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This document discusses the importance of a scientific approach in the field of abdominal wall surgery. It emphasizes the need for a combination of factors, including personal experience, guidelines, and analysis of scientific literature, in order to provide patients with the best possible care. The document also highlights the complexity of the field and the value of research in addressing challenging situations. This special issue of the journal Hernia, guest edited by international experts, aims to provide surgeons with valuable insights and support in their daily practice. [Extracted from the article]

Hills and mountain fields have a high proportion in coastal areas around the world. Especially in China, lots of low-rise buildings are in complex mountain terrain. Compared with the flat topography under typhoons, due to the change caused by complex topography, the damage ratio of low-rise buildings is much larger. This paper investigates the wind pressure distribution in three different configurations of typical mountain terrain on low-rise buildings in coastal areas by wind tunnel tests. At the same time, the results are compared with the wind pressure distribution of low-rise buildings without surrounding structures. The variation of the average pressure coefficient and shape coefficient with the change of hillside height under a wind attack angle of 0° and the trends of average wind pressure coefficients of a low-rise building under wind attack angles of 0° – 90° are studied. The results show that the distribution of pressure in low buildings is significantly affected by the height of the mountain. When the hillside height is half of the scale physical model, the influence coefficient from the mountain to each surface of the whole building is within 50%. When the hillside height is four times that of the model, the influence factor from the mountain to each surface of the whole building is obvious and is most significantly influenced by the leeward roof. The mean design criteria of the low-rise building, such as windward midline, leeward roof, and windward roof in these three typical mountain terrains, should be designed for their higher absolute value of the average pressure coefficient. The mean pressure coefficient under different wind angles and mountain environments has a significant relationship. The most unfavorable wind angle of wind load calculations should be considered when designing low-rise buildings. [ABSTRACT FROM AUTHOR]

Topography can strongly affect ground motion, and studies of the quantification of hill surfaces' topographic effect are relatively rare. In this paper, a new quantitative seismic topographic effect prediction method based upon the BP neural network algorithm and three-dimensional finite element method (FEM) was developed. The FEM simulation results were compared with seismic records and the results show that the PGA and response spectra have a tendency to increase with increasing elevation, but the correlation between PGA amplification factors and slope is not obvious for low hills. New BP neural network models were established for the prediction of amplification factors of PGA and response spectra. Two kinds of input variables' combinations which are convenient to achieve are proposed in this paper for the prediction of amplification factors of PGA and response spectra, respectively. The absolute values of prediction errors can be mostly within 0.1 for PGA amplification factors, and they can be mostly within 0.2 for response spectra's amplification factors. One input variables' combination can achieve better prediction performance while the other one has better expandability of the predictive region. Particularly, the BP models only employ one hidden layer with about a hundred nodes, which makes it efficient for training. [ABSTRACT FROM AUTHOR]

The aim of this paper was to investigate intumescent coatings based on polyfurfuryl alcohol (PFA) resin as a binder benefiting from high char yield and low smoke emission. To this end, the coatings composition in terms of PFA binder resin, long oil alkyd plasticizing resin, TiO2 pigment, and flame-retardant additives (FR) was changed as input parameters according to a mixture design-of-experiments. The corresponding changes in the backside temperature of mild steel substrate (Tb), residual char expansion ratio, limiting oxygen index, and char residue (wt% @1000 °C) were studied as the response variables describing fire performance characteristics of the coatings. The results showed that the backside temperature of the plate increased and the expansion ratio decreased with increasing in the alkyd resin concentration. Also, the flame-retardant efficiency of coatings strongly depends on the content of FR additives. When the content of PFA and alkyd resin was increased at a high level (35 and 4 wt%, respectively), the Tb of the coated plates reached 415 °C rapidly, due to the cracking of the coating and the lower concentration of FR additives. However, the formula with higher FR content, i.e., 68 wt%, showed the lowest Tb value ca. 128 °C. Flame-retardant characteristics directly depended on the expansion ratio of the coatings and the morphology of the char layer remaining on the substrate after the flame test; therefore, coatings with a higher expansion ratio showed lower backside temperature. The findings were supported by examining of the remaining char morphology after a flame test by optical microscopy and validated by comparing the predicted and actual responses for optimization. The value of absolute relative deviation was obtained in the range of 1.6–7.9, which indicates a good agreement between the proposed and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving the generalized absolute value equations (GAVE). We present a new method named as modulus-based block triangular splitting iteration (MBTS) method based on the block matrix structure resulting from the transformation of the GAVE into two equations. This method is developed by decomposing the matrix into diagonal and triangular matrices, as well as applying a series of suitable combination and modification techniques. The advantage of the MBTS method is that it is not necessary to solve the inverse of the coefficient matrix of the linear equation system during each iteration, which greatly improves the computational speed and reduces its storage requirements. In addition, we present some convergent theorems proving by different techniques and the estimate of the required number of iteration steps. Furthermore, in the accompanying corollaries, we provide some estimations for choosing appropriate parameter values. Finally, we validated the effectiveness and efficiency of our newly developed method through two numerical examples of the GAVE. [ABSTRACT FROM AUTHOR]

