Recursive Evaluation Research Articles

Recursive two-stage evaluation model for dynamic decision making under ambiguity

In this paper, the two-stage-evaluation (TSE) model for decision making under ambiguity (He 2021) is extended to intertemporal setting in an axiomatic approach. The first set of axioms employed are commonly adopted for dynamic non-expected utility models in the literature. Besides these regular axioms, I also assume dynamic consistency and conditions which deliver a static TSE for consumption plans only pay non-zero consequences for one period. It is shown that these axioms hold if and only if these exists a recursively defined evaluation utility model representing decision maker (DM)’s preferences over consumption plans conditional on arriving at any node in an event tree. Such a recursive form implies that one can apply dynamic programming technique (rolling back the decision tree) to solve a dynamic decision making problem under TSE model. It can be shown that the solution for the recursively defined dynamic TSE model exists uniquely. Due to the “small domain” setup, the agent is short-sighted in the sense that they only process subjective probabilities over events defined on one period uncertainty over next period states, which differs from “far-sighted” assumption in most extant models that assume subjective probabilities exist over events defined on multiple periods. It is shown that under some extra conditions, our DM applies Bayes’ rule “updating’ her subjective beliefs.

Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors

Abstract We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant (or equi-variant) under permutations and rotations. This task arises in the evaluation linear models as well as equivariant neural network models of many-particle systems. The theoretical bottleneck is the contraction of a high-dimensional symmetric and sparse tensor with a specific sparsity pattern that is directly related to the symmetries imposed on the polynomial. The sparsity of this tensor makes it challenging to construct a highly efficient evaluation scheme. The references [10, 11] introduced a recursive evaluation strategy that relied on a number of heuristics, but performed well in tests. In the present work, we propose an explicit construction of such a recursive evaluation strategy and show that it is in fact optimal in the limit of infinite polynomial degree.

A neural builder for spatial subdivision hierarchies

Spatial data structures, such as k-d trees and bounding volume hierarchies, are extensively used in computer graphics for the acceleration of spatial queries in ray tracing, nearest neighbour searches and other tasks. Typically, the splitting strategy employed during the construction of such structures is based on the greedy evaluation of a predefined objective function, resulting in a less than optimal subdivision scheme. In this work, for the first time, we propose the use of unsupervised deep learning to infer the structure of a fixed-depth k-d tree from a constant, subsampled set of the input primitives, based on the recursive evaluation of the cost function at hand. This results in high-quality upper spatial hierarchy, inferred in constant time and without paying the intractable price of a fully recursive tree optimisation. The resulting fixed-depth tree can then be further expanded, in parallel, into either a full k-d tree or transformed into a bounding volume hierarchy, with any known conventional tree builder. The approach is generic enough to accommodate different cost functions, such as the popular surface area and volume heuristics. We experimentally validate that the resulting hierarchies have competitive traversal performance with respect to established tree builders, while maintaining minimal overhead in construction times.

Use of a Deep Learning Approach for the Evaluation of Students' Online Learning Cognitive Ability

The cognitive ability evaluation of college students' online learning still faces many challenges. Evaluation of college students' online learning cognitive ability is helpful to monitor the learning effect and progress of students, so as to detect problems in time, make suggestions and take corresponding measures to improve. However, the existing evaluation methods for the cognitive ability of college students' online learning often only focus on the degree of knowledge mastery of students, while ignoring the performance of students' learning strategies, autonomous learning ability and emotional attitude in the online learning process. And it is often impossible to understand the learning status of students in real time. To this end, this article studies the evaluation method of college students’ online learning cognitive ability based on deep learning. The evaluation of online learning cognitive ability of college students is divided into two parts: online learning ability evaluation and learning recursive ability evaluation. By introducing the learning ability layer and the learning recursive ability layer into the dynamic key-value memory network and constructing the corresponding evaluation model, it’s better to evaluate the online learning cognitive ability of college students. Based on the historical learning behavior data of students in the online learning process, the online learning cognitive state is predicted, and the performance of the model is further improved through data enhancement and self-attention mechanism. Experimental results verify the validity of the constructed model.

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals.

To improve the efficiency of Gaussian integral evaluation on modern accelerated architectures, FLOP-efficient Obara-Saika-based recursive evaluation schemes are optimized for the memory footprint. For the 3-center 2-particle integrals that are key for the evaluation of Coulomb and other 2-particle interactions in the density-fitting approximation, the use of multiquantal recurrences (in which multiple quanta are created or transferred at once) is shown to produce significant memory savings. Other innovations include leveraging register memory for reduced memory footprint and direct compile-time generation of optimized kernels (instead of custom code generation) with compile-time features of modern C++/CUDA. Performance of conventional and CUDA-based implementations of the proposed schemes is illustrated for both the individual batches of integrals involving up to Gaussians with low and high angular momenta (up to L = 6) and contraction degrees, as well as for the density-fitting-based evaluation of the Coulomb potential. The computer implementation is available in the open-source LibintX library.

Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the demand nodes and generators. To reach the solution for the OPF problem a recursive evaluation of the model that determines the voltage variables at the iteration t+1 (vt+1) by using the information of the voltages at the iteration t (vt) is proposed. To finish the recursive solution process of the OPF problem via the convex relaxation, the difference between the voltage magnitudes in two consecutive iterations less than the predefined tolerance is considered as a stopping criterion. The numerical results in the 85-bus grid demonstrate that the proposed recursive convex model can solve the classical power flow problem in monopolar DC networks, and it also solves the OPF problem efficiently with a reduced convergence error when compared with semidefinite programming and combinatorial optimization methods. In addition, the proposed approach can deal with radial and meshed monopolar DC networks without modifications in its formulation. All the numerical implementations were in the MATLAB programming environment and the convex models were solved with the CVX and the Gurobi solver.

A piecewise recursive semi-analytical method for effective evaluation of heterogeneous aging viscoelastic materials

A novel semi-analytical method in the time domain is proposed to predict the effective properties of heterogeneous aging viscoelastic materials. By virtue of a series expansion in a discretized time interval, variables and time varying constitutive coefficients can temporally be described more precisely, and a piecewise variable separation is realized. Consequently, a set of recursive constitutive equations are derived from a second-order differential constitutive equation with time-varying coefficients, and a spatially and temporally coupled effective evaluation is decoupled into a series of recursive spatial effective evaluations which can be tackled with Mori–Tanaka method (M–T), self-consistent method (SC), or other well developed skills, providing time-varying effective strain/stress. A recursive adaptive algorithm is stressed, so as to ensure stable temporal solution accuracy for different step sizes, and avoid the temporal inaccuracy caused either by the relatively lower truncation order or improper step size. Four numerical examples are provided to verify the effectiveness of the proposed approach by comparing the prediction results with reference solutions.

Vibrational description of the LiAr molecule in its X 2Σ+ and A 2Π electronic states in the framework of an algebraic model

In this work, the vibrational energy levels, the kinetic energy and the potential energy of the LiAr molecule in its X 2Σ+ and A 2Π electronic states are studied using the Morse potential and so(2, 1) spectrum generating algebra approach. An algorithm for the recursive evaluation of the expectation value of for a given state of Li (X 2Σ+) Ar and Li (A 2Π) Ar are proposed. As an application closed-form estimations for the value of Li (X 2Σ+) Ar and Li (A 2Π) Ar were derived using Jensen’s inequality. This allows us to obtain several inequalities relating the radial expectation value of Li (X 2Σ+) Ar and Li (A 2Π) Ar at the logarithme of the expectation value of . These obtained outcomes are compared to the published results, both theoretical and experimental, and show a good agreement.

Analytic expressions for the moving infinite line source model

Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes. Solution of this model involves a relatively heavy numerical quadrature. Contrarily to the infinite line source model, there is currently no known first-order approximation that could be useful for many practical applications. In this paper, known analytical expressions of the Hantush well function and generalized incomplete gamma function are first revisited. A clear link between these functions and the moving infinite line source model is then established. Then, two new exact and integral-free analytical expressions are proposed, along with two new first-order approximations. The new analytical expressions proposed take the form of convergent power series involving no recursive evaluations. It is shown that relative errors less than 1% can be obtained with only a few summands. The convergence properties of the series, their accuracy and the validity domain of the first-order approximations are also presented and discussed.

Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

We report on accurate variational calculations of the Born–Oppenheimer potential for excited states of the hydrogen molecule with , and Φ symmetries. The obtained potential energy curves reach the relative precision of or better along internuclear distances of 0.01–20 au. Calculations rely on the recursive evaluation of two-centre two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first-ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.

Novel Self-Adaptive Shale Gas Production Proxy Model and Its Practical Application.

