Standard Element Research Articles

MP06-12 STANDARDIZATION AND VISUALIZATION OF THE SURGICAL TIME OUT ACROSS SURGICAL SUBSPECIALTIES

You have accessJournal of UrologyCME1 Apr 2023MP06-12 STANDARDIZATION AND VISUALIZATION OF THE SURGICAL TIME OUT ACROSS SURGICAL SUBSPECIALTIES Brittany Levy, Sherry Lantz, Wesley Wilt, and Andrew Harris Brittany LevyBrittany Levy More articles by this author , Sherry LantzSherry Lantz More articles by this author , Wesley WiltWesley Wilt More articles by this author , and Andrew HarrisAndrew Harris More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003217.12AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: The timeout (TO) can prevent adverse events but is subject to TO engagement. We hypothesize transforming the TO to an auditable, active process will improve compliance and engagement. METHODS: The passive nature of the current TO was identified as a potential safety issue on staff patient safety culture surveys. Subsequently, the Time Out Engagement and Standardization (TOES) quality improvement initiative was developed. 11 TOs were audited concerning engagement and content. Leadership and frontline stakeholders were engaged as members of the TOES team to determine potential interventions. A TO consisting of 15 elements utilizing a TO whiteboard with role specific objectives was developed. Plan, Do, Study, Act (PDSA) cycles commenced. Following implementation, 17 TOs in urology, general surgery, and vascular surgery were audited based on engagement and content. RESULTS: Engagement varied with nurse participating in 100% compared to anesthesia provider or surgeon participating in 18%. No TO included all 15 elements and only 13% of elements were standardized across TOs. Overall, 40% of the elements were discussed in 80% of TOs. Post-implementation of TOES, nursing, anesthesia, and surgeon participated in 100% of TOs. The 15 standardized elements of the TO were discussed 90% of the time. Voice of the customer audits revealed widespread acceptance of the active TO. Within the robotic OR, urologists noted a particular improvement in preoperative planning communication across the surgical team. CONCLUSIONS: We identified a need for increased engagement of the TO based on staff concerns which were verified through auditing. Implementation of a team driven intervention and rapid PDSA cycles led to measurable improvement of the surgical TO. Source of Funding: None © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e57 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Brittany Levy More articles by this author Sherry Lantz More articles by this author Wesley Wilt More articles by this author Andrew Harris More articles by this author Expand All Advertisement PDF downloadLoading ...

지리교육에서의 교수·학습 자료로써 드론 기반 3차원 지형 모델 활용:지형학적 성취기준 및 학습 요소를 중심으로

지리교육에서의 교수·학습 자료로써 드론 기반 3차원 지형 모델 활용:지형학적 성취기준 및 학습 요소를 중심으로

A simple and efficient lagrange multiplier based mixed finite element for gradient damage

A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a Lagrange multiplier based mixed finite element formulation for finite strains. Thereby, no numerical stabilization or penalty parameters are required. On the other hand, no additional degrees of freedom appear for the Lagrange multiplier which is achieved through a suitable FE-interpolation scheme allowing for static condensation. In contrast to competitive approaches from the literature with similar efficiency, the proposed formulation does not require cross-element information and thus, a straightforward implementation using standard element routine interfaces is enabled. Numerical tests show mesh-independent solutions, robustness of the solution procedure for states of severe damage and under cyclic loading conditions. It is demonstrated that the computing time of the gradient damage calculations exceeds the one of purely elastic computations only by an insignificant amount. Furthermore, an improved convergence behavior compared to alternative approaches is shown.