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in multiple access communication systems in code division. Firstly, this paper studies the Jacobi sums over Galois rings of arbitrary characteristics and completely determines their absolute values. This extends the work by Li et al. (Sci China 56(7):1457–1465, 2013), where the Jacobi sums over some Galois rings with characteristics of a prime square were discussed. It is worth mentioning that the generalization is not trivial, as the Galois rings of arbitrary characteristics have a more complicated structure. Our deterministic construction of codebooks is based on Jacobi sums over Galois rings of arbitrary characteristics, producing asymptotically optimal codebooks for the Welch bound. Finally, compared to the literature, this article proposes for the first time design of codebooks based on Jacobi sums over Galois rings. In addition, the parameters of the presented codebooks are new. [ABSTRACT FROM AUTHOR]

Time series forecasting is an important application of many statistical methods. When it is appropriate to assume that the data may be projected towards the future based on the past history of the dataset, a preliminary examination is usually required to ensure that the data sequence is autocorrelated. This is a quite obvious assumption that has to be made and can be the object of a formal test of hypotheses. The most widely used test is the portmanteau test, i.e., a sum of the squared standardized autocorrelations up to an appropriate maximum lag (the truncation point). The choice of the truncation point is not obvious and may be data-driven exploiting supplementary information, e.g. the largest autocorrelation and the lag where such maximum is found. In this paper, we propose a portmanteau test with a truncation point equal to the lag of the largest (absolute value) estimated autocorrelation. Theoretical and simulation-based comparisons based on size and power are performed with competing portmanteau tests, and encouraging results are obtained. [ABSTRACT FROM AUTHOR]

Consider a quantum cat map M associated with a matrix A ∈ Sp (2 n , Z) , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue of A of largest absolute value and (2) the characteristic polynomial of A is irreducible over the rationals. This is similar to previous work (Dyatlov and Jin in Acta Math 220(2):297–339, 2018; Dyatlov et al. in J Am Math Soc 35(2):361–465, 2022) on negatively curved surfaces and (Schwartz in The full delocalization of eigenstates for the quantized cat map, 2021) on quantum cat maps with n = 1 , but this paper gives the first results of this type which apply in any dimension. When condition (2) fails we provide a weaker version of the result and discuss relations to existing counterexamples. We also obtain corresponding statements regarding semiclassical measures and damped quantum cat maps. [ABSTRACT FROM AUTHOR]

Stochastic adaptive gradient decent algorithms, such as AdaGrad and Adam, are extensively used to train deep neural networks. However, randomly sampling gradient information introduces instability to the learning rates, leading to adaptive methods with poor generalization. To address this issue, the ABNGrad algorithm, which leverages the absolute value operation and the normalization technique, is proposed. More specifically, the absolute value function is first incorporated into the iteration of the second-order moment estimate to ensure that it monotonically increases. Then, the normalization technique is employed to prevent a rapid decrease in the learning rate. In particular, the techniques used in this paper can also be integrated into other existing adaptive algorithms, such as Adam, AdamW, AdaBound, and RAdam, yielding good performance. Additionally, it is shown that ABNGrad can attain the optimal regret bound for solving online convex optimization problems. Finally, many experimental results illustrate the effectiveness of ABNGrad. For a comprehensive exploration of the advantages of the proposed approach and the specifics of its detailed implementation, the readers are referred to the following https://github.com/Wenhan-Jiang/ABNGrad.git [ABSTRACT FROM AUTHOR]

