Set Of Points Research Articles

Stratified sample tiling

The paper introduces a practical method for the construction of large-scale point sets for analysis of computer models. The constructed experimental design is useful for (probabilistic) integration, construction of approximation or a screening. The essence of the presented approach is the stratification of the design domain into an orthogonal grid of substrata and a subsequent tiling with tiles of points. If optimized, such tiles experience a major reduction of the number of degrees of freedom in the optimization process. That way, optimal or near-optimal point patterns can be feasibly identified and are further utilized for construction of larger point sets, thanks to the idea of self-similarity and structured space stratification The space-filling properties of the resulting point sets may be further enhanced by various “scrambling” strategies, which may remove the undesired sample collapsibility achieved via regular tiling. The performance of the constructed point sets is compared to Quasi Monte Carlo (QMC), Randomized Quasi Monte Carlo (RQMC) sequences, which are still today considered by engineers and even scientists as choices for variance reduction of numerical integration Further, the mentioned sampling strategies are compared in the terms of robustness when integrating a multivariate function with a localized feature. It is concluded that the proposed sampling approach reaches a superior performance in numerical integration and identification of function extremes as compared to sampling methods used by practicing researchers and engineers. Additionally, the reader is supplied with the open-access, ready-to-use implementation of the presented algorithm named SampleTiler.

DS-partial metric spaces and domain theory

In this paper, we establish some connections between partial metric spaces and domain theory, and give a characterization of stable partially metrizable d-spaces. First, the concept of S-partial metrics on posets is introduced. Then it is demonstrated that the open ball topology is coarser than the Scott topology in an S-partial metric space, and that the partially metrizable d-space is exactly the DS-partial metric space. In addition, some conditions are provided to ensure that the open-ball topology and the Scott topology coincide in an S-partial metric space. Moreover, we prove that, for an S-partial metric space (X,≤,p), (X,Op(X)) is sober iff the set of all limit points of every self-convergent sequence is directed. Finally, we propose the notion of DS-valuation space and obtain the result that there is a bijection between stable DS-partial metric spaces and DS-valuation spaces, thereby giving the characterization of stable partially metrizable d-spaces.

The Optimal Transportation Option in an Underground Hard Coal Mine: A Multi-Criteria Cost Analysis

The issue of transport in underground hard coal mines is very rarely described in the literature. The financial aspects of this issue are even less often analyzed. Publications in this area focus on technical issues and the safety of mining crews. More attention is paid to transport in open-pit mines. The above premises and practical needs imply the need to conduct economic analyses of transport systems in underground hard coal mines. This paper is a scientific communication, which presents the concept of a multi-criteria cost analysis as a tool to support the selection of the optimal transportation option in an underground hard coal mine. Considerations in this area have not been carried out in the relevant literature, and the problem of selecting a transportation option is a complex and necessary issue in the practice of underground mines with extensive mine workings. The methodology presented includes five cost criteria (costs of carrying out the transportation task; route expansion costs; rolling stock maintenance costs; depreciation costs; and additional personnel costs). The simultaneous application of criteria relating to utility properties in addition to cost criteria makes it possible to adopt a specific technical and organizational model of the transportation system based on the indication of the optimal solution, resulting from the mathematical construction of functions of objectives relating to utility and cost. The optimal variant of the designed system and configuration of the material transportation system in underground workings takes into consideration the following: (1) seven utility criteria (KU1—transportation task completion time; KU2—compatibility of transportation systems; KU3—continuous connectivity; KU4—co-use with other transportation tasks; KU5—safety; KU6—inconvenience; KU7—operation under overplanning conditions) and (2) five cost criteria (KK1—costs of implementing the transportation task; KK2—costs of route expansion; KK3—rolling stock maintenance costs; KK4—depreciation costs; KK5—additional personnel costs). Based on the aforementioned criteria, two objective functions are built for each option: utility and cost. They present divergent goals; therefore, they are non-cooperative functions. Both utility and costs strive for the maximum. In the developed methodology, an ideal point is usually a fictitious solution representing a set of maximum values among all the achievable values in a set of solutions, but it is impossible to achieve this simultaneously based on all the criteria. This point illustrates the maximum utility and lowest cost among the alternatives considered, which is obviously impossible for any of the variants to meet at the same time, although it indicates the possibilities of the technique and the range of costs. For the developed method, a so-called “PND” nadir point is also determined, representing the least-preferred level of achievement of all goals simultaneously, determined from the set of optimal points in the Pareto sense. The originality of the conceptual considerations undertaken stems from: filling the gap in the economic methodology of complex transportation systems evaluation; embedding considerations in the trend concerning complex transportation systems of underground mines; and focusing considerations on the pre-investment phase, making it possible to optimize costs before expenditures are incurred.

Hypothalamic Thyroid Hormone Receptor α1 Signaling Controls Body Temperature.

Background: The importance of thyroid hormones (THs) for peripheral body temperature regulation has been long recognized, as medical conditions such as hyper- and hypothyroidism lead to alterations in body temperature and energy metabolism. In the past decade, the brain actions of THs and their respective nuclear receptors, thyroid hormone receptor α1 (TRα1) and thyroid hormone receptor beta (TRβ), coordinating body temperature regulation have moved into focus. However, the exact roles of the individual TR isoforms and their precise neuroanatomical substrates remain poorly understood. Methods: Here we used mice expressing a mutant TRα1 (TRα1+m) as well as TRβ knockouts to study body temperature regulation using radiotelemetry in conscious and freely moving animals at different ambient temperatures, including their response to oral 3,3',5-triiodothyronine (T3) treatment. Subsequently, we tested the effects of a dominant-negative TRα1 on body temperature after adeno-associated virus (AAV)-mediated expression in the hypothalamus, a region known to be involved in thermoregulation. Results: While TRβ seems to play a negligible role in body temperature regulation, TRα1+m mice had lower body temperature, which was surprisingly not entirely normalized at 30°C, where defects in facultative thermogenesis or tail heat loss are eliminated as confounding factors. Only oral T3 treatment fully normalized the body temperature profile of TRα1+m mice, suggesting that the mutant TRα1 confers an altered central temperature set point in these mice. When we tested this hypothesis more directly by expressing the dominant-negative TRα1 selectively in the hypothalamus via AAV transfection, we observed a similarly reduced body temperature at room temperature and 30°C. Conclusion: Our data suggest that TRα1 signaling in the hypothalamus is important for maintaining body temperature. However, further studies are needed to dissect the precise neuroanatomical substrates and the downstream pathways mediating this effect.

An errors-unidentified hand-eye calibration method via robot relocalization and iterative combinatorial refinement

The accuracy of hand-eye calibration is easily affected by robot kinematic error, measurement error, random error, etc., and can be to a certain extent enhanced by the complicated error identification. To address this problem, we propose a novel errors-unidentified hand-eye calibration method. A relocalization-based hand-eye calibration is implemented to overcome the challenge from robot kinematics at first owing to the high robot relocalization accuracy. The tool center point (TCP) coordinates are then obtained based on an iterative reweighted least squares (IRLS) spherical fitting algorithm. An iterative combinatorial refinement algorithm is finally presented to search the solutions in the form of permutation and combination when solving the rigid transformation matrix. Experiments on criterion sphere and blade demonstrate that by converting the hand-eye matrix solving problem into a point set matching problem, the accuracy of the proposed method is enhanced by 60% on average compared with three state-of-the-art hand-eye calibration methods.

Design of a feedback linearizing controller for a CSTR reactor

The design of a controller for a chemical reactor was studied. Based on the input-output feedback linearization, the controller was designed for a situation where the output of the system is the concentration. The reaction in the reactor is of the first-order type. First, the reactor is modeled and presented, and then a controller for this system is designed. The control system was implemented in Simulink MATLAB. The simulation results show that the designed controller is able to control the concentration in a wide range and its performance is desirable for changing either the disturbances or the set point.

A Multi-Fidelity Bayesian Optimization Approach for Constrained Multi-Objective Optimization Problems

Abstract In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multiobjective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none is available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multiobjective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions.

A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ a combined global-local approach in building the approximation. Our framework uses a subset-of-data approach where the subset is a union of a set of global points designed to capture the global trend in the data, and a set of local points specific to a given testing location to capture the local trend around the testing location. The correlation function is also modeled as a combination of a global, and a local kernel. The predictive performance of our framework, which we refer to as TwinGP, is comparable to the state-of-the-art GP modeling methods, but at a fraction of their computational cost.