2D physically unclonable functions of the arbiter type

Objectives. The problem of constructing a new class of physically unclonable functions of the arbiter type (APUF) is being solved, based on the difference in delay times for the inputs of numerous modifications of the base element, due to both an increase in the number of inputs and the topology of their connection. Such an approach allows building two-dimensional physically unclonable functions (2D-APUF), in which, unlike classical APUF, the challenge generated for each basic element selects a pair of paths not from two possible, but from a larger number of them. The relevance of such a study is associated with the active development of physical cryptography. The following goals are pursued in the work: the construction of the basic elements of the APUF and their modifications, the development of a methodology for constructing 2D-APUF.Methods. The methods of synthesis and analysis of digital devices are used, including those based on programmable logic integrated circuits, the basics of Boolean algebra and circuitry. Results. It is shown that the classical APUF uses a standard basic element that performs two functions, namely, the function of choosing a pair of paths Select and the function of switching paths Switch, which, due to their joint use, allow achieving high performance. First of all, this concerns the stability of the APUF functioning, which is characterized by a small number of challenge, for which the response randomly takes one of two possible values 0 or 1. Modifications of the base element in terms of the implementations of its Select and Switch functions are proposed. New structures of the base element are presented in which the modifications of their implementations are made, including in terms of increasing the number of pairs of paths of the base element from which one of them is selected by the challenge, and the configurations of their switching. The use of various basic elements makes it possible to improve the main characteristics of APUF, as well as to break the regularity of their structure, which was the main reason for hacking APUF through machine learning. Conclusion. The proposed approach to the construction of physically unclonable 2D-APUF functions, based on the difference in signal delays through the base element, has shown its efficiency and promise. The effect of improving the characteristics of such PUFs has been experimentally confirmed with noticeable improvement in the stability of their functioning. It seems promising to further develop the ideas of constructing two-dimensional physically unclonable functions of the arbiter type, as well as experimental study of their characteristics, as well as resistance to various types of attacks, including using machine learning.

Microvariation in the Distribution of Resumptive Pronouns in the Left Dislocation Construction in Two Tyrolean Dialects of Northern Italy

In this paper we document a so-far neglected case of microvariation involving resumptive pronouns in the left-dislocation construction in Meranese, spoken in South Tyrol, and Mòcheno, spoken in the Fersina valley (Trentino). While in standard German resumptive elements in this construction belong to the class of D-pronouns, the two Tyrolean dialects considered in the paper exhibit, as resumptive pronouns, both (i) D-pronouns and (ii) pronominal usages of the distal demonstrative formed by the definite article (D) and sèll corresponding to ‘that one’. We show that in both languages D+sèll forms overlap with German D-pronouns in most contexts, whereas D-pronouns only superficially, but not functionally, correspond to German D-pronouns, and have undergone a weakening process. While the weakening process is in nuce in Meranese, it seems to be nearly completed in Mòcheno, where D-pronouns appear to have acquired a status close to that of subject clitics of Northern Italian varieties.

A Meta-Analysis of Behavior Interventions for Students With Emotional-Behavioral Disorders in Self-Contained Settings

Students with emotional-behavioral disorders (EBDs) often learn in alternative classroom settings to provide more intensive instruction that meets their educational needs. Although research has demonstrated promise for several behavior intervention practices in general education settings, the generalizability of these practices to more restricted environments is unknown. Thus, this meta-analysis aimed to examine the class-wide behavior interventions tested in self-contained learning environments for students with EBDs. Studies investigating behavioral interventions in alternative elementary settings were systematically screened. Fifteen studies with 20 effect sizes met inclusion criteria and results from each study were synthesized. An estimated average effect was calculated ( g = 0.93, SE = 0.16), demonstrating that tested interventions are typically effective in self-contained learning environments to improve student behaviors. A thematic analysis and multi-level meta-regression were conducted to determine which elements are most beneficial to students in these unique learning environments. Results indicated that interventions that included relational supports, such as daily parent communication, differentially benefited students ( B = 1.26, SE = 0.15). Limitations include the small number of studies meeting inclusion criteria that have investigated behavior interventions in self-contained settings and the need for improved research quality. Implications suggest support for adapting standardized practice elements, such as group contingencies, to improve student behaviors in multiple learning environments.

ReLU Neural Network Galerkin BEM

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dimensions. We adopt a Galerkin formulation-based method, in polygonal domains with a finite number of straight sides. Trial spaces used in the Galerkin discretization of the BIEs are built by using NNs that, in turn, employ the so-called Rectified Linear Units (ReLU) as the underlying activation function. The ReLU-NNs used to approximate the solutions to the BIEs depend nonlinearly on the parameters characterizing the NNs themselves. Consequently, the computation of a numerical solution to a BIE by means of ReLU-NNs boils down to a fine tuning of these parameters, in network training. We argue that ReLU-NNs of fixed depth and with a variable width allow us to recover well-known approximation rate results for the standard Galerkin Boundary Element Method (BEM). This observation hinges on existing well-known properties concerning the regularity of the solution of the BIEs on Lipschitz, polygonal boundaries, i.e. accounting for the effect of corner singularities, and the expressive power of ReLU-NNs over different classes of functions. We prove that shallow ReLU-NNs, i.e. networks having a fixed, moderate depth but with increasing width, can achieve optimal order algebraic convergence rates. We propose novel loss functions for NN training which are obtained using computable, local residual a posteriori error estimators with ReLU-NNs for the numerical approximation of BIEs. We find that weighted residual estimators, which are reliable without further assumptions on the quasi-uniformity of the underlying mesh, can be employed for the construction of computationally efficient loss functions for ReLU-NN training. The proposed framework allows us to leverage on state-of-the-art computational deep learning technologies such as TENSORFLOW and TPUs for the numerical solution of BIEs using ReLU-NNs. Exploratory numerical experiments validate our theoretical findings and indicate the viability of the proposed ReLU-NN Galerkin BEM approach.

