Approximation Method Research Articles

Food waste and its causes in higher education cafeterias and canteens: an exploratory study in the province of Santiago (Chile)

ABSTRACT Food waste (FW) is the decrease in the mass of edible food during retail, food service, and final consumption. In recent years, research related to this topic has spread. However, there are still few references about food waste in the service sector in developing countries, which is a concern for three reasons: first, due to the overgrew of food consumption out of the home before the COVID-19 pandemic; secondly, due to the interest in carrying out this research at the local level avoiding regional or global generalizations and, finally for the nutritional implications derived from this research. With this background, this paper fills this gap and aims to evaluate food waste in the service sector, concretely in higher education cafeterias and canteens (HECC). Our specific objectives include obtaining information on the causes of FW in HECC in Santiago (Chile) using approximation methods that are better suited to the purposes of this paper. The study employed the qualitative research paradigm to analyze primary data and comprises a structured questionnaire survey and a qualitative semi-structured interview of HECC managers. Non-probabilistic sampling was used as a convenience sampling technique to select the HECC to be surveyed (n = 17). The results show a total FW by year comprised 309 tons of FW generated in the higher education canteens surveyed and 115 tons generated in the higher education cafeterias surveyed, representing 425 tons of FW annually. Divided by the total FW by the working days of HECC, the average FW generated daily is 1381 kg, corresponding to 1005 kg per day in higher education canteens and 376 kg per day in higher education cafeterias.

Improving horizon computation algorithm with quasirandom sequences

The topographic horizon can be used to estimate shading for applications requiring an accurate solar resource estimate, including the effects of the local terrain. With high-resolution topography data, horizon estimation significantly contributes to the computation time needed for irradiance simulations. Approximate horizon algorithms have been proposed previously, sampling topography in a finite number of directions. This paper extends this idea by presenting a sampling approach based on the quasirandom sequences. The sampling strategy is optimized with 300,000 km2 of topography data from Europe and the USA. We demonstrate that our algorithm is several orders of magnitude faster than the precise horizon calculation and significantly improves the previous approximate algorithms. In particular, at the ground level with a topography resolution of 1 m/pixel, the proposed method achieved the same accuracy as the old approximate method four times faster. The horizon is one of the key methods in geographical information science and a part of many modeling tools in the built environment. Improvements in computation time benefit all applications that require irradiance modeling, e.g., the yield of vehicle- and building-integrated photovoltaic or temperature modeling of buildings.

Inaccurate search based sequential approximate constrained optimization method for Solid Rocket Motor design

Surrogate based constrained optimization methods are widely utilized in practical solid rocket motor (SRM) design problems. To improve the design performance, this paper proposes an inaccurate search based sequential approximate constrained optimization (ISSACO) method consisting of an efficient recursive evolution Latin hypercube design (RELHD) method and a three-stage constrained sampling method. The RELHD method divides large-sample experiment design problem into several small-sample design problems to ensure the computational efficiency and the design uniformity at the same time. The three-stage constrained sampling method employs the elite archives mechanism to balance the feasibility and the optimality in optimization. Results of the numerical cases indicate that the proposed ISSACO algorithm is competitive with other state-of-art constrained optimization method in efficiency and effectiveness. The finocyl grain design and the impulse mass ratio optimization are also conducted to make further verifications, and the ISSACO method can efficiently obtain feasible optimum and proves to be a potential method for computationally intensive solid rocket motor design problems.

Grid Point Approximation for Distributed Nonparametric Smoothing and Prediction

Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we find that the popularly used one-shot type estimator is highly inefficient for prediction purposes. To this end, we propose a novel grid point approximation (GPA) method, which has the following advantages. First, the resulting GPA estimator is as statistically efficient as the global estimator under mild conditions. Second, it requires no communication and is extremely efficient in terms of computation for prediction. Third, it is applicable to the case where the data are not randomly distributed across different machines. To select a suitable bandwidth, two novel bandwidth selectors are further developed and theoretically supported. Extensive numerical studies are conducted to corroborate our theoretical findings. Two real data examples are also provided to demonstrate the usefulness of our GPA method.