Recently, production optimization has gained increasing interest in the petroleum industry. The most computationally intensive and critical part of the production optimization process is the evaluation of the production function performed by the numerical reservoir simulator. Employing proxy models as a substitute for the reservoir simulator is proposed for alleviating this high computational cost. In this study, a new approach to construct adaptive proxy models for production optimization problems is proposed. An adaptive difference evolution algorithm (SaDE) optimized least-squares support vector machine (LSSVM) is used as an approximation function, while training is performed using a self-adaptive response surface experimental design (SaRSE). SaDE selects the optimal hyperparameters of LSSVM during the training process to improve the prediction accuracy of the proxy model. Cross-validation methods are used in the recursive training and network evaluation phases. The developed method is used to optimize the production of block gas reservoir models. Computational results confirm that the developed adaptive proxy model outperforms traditional regression methods. It is further verified that when the experimental data are updated, the alternative model still has high prediction accuracy when performing the objective function evaluation. The results show that the proposed proxy modeling approach enhances the entire optimization process by providing a fast approximation of the actual reservoir simulation model with better accuracy.

Optimal Integration of Dispersed Generation in Medium-Voltage Distribution Networks for Voltage Stability Enhancement

This study addresses the problem of the maximization of the voltage stability index (λ-coefficient) in medium-voltage distribution networks considering the optimal placement and sizing of dispersed generators. The problem is formulated through a mixed-integer nonlinear programming model (MINLP), which is solved using General Algebraic Modeling System (GAMS) software. A numerical example with a 7-bus radial distribution network is employed to introduce the usage of GAMS software to solve the proposed MINLP model. A new validation methodology to verify the numerical results provided for the λ-coefficient is proposed by using recursive power flow evaluations in MATLAB and DigSILENT software. The recursive evaluations allow the determination of the λ-coefficient through the implementation of the successive approximation power flow method and the Newton–Raphson approach, respectively. It is effected by fixing the sizes and locations of the dispersed sources using the optimal solution obtained with GAMS software. Numerical simulations in the IEEE 33- and 69-bus systems with different generation penetration levels and the possibility of installing one to three dispersed generators demonstrate that the GAMS and the recursive approaches determine the same loadability index. Moreover, the numerical results indicate that, depending on the number of dispersed generators allocated, it is possible to improve the λ-coefficient between 20.96% and 37.43% for the IEEE 33-bus system, and between 18.41% and 41.98% for the IEEE 69-bus system.

Amplitude recursions with an extra marked point

The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at genus zero: open-string N-point amplitudes can be obtained from those at N-1 points. We establish a similar formalism at genus one, which allows the recursive calculation of genus-one Selberg integrals using an extra marked point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby genus-one Selberg integrals are related to genus-zero Selberg integrals. Accordingly, N-point open-string amplitudes at genus one can be obtained from (N+2)-point open-string amplitudes at tree level. The construction is related to and in accordance with various recent results in intersection theory and string theory.

Linearization of periodic power electronic-based power systems for small-signal analysis

Integrating power electronics to the grid has introduced new small signal–signal stability challenges, which are commonly studied with average time-invariant models and, more recently, with harmonic state–space models. In both approaches, it is common to obtain the models by following an analytical formulation, which can be tedious and impractical in systems with different controllers and topologies, just to mention a few examples. This paper proposes a numerical approach based on shooting methods and the recursive evaluation of the time-variant Jacobian along the steady-state orbits to construct automatically a periodic linear time-variant model and its respective linear time-invariant model using the extended harmonic domain; these models include explicitly the harmonic components. The proposed modeling approach can be applied to systems with different converter topologies, controllers, and modulation techniques. A nonlinear periodic switched system (grid-connected parallel inverter-based microgrid) is used to validate the proposed linearization approach.

Gel’fand–Yaglom type equations for calculating fluctuations around instantons in stochastic systems

In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. In this paper, we derive a general, closed form expression for the leading prefactor contribution of the fluctuations around the instanton trajectory for the computation of probability density functions of general observables. The key technique is applying the Gel’fand–Yaglom recursive evaluation method to the suitably discretized Gaussian path integral of the fluctuations, in order to obtain matrix evolution equations that yield the fluctuation determinant. We demonstrate agreement between these predictions and direct sampling for examples motivated from turbulence theory.

Politeness as normative, evaluative and discriminatory: the case of verbal hygiene discourses on correct honorifics use in South Korea

Abstract This paper uses the concept of “verbal hygiene” (Cameron, Deborah. 1995. Verbal hygiene. Abingdon, UK: Routledge) to analyze metadiscourses in South Korea regarding a recent innovation in the use of subject honorific markers in the service industry. This innovation, commonly referred to as samwul contay ‘inanimate object respect’ involves using honorifics when the grammatical subject of the sentence is an inanimate object, typically the products or services being offered to the customer. Critical discourse analysis was conducted of materials produced by language authorities and mainstream media, as well as layperson-produced blogs and reader comments. The analysis shows that the materials mobilized discourses of ungrammaticality and immorality to delegitimize samwul contay, and stigmatize the sales personnel who used it. By applying the concept of “verbal hygiene” to politeness-related metadiscourses, the current paper advances the perspective that politeness is occasioned through the recursive evaluation of linguistic behavior. Rather than being idiosyncratic, these evaluations appeal to established language norms and moral orders. The way that verbal hygiene discourses promote the language usage of the powerful while stigmatizing the powerless demonstrates that politeness relies inherently on socio-historically imbedded discriminatory practices of placing value on the language usage of certain groups, while delegitimizing that of others.