Experimental and numerical studies of screwed connections with hot-rolled steel plate and cold-formed steel sheet

This paper presents a test and numerical program on screwed connections of cold-formed steel (CFS) sheets and hot-rolled steel (HRS) plates. The shear strength, load–deformation relationship, and failure mode of the specimens were obtained. The test results were compared with the results predicted by the North American Specification (AISI S 100–16), European Standard (EN1993-1–3), and finite element (FE) models. The influence of the fastener diameter and thickness of the CFS sheet and HRS plate on the specimens was discussed. In addition, a new method of calculating the bearing capacity of the connections with thicker plates was proposed. The results showed that bearing failure, shear failure, and combined bearing/shear failure were observed in the specimens. The nominal strengths predicted by AISI S 100 and EN 1993–1–3 for specimens are generally conservative. The numerical models can predict the failure modes and load–deformation relationships of the specimens with good agreement. In addition, the proposed method for the bearing capacity has better accuracy when the connections have thicker HRS plates.

The impact of tableside ordering technologies on alcohol sales to the intoxicated.

The impact of tableside ordering technologies on alcohol sales to the intoxicated.

X‐ray fluorescence analysis using ultrasonic levitation technique

AbstractA thin film is used as the sample holder for analyzing solutions and solid samples using x‐ray fluorescence (XRF). The incident x‐rays are scattered on the sample and thin film, and the scattered x‐rays serve as background signals in the XRF spectra. To reduce the intensity of the background signal, an ultrasonic levitation method was developed herein for XRF measurements. The ultrasonic levitation device is equipped with a transducer (horn) and reflector, and a small‐size sample is levitated around a node of a generated standing wave; thus, a sample holder is not necessary. Fe solution (2 μL) was analyzed to evaluate the developed instrument. The results obtained using levitation times of 0 and 60 min were compared. The solvent droplet almost evaporated during ultrasonic levitation; therefore, the absorption effects of XRFs and incident x‐rays and the scattering effect of incident x‐rays were reduced. At a levitation time of 60 min, the net intensity of the Fe Kα peak was increased, and the background intensity decreased. The relationship between the levitation time and the net or background intensities of the Fe Kα peak was defined; thus, condensation of the sample droplet was successfully observed. Quantitative analysis was performed using an internal standard method. The relative intensity (ratio of the net intensities of the target and internal standard elements) was proportional to the concentration ratio. Therefore, this method is useful for measuring trace elements at low background intensity and elucidating the process of condensation of a sample droplet.

Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: An experimental validation

Owing to ever-increasing complexity of engineering structures, developing a methodology for the early detection of defects has become crucial to ensure their long-term safety and reliability with the least amount of expense. There are always discrepancies between experimental and numerical modal data because of unknown structural parameters and uncertainties. The finite element (FE) model updating techniques attempt to minimize the differences by adjusting the unknown parameters of the FE model. Therefore, the FE model updating methods are essential for developing a baseline model and accurate damage identifications in subsequent steps. This paper employs the semi-rigidly connected frame element (S-RCFE) instead of the standard Euler-Bernoulli beam element for assembling the FE model of the experimental beam and establishing a high-fidelity numerical model. The S-RCFE with extra design parameters, including the end fixity factor of all connections, enables us to achieve a reasonable agreement between experimental and numerical models through the optimization-based procedure. In FE model updating step, two objective functions based on modified total modal assurance criterion (MTMAC) and changes in natural frequencies are used to minimize by three optimization algorithms, viz, grey wolf optimizer (GWO), gradient-based optimization (GBO), and an improved version of GWO (IGWO). The influence of the S-RCFE and standard Euler-Bernoulli beam on the model updating accuracy is also examined, and the efficiency of S-RCFE is evaluated. The statistical results reveal that GWO-MTMAC and IGWO-MTMAC can be successfully implemented for FE model updating with almost the same performance. However, IGWO provides the most reliable results with a relatively extensive computation time for damage identification in all scenarios. In some damage scenarios, the GWO and GBO perform comparably with very similar running time. Data used in this article can be found at https://github.com/Samir-Khatir/Data-modal-analysis-of-healthy-and-cracked-beam.git