Sensor placement method for water distribution networks based on sampling of non-bandlimited graph signals

Monitoring water distribution networks (WDNs) requires careful consideration of sensor placement, which is essential for obtaining comprehensive information about the network. A natural graphical structure underlies WDN, making graph sampling theory advantageous for selecting monitoring nodes. However, graph sampling theory is only applied only to restrictive band-limited signals, while the pressure data of WDN is a restrictive non-band-limited signal. To address this issue, this paper presents an approximate conversion method for transforming non-band-limited signals into band-limited signals, accompanied by an optimal spectrum threshold formula. This formula is used to perform spectral screening in the graph frequency domain, effectively converting non-band-limited signals into band-limited signals that preserve the major frequency components while ignoring smaller-value frequency components. By sampling band-limited signal, we identify sampling nodes that perfectly recover the signal. These sampling nodes act as monitoring nodes that can perform a comprehensive inspection of the WDN and accurately locate leaks. The accuracy of our method in recovering the signal and locating the leak is demonstrated by comparing it with two existing sensor placement optimization methods.

Enhanced MRI brain tumor detection and classification via topological data analysis and low-rank tensor decomposition

The advent of artificial intelligence in medical imaging has paved the way for significant advancements in the diagnosis of brain tumors. This study presents a novel ensemble approach that uses magnetic resonance imaging (MRI) to identify and categorize common brain cancers, such as pituitary, meningioma, and glioma. The proposed workflow is composed of a two-fold approach: firstly, it employs non-trivial image enhancement techniques in data preprocessing, low-rank Tucker decomposition for dimensionality reduction, and machine learning (ML) classifiers to detect and predict the type of brain tumor. Secondly, persistent homology (PH), a topological data analysis (TDA) technique, is exploited to extract potential critical areas in MRI scans. When paired with the ML classifier output, this additional information can help domain experts to identify areas of interest that might contain tumor signatures, improving the interpretability of ML predictions. When compared to automated diagnoses, this transparency adds another level of confidence and is essential for clinical acceptance. The performance of the system was quantitatively evaluated on a well-known MRI dataset, with an overall classification accuracy of 97.28% using an extremely randomized trees model. The promising results show that the integration of TDA, ML, and low-rank approximation methods is a successful approach for brain tumor identification and categorization, providing a solid foundation for further study and clinical application.

Encyclopædia Inflationaris: Opiparous Edition

The current flow of high-accuracy astrophysical data, among which are the Cosmic Microwave Background (CMB) measurements by the Planck satellite, offers an unprecedented opportunity to constrain the inflationary theory. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. Given that there is currently no observational evidence for primordial non-Gaussianities, isocurvature perturbations or any other non-minimal extension of the inflationary paradigm, a reasonable approach is to consider the simplest models first, namely the slow-roll single-field models with minimal kinetic terms. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. It has been customary to tackle this problem by means of approximate model-independent methods while a more ambitious alternative is to study the inflationary scenarios one by one. We have developed the publicly available runtime library ASPIC11https://github.com/cosmicinflation/aspic. to implement this last approach. The ASPIC code provides all routines needed to quickly derive reheating-consistent observable predictions within this class of scenarios. ASPIC has been designed as an evolutive code which presently supports 118 different models. In this paper, for each of the ASPIC models, we present and collect new results in a systematic manner, thereby constituting the first Encyclopædia Inflationaris.