Gabor phase retrieval is the problem of recovering a signal from the absolute values of Gabor transform, which has turned into a very active research area. In the paper, we define a generalized Paley–Wiener space, which is obtained by applying the special affine Fourier transform to L p ([ - B , B ]) (2 ≤ p ≤ ∞) and provide the uniqueness of the Gabor phase retrieval in the generalized Paley–Wiener space. When the window function ψ is the inverse special affine Fourier transform of ϕ = 2 1 4 e - π x 2 , we show that every signal in the generalized Paley–Wiener space can be uniquely recovered, up to a global sign, from its the magnitudes of Gabor measurement sampled on a rectangular lattice. Recently, Grohs, Liehr and Wellershoff studied the Gabor phase retrieval problems in the conventional Paley–Wiener space. The paper extends their results to the generalized Paley–Wiener space. Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the applied range of the Gabor phase retrieval. [ABSTRACT FROM AUTHOR]

In this paper, two new iterative methods for solving generalized absolute value equations (GAVEs) are proposed and investigated using the single-step iteration (SSI) approach. The proposed iterative methods are Picard-SSI and nonlinear SSI-like methods. In the implementation of the Picard-SSI method, we have used the SSI method as an inner solver. The convergence of the proposed method for solving GAVE is analyzed under reasonable constraints. Several numerical examples are given to illustrate the efficiency and implementation of the proposed methods. [ABSTRACT FROM AUTHOR]

Most measures of agreement are chance-corrected. They differ in three dimensions: their definition of chance agreement, their choice of disagreement function, and how they handle multiple raters. Chance agreement is usually defined in a pairwise manner, following either Cohen's kappa or Fleiss's kappa. The disagreement function is usually a nominal, quadratic, or absolute value function. But how to handle multiple raters is contentious, with the main contenders being Fleiss's kappa, Conger's kappa, and Hubert's kappa, the variant of Fleiss's kappa where agreement is said to occur only if every rater agrees. More generally, multi-rater agreement coefficients can be defined in a g-wise way, where the disagreement weighting function uses g raters instead of two. This paper contains two main contributions. (a) We propose using Fréchet variances to handle the case of multiple raters. The Fréchet variances are intuitive disagreement measures and turn out to generalize the nominal, quadratic, and absolute value functions to the case of more than two raters. (b) We derive the limit theory of g-wise weighted agreement coefficients, with chance agreement of the Cohen-type or Fleiss-type, for the case where every item is rated by the same number of raters. Trying out three confidence interval constructions, we end up recommending calculating confidence intervals using the arcsine transform or the Fisher transform. [ABSTRACT FROM AUTHOR]

The technique for order preference by similarity to ideal solution (TOPSIS) is a popular multi-attribute decision making method. However, the increasing uncertain information with probability and the psychological factor of regret aversion of experts in some complicated situations bring new challenges to the application of traditional TOPSIS. The probabilistic hesitant fuzzy set (P-HFS) is an effective tool to depict the hesitant fuzzy information with the corresponding probability, which can remain more information. In addition, the regret theory indicates that experts may care more about the regret values than the absolute values of alternatives under the fuzzy environment. This paper investigates a new probabilistic hesitant fuzzy TOPSIS (PHFTOPSIS) method based on the regret theory. We propose the corresponding concepts of utility function, reject–rejoice function and perceived utility value of the probabilistic hesitant fuzzy element (P-HFE). The maximum deviation model under the probabilistic hesitant fuzzy environment is presented to determine the weights of attributes. The detailed implementation process of the PHFTOPSIS method based on the regret theory is also provided. Moreover, we apply the proposed method to the investment strategy. Compared with earlier methods, the proposed method can consider both the probabilistic hesitant fuzzy information and regret aversion of experts at the same time in actual applications. A comparative analysis with traditional TOPSIS and probabilistic hesitant fuzzy weighted averaging (PHFWA) operator is further conducted to illustrate its advantages. [ABSTRACT FROM AUTHOR]