Шляхи адаптації та модернізації випробувального обладнання для відтворення ударних навантажень виходячи з вимог стандарту MIL-STD-810

The subject matter of the article is the process of testing the objects of general use, aviation and space industry, railway transport, electric power industry, and nuclear industry on the impact of shock loads. The goal is to implement modern international standards, in particular MIL-STD-810, in the practice of testing laboratories. The tasks to be solved are: to study the possibility of using vibration stands in impact testing and to modernize the existing test equipment by developing a new software for control systems based on existing and proven algorithms. To achieve this goal, the analysis of current regulatory documents was carried out and the existing experience in the conformity assessment was adapted. The following results were obtained: a research test stand was created using the technical capabilities of the Test & Certification Center of RPI “HARTRON-ARKOS” LTD. The software was developed using standard library elements from the SCADA system. The capacity of using a vibrating stand during impact testing was taken into account, and an iterative impact control mode was implemented. The operability of the modernized test equipment was confirmed by full-scale verification of all parameters with a positive result, and approbation was passed during real tests in various modes for complex test objects. This paper formulates proposals for expanding the capabilities of the existing laboratory and testing base when implementing MIL-STD-810. The proposed approach to software development allows the replication of the code in any other software environment. A comparative assessment of financial and time costs for the purchase of new and modernization of existing equipment confirms the economic feasibility of the described approach. The perceptiveness of the adoption of the MIL-STD-810 standard as a state standard of Ukraine was defined. It is proposed to use this standard in the practice of testing laboratories to conform the requirements of developers and manufacturers in various industries, as well as a basis for industry standards, which ensures the replacement of outdated and canceled standards.

Linear viscoelastic response of the vertex model with internal and external dissipation: Normal modes analysis

We use the normal mode formalism to study the shear rheology of the vertex model for epithelial tissue mechanics in the overdamped linear response regime. We consider systems with external (e.g., cell-substrate) and internal (e.g., cell-cell) dissipation mechanisms, and derive expressions for stresses on cells due to mechanical and dissipative forces. The semi-analytical method developed here is, however, general and can be directly applied to study the linear response of a broad class of soft matter systems with internal and external dissipation. It involves normal mode decomposition to calculate linear loss and storage moduli of the system. Specifically, displacements along each normal mode produce stresses due to elastic deformation and internal dissipation, which are in force balance with loads due to external dissipation. Each normal mode responds with a characteristic relaxation timescale, and its rheological behavior can be described as a combination of a standard linear solid element due to elastic stresses and a Jeffreys model element due to the internal dissipative stresses. The total response of the system is then fully determined by connecting in parallel all the viscoelastic elements corresponding to individual normal modes. This allows full characterization of the potentially complex linear rheological response of the system at all driving frequencies and identification of collective excitations. We show that internal and external dissipation mechanisms lead to qualitatively different rheological behaviors due to the presence or absence of Jeffreys elements, which is particularly pronounced at high driving frequencies. Our findings, therefore, underscore the importance of microscopic dissipation mechanisms in understanding the rheological behavior of soft materials and tissues, in particular.

INDONESIA'S SPATIAL DATA INFRASTRUCTURE (CASE STUDY: BANGKALAN, SAMPANG AND BLITAR REGENCIES)

The paper examines the current state of Spatial Data Infrastructure (SDI) in Indonesia, with a focus on identifying strengths, weaknesses, and organizational structures of the national SDIs. This paper aims to inform the design and implementation of a future regional SDI for the local government especially at the Bangkalan, Sampang and Blitar Regency. The evaluation is conducted using a survey with 46 questions, which assess the factors that affect execution the of SDI in the region. The survey is classified according to the five basic components of an SDI: policy elements, institutional elements, human resources, standard elements, geospatial data and information, and technology elements. The results of the survey are analyzed to identify the current state of SDI implementation in the region and to serve as a reference point for future updates. The paper concludes by highlighting the need for technical and organizational solutions to address present problems in the geospatial data management and interoperability in order to fully exploit the potential of geospatial information in decision making.