U-TPE: A universal approximate thumbnail-preserving encryption method for lossless recovery

Due to the limited local storage space, more and more people are accustomed to uploading images to the cloud, which has aroused concerns about privacy leaks. The traditional solution is to encrypt the images directly. However, in this way, users cannot easily browse the images stored in the cloud. Obviously, the traditional method has lost the visual usability of cloud images. To solve this problem, the Thumbnail-Preserving Encryption (TPE) method is proposed. Although approximate-TPE is more efficient than ideal TPE, it cannot restore the original image without damage and cannot encrypt some images with texture features. Inspired by the above, we propose a universal approximate thumbnail-preserving encryption method with lossless recovery. This method divides the image into equal-sized chunks, each of which is further divided into an embedding area and an adjustment area. The pixels of the embedding area are recorded by prediction. Then, the auxiliary information necessary to restore the image is encrypted and hidden in the embedding area of the encrypted image. Finally, the pixel values of the adjustment area in each block are adjusted so that the average value is close to the original block. Experimental results show that the proposed method can not only restore images losslessly but also process images with different texture features, achieving good generality. On the BOWS2 dataset, all images can be encrypted by adjusting the block size. In addition, it can resist third-party face recognition and comparison, achieving satisfactory results in balancing privacy and visual usability.

Comparison of methods for modeling the gas-dynamic characteristics of high-pressure centrifugal compressors that ensure the operation of field low-temperature separation units using the example of a modification with a pressure ratio of up to 1.9...2.1

Objective. Currently, for the development of Valanginian and other deeplying (compared to the Cenomanian) deposits, low-temperature separation (LTS) units with turboexpander units (TDA) are used, and the booster compressor station (BCS) is one of the key technological facilities necessary to ensure the efficient operation of promising technologies for gas preparation using the NTS method with TDA turboexpander units for transport. The purpose of the study is to substantiate optimal operating modes, as well as to develop measures for the technological development of a booster compressor station based on the use of methods for modeling the operation of centrifugal compressors, gas pumping units and, directly, the booster compressor station. Method. The following methods were used: the method of reduced characteristics, the refined method of reduced characteristics, and the two-dimensional approximation method. The basis of the mathematical model of the research objects is the gas-dynamic characteristics of centrifugal compressors. Result. The results of a comparison of methods for modeling HDC (reduced characteristics method, refined method of reduced characteristics, two-parameter approximation method) of high-pressure pulp and paper mills are presented using the example of a pulp and paper mill with a pressure ratio of up to 1.9...2.1, intended for equipping gas compressor units with a unit power of 16.0 MW as part of field operations. DKS. An analysis and comparison of the obtained modeling results with actual data was carried out. Conclusion. The accuracy of the mathematical model of the GDC PPM as part of the field booster compressor stations that ensure the operation of NTS installations with TDA determines the accuracy of the assessment of energy consumption and the technical condition of the gas pumping units, as well as calculations of future operating modes of gas pumping equipment, which are carried out to solve a number of applied problems, including determining the timing of equipment modernization or reconstruction of the station.

Discontinuous Galerkin finite element method for the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes

Context. The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to handle numerically, they often fail to accurately describe the radiation field inside complex geometries. For these cases, it is necessary to directly solve the radiative transfer equation numerically. Aims. We investigate the accuracy of the discontinuous Galerkin finite element method (DGFEM hereafter) applied to the frequency-dependent two-dimensional radiative transfer problem, and coupled with the radiative equilibrium equation. We next used this method in the context of axis-symmetric circumstellar envelopes. Methods. The DGFEM is a variant of finite element methods. It employs discontinuous elements and flux integrals along their boundaries, ensuring local flux conservation. However, as opposed to the classical finite element methods, the solution is discontinuous across element edges. We implemented this approach in a code and tested its accuracy by comparing our results with the benchmarks from the literature. Results. For all the tested cases, the temperatures profiles agree within one percent. Additionally, the emerging spectral energy distributions (SEDs) and images, obtained by ray-tracing techniques from the DGFEM emissivity, agree on average within 5% and 10%, respectively. Conclusions. We show that the DGFEM can accurately describe the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes. Consecutively the emerging SEDs and images are also well reproduced. The DGFEM provides an alternative method (other than Monte-Carlo methods for instance) for solving the radiative transfer equation, and it could be used in cases that are more difficult to handle with the other methods.