Partitions for stratified sampling

Abstract Classical jittered sampling partitions [ 0 , 1 ] d {[0,1]^{d}} into m d {m^{d}} cubes for a positive integer m and randomly places a point inside each of them, providing a point set of size N = m d {N=m^{d}} with small discrepancy. The aim of this note is to provide a construction of partitions that works for arbitrary N and improves straight-forward constructions. We show how to construct equivolume partitions of the d-dimensional unit cube with hyperplanes that are orthogonal to the main diagonal of the cube. We investigate the discrepancy of such point sets and optimise the expected discrepancy numerically by relaxing the equivolume constraint using different black-box optimisation techniques.

SatellStitch: Satellite Imagery-Assisted UAV Image Seamless Stitching for Emergency Response without GCP and GNSS

Rapidly stitching unmanned aerial vehicle (UAV) imagery to produce high-resolution fast-stitch maps is key to UAV emergency mapping. However, common problems such as gaps and ghosting in image stitching remain challenging and directly affect the visual interpretation value of the imagery product. Inspired by the data characteristics of high-precision satellite images with rich access and geographic coordinates, a seamless stitching method is proposed for emergency response without the support of ground control points (CGPs) and global navigation satellite systems (GNSS). This method aims to eliminate stitching traces and solve the problem of stitching error accumulation. Firstly, satellite images are introduced to support image alignment and geographic coordinate acquisition simultaneously using matching relationships. Then a dynamic contour point set is constructed to locate the stitching region and adaptively extract the fused region of interest (FROI). Finally, the gradient weight cost map of the FROI image is computed and the Laplacian pyramid fusion rule is improved to achieve seamless production of the fast-stitch image map with geolocation information. Experimental results indicate that the method is well adapted to two representative sets of UAV images. Compared with the Laplacian pyramid fusion algorithm, the peak signal-to-noise ratio (PSNR) of the image stitching results can be improved by 31.73% on average, and the mutual information (MI) can be improved by 19.98% on average. With no reliance on CGPs or GNSS support, fast-stitch image maps are more robust in harsh environments, making them ideal for emergency mapping and security applications.

A reinforcement learning-based temperature control of fluidized bed reactor in gas-phase polyethylene process

This study investigates using deep reinforcement learning (DRL) with proportional-integral-derivative (PID) control for temperature cascade control in a fluidized bed reactor within a commercial gas-phase polyethylene process. The heat exchange system's nonlinearity and frequent disturbances pose challenges for PID controllers, particularly under varying conditions. To address this, a PID-DRL cascade control scheme is developed, where a DRL controller is used in the secondary loop. The DRL controller, designed using the actor-critic framework, is trained using the Deep Deterministic Policy Gradient algorithm. The DRL controller is evaluated in three stand-alone secondary loop experiments, as well as three cascade control experiments. Results reveal the DRL controller surpass the traditional PID controller in both scenarios. The DRL controller shows better set point tracking and interference suppression, indicated by lower integral absolute error (IAE) values. The proposed cascade control structure can be used to enhance reactor stability and product quality in gas-phase polyethylene processes.

Advanced plant-wide control design tools applied to the fluid catalytic cracker-fractionator benchmark

In this work two advanced multivariable control structure design tools are applied on the recently appeared fluid catalytic cracking (FCC)-fractionator benchmark process. Indeed, the partial least squares-based sum of squared deviations (PLS-based SSD) approach and the control allocation (CA) with measurement combination procedure are proposed here to develop new control policies. The minimally invasive feature of PLS-based SSD, allows to obtain an open-loop steady-state model of the process by using closed-loop normal data and to perform a performance/feasibility assessment of the already installed control structure. In this regard, the procedure identified some global integrity problems of the industrial-based control structure proposed in previous works and, therefore, new plant-wide control structures (with different sizing and input/output pairings) were proposed, where the SSD indexes have improved in the range of 50% to 90% and the matrix conditioning guaranteed. The proposed control structures were dynamically tested under typical set point and disturbance variations.

Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.