Determination of Chromium in Contaminated Water Samples Using Chemically Modified Nanoadsorbent: A Computational and Experimental Study

AbstractIn the reported work, a solid phase extraction method for speciation of chromium species in contaminated industrial and river water samples has been studied by using both experimental and computational methods. Multiwalled carbon nanotubes (MWCNTs) functionalized with tris(2‐aminoethyl)amine (TREN) was used as a solid phase extractant for the hyphenated preconcentration of chromium species. The characterization of the immobilized MWCNTs was done by FTIR and SEM analysis. This hyphenated system significantly improves the overall analytical performance by reducing sample consumption and sampling time. The computational results supported the experimental findings. The negative adsorption energy (−2.71 eV) suggested that the interaction process between chromium and modified nanoadsorbent is spontaneous. The system showed a limit of detection of 0.07 μg L−1 at optimized condition with an RSD value of 1.2 %. Adsorption capacity was measured using Lagergren's equation which showed that adsorption kinetics follows pseudo second‐order. The suggested method was applied to contaminated real water samples by performing spike recovery tests. The validation of the reported system was done by analysing NIST Standard Reference Material Trace Elements in Natural Water 1640a.

Experimental research on standardized bamboo culm components for developing prefabricated bamboo building

Bamboo culm structures are useful for areas with limited access to structural wood, especially for remote bamboo forest areas. This study focuses on developing standardized bamboo culm components for the prefabricated bamboo building, which is potential to replace timber components made of dimension lumber used in modern timber buildings. The basic material properties of Moso bamboo and bamboo culm elements were investigated. Test results show that the main mechanical properties of bamboo culm are comparable to some coniferous wood, such as TC-13A grade (in Chinese standard). Several types of simple and reliable connectors were designed for connecting bamboo culms, attempting to provide standardized bamboo culm elements. The prefabricated shear wall elements were designed with bamboo culms as studs and glubam lumber as perimeter frame for regulate the dimension. Three shear wall models were tested under monotonic and cyclic lateral loading. It was found that the lateral resistance capacity of bamboo culm shear wall is about 64% of that of the similar lightweight wood frame shear walls. Three specimens of bamboo culm trusses were also tested to obtain the design capacity of the roof system. Based on the experimental test results, a prototype single-story building was designed and constructed to assess the feasibility of the constructional details. Carbon dioxide emission analysis revealed the environmentally friendly advantages of this type of bamboo building.

RISK FACTORS OF UMBILICAL CORD PATHOLOGY AND FACTORS OF NEGATIVE PERINATAL CONSEQUENCES AND NEWBORN INCIDENCE

According to literature sources, the real frequency of many umbilical cord pathologies differs significantly from the statistical data indicated by researchers in their works (from 15% to 38%). The implementation of a system of diagnostic and treatment and preventive measures, based on mandatory antenatal and postnatal assessment of the features and characteristics of the umbilical cord, allows to improve perinatal outcomes and reduce perinatal morbidity. The aim of the work was to identify the main risk factors of umbilical cord pathology and negative perinatal consequences; to develop elements of standardization of antenatal and postnatal diagnosis of umbilical cord pathology. Research materials and methods. A retrospective assessment of medical documentation data (3,280 individual medical records of pregnant women) made it possible to establish the frequency of umbilical cord pathology in the population. In the future, a more detailed extended antenatal and postnatal examination of the umbilical cord and placenta after delivery was carried out in 637 patients of reproductive age with pregnancy complicated by pathology of the umbilical cord (main group). The control group was formed by 40 patients with an uncomplicated course of pregnancy and live birth of full-term healthy children. The study was conducted taking into account the main principles of the Helsinki Declaration on Biometric Research and the powers of the GCH ICH, in accordance with biometric norms with compliance with the principles of confidentiality and ethics (excerpt from protocol No. 128/22 of the meeting of the Bioethics Commission dated September 29, 2022, Ivano-Frankivsk National Medical University, Ministry of Health of Ukraine).Data analysis was performed using the Statistica 7.0 package of statistical programs (StatSoftInc., USA). The association of independent variables with the condition being studied is presented as odds ratio (OR) and 95% confidence interval (CI).The materials of the article are the result of the research of the complex research work fragment of the Department of Obstetrics and Gynecology named after I.D. Lanovyi of the Ivano-Frankivsk National Medical University: “Development of diagnostic tactics and pathogenetic substantiation of effective methods of preserving and restoring reproductive potential and improving parameters of a woman’s quality of life in obstetric and gynecological pathology” (state registration number 0121U109269, implementation dates 2021-2026 ), the author is a co-executor of the topic.Research results and their discussion. The following data were noted: an excess of the population norm of the length of the umbilical cord, a high proportion of eccentric and marginal insertion of the umbilical cord (22.14%) and umbilical cord coiling (33.28%), a decrease in the proportion of the reference limits of the umbilical cord tortuosity index (15.86%), in 56.7% of observations, the specific gravity of the umbilical cord was lower. Probable risk factors for umbilical cord pathology with a predominance of age over 35 years, nicotine addiction in pregnant women, multiple fertility, use of IVF programs, change in the amniotic fluid index, overweight and obesity, other clinical conditions associated with metabolic disorders (gestational diabetes, insulin resistance) were identified. Conclusion. The share of the umbilical cord pathology both in the isolated type and in the combination of characteristic features of the umbilical cord is 40.98%. The increase in the risk of negative perinatal consequences has a close relationship with the umbilical cord pathology and the combination of different types of pathology, as well as the addition of gestational complications, which allows for the formation of screening programs and optimization of the diagnostic algorithm.