Functional analytic methods for discrete approximations of subwavelength resonator systems

Functional analytic methods for discrete approximations of subwavelength resonator systems

Harnessing 12-lead ECG and MRI data to personalise repolarisation profiles in cardiac digital twin models for enhanced virtual drug testing

Cardiac digital twins are computational tools capturing key functional and anatomical characteristics of patient hearts for investigating disease phenotypes and predicting responses to therapy. When paired with large-scale computational resources and large clinical datasets, digital twin technology can enable virtual clinical trials on virtual cohorts to fast-track therapy development. Here, we present an open-source automated pipeline for personalising ventricular electrophysiological function based on routinely acquired magnetic resonance imaging (MRI) data and the standard 12-lead electrocardiogram (ECG).Using MRI-based anatomical models, a sequential Monte-Carlo approximate Bayesian computational inference method is extended to infer electrical activation and repolarisation characteristics from the ECG. Fast simulations are conducted with a reaction-Eikonal model, including the Purkinje network and biophysically-detailed subcellular ionic current dynamics for repolarisation. For each patient, parameter uncertainty is represented by inferring an envelope of plausible ventricular models rather than a single one, which means that parameter uncertainty can be propagated to therapy evaluation. Furthermore, we have developed techniques for translating from reaction-Eikonal to monodomain simulations, which allows more realistic simulations of cardiac electrophysiology. The pipeline is demonstrated in three healthy subjects, where our inferred pseudo-diffusion reaction-Eikonal models reproduced the patient's ECG with a median Pearson's correlation coefficient of 0.9, and then translated to monodomain simulations with a median correlation coefficient of 0.84 across all subjects. We then demonstrate our digital twins for virtual evaluation of Dofetilide with uncertainty quantification. These evaluations using our cardiac digital twins reproduced dose-dependent QTc and T peak to T end prolongations that are in keeping with large population drug response data.The methodologies for cardiac digital twinning presented here are a step towards personalised virtual therapy testing and can be scaled to generate virtual populations for clinical trials to fast-track therapy evaluation. The tools developed for this paper are open-source, documented, and made publicly available.

Anomaly Detection and Approximate Similarity Searches of Transients in Real-time Data Streams

We present Lightcurve Anomaly Identification and Similarity Search (LAISS), an automated pipeline to detect anomalous astrophysical transients in real-time data streams. We deploy our anomaly detection model on the nightly Zwicky Transient Facility (ZTF) Alert Stream via the ANTARES broker, identifying a manageable ∼1–5 candidates per night for expert vetting and coordinating follow-up observations. Our method leverages statistical light-curve and contextual host galaxy features within a random forest classifier, tagging transients of rare classes (spectroscopic anomalies), of uncommon host galaxy environments (contextual anomalies), and of peculiar or interaction-powered phenomena (behavioral anomalies). Moreover, we demonstrate the power of a low-latency (∼ms) approximate similarity search method to find transient analogs with similar light-curve evolution and host galaxy environments. We use analogs for data-driven discovery, characterization, (re)classification, and imputation in retrospective and real-time searches. To date, we have identified ∼50 previously known and previously missed rare transients from real-time and retrospective searches, including but not limited to superluminous supernovae (SLSNe), tidal disruption events, SNe IIn, SNe IIb, SNe I-CSM, SNe Ia-91bg-like, SNe Ib, SNe Ic, SNe Ic-BL, and M31 novae. Lastly, we report the discovery of 325 total transients, all observed between 2018 and 2021 and absent from public catalogs (∼1% of all ZTF Astronomical Transient reports to the Transient Name Server through 2021). These methods enable a systematic approach to finding the “needle in the haystack” in large-volume data streams. Because of its integration with the ANTARES broker, LAISS is built to detect exciting transients in Rubin data.

Efficiency high-order discontinuous Galerkin method for low speeds flows with time-derivative preconditioning

A local preconditioning high-order discontinuous Galerkin (DG) method is introduced to enhance the efficiency and accuracy of the density-based approach for low-speed flows. The method is based on the time-derivative preconditioning technique typically employed in finite volume methods. Traditional approximation methods that only precondition low-order derivatives lead to incompatibility of the equations. To extend the preconditioning technique to the DG method, we employ an analytic preconditioning mass matrix derived from the DG formulation of the preconditioned Navier–Stokes equations. Modified numerical flux functions and a self-adaptive local velocity truncation parameter are employed for DG systems with preconditioning. We demonstrate the efficiency and accuracy of the preconditioned DG method using explicit and implicit schemes for steady flows and a dual-time scheme for unsteady flows. The method has been implemented and used to compute a variety of flow problems, including inviscid and laminar flows, utilizing various degrees of polynomial approximations. Computations with and without preconditioning are performed to analyze the influence of spatial discretization on the accuracy and convergence of the DG solutions at low Mach numbers. Numerical results underscore the enhanced accuracy and convergence properties of the proposed method for low-speed flows, indicating significant performance improvements over traditional methods.

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

Spectral densities, structured noise and ensemble averaging within open quantum dynamics.

Although recent advances in simulating open quantum systems have led to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely, the numerical integration of Schrödinger equation (NISE). First, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed thermalized NISE. Second, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics.

The JCSS probabilistic model Code, future developments

To assess and verify the reliability of structures, reliability based building codes allow for the application of full-probabilistic methods and semi-probabilistic methods (i.e. the partial factor method). In principle, both methods should be equivalent and lead to (approximately) the same reliability level. Therefore partial factors should be as much as possible determined based on a probabilistic background and calibration exercises. On the other hand, as the probabilistic design method may be considered as more rational and consistent than the partial factor design, there is a tendency to use probabilistic methods directly in the assessment of special of important new structures and also in the assessment of existing structures. In both the calibration exercise and in the full probabilistic assessment of structures, we face the problem that many assumptions have to be made. In particular in regard to the statistical modelling of random variables and in regard to accepted approximative methods of calculation. This often brings the engineer to a challenging position. In the past years the JCSS probabilistic model code (PMC) has served as an often-consulted operational code for this purpose. In the present paper, the JCSS PMC and its future developments are presented and discussed.

Identification of sparse nonlinear controlled variables for near‐optimal operation of chemical processes

AbstractFor optimal operation of chemical processes, the selection of controlled variables plays an important role. A previous proposal is to approximate the necessary conditions of optimality (NCO) as the controlled variables, such that process optimality is automatically maintained by tracking constant zero setpoints. In this paper, we extend the NCO approximation method by identifying sparse nonlinear controlled variables, motivated by the fact that simplicity is always favoured for practical implementations. To this end, the ‐regularization is employed to approximate the NCO, such that the controlled variables are maintained simple, even they are specified as nonlinear functions. The sparse controlled variables are solved using the proximal gradient method, implemented within a tailored Adam algorithm. Two case studies are provided to illustrate the proposed approach.

Estimation of the domain of attraction for continuous-time saturated positive polynomial fuzzy systems based on novel analysis and convexification strategies

In this paper, the domain of attraction (DOA) of the continuous-time positive polynomial fuzzy systems subject to input saturation is estimated by using the level set of the linear copositive Lyapunov function. To relax the estimation of DOA, the restriction on the level set is removed by embedding the expression of the level set into the stability conditions and positivity conditions. Referring to the nonconvex terms caused by above novel analysis strategy, some polynomial inequality lemmas are proposed to handle them; the nonconvex terms caused by imperfect premise matching (IPM) nonlinear membership functions are dealt with by sector nonlinear methods and advanced Chebyshev membership-function-dependent (MFD) methods. In this advanced MFD method, the state space segmentation and polynomial order selection of the Chebyshev approximation method are improved based on breakpoints of the first derivative and curvature, respectively, which is helpful to reduce the conservatism and computational burden of the result. Thus, this advanced Chebyshev MFD method not only optimizes the convexification strategy, but also can further be extended to estimate the DOA when it is used to introduce the membership functions information for convex stability and positivity conditions. Finally, a numerical example and the lipoprotein metabolism and potassium ion transfer nonlinear model are presented to validate the effectiveness and feasibility of the aforementioned analysis and convexification strategies in the expansion of DOA estimation.

Numerical solutions of stochastic delay integro-differential equations by block pulse functions

This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy.