Entire Curve Research Articles

TL-SDA: A designed toolkit for the deconvolution analysis of thermoluminescence glow curves

In the present study, a graphical user interface (GUI) toolkit has been developed to analyze the thermoluminescence (TL) glow-curve and evaluate the trapping parameters using TL expression based on the one-trap one-recombination model. The basic idea of the deconvolution analysis in the developed toolkit is based on performing a sequence of successful fits, where the information provided by each fit is used by the next fit until the deconvolution of the entire glow curve approaches an optimum solution. The starting values and ranges of the fitting parameters can be controlled and adjusted to improve the deconvolution analysis of complex structure glow curves. The designed toolkit is also supported by the background-subtraction option to improve the analysis at low irradiation dose levels. The expanded uncertainty at the 95 % confidence level of the fitted trapping parameters is also provided. All the evaluations performed using the designed toolkit are allowed to be extracted into an Excel spreadsheet. The TL-SDA toolkit can be freely downloaded from: TLSDA_v1 - File Exchange - MATLAB Central (https://www.mathworks.com/matlabcentral/fileexchange/154136-tlsda_v1-1)

Analytic Ax–Schanuel for semi-abelian varieties and Nevanlinna theory

Let $A$ be a semi-abelian variety with an exponential map $\exp : \mathop{\mathrm{Lie}}(A) \to A$. The purpose of this paper is to explore Nevanlinna theory of the entire curve $\hskip1pt{\widehat{\mathrm{exp}}}\hskip2pt f := (\exp f, f) : \mathbf{C} \to A \times \mathop{\mathrm{Lie}}(A)$ associated with an entire curve $f : \mathbf{C} \to \mathop{\mathrm{Lie}}(A)$. Firstly we give a Nevanlinna theoretic proof to the analytic Ax–Schanuel Theorem for semi-abelian varieties, which was proved by J. Ax 1972 in the case of formal power series (Ax–Schanuel Theorem). We assume some non-degeneracy condition for $f$ such that the elements of the vector-valued function $f(z) - f(0) \in \mathop{\mathrm{Lie}}(A) \cong \mathbf{C}^n$ are $\mathbf{Q}$-linearly independent in the case of $A = (\mathbf{C}^{*})^{n}$. Our proof is based on the Log Bloch–Ochiai Theorem and a key estimate which we show. Our next aim is to establish a Second Main Theorem for $\hskip1pt{\widehat{\mathrm{exp}}}\hskip2pt f$ and its $k$-jet lifts with truncated counting functions at level one. We give some applications to a problem of a type raised by S. Lang and the unicity. The results clarify a relationship between the problems of Ax–Schanuel type and Nevanlinna theory.

Weakly Kähler hyperbolic manifolds and the Green–Griffiths–Lang conjecture

Abstract We introduce the notion of weakly Kähler hyperbolic manifold which generalizes that of Kähler hyperbolic manifold given in the early 1990s by M. Gromov, and establish its basic features. We then investigate its spectral properties and show a spectral gap result (on a suitable modification). As applications, we prove that weakly Kähler hyperbolic manifolds are of general type and we study the geometry of their subvarieties and entire curves, verifying – among other things – various aspects of the Lang and the Green–Griffiths conjectures for this class of manifolds.

An alternative and robust formulation of the fatigue crack growth rate curve for long cracks

Crack growth simulations are an important method for estimating the remaining service life of components and structures with cracks under cyclic loading. In particular, the evaluation of cracks emanating from clinched joints is a major challenge because the fracture mechanical properties of the sheet materials can change locally due to the joining process. Special specimens are used to determine the relevant crack growth rate curves. For the application of these curves within simulation programs, they are described using crack propagation equations. This requires an accurate formulaic description of the entire crack curve with clearly identifiable parameters that unambiguously describe certain characteristics of the crack growth rate curve. Known approaches either describe only parts of the crack growth rate curve or the single parameters affect different characteristics of the curve and thus influence each other. Therefore, a new alternative and robust mathematical fit of the crack growth rate curve is developed and validated with experimental results.

On a Hierarchy of Vector Derivative Nonlinear Schrödinger Equations

We propose a new hierarchy of the vector derivative nonlinear Schrödinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves Γ={(μ,λ)} of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution τ. The type of this involution depends on the genus of the spectral curve. Or the involution has the form τ:(μ,λ)→(μ,−λ), or τ:(μ,λ)→(−μ,−λ). The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve Γ, but by its factor Γ/τ, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector p=(p1,p2)t is determined, first of all, by the dynamics of its length |p|. Independent equations determine the dependence of the direction of the vector p from its length. In cases where the direction of the vector p is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

Changes in the force-time curve during a repeat power ability assessment using loaded countermovement jumps.