Analytical Approach to Current Rating of Three-Phase Power Cable with Round Conductors

The continuous increase in the demand for electricity makes it necessary to modernize or build new transmission lines. This, in turn, results in research that is still being carried out on the optimal use of power cables. In the paper, an improved analytical method for the determination of the current rating of power cables was proposed. The method for determining the ampacity of the power cable presented in the IEC standard assumes that power losses in the phase conductors and screens are determined by taking into account skin and the proximity effects on the basis of tabulated coefficients. The methodology proposed in the paper is based on the method presented in the IEC standard, but the power losses in the conductive elements of the cable are determined analytically, which offers higher accuracy. In order to validate the analytical method proposed in this paper, numerical calculations based on the finite element method with very fine mesh were also performed. Exemplary calculations carried out for three types of cables with use of the proposed method, IEC standard and finite elements showed very good agreement in the results. The proposed method requires more computational effort, but it offers more accurate results than the IEC standard and can be used when higher accuracy is required. It can also serve as a reference point for simplified calculations.

A unified enrichment approach of the standard three-node triangular element

The aim of this paper is to unify the ideas and to extend to a more general setting the work done in (Dell'Accio et al., 2023 [14]) for a polynomial enrichment of the standard three-node triangular element (triangular linear element) using line integrals and quadratic polynomials. More precisely, we introduce a new class of nonconforming finite elements by enriching the class of linear polynomial functions with additional functions which are not necessarily polynomials. We provide a simple condition on the enrichment functions, which is both necessary and sufficient, that guarantees the existence of a family of such enriched elements. Several sets of admissible enriched functions that satisfy the admissibility condition are also provided, together with the explicit expression of the related approximation error. Our main result shows that the approximation error can be decomposed into two parts: the first one is related to the linear triangular element while the second one depends on the enrichment functions. This representation of the approximation error allows us to derive sharp error bounds in both L∞ and L1 norms, with explicit constants, for continuously differentiable functions with Lipschitz continuous gradients. These bounds are proportional to the second and the fourth power of the circumcircle radius of the triangle, respectively. We also provide explicit expressions of these bounds in terms of the circumcircle diameter and the sum of squares of the triangle edge lengths.

The frequency of dysplastic branching crypts in colorectal polypoid tubular adenomas.

Dysplastic crypt branching (DCB) was recently found in ulcerative colitis-associated dysplasia. The aim was to assess the frequency and the branching phenotype of DCB in polypoid colorectal tubular adenomas (TA). A total of 3956 DCB were found in the 139 TA: 98% were in asymmetric branching (DCAB) and the remaining 2% in symmetric branching (DCSB). A linear correlation was found between DCB frequency and the increasing digital size in TA (p < .05). Using a digital ruler, adenomas were divided into small TA (<5 mm) and larger TA (≥5 mm). The difference between the frequency of DCB in small TA (n=75) vs. larger TA (n=64), was significant (p < .05). DCB frequency was not influenced by age, gender or TA localization. In the normal colorectal mucosa (≈2 m2 ), only occasional CSB is found and no CAB. And yet, multiple DCB (mean 16.7 DCB), mostly DCAB, was found in small TA, occupying <5 mm of the mucosal area. In larger TA, as many as 42.1 DCB (mean), mostly DCAB, occurred in merely 7.8 mm (mean) of the colon mucosa. Thus it is suggestedthat DCB is a standard histologic element of TA. The natural expansion of the adenomatous tissue in larger TA appears to be follow on from newly produced, mostly DCAB, by DCSB and by the accumulation of their dysplastic offspring's progenies. The findings strongly suggest that DCB is a central microstructure in the histological events unfolding in polypoid colorectal TA.