For the period of satellite altimetry observation 1993–2018, a comparison was made of estimates of the linear meridional shifts of the jet structure and variations in current intensity in the sector of the Antarctic Circumpolar Current (ACC) south of Africa (10° E–25° W), obtained on the basis of the parameters derived from the module of the absolute dynamic topography (ADT) gradient : directly , module of the velocity of geostrophic current |u| on the ocean surface, half of square of the ADT gradient , and specific kinetic energy . The analysis was carried out by a method developed earlier and refined in this paper using linear regression analysis. It is shown that qualitatively the characters of the meridional shifts (displacement of the curves of these parameters averaged over latitude and for each year) in latitude and the corresponding current intensity variations (i.e., variations in the parameters themselves) over 26-year observations, when calculated through each of the four parameters, turned out to be similar. The same similarity was obtained from the calculations with respect to the ADT scale. Meanwhile, the quantitative differences between calculations for different pairs of parameters can be significant even in the and pair. In quantitative terms, the absolute values of shifts of the jet structure and variations in the intensity of currents in the ACC band in the studied sector of the Southern Ocean generally increase from those linearly dependent on the ADT gradient module to quadratically dependent ones. [ABSTRACT FROM AUTHOR]

Most of the plant diseases severely affect the plant leaves and thus can be identified from infected leaf images using modern computer vision techniques. During the last decade, various machine learning methods have been developed to detect and analyze plant leaf disease accurately. Hence, developing an effective machine learning prediction method for plant disease identification at an early stage arises enormous interest in computer vision research. Diagnosing plant leaf diseases is a challenging area of research, mainly because leaf images exhibit complexity arising from irregular shapes, uneven colors, a mixture of normal and abnormal regions, and are often accompanied by complex backgrounds. In this paper, a new feature descriptor titled as the local triangular-ternary pattern (LTriTP) for plant leaf disease detection is proposed. The proposed method extracts feature vectors using the triangular shape descriptor to enable efficient extraction and representation of features from the leaf images. To apply the ternary pattern, an absolute mean value based dynamic threshold is computed, which supports the sensitive analysis of plant leaf image texture information by producing highly relevant and diverse values. Since plant disease can appear at any orientation on a leaf image, therefore in each triangle, a histogram of the gradient is also computed in four directions (00, 450, 900, and 1350) to find the gradient change of infected regions in contrast to healthy areas. This is what we termed as the triangular histogram of gradient (T-HOG), which makes the proposed method orientation invariant. Fusion of T-HOG and LTriTP features has shown better disease detection performance. Multimodal classification is performed using 6 disease classes of tomato leaf images. The performance of the proposed method is compared with renowned methods like Local Binary Pattern, and Local Ternary Pattern using the publicly available PlantVillage dataset of tomato images. The classification accuracy varies from 94.50% to 97.80% with respect to different classifiers, where the error rate varies from 2.03% to 5.03%. [ABSTRACT FROM AUTHOR]

Newton-type methods have been successfully applied to solve the absolute value equation Ax − |x| = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [A − I, A + I] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs. [ABSTRACT FROM AUTHOR]

