Continuous Approximation Research Articles

Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Wasserstein barycenter, built on the theory of Optimal Transport (OT), provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it is often intractable to precisely compute, especially for high dimensional and continuous settings. To alleviate this problem, we develop a novel regularization by using the fact that c-cyclical monotonicity is often necessary and sufficient conditions for optimality in OT problems, and incorporate it into the dual formulation of Wasserstein barycenters. For efficient computations, we adopt a variational distribution as the approximation of the true continuous barycenter, so as to frame the Wasserstein barycenters problem as an optimization problem with respect to variational parameters. Upon those ideas, we propose a novel end-to-end continuous approximation method, namely Variational Wasserstein Barycenters with c-Cyclical Monotonicity Regularization (VWB-CMR), given sample access to the input distributions. We show theoretical convergence analysis and demonstrate the superior performance of VWB-CMR on synthetic data and real applications of subset posterior aggregation.

Machine learning approach for impedance locus uncertainties

Abstract This work deals with the determination of the uncertainty of measurement data, determined by electrical impedance spectroscopy. Four different types of sand were measured impedimetrically in a measuring cell designed as a plate capacitor in a frequency range from 20 Hz to 1 MHz. The measuring cell was filled ten times with each sand and 20 impedance spectra were recorded for each filling. The uncertainty at each frequency was determined from the measurement data. It was found that the measurement data variance with a given measuring-cell filling was negligibly small. However, it increased by a factor of up to 100 when the measuring cell was repeatedly emptied and re-filled with the same material. We propose a way to estimate a continuous approximation of the uncertainty band of the impedance locus in the complex plane from the discrete uncertainties at each frequency. It uses a Support Vector Machine (SVM) to generate a regression curve using the discrete uncertainties. The result of the regression was used to estimate the uncertainties of an average impedance locus. The said machine learning tool can handle large amounts of data, classes, and influencing variables. In this manner, it can help to identify cause-effect relationships. Furthermore, at the end of this work a possibility to estimate a continuous uncertainty band along the impedance locus curve via SVM regression is shown. This is an extension to the common methodology in literature, where the uncertainty is only determined at selected individual points of the impedance spectrum.

Meta-learning representations for clustering with infinite Gaussian mixture models

Appropriate representations are critical for a better clustering performance. Although many neural network-based clustering methods have been proposed, they do not directly train neural networks to improve the clustering performance. We propose a method that can meta-learn knowledge for clustering from various labeled data and uses the knowledge for clustering unseen unlabeled data. The proposed method trains neural networks to obtain representations such that the clustering performance improves when the representations are clustered by variational Bayesian (VB) inference with an infinite Gaussian mixture model. For the objective function, we propose a continuous approximation of the adjusted Rand index (ARI) by which we can evaluate the clustering performance from soft clustering assignments. Since the approximated ARI and the VB inference procedure are differentiable, we can backpropagate the objective function through the VB inference procedure to train the neural networks. With experiments using text and image datasets, we demonstrate that our proposed method has a higher adjusted Rand index than the existing methods.

A Tenth-Order Sixth-Derivative Block Method for Directly Solving Fifth-Order Initial Value Problems

This work proposes a hybrid block numerical method of tenth order for the direct solution of fifth-order initial value problems. The formulas that constitute the block method are derived from a continuous approximation obtained through interpolation and collocation techniques. In order to obtain better accuracy, sixth-order derivatives are incorporated to develop the formulas. The main characteristics of the method are analyzed, namely, the order, local truncation errors, zero-stability, consistency and convergence. The proposed strategy performs well, as shown by some numerical examples and the corresponding efficiency curves. Compared to existing numerical methods in the literature, the proposed method is competitive and the numerical approximations it provides are significantly close to the precise solutions.

Continuous time approximation of Nash equilibria in monotone games

We consider the problem of approximating Nash equilibria of [Formula: see text] functions [Formula: see text] of [Formula: see text] variables. In particular, we show systems of the form [Formula: see text] [Formula: see text] are well-posed and the large time limits of their solutions [Formula: see text] are Nash equilibria for [Formula: see text] provided that these functions satisfy an appropriate monotonicity condition. To this end, we will invoke the theory of maximal monotone operators on a Hilbert space. We will also identify an application of these ideas in game theory and show how to approximate equilibria in some game theoretic problems in function spaces.

