using strict clinical diagnostic criteria. To emulate real-world populations with varying CSMFs, we evaluated the KL estimations for 500 different test datasets of varying cause distribution. We assessed the quality of these estimates in terms of CSMF accuracy as well as linear regression and compared this with the results of PCVA.ResultsKL performance is similar to PCVA in terms of CSMF accuracy, attaining values of 0.669, 0.698, and 0.795 for adult, child, and neonatal age groups, respectively, when health care experience (HCE) items were included. We found that the length of the cause list has a dramatic effect on KL estimation quality, with CSMF accuracy decreasing substantially as the length of the cause list increases. We found that KL is not reliant on HCE the way PCVA is, and without HCE, KL outperforms PCVA for all age groups.ConclusionsLike all computer methods for VA analysis, KL is faster and cheaper than PCVA. Since it is a direct estimation technique, though, it does not produce individual-level predictions. KL estimates are of similar quality to PCVA and slightly better in most cases. Compared to other recently developed methods, however, KL would only be the preferred technique when the cause list is short and individual-level predictions are not needed.

An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit

The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low. The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm.

Estimation of Time to Hard Failure Distributions Using a Three-Stage Method

Degradation analysis is a tool for assessing the lifetime distribution in reliability analysis. The lifetime of a product, in degradation analysis, is defined as the time when the value of a chosen degradation characteristic reaches a predetermined threshold. This kind of failure is called a soft failure, in contrast with a hard failure which means that the product is not functioning at any positive performance level. In this article, we introduce the idea of considering the threshold for the degradation characteristic as random. The difference between the time to soft failure and hard failure is then modeled. We modify Lu & Meeker's two-stage method, and a new approach named the three-stage method is developed. We apply both the two- and three-stage methods to a simulation study. From the simulation study, we conclude that when the time to soft failure is very different from the time to hard failure, the three-stage method leads to a better performance than the two-stage method. Fatigue-crack growth data are analysed at the end.