Nanocelluloses are highly interesting structures due to a variety of inherent properties, such as high surface area and porosity; hence, there is a need to investigate new sources of raw materials for their production. From this perspective, this paper presents a study on the obtainment of nanocelluloses from the cashew apple bagasse by evaluating the influence of the biomass pretreatment on the properties of the obtained structures. The cashew apple bagasse (CAB) was previously submitted to alkaline and acid–alkali pretreatments and the solid named CAB-PTA and CAB-PT-HA, respectively. The nanocellulosic fractions were obtained by hydrolysis using sulfuric acid combined with an ultrasonic treatment under different reaction times (1 h and 5 h). The highest nanocellulose yield was achieved using CAB-PT-HA, and the nanocrystals were rod-shaped and presented diameters of 30 to 40 nm. In the production of nanocelluloses using CAB-PTA, reaction time influenced the shape and size of the nanostructures, and the chemical composition analysis indicated the presence of residual lignin in those structures, which showed higher thermal stability. All obtained nanocelluloses presented zeta potentials greater than 30 mV in absolute values, indicating stable suspensions. Thus, this study can confirm the feasibility of the use of CAB as a novel renewable source for producing cellulose nanocrystals that possess great potential to be used as valuable biomaterials to this end. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of different materials has been widely studied using the split Hopkinson pressure bar (SHPB) testing. The striker bar's velocity (SV) and the incident bar's impact surface are well known to have a significant impact on producing a clear signal in the compressive SHPB studies. Several times, the shape of the incident strain signal differs from an ideal state, and the reason is difficult to find. In this paper, a parametric investigation of such understudied instances is carried out utilising Abaqus software for finite element analysis (FEA). The numerically obtained incident strain pulse for a perfectly aligned SHPB setup with different SV was validated experimentally on compressive SHPB apparatus. The numerical output was found to have good agreement with experimental results. Further, plots of incident strain were evaluated numerically for Sv (10, 15, 20, 25 and 30 in m/s) which was used for polynomial fitting using MATLAB's curve fitting tool. A similar method was adopted for symmetrically plane non-parallel impact surface on the incident bar. The angles chosen for FEA calculations were 5°, 10°, 15° and 20°. Filleted impact surface with radius (r) 1.5, 3, 4.5 and 6 mm was also studied. The study of the variation of impact surface shape was done at a striker velocity of 25 m/s. It was observed from this study that when striker velocity increases, the absolute magnitude of incident strain at peak increases while rise time remained constant. In turn, when the symmetrically non-parallel plane surface angle and fillet radius grow, the absolute value of incident strain at peak almost stays the same but the rising time lengthens. This study can help understand the nature and discrepancy of the incident strain signal obtained in the compressive SHPB setup and find its root cause. [ABSTRACT FROM AUTHOR]

In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016). [ABSTRACT FROM AUTHOR]

The Dunhuang murals, a significant part of Chinese heritage, have suffered deterioration primarily due to environmental and chemical factors, notably salt damage. This study proposes a sophisticated method that synergizes Fractional Order Differentiation (FOD) and Partial Least Squares Regression (PLSR) to accurately invert the phosphate content in the mural plaster of the Dunhuang paintings. The focal points of the research include: (1) To address the issue of information loss and reduced modeling precision caused by integer-order differentiation algorithms, the FOD method is employed for preprocessing spectral data. This approach ensures the fine spectral differences in the phosphate content of the mural plaster are precisely captured, (2) Utilizing PLSR, the study models the spectral bands identified at a significance level of 0.01 with measured conductivity values, thereby enabling the precise prediction of the phosphate content in the murals. The research outcomes reveal: (1) The FOD method can elucidate the nonlinear characteristics and variation patterns of the mural samples in the spectral data. As the order increases from zero to two, the number of spectral bands meeting the 0.01 significance test initially decreases and then increases. The highest absolute value of the positive correlation coefficient is observed at the 1.9 order, corresponding to the 2077 nm band, (2) For predicting the phosphate content in the murals, the model at the 1.9 order is most suitable for inversion. This model, after cross-validation, achieves a maximum R2 value of 0.861. This study created an efficient FOD-based model for estimating phosphate in mural plaster. [ABSTRACT FROM AUTHOR]

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value. [ABSTRACT FROM AUTHOR]

The SOR-like iteration method for solving the system of absolute value equations of finding a vector x such that A x - | x | - b = 0 with ν = ‖ A - 1 ‖ 2 < 1 is investigated. The convergence conditions of the SOR-like iteration method proposed by Ke and Ma (Appl. Math. Comput., 311:195–202, 2017) are revisited and a new proof is given, which exhibits some insights in determining the convergent region and the optimal iteration parameter. Along this line, the optimal parameter which minimizes ‖ T ν (ω) ‖ 2 with T ν (ω) = | 1 - ω | ω 2 ν | 1 - ω | | 1 - ω | + ω 2 ν and the approximate optimal parameter which minimizes an upper bound of ‖ T ν (ω) ‖ 2 are explored. The optimal and approximate optimal parameters are iteration-independent, and the bigger value of ν is, the smaller convergent region of the iteration parameter ω is. Numerical results are presented to demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo et al. (Appl. Math. Lett., 97:107–113, 2019). [ABSTRACT FROM AUTHOR]