Eco-friendly transparent glass prepared from rice straw ash for neutron and charged particle radiation shielding

The current study aimed to fabricate and investigate new glass system incorporating silica from rice straw ash (RSA). The effect of adding different concentrations of bismuth oxide (Bi2O3) on the glass's structure was examined using FTIR. The A.C. conductivity of the prepared glasses over the frequency range (120 Hz − 100 kHz) and the temperature range (300–620 oK) have been measured. Based on its electron density, a substance's electrical conductivity can alter as photon energy increases. For the current investigated glasses, the electron density (Neff) and electrical conductivity relation over the energy range (0.015–10 MeV) were calculated. Glass samples' ability to attenuate radiation such as neutrons, electrons, protons, and alpha particles has been investigated. For neutrons, the effective removal cross-section (∑R, cm−1) and the total macroscopic cross-section (∑T, cm−1) are calculated. For charged particles like protons (H+) and alpha (He2+), SRIM software has been used to determine the glass Mass Stopping Power (MSP) and the Projected Range (PR). For electrons (β−), MSP and the Continuous Stopping Down Approximation (CSPA) were calculated using ESTAR (NIST). On the other hand, Phy X/Zextra software was used to determine glasses effective atomic numbers (Zeff) over a broad energy range. As a result, BSiBi20 glass with the highest Bi2O3 concentrations (20 mol. %) shows superior shielding features for fast neutrons (∑R = 0.128 cm−1) compared to the competitors like ordinary concrete (O.C.). For charged particles, BSiBi20 glass achieves the lowest MSP, CSPA, and the highest Zeff values over the entire energy range. The KERMA (Kinetic Energy Released per unit Mass of the Absorbing material) calculations indicated a significant influence on the elemental composition of the glass system in the intermediate photon energy regime.

Towards [formula omitted]-Continuous Multi-Strip Path-Planning for 5-Axis Flank CNC Machining of Free-Form Surfaces Using Conical Cutting Tools

Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets G1 (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve G1 continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the G1 connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness.

Prediction of oxygen distribution in the waste mass from an aeration well in bioreactor landfills.

The key to upgrade the efficiency of aerobic remediation of landfills is to determine the distribution characteristics of oxygen concentration during aerobic ventilation. This study discusses the distribution law of oxygen concentration with time and radial distance based on a single-well aeration test at an old landfill site. The transient analytical solution of the radial oxygen concentration distribution was deduced using the gas continuity equation and approximation of calculus and logarithmic functions. Oxygen concentration data from the field monitoring were compared with the results predicted by the analytical solution. The results indicated that the oxygen concentration initially increased and then decreased with prolonged aeration time. With an increase in radial distance, the oxygen concentration rapidly declined, followed by a gradual decrease. The influence radius of the aeration well increased slightly when the aeration pressure increased from 2 to 20 kPa. The field test data agreed with the analytical solution prediction results, preliminarily verifying the reliability of the oxygen concentration prediction model. Results from this study provide a basis of guidelines for the design, operation and maintenance management of a landfill aerobic restoration project.

Snap-through instability during transmission of rotation by a flexible shaft with initial curvature

The geometric imperfection of a flexible shaft transmitting rotary motion along a curved path may result in a highly nonlinear relation between the rotation angles at the driving and driven ends. If the intrinsic curvature of the shaft surpasses a specific threshold, even snap-through instability becomes possible. Previously, the problem has been considered for the case when the shaft is confined in a rigid channel such that only the rotary motion is possible along its entire length. The present study focuses on the case of the freely deformable axis of the shaft. Just the locations and the tangential directions of its ends are fixed. We investigate the response of the shaft, in terms of rotation at the driven end, by combining analytical solutions using incremental equations from the theory of Kirchhoff rods and a finite element model that features a C1 continuous approximation of deflections and rotations. Comparison to the constrained case shows that the impact of the deformability of the axis grows both with the intrinsic curvature of the shaft and its angular length.

Exciton binding energy and radiation lifetime in CdTe/Cd1−xZnxS strained core/shell spherical quantum dots under pressure

In this paper, the exciton binding energy and radiation lifetime in type I and II structures of CdTe/Cd[Formula: see text]ZnxS strained core/shell spherical quantum dots under the hydrostatic pressure have been studied by using the variational method within the continuous dielectric model and effective mass approximation. The results show that for these two structures, the exciton binding energies with and without strain decrease with the increasing core radius but increase with the increasing pressure. The exciton binding energy with strain is smaller than that without strain. For type I structure, the effect of strain is small, and the radiation lifetime decreases monotonically with the increasing pressure. By contrast, for type II structure, the effects of shell radius and strain on the exciton binding energy are obvious, and the radiation lifetime increases first and then decreases with the increasing pressure.

Adaptive transit design: Optimizing fixed and demand responsive multi-modal transportation via continuous approximation

Adaptive transit design: Optimizing fixed and demand responsive multi-modal transportation via continuous approximation

Determining an optimal sensor system for smart buildings with uncertain energy supply and demand

The increased smartness of buildings and new technology are expected to mitigate the impact of climate change through renewable energy usage, efficient energy management, and greenhouse gas emission reduction. Using internet of things, sensors, and data analysis, energy management can substantially optimize the use of energy and balance energy supply and demand. However, a distributed sensor system is complex and needs to be located well to make the system efficient. The present study proposes a continuous approximation approach to determine the number of sensors required and the location to set them up in a building as well as the smartness level of each sensor while minimizing the total network cost. We also conducted a numerical analysis to illustrate the model and obtain management insights. Interestingly, in our example, we found that the basement floor of a building should have more sensors installed than other floors.

A New Distributed Robust Power Control for Two-Layer Cooperative Communication Networks in Smart Grids with Reduced Utility Costs

The packet loss during transmission of load control commands can lead to regulation errors in the smart grid and increase the cost of utility agencies due to the purchase of additional automatic generation control (AGC) services. In this paper, a two-layer cooperative communication network between the utility company and relays is presented. The utility company rents the relay to assist with the downlink transmission to improve the reliability of communication and reduce the data transmission cost due to packet loss. Furthermore, the uncertainty of channel gain is considered, and a two-tier game model is established. A distributed robust power control algorithm based on the continuous convex approximation method is proposed to obtain the optimal relay power allocation and price. Through the simulation analysis of the proposed scheme and the two comparison schemes, the cost of the utility company was reduced by 6% and 21%, and the standard deviation of income value between the relays was reduced by 40% and 48%, respectively.

An information extraction method based on improved mixed text density web pages

AbstractTo improve the effect of web page information extraction, this paper proposes an improved information extraction method of mixed text density grids. Under various power constraints of the relay node itself, this paper proposes a design scheme of joint beamforming and artificial noise based on safety and rate maximisation. Furthermore, with the help of semidefinite relaxation techniques and first‐order approximations, it can be approximated as a semidefinite programming problem that is easy to solve. In addition, this paper uses an iterative algorithm based on a continuous convex approximation to process data to improve the accuracy of web page data extraction. The experimental results show that the information extraction method based on improved mixed text density webpages proposed in this paper has a good information extraction effect.

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

Discounting money and health effects from communicable and noncommunicable diseases in Thailand