Repeat power ability (RPA) assessments traditionally use discrete variables, such as peak power output, to quantify the change in performance across a series of jumps. Rather than using a discrete variable, the analysis of the entire force-time curve may provide additional insight into RPA performance. The aims of this study were to (1) analyse changes in the force-time curve recorded during an RPA assessment using statistical parametric mapping (SPM) and (2) compare the differences in the force-time curve between participants with low and high RPA scores, as quantified by traditional analysis. Eleven well-trained field hockey players performed an RPA assessment consisting of 20 loaded countermovement jumps with a 30% one repetition maximum half squat load (LCMJ20). Mean force-time series data was normalized to 100% of the movement duration and analysed using SPM. Peak power output for each jump was also derived from the force-time data and a percent decrement score calculated for jumps 2 to 19 (RPA%dec). An SPM one-way ANOVA with significance accepted at α=0.05, was used to identify the change in the force-time curve over three distinct series of jumps across the LCMJ20 (series 1 = jumps 2-5, series 2 = jumps 9-12 and series 3 = jumps 16-19). A secondary analysis, using an independent T-test with significance accepted at p<0.001, was also used to identify differences in the force-time curve between participants with low and high RPA%dec. Propulsive forces were significantly lower (p<0.001) between 74-98% of the movement compared to 0-73% for changes recorded during the LCMJ20. Post hoc analysis identified the greatest differences to occur between jump series 1 and jump series 2 (p<0.001) at 70-98% of the movement and between jump series 1 and jump series 3 (p<0.001) at 86-99% of the movement. No significant differences were found between jump series 2 and jump series 3. Significant differences (p<0.001) in both the braking phase at 44-48% of the jump and the propulsive phase at 74-94% of the jump were identified when participants were classified based on low or high RPA%dec scores (with low scores representing an enhanced ability to maintain peak power output than high scores). A reduction in force during the late propulsive phase is evident as the LCMJ20 progresses. SPM analysis provides refined insight into where changes in the force-time curve occur during performance of the LCMJ20. Participants with the lower RPA%dec scores displayed both larger braking and propulsive forces across the LCMJ20 assessment.

Determining the stability region in the plane of parameters and quality indicators of linear discrete automatic control systems by D-partitioning method

The problem of constructing the boundary of the stability region (BSR) of linear discrete automatic control systems in the plane of the system parameters, which are linearly included in the coefficients of the characteristic equation, and quality indicators of the transient process (stability degree, fluctuation degree or attenuation factor) by the D-partition method is considered. The shifted and fictitious characteristic equations for BSR construction in the area of parameters and quality indicators are introduced. It is shown that the quality indicators are non-linearly included in the coefficients of the characteristic equation, therefore it is impossible to construct the BSR of discrete automatic control system using the classical D-partition method. Constructing of digital control system BSR of spaceship state using one coordinate in the plane of the system parameter- stability degree is considered. The BSR is obtained using the previously proposed by the authors method of constructing the region of stability in the plane of two parameters, one of which is nonlinearly included in the system equation. At the same time, the construction of the entire D-partition curve, special straight lines, and the use of Neimark hatching is excluded, and computer realization of the limit of stability region is ensured. The obtained BSR family in the plane of the parameter and at different values of another system parameter which is nonlinearly included in the coefficients of the shifted characteristic equation makes it possible to estimate, and for the parameter values on the boundary of the stability region of the BSR family, to determine the stability degree.

On Defects of Entire Curves of Finite Lower Order

On Defects of Entire Curves of Finite Lower Order

Method for predicting lifetime of ion exchange resin in PWR primary loop based on nuclide distribution measurement