The letter is a response to comments made on a recently published paper about thrombocytopenia in the intensive care unit (ICU). The authors acknowledge that thrombocytopenia is a complex condition with various contributing factors and that its impact on prognosis may vary between different patient populations. The study focused on defining thrombocytopenia and its association with outcomes, rather than investigating its causes or management. The authors suggest that further research is needed to explore the association between thrombocytopenia and mortality in a broader ICU population and to gather randomized data on the use of platelet transfusions in ICU patients. [Extracted from the article]

According to archival data for the period from 1923 to 2022, the long-term (interdecadal and interannual) variability of the dissolved oxygen concentration and temperature in the surface layer of the Black Sea in the spring hydrological season (from May to June) is analyzed. The lowest oxygen concentrations over the entire period of instrumental observations (approximately 100 years) were observed on the northwestern shelf and in the open part of the Black Sea for the period from 1923 to 1932. The negative anomalies of dissolved oxygen exceeded (in absolute value) the corresponding anomalies noted during the period of eutrophication of the Black Sea waters in the last decades of the 20th century. The main reason for the extreme anomalies discovered in the 1920s is the increase in the temperature of the surface layer of the Black Sea waters during this period. [ABSTRACT FROM AUTHOR]

Thermal-integrated pumped thermal electricity storage (TI-PTES) could realize efficient energy storage for fluctuating and intermittent renewable energy. However, the boundary conditions of TI-PTES may frequently change with the variation of times and seasons, which causes a tremendous deterioration to the operating performance. To realize efficient and flexible energy storage in operating conditions, a novel composition-adjustable TI-PTES is proposed, and the operating performance is investigated and compared with composition-fixed TI-PTES. Simulation results show that, compared to composition-fixed TI-PTES, the energy storage efficiency of TI-PTES could be enhanced by the absolute value of 4.4–18.3% by introducing composition adjustment method under various boundary conditions. Besides, tuning sub-system composition could simultaneously adjust the capacities of power input, heat storage and power output, realizing a more flexible operating range for TI-PTES. A case study for an isolated energy community shows that composition-adjustable TI-PTES could realize 100% conversion of off-peak electric energy and reduce daily investment by 35.6% compared with composition-fixed TI-PTES. [ABSTRACT FROM AUTHOR]

Suppose A = { a 1 , ... , a n + 2 } ⊂ Z n has cardinality n + 2 , with all the coordinates of the a j having absolute value at most d, and the a j do not all lie in the same affine hyperplane. Suppose F = (f 1 , ... , f n) is an n × n polynomial system with generic integer coefficients at most H in absolute value, and A the union of the sets of exponent vectors of the f i . We give the first algorithm that, for any fixedn, counts exactly the number of real roots of F in time polynomial in log (d H) . We also discuss a number-theoretic hypothesis that would imply a further speed-up to time polynomial in n as well. [ABSTRACT FROM AUTHOR]

We consider a mathematical model of the initiation and development of atherosclerosis in the early stage, defined in different domains. The existence of nonnegative weak solutions is proved via studying an auxiliary system with absolute value terms and applying a novel semi-discrete, operator splitting numerical scheme. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify our assumptions in model building and theoretical analysis. The framework we developed can also be used for nonlinear reaction–diffusion systems defined in other different domains with more complex coupling conditions. [ABSTRACT FROM AUTHOR]