The purpose of this study was to determine the discount rates for money and health outcomes in the Thai context, including the discount rates for communicable and non-communicable diseases. Moreover, this study aimed to explore the socio-demographic characteristics that influence discounting. The computer-based experimental design was used to obtain time preferences for money and health in a total of 1202 Chiang Mai province population, aged 25–50, individually interviewed by trained interviewers. Money-related questions were carried out in all subjects. For health-related questions, all subjects were randomly assigned in a 1:1 ratio for response to questions about Coronavirus Disease 2019 (COVID-19) (N = 602) and air pollution (N = 600). A choice-based elicitation procedure was performed in the experiment to obtain the indifference values from subjects’ time preferences. The cumulative weighting functions were generated using the indifference values to indicate the degree of discounting. The discount factors were computed from the cumulative weighting functions. The discount rates were estimated using a continuous approximation based on the relationship between the discount factors and the parameters governing the discounting model. The Tobit model was applied to investigate the relationships between discounting and socio-demographic characteristics. Discounting for money was greater than discounting for health. Money and health had annual discount rates of 6.2% and 1.3%, respectively. Furthermore, in the COVID -19 situation, the annual discount rate for health was higher than that in the air pollution situation (2.4% vs. 0.7%). Generation X subjects (aged 42 years and above), children under the age of 15 in the household, and underlying diseases were positively related to discounting, while household income was negatively related to discounting. Health should be discounted at a lower rate than money. Moreover, different discount rates should be considered for different types of diseases.

Who has access to e-commerce and when? Time-varying service regions in same-day delivery

We study the design of same-day delivery (SDD) systems under the assumption that service regions are allowed to vary over the course of the day; equivalently, that customers in different locations may have access to SDD for different lengths of time over the service day or may have no access at all. This contrasts with the bulk of the literature, in which a service region is defined in advance and all customers in the service region can place SDD orders during the same time window. Leveraging continuous approximation techniques to capture average-case system behavior, we derive optimal service region areas and corresponding SDD order cutoff times to maximize the expected number of orders served per day. We quantify the benefit of allowing the service regions to vary, both theoretically and empirically, and discuss related equity issues in SDD systems. We illustrate and validate our results with a case study set in the Phoenix, Arizona metropolitan area.

Assessing last-mile distribution resilience under demand disruptions

The COVID-19 pandemic led to a significant breakdown of the traditional retail sector resulting in an unprecedented surge in e-commerce demand for the delivery of essential goods. Consequently, the pandemic raised concerns pertaining to e-retailers’ ability to maintain and efficiently restore level of service in the event of such low-probability high-severity market disruptions. Thus, considering e-retailers’ role in the supply of essential goods, this study assesses the resilience of last-mile distribution operations under disruptions by integrating a Continuous Approximation (CA) based last-mile distribution model, the resilience triangle concept, and the Robustness, Redundancy, Resourcefulness, and Rapidity (R4) resilience framework. The proposed R4 Last Mile Distribution Resilience Triangle Framework is a novel performance-based qualitative-cum-quantitative domain-agnostic framework. Through a set of empirical analyses, this study highlights the opportunities and challenges of different distribution/outsourcing strategies to cope with disruption. In particular, the authors analyzed the use of an independent crowdsourced fleet (flexible service contingent on driver availability); the use of collection-point pickup (unconstrained downstream capacity contingent on customer willingness to self-collect); and integration with a logistics service provider (reliable service with high distribution costs). Overall, this work recommends the e-retailers to create a suitable platform to ensure reliable crowdsourced deliveries, position sufficient collection-points to ensure customer willingness to self-collect, and negotiate contracts with several logistics service providers to ensure adequate backup distribution.

A hybrid finite element–finite volume method for conservation laws

We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. To lowest (3rd) order this method reduces to the Active Flux method. The update of the moments is achieved immediately by integrating the conservation law over the cell, integrating by parts and employing the continuity across cell interfaces. We propose two ways how the point values can be updated in time: either by first deriving a semi-discrete method that uses a finite-difference-type formula to approximate the spatial derivative, and integrating this method e.g. with a Runge-Kutta scheme, or by using a characteristics-based update, which is inspired by the original (fully discrete) Active Flux method. We analyze stability and accuracy of the resulting methods.

On the Klimontovich description of complex (dusty) plasmas

AbstractThe numerous idealizations that are involved in the exact microscopic statistical description of complex (dusty) plasmas are discussed in detail. The two prevailing approaches in the Klimontovich description of dusty plasmas are reviewed in a pedagogical manner. The continuous phase space approximation is introduced, within which the more rigorous treatment should collapse to the more heuristic treatment. The plasma Klimontovich equations are shown to be identical, but there are marked differences in the dust Klimontovich equations whose origin is analysed in depth.