Discrete Points Research Articles

A curved layering algorithm based on voxelization and geodesic distance for robotic GMA additive manufacturing

ABSTRACT Curved layering has become one of the current research hotspots for its unique advantages. In order to improve the adaptability and accuracy, this paper proposes a new curved layering and path planning algorithm based on voxelization and geodesic distance. High density discrete points are used to approximate the shortest path, voxelization and new optimized search algorithm are adopted to obtain the geodesic distance field within stereolithography (STL) model. Curved layers are formed from points with equal geodesic distance values. The developed algorithm overcomes the limitations of the existing facet offsetting method. Moreover, robot positioner angle planning strategies are exploited to achieve good formation for support-free curved layers of spatial overhang characteristics. The results of comparative analysis and verification experiment indicate that the algorithm accuracy is not affected by the size and intersection angle of the triangles, satisfies the high-precision requirements for parts with curved surface in robotic GMA additive manufacturing.

A transformer model for cause-specific hazard prediction

BackgroudModelling discrete-time cause-specific hazards in the presence of competing events and non-proportional hazards is a challenging task in many domains. Survival analysis in longitudinal cohorts often requires such models; notably when the data is gathered at discrete points in time and the predicted events display complex dynamics. Current models often rely on strong assumptions of proportional hazards, that is rarely verified in practice; or do not handle sequential data in a meaningful way. This study proposes a Transformer architecture for the prediction of cause-specific hazards in discrete-time competing risks. Contrary to Multilayer perceptrons that were already used for this task (DeepHit), the Transformer architecture is especially suited for handling complex relationships in sequential data, having displayed state-of-the-art performance in numerous tasks with few underlying assumptions on the task at hand.ResultsUsing synthetic datasets of 2000–50,000 patients, we showed that our Transformer model surpassed the CoxPH, PyDTS, and DeepHit models for the prediction of cause-specific hazard, especially when the proportional assumption did not hold. The error along simulated time outlined the ability of our model to anticipate the evolution of cause-specific hazards at later time steps where few events are observed. It was also superior to current models for prediction of dementia and other psychiatric conditions in the English longitudinal study of ageing cohort using the integrated brier score and the time-dependent concordance index. We also displayed the explainability of our model’s prediction using the integrated gradients method.ConclusionsOur model provided state-of-the-art prediction of cause-specific hazards, without adopting prior parametric assumptions on the hazard rates. It outperformed other models in non-proportional hazards settings for both the synthetic dataset and the longitudinal cohort study. We also observed that basic models such as CoxPH were more suited to extremely simple settings than deep learning models. Our model is therefore especially suited for survival analysis on longitudinal cohorts with complex dynamics of the covariate-to-outcome relationship, which are common in clinical practice. The integrated gradients provided the importance scores of input variables, which indicated variables guiding the model in its prediction. This model is ready to be utilized for time-to-event prediction in longitudinal cohorts.

Reconstruction of measurement data with multiple outliers using novel domain-based RBF

Due to the high accuracy of computation, radial basis function (RBF) is widely recognized as a versatile and effective method for interpolating and approximating discrete points in various fields. However, RBF is quite sensitive to outliers, which can easily lead to distorted results. In this article, a novel overlapped domain-based RBF (ODRBF) method is proposed, in which the concept of effective domain is introduced to build a moving model, and Student’s t-regression and Gaussian mixture model (GMM) clustering are used for dealing with local anomalies. By introducing the effective domain, the estimated points and domain radius are constructed and the global model can be transformed into local estimation models. In each effective domain, a series of estimation models are iteratively generated through Student’s t-regression, and based on the distances between the estimation model and discrete points, GMM clustering is used to subsequently select the data as the input of the next regression. This iterative strategy in each effective domain ensures the removal of multiple outliers. Then, the preserved points in the processed effective domain are used to obtain local estimated value by RBF. The proposed method demonstrates strong robustness to highly contaminated dataset in the reconstruction of the simulation and experimental datasets.