Ion exchange resins are commonly utilized for water treatment in pressurized water reactors' primary loop. These resins have the ability to adsorb radioactive cations present in the primary loop coolant, leading to a purification effect. However, the resin becomes radioactive post-purification and cannot be regenerated, thus requiring regular replacement. As the process of resin replacement exposes personnel to radiation, it is crucial to enhance the resin's utilization. This paper aims to investigate a non-destructive testing method for evaluating the lifetime of resin in pressurized water reactor purification units. It also aims to offer guidance for safe resin replacement. The resin is contained in a column (commonly referred to as ion exchange columns) and consumed from top to bottom, with radioactivity decreasing in intensity from top to bottom. The study utilizes the longitudinal radioactivity distribution characteristics of ionic resins to build a gamma-ray detection system with high resistance to interlayer interference and good longitudinal resolution. In this study, a two-stage resin column was utilized to capture common fission product nuclides and corrosion-activated nuclides, such as 60Co, 137Cs, 54Mn, and 124Sb, from the effluent of a pressurized water reactor. The distribution of these nuclides was measured using this device. The results indicate that the activity levels of 60Co, 137Cs, and 54Mn reached their peak in the column before rapidly declining. The height of the resin layer corresponding to the highest activity level of each nuclide varied, indicating the resin's adsorption selectivity. After processing an additional 10 tons of wastewater, a second measurement was taken which showed that the failure range of the resin expanded downwards as the treated water volume increased. The entire distribution curve of the nuclides within the exchange column also shifted upwards and to the right. By comparing the first and second observations, we discovered that the bottom part of the resin will fail when the activity of the most penetrating nuclide in the wastewater surpasses a specific threshold. This research suggests a novel approach to predicting the lifetime of resin, which generalizes the trend of radionuclide intensity inside the ion exchange column.

A relationship between orthogonal regression and the coefficient of determination under rotation of data sets

In this article, we explore patterns of R 2 across data sets to reveal a fundamental equivalence. If any set of bivariate data is rotated, the R 2 value changes and defines a curve as a function of the rotation angle θ. We show that for any data set whose rotated R 2 curve has the same maximum value, the entire curve is identical up to a shift in the rotation angle. We also find that a recently introduced measure of linearity, Q 2, provides a definitive relation between these data sets, with equal Q 2 values resulting in identically rotated R 2 curves. Finally, we also show that we can consider R 2 as the combination of two components, the linearity of the data and a rotation angle. While rotating data or axes for non spatial data loses the specific meaning of the variables, these results may provide additional understanding of the relationships within the data and can reveal similarities between data sets, the role of sensitivity in correlation, and the nature of correlation itself.

Novel experimental technique to model impression piles in centrifuge testing

A novel experimental technology for small-scale centrifuge tests on piled foundations has been investigated. The technology is suitable for bored piles where the pile shaft has been profiled to improve bearing capacity, such as with the impression pile which has an enhanced shaft capacity owing to the small impressions created along the shaft. In previous centrifuge testing, impression piles have been created by pouring resin into a profiled bore. However, in the technique described, a pile made from three-dimensionally (3D)-printed rigid plastic components with a mandrel mechanism is used to create a nodular shaft surface during model making. Once assembled the pile has the same geometry as the cast-in-situ impression pile. 3D-printed plastic piles allow for fast model making and demonstrate excellent repeatability. Because of the ductile behaviour of the soil–plastic interface the impressions improve the performance of a pile over the entire load settlement curve, not just at ultimate capacity. In addition, a greater increase in ultimate capacity was registered for the 3D-printed plastic impression piles compared to similar resin impression piles. At working load, the 3D-printed plastic impression piles outperformed traditional straight-shafted piles by 90%.

Standardized longitudinal strain curves stratified by age and sex in healthy individuals: The Copenhagen City Heart Study

Abstract Introduction Speckle-tracking echocardiography has gained widespread use, and strain parameters such as global longitudinal strain (GLS) and strain rates are strongly associated with risk of heart failure and cardiovascular death. Such strain measures, however, only represent limited features of the complete longitudinal strain (LS) curve. Thus, interpretation of entire curves might provide additional insight. Purpose To establish normal standardized LS curves over an entire heart cycle for healthy subjects stratified by age and sex. Furthermore, to assess how these curves vary with age and to compare this with conventional strain measures. Methods The study population consisted of 1790 healthy subjects free of cardiovascular disease and risk factors including diabetes mellitus and hypertension at baseline. Subjects were stratified by sex and further by age in groups as defined in the SCORE risk chart. Subjects underwent echocardiography, and LS curves from the apical four-chamber view were derived and standardized in length using linear interpolation. Terms to describe qualitative findings in the standardized strain curves were established (Figure 1). Early diastolic strain (EDS) was defined as the difference in strain from peak LS to maximal curvature after early diastolic filling, while late diastolic strain (LDS) was defined as the difference in strain from the plateau phase in late passive diastole to maximal curvature in active diastole. Conventional strain measures included GLS, systolic strain rate (SRS), early diastolic strain rate (SRE), and late diastolic strain rates (SRA). The association between these and age group were investigated using univariable linear regression for each sex. Results In the study population, 1101 (61.5%) subjects were female. The standardized strain curves (Figure 2) showed that aging primarily manifested in the diastolic part of the strain curve. Decreasing EDS was associated with increasing age group, while the opposite was true for LDS. In linear regression, both SRE (female: beta=-0.13; p&amp;lt;0.001, male: beta=-0.1; p&amp;lt;0.001) and SRA (female: beta=0.09; p&amp;lt;0.001, male: beta=0.09; p&amp;lt;0.001) were associated with age group for both sexes. Peak LS did not change notably with age, and in linear regression, GLS and SRS were only significantly associated with age for women (GLS: beta=0.12; p&amp;lt;0.001, SRS: beta=0.01; p&amp;lt;0.001). Conclusion We derived normal standardized LS curves for healthy individuals stratified by age and sex, which can serve as normal values in future studies. In addition, these showed that age was primarily associated with changes in the diastolic part of the strain curve in both sexes, which was consistent with conventional strain measures.Figure 1:Overview of termsFigure 2Standardized longitudinal strai

Entire Curves Producing Distinct Nevanlinna Currents

Abstract First, inspired by a question of Sibony, we show that in every compact complex manifold $Y$ with certain Oka property, there exists some entire curve $f: \mathbb {C}\rightarrow Y$ generating all Nevanlinna/Ahlfors currents on $Y$, by holomorphic disks $\{f\restriction _{\mathbb {D}(c, r)}\}_{c\in \mathbb {C}, r&amp;gt;0}$. Next, we answer positively a question of Yau, by constructing some entire curve $g: \mathbb {C}\rightarrow X$ in the product $X:=E_{1}\times E_{2}$ of two elliptic curves $E_{1}$ and $E_{2}$, such that by using concentric holomorphic disks $\{g\restriction _{\mathbb {D}_{ r}}\}_{r&amp;gt;0}$ we can obtain infinitely many distinct Nevanlinna/Ahlfors currents proportional to the extremal currents of integration along curves $[\{e_{1}\}\times E_{2}]$, $[E_{1}\times \{e_{2}\}]$ for all $e_{1}\in E_{1}, e_{2}\in E_{2}$ simultaneously. This phenomenon is new, and it shows tremendous holomorphic flexibility of entire curves in large scale geometry. Dedicated to Julien Duval with admiration

Examining the Quasi-Static Uniaxial Compressive Behaviour of Commercial High-Performance Epoxy Matrices.

Four commercial high-performance aerospace aromatic epoxy matrices, CYCOM®890, CYCOM®977-2, PR520, and PRISM EP2400, were cured to a standardised 2 h, 180 °C cure cycle and evaluated in quasi-static uniaxial compression, as well as by dynamic scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The thermoplastic toughened CYCOM®977-2 formulation displayed an overall increase in true axial stress values across the entire stress-strain curve relative to the baseline CYCOM®890 sample. The particle-toughened PR520 sample exhibited an overall decrease in true axial stress values past the yield point of the material. The PRISM EP2400 resin, with combined toughening agents, led to true axial stress values across the entire plastic region of the stress-strain curve, which were in line with the stress values observed with the CYCOM®890 material. Interestingly, for all formulations, the dilation angles (associated with the volume change during plastic deformation), recorded at 0.3 plastic strain, were close to 0°, with the variations reflecting the polymer structure. Compression data collected for this series of commercial epoxy resins are in broad agreement with a selection of model epoxy resins based on di- and tetra-functional monomers, cured with polyamines or dicarboxylic anhydrides. However, the fully formulated resins demonstrate a significantly higher compressive modulus than the model resins, albeit at the expense of yield stress.

Approximation of holomorphic Legendrian curves with jet-interpolation

We prove several interpolation results for holomorphic Legendrian curves lying in an odd dimensional complex Euclidean space with the standard contact structure. In particular, we show that an arbitrary countable set of points in C2n+1 lies on an injectively immersed isotropic surface with a prescribed complex structure. If the set has no accumulation points, the surface may be taken properly embedded. We also prove a Carleman-type theorem for holomorphic Legendrian curves with interpolation. Namely, a Legendrian curve, defined on a certain type of unbounded closed set in a given open Riemann surface R, may be approximated in the C0-topology by an entire Legendrian curve with prescribed finite-order Taylor polynomials at a closed discrete set of points in R. Under suitable conditions, the approximating map may be made into a proper embedding.

Clot-based time attenuation curve as a novel imaging predictor of mechanical thrombectomy functional outcome in acute ischemia stroke.

To investigate whether a novel assessment of thrombus permeability obtained from perfusion computed tomography (CTP) can act as a more accurate predictor of clinical response to mechanical thrombectomy (MT) in acute ischemic stroke (AIS). We performed a study including two cohorts of AIS patients who underwent MT admitted to a single-center between April 2018 and February 2022: a retrospective development cohort (n = 71) and a prospective independent validation cohort (n = 96). Thrombus permeability was determined in terms of entire thrombus time-attenuation curve (TAC) on CTP. Association between thrombus TAC distributions and histopathological results was analyzed in the development cohort. Logistic regression was used to assess the performance of the TAC for predicting 90-day modified Rankin Scale (mRS) score, and good outcome was defined as a mRS score of ≤ 2. Basic clinical characteristics was used to build a routine clinical model. A combined model gathered TAC and basic clinical characteristics was also developed. The performance of the three models is compared on the independent validation set. Two TAC distributions were observed-unimodal (uTAC) and linear (lTAC). TAC distributions achieved strong correlations (|r|= 0.627, p < 0.001) with histopathological results, in which uTAC associated with fibrin- and platelet-rich clot while lTAC associated with red blood cell-rich clot. The uTAC was independently associated with poor outcome (odds ratio, 0.08 [95% confidence interval (CI), 0.02-0.31]; p < 0.001). TAC distributions yielded an AUC of 0.78 (95% CI, 0.70-0.87) for predicting clinical outcome. When combined clinical characteristics, the performance was significantly improved (AUC, 0.85 [95% CI, 0.76-0.93]; p < 0.001) and higher than routine clinical model (AUC, 0.69 [95% CI, 0.59-0.83]; p < 0.001). Thrombus TAC on CTP were found to be a promising new imaging biomarker to predict the outcomes of MT in AIS. This study revealed that clot-based time attenuation curve based on admission perfusion CT could reflect the permeability and composition of thrombus and, also, provide valuable information to predict the clinical outcomes of mechanical thrombectomy in patients with acute ischemia stroke. • Two time-attenuation curves distributions achieved strong correlations (|r|= 0.627, p < 0.001) with histopathological results. • The unimodal time-attenuation curve was independently associated with poor outcome (odds ratio, 0.08 [0.02-0.31]; p < 0.001). • The time-attenuation curve distributions yielded a higher performance for detecting clinical outcome than routine clinical model (AUC, 0.78 [0.70-0.87] vs 0.69 [0.59-0.83]; p < 0.001).

Noninvasive assessment of left ventricular end-diastolic pressure using machine learning-derived phasic left atrial strain.

While transthoracic echocardiography (TTE) assessment of left ventricular end-diastolic pressure (LVEDP) is critically important, the current paradigm is subject to error and indeterminate classification. Recently, peak left atrial strain (LAS) was found to be associated with LVEDP. We aimed to test the hypothesis that integration of the entire LAS time curve into a single parameter could improve the accuracy of peak LAS in the noninvasive assessment of LVEDP with TTE. We retrospectively identified 294 patients who underwent left heart catheterization and TTE within 24 h. LAS curves were trained using machine learning (100 patients) to detect LVEDP ≥ 15 mmHg, yielding the novel parameter LAS index (LASi). The accuracy of LASi was subsequently validated (194 patients), side by side with peak LAS and ASE/EACVI guidelines, against invasive filling pressures. Within the validation cohort, invasive LVEDP was elevated in 116 (59.8%) patients. The overall accuracy of LASi, peak LAS, and American Society of Echocardiography/European Association for Cardiovascular Imaging (ASE/EACVI) algorithm was 79, 75, and 76%, respectively (excluding 37 patients with indeterminate diastolic function by ASE/EACVI guidelines). When the number of LASi indeterminates (defined by near-zero LASi values) was matched to the ASE/EACVI guidelines (n = 37), the accuracy of LASi improved to 87%. Importantly, among the 37 patients with ASE/EACVI-indeterminate diastolic function, LASi had an accuracy of 81%, compared with 76% for peak LAS. LASi allows the detection of elevated LVEDP using invasive measurements as a reference, at least as accurately as peak LAS and current diastolic function guideline algorithm, with the advantage of no indeterminate classifications in patients with measurable LAS.

An interpretable AI model for recurrence prediction after surgery in gastrointestinal stromal tumour: an observational cohort study

There are several models that predict the risk of recurrence following resection of localised, primary gastrointestinal stromal tumour (GIST). However, assessment of calibration is not always feasible and when performed, calibration of current GIST models appears to be suboptimal. We aimed to develop a prognostic model to predict the recurrence of GIST after surgery with both good discrimination and calibration by uncovering and harnessing the non-linear relationships among variables that predict recurrence. In this observational cohort study, the data of 395 adult patients who underwent complete resection (R0 or R1) of a localised, primary GIST in the pre-imatinib era at Memorial Sloan Kettering Cancer Center (NY, USA) (recruited 1982-2001) and a European consortium (Spanish Group for Research in Sarcomas, 80 sites) (recruited 1987-2011) were used to train an interpretable Artificial Intelligence (AI)-based model called Optimal Classification Trees (OCT). The OCT predicted the probability of recurrence after surgery by capturing non-linear relationships among predictors of recurrence. The data of an additional 596 patients from another European consortium (Polish Clinical GIST Registry, 7 sites) (recruited 1981-2013) who were also treated in the pre-imatinib era were used to externally validate the OCT predictions with regard to discrimination (Harrell's C-index and Brier score) and calibration (calibration curve, Brier score, and Hosmer-Lemeshow test). The calibration of the Memorial Sloan Kettering (MSK) GIST nomogram was used as a comparative gold standard. We also evaluated the clinical utility of the OCT and the MSK nomogram by performing a Decision Curve Analysis (DCA). The internal cohort included 395 patients (median [IQR] age, 63 [54-71] years; 214 men [54.2%]) and the external cohort included 556 patients (median [IQR] age, 60 [52-68] years; 308 men [55.4%]). The Harrell's C-index of the OCT in the external validation cohort was greater than that of the MSK nomogram (0.805 (95% CI: 0.803-0.808) vs 0.788 (95% CI: 0.786-0.791), respectively). In the external validation cohort, the slope and intercept of the calibration curve of the main OCT were 1.041 and 0.038, respectively. In comparison, the slope and intercept of the calibration curve for the MSK nomogram was 0.681 and 0.032, respectively. The MSK nomogram overestimated the recurrence risk throughout the entire calibration curve. Of note, the Brier score was lower for the OCT compared to the MSK nomogram (0.147 vs 0.564, respectively), and the Hosmer-Lemeshow test was insignificant (P=0.087) for the OCT model but significant (P<0.001) for the MSK nomogram. Both results confirmed the superior discrimination and calibration of the OCT over the MSK nomogram. A decision curve analysis showed that the AI-based OCT model allowed for superior decision making compared to the MSK nomogram for both patients with 25-50% recurrence risk as well as those with >50% risk of recurrence. We present the first prognostic models of recurrence risk in GIST that demonstrate excellent discrimination, calibration, and clinical utility on external validation. Additional studies for further validation are warranted. With further validation, these tools could potentially improve patient counseling and selection for adjuvant therapy. The NCI SPORE in Soft Tissue Sarcoma and NCI Cancer Center Support Grants.

Adverse impact reduction and job performance optimization via pareto-optimal weighting: A shrinkage formula and regularization technique using machine learning.

In personnel selection practice, one useful technique for reducing adverse impact and enhancing diversity is the Pareto-optimal weighting approach of De Corte et al. (2007). This approach produces a series of hiring solutions that characterize a diversity-job performance trade-off and can lead to more optimal selection outcomes (sometimes doubling the number of job offers for minority applicants without changing the job performance outcomes of personnel selection). Despite these advantages, recent research has identified a potential problem with the Pareto-weighting technique-Pareto solutions suffer from shrinkage upon cross-validation. To address the problem of shrinkage in the Pareto trade-off curve (i.e., diversity shrinkage and validity shrinkage), we offer two contributions. First, a shrinkage approximation formula is introduced (similar to a formula for adjusted R², but applicable to the entire Pareto trade-off curve). Second, we derive a novel technique for the regularization of Pareto-optimal predictor weights (borrowed from the field of machine learning), which is designed to produce predictor weights that are less vulnerable to shrinkage (similar to ridge regression and adapted from the elastic net technique). Both approaches-the proposed Pareto shrinkage formula and the proposed regularization technique-are then evaluated using Monte Carlo simulation. Recommendations are provided for approximating potential diversity-performance trade-off curves in personnel selection, while accounting for shrinkage. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Dense entire curves in rationally connected manifolds (with an appendix by János Kollár)

Dense entire curves in rationally connected manifolds (with an appendix by János Kollár)