SPECTRAL PROPERTIES AND INVERSE NODAL PROBLEMS FOR SINGULAR DIFFUSION EQUATION

In this study, some properties for the pencils of singular Sturm-Liouville operators are investigated. Firstly, the behaviors of eigenvalues were learned, then the solutions of the inverse problem were given to determine the potential function and parameters of the boundary condition with the help of a dense set of nodal points and lastly we obtain a constructive solution to the inverse problems of this class.

The Spherical Cap Discrepancy of Healpix Points

In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of the unit 2-sphere is lower and upper bounded by order square root of the number of points, and compute explicit constants. This adds to the currently known (short) collection of explicitly constructed sets whose discrepancy converges with order 𝑁−1/2, matching the asymptotic order for i.i.d. random point sets. We describe the HEALPix framework in more detail and give explicit formulas for the boundaries and pixel centers. We then introduce the notion of an 𝑛-convex curve and prove an upper bound on how many fundamental domains are intersected by such curves, and in particular we show that boundaries of spherical caps have this property. Lastly, we mention briefly that a jittered sampling technique works in the HEALPix framework as well.

Paracrine signalling by pancreatic δ cells determines the glycaemic set point in mice.

While pancreatic β and α cells are considered the main drivers of blood glucose homeostasis through insulin and glucagon secretion, the contribution of δ cells and somatostatin (SST) secretion to glucose homeostasis remains unresolved. Here we provide a quantitative assessment of the physiological contribution of δ cells to the glycaemic set point in mice. Employing three orthogonal mouse models to remove SST signalling within the pancreas or transplanted islets, we demonstrate that ablating δ cells or SST leads to a sustained decrease in the glycaemic set point. This reduction coincides with a decreased glucose threshold for insulin response from β cells, leading to increased insulin secretion to the same glucose challenge. Our data demonstrate that β cells are sufficient to maintain stable glycaemia and reveal that the physiological role of δ cells is to provide tonic feedback inhibition that reduces the β cell glucose threshold and consequently lowers the glycaemic set point in vivo.

A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels.

Minimally sufficient experimental design using identifiability analysis

Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data.

Sleep restores an optimal computational regime in cortical networks.

Sleep is assumed to subserve homeostatic processes in the brain; however, the set point around which sleep tunes circuit computations is unknown. Slow-wave activity (SWA) is commonly used to reflect the homeostatic aspect of sleep; although it can indicate sleep pressure, it does not explain why animals need sleep. This study aimed to assess whether criticality may be the computational set point of sleep. By recording cortical neuron activity continuously for 10-14 d in freely behaving rats, we show that normal waking experience progressively disrupts criticality and that sleep functions to restore critical dynamics. Criticality is perturbed in a context-dependent manner, and waking experience is causal in driving these effects. The degree of deviation from criticality predicts future sleep/wake behavior more accurately than SWA, behavioral history or other neural measures. Our results demonstrate that perturbation and recovery of criticality is a network homeostatic mechanism consistent with the core, restorative function of sleep.

Dissecting the rationale for thromboprophylaxis in challenging surgical cases

Pulmonary embolism (PE) is a leading preventable cause of death in surgical patients, and rates of fatal PE are increasing. Individual assessment, to balance the risks of thrombosis and bleeding, is the key to providing appropriate prophylaxis. The risk assessment process includes use of evidence-based guidelines, literature published since the latest guidelines, large registries, and risk scoring systems together with clinical experience and judgment. Risk assessment is a dynamic process and needs to be updated both during the hospital stay and just prior to discharge since clinical events may change the level of risk. The final assessment may identify patients who require ongoing anticoagulant prophylaxis after discharge. The Caprini risk score is widely used in surgical patients and is a composite of the number of risk factors and their relative weights. The Caprini risk score set point for risk levels requiring anticoagulant prophylaxis varies depending on the type of surgical procedure, surgical population, and number of risk factors. Mandatory implementation of evidence-based care pathways is helpful in lowering PE-related mortality. This review presents several challenging cases, emphasizing the importance of employing all available assessment tools, including dynamic assessment of risk during hospitalization. Finally, the limitations of evidence-based guidelines in complex scenarios and the need to employ all available tools to properly protect very high–risk patients are emphasized.