Active control and prediction model for the dynamic shape of laminated plate/shell structures with piezoelectric actuators

This study establishes an active control and prediction model for the dynamic shape of laminated plates/shells with piezoelectric actuators. Firstly, transient responses of shell structures are numerically calculated by adopting the finite element method (FEM) and the Newmark formulae, then the Kuhn-Tucker equation is utilized to get the time-varying voltage values with a minimum shape control error. Subsequently, a backpropagation neural network (BPNN) is constructed to predict the control precision for cases with different piezoelectric actuator layouts. Finally, the proposed control model is demonstrated through numerical examples with a maximum relative control error of only 0.023% for a given desired shape and the average error of the prediction model with 98 input neurons is 18%, thereby satisfying the application requirements. Furthermore, for a model with 3870 degrees of freedom and 21 discrete time points, the computational time is reduced significantly from 8.24 s to 0.002 s through the prediction model, making it highly suitable for optimization problems by utilizing heuristic algorithms.

Optimization method to construct multiple acoustic vortices for holograms

In this study, the novel optimization method of holograms based on spin density is developed by introducing a new degree of freedom—spin angular momentum density into the direct search method. This approach leverages the programmability of numerous pixels in holograms and eliminates the need for meticulous management of amplitude and phase at discrete points, facilitating the construction of multiple first-order acoustic vortices. We efficiently construct a pattern of 40 vortices within a plane and vortices with different intensities and structures using this approach. We also illustrate the practical application of our design methodology by showcasing its ability to manipulate particles through the transfer of angular momentum from vortices to particles. This work not only advances our understanding of acoustic vortices but also explore a new degree of freedom in designing holograms, potentially enhancing the capacity of holograms.

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO2 sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

Synthesizing polarization singularity lattices using phase ramps

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

Inter-observer variation of head and foot point selection for subject height determination.

The purpose of this study was to examine factors affecting video analysts' decisions in marking the vertex of the head and foot point and corresponding inter-observer marking variances when conducting height analysis on individuals seen in video. Nineteen video analysts participated in an exercise at the 2022 Ontario Forensic Video Analysts' Association (OFVAA) conference where they were asked to mark the vertex of the head and a corresponding foot point of a "suspect" on extracted video frames in a variety of positions and with different headwear (no headwear, baseball cap, and hoodie). A height scale with discrete marking points located at the same positions as where the suspect was positioned was also included in a separate image set, offering a comparison to the suspect. Marked points for all analysts were overlayed onto the respective image frame for visual observations. Summary statistics were used for data interpretation. This study demonstrated that factors such as the suspect's proximity to the camera and suspect's headwear affected the variability and range of marking, which has a direct correlation to the estimated height of the suspect. In general, when the region to be marked was larger, the variability was also larger. This study also demonstrates that marking errors were significantly reduced when discrete marking locations were present such as on a height scale. The average percentage difference of height was most notable, approximately 3%, when the suspect was wearing a hoodie and was at a position closest to the camera. The range of the percentage difference was also the highest at this position, which was 10.6%. In comparison, the height scale had a maximum percent height difference of 0.6% at position D-5, the furthest position from the camera. The range at this location was approximately 2%, which was also the highest range value for the height scale. Future studies should consider suspect posture and look at how these errors may be minimized by examining the best locations to mark the head and foot points under different scenarios.

Tracking Fibrinolysis of Chandler Loop-Formed Whole Blood Clots Under Shear Flow in An In-Vitro Thrombolysis Model.

Thromboembolism and related complications are a leading cause of morbidity and mortality worldwide and various assays have been developed to test thrombolytic drug efficiency both in vitro and in vivo. There is increasing demand for more physiologically relevant in-vitro clot models for drug development due to the complexity and cost associated with animal models in addition to their often lack of translatability to human physiology. Flow, pressure, and shear rate are important characteristics of the circulatory system, with clots that are formed under flow displaying different morphology and digestion characteristics than statically formed clots. These factors are often unrepresented in conventional in-vitro clot digestion assays, which can have pharmacological implications that impact drug translational success rates. The Real-Time Fluorometric Flowing Fibrinolysis (RT-FluFF) assay was developed as a high-fidelity thrombolysis testing platform that uses fluorescently tagged clots formed under shear flow, which are then digested using circulating plasma in the presence or absence of fibrinolytic pharmaceutical agents. Modifying the flow rates of both clot formation and clot digestion steps allows the system to imitate arterial, pulmonary, and venous conditions across highly diverse experimental setups. Measurements can be taken continuously using an in-line fluorometer or by taking discrete time points, as well as a conventional end point clot mass measurement. The RT-FluFF assay is a flexible system that allows for the real-time tracking of clot digestion under flow conditions that more accurately represent in-vivo physiological conditions while retaining the control and reproducibility of an in-vitro testing system.

A novel experimental vignette methodology: SMART vignettes

We motivate and present the methodology of vignette