Background: The responsible use of 3D-printing in medicine includes a context-based quality assurance. Considerable literature has been published in this field, yet the quality of assessment varies widely. The limited discriminatory power of some assessment methods challenges the comparison of results. The total error for patient specific anatomical models comprises relevant partial errors of the production process: segmentation error (SegE), digital editing error (DEE), printing error (PrE). The present review provides an overview to improve the general understanding of the process specific errors, quantitative analysis, and standardized terminology. Methods: This review focuses on literature on quality assurance of patient-specific anatomical models in terms of geometric accuracy published before December 4th, 2022 (n = 139). In an attempt to organize the literature, the publications are assigned to comparable categories and the absolute values of the maximum mean deviation (AMMD) per publication are determined therein. Results: The three major examined types of original structures are teeth or jaw (n = 52), skull bones without jaw (n = 17) and heart with coronary arteries (n = 16). VPP (vat photopolymerization) is the most frequently employed basic 3D-printing technology (n = 112 experiments). The median values of AMMD (AMMD: The metric AMMD is defined as the largest linear deviation, based on an average value from at least two individual measurements.) are 0.8 mm for the SegE, 0.26 mm for the PrE and 0.825 mm for the total error. No average values are found for the DEE. Conclusion: The total error is not significantly higher than the partial errors which may compensate each other. Consequently SegE, DEE and PrE should be analyzed individually to describe the result quality as their sum according to rules of error propagation. Current methods for quality assurance of the segmentation are often either realistic and accurate or resource efficient. Future research should focus on implementing models for cost effective evaluations with high accuracy and realism. Our system of categorization may be enhancing the understanding of the overall process and a valuable contribution to the structural design and reporting of future experiments. It can be used to educate specialists for risk assessment and process validation within the additive manufacturing industry. Context of the figures in this review. Center: Fig. 5+ 7; top (blue): Fig. 8; right (green): Fig. 9; bottom (yellow): Fig. 10; left (red): Fig. 11. A version in high resolution can be found online in the supplementary material. [ABSTRACT FROM AUTHOR]

This study extends the previous fatigue test method under constant stress amplitude based on Paris' law with two unknown parameters to evaluate the fatigue lifetime of polysilicon thin films under cyclic loading with gradually increasing stress amplitude, which gives more efficient manner. The extended method is applied to the experimental data obtained from the tests for the three specimen types with different shapes, which induce non-uniform stress distribution. The two unknown parameters in Paris' law are evaluated by statistical analysis with maximum likelihood method based on the experimental data obtained from the fatigue tests with the gradually increasing stress amplitudes at different rates. They are then compared to those obtained by the tests with constant stress amplitudes. The confidence bounds are calculated for the two unknown parameters and give the statistical difference level at 32.8%. The lifetime difference of the fatigue curves is also analyzed with the error of the absolute value of cyclic number in logarithmic scale to be smaller than 1. The results show that the fatigue curve of polysilicon thin films could be estimated by using the two unknown parameters of the Paris' law obtained from the new fatigue experiments with gradually increasing stress amplitude. [ABSTRACT FROM AUTHOR]

A Boolean function f on n variables is said to be a bent function if the absolute value of all its Walsh coefficients is 2 n / 2 . Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana–McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into 2-dimensional affine and linear subspaces. [ABSTRACT FROM AUTHOR]

The solid-on-solid model is a model of height functions, introduced to study the interface separating the + and − phase in the Ising model. The planar solid-on-solid model thus corresponds to the three-dimensional Ising model. Delocalisation of this model at high temperature and at zero slope was first derived by Fröhlich and Spencer, in parallel to proving the Berezinskii-Kosterlitz-Thouless phase transition. The first main result of this article consists of a simple, alternative proof of delocalisation of the solid-on-solid model. In fact, the argument is more general: it works on any planar graph—not just the square lattice—and implies that the interface delocalises at any slope rather than exclusively at the zero slope. The second main result, proved independently, is that the absolute value of the height function in this model satisfies the FKG lattice condition. This property is believed to be intimately linked to the (quantitative) understanding of delocalisation, given the recent successes in the context of the square ice and (more generally) the six-vertex model, and it has already been used elsewhere in a new proof of the BKT transition. The new FKG inequality is shown to hold true for both the solid-on-solid model as well as for the discrete Gaussian model, which in this article implies that the two notions of delocalisation, namely delocalisation in finite volume and delocalisation of shift-invariant Gibbs measures, coincide. [ABSTRACT FROM AUTHOR]