Inter-Collateral Diabetic Retinopathy Extraction and Evaluation Using Trained Datasets of Multiple Feature Set

Diabetic Retinopathy (DR) is caused due to un-mounted diabetic comorbidities. The patients suffer complete vision blindness if untreated or diagnosed on later stage. In this article, we propose a novel approach for early detection and prediction using trained datasets of multiple features. The process expansion is resultant of multiple stage attribute extraction via a series of inter-collateral parameters of diabetics. Typically, the proposed technique is designed and developed on a multi-value and multi-dimension datasets such as comorbidities history of patient encountered during diabetics. The proposed technique uses collateral attributes in evaluating retinopathy status and thereby validates the extracted DR under threshold value comparisons. The results are computed using HADOOP framework for recursive pattern and feature evaluation. The trial is processed on UCL digital library datasets with estimated performance of 98.7% with extraction and 92.34% with value True-Positive (TP) prediction.

A Recursive Characteristics Analysis-Based Stationarity Evaluation Model for Friction-Induced Attractors in the Sliding Friction Process

Abstract In this study, the coefficient of friction (COF) signals throughout the running-in process were examined by sliding a ring against a static disc. By reconstructing the scalar time-series into multi-dimensional phase spaces, friction-induced attractors were obtained and quantified by recursive characteristics analysis, which can effectively realize the running-in status identification. Moreover, a recursive characteristics analysis-based evaluation model was established to investigate the stationarity of the friction-induced attractors based on the recurrence quantification analysis (RQA) measures. The analyses of the numerically simulated signals and experimental results indicate that the extracted model is an intuitive and effective method. Furthermore, to improve the stationary of the friction-induced attractors, the normal pressure should be low, whereas the relative sliding velocities should be increased appropriately. These results would contribute to the revelation of the recursive characteristics of the tribosystem and the improvement of the stationarity of friction-induced attractors.

On the convergence of recursive SURE for total variation minimization

Abstract Recently, total variation (TV) regularization has become a standard technique for image recovery. The mean squared error (MSE) of the reconstruction can be reliably estimated by Stein’s unbiased risk estimate (SURE). In this work, we develop two recursive evaluations of SURE, based on Chambolle’s projection method (CPM) for TV denoising and alternating direction method of multipliers (ADMM) for TV deconvolution, respectively. In particular, from the proximal point perspective, we provide the convergence analysis for both iterative schemes and the corresponding Jacobian recursions, in terms of the solution distance, from which follows the convergence of noise evolution of Monte-Carlo simulation in practical computations. The theoretical analysis is supported by numerical examples.

Assessment and treatment planning for schizotypal personality disorder: A metacognitively oriented point of view.

The aim of this study was to pilot test a novel assessment and treatment plan for patients with a schizotypal personality disorder by integrating the Diagnostic and Statistical Manual of Mental Disorders (5th ed.) alternative model of personality disorders, metacognitively oriented psychotherapies, and recovery approaches. I recruited 12 patients diagnosed with schizotypal personality disorder. I report results from the global assessment including measures on symptoms, maladaptive traits, Big Five personality traits, schizophrenia proneness, and metacognition. I also describe how I planned treatment to promote an individualized understanding of a person's agenda and recovery. The treatment plans were also evaluated through in-depth qualitative interviews at the end of the intervention. Interviews were analyzed through a phenomenological framework and a computer-aided qualitative analysis software. Assessment results and qualitative interviews highlight the importance of a multilevel, progressive treatment plan aimed at considering the personality functioning from a recovery-oriented, nonpathologizing approach. On 1 hand, an assessment that focuses on both healthy and maladaptive traits fosters a progressive redefinition of the therapeutic agenda. On the other hand, a constant and recursive evaluation of metacognition and personality traits offers a treatment strategy that supports my core assumption that recovery from schizotypal personality disorder is possible. A twofold focus on personality traits and metacognition seems to represent a viable strategy for treating patients with schizotypal personality disorder. A metacognitively oriented rehabilitation may be a flexible, personalized and effective approach toward recovery. (PsycInfo Database Record (c) 2020 APA, all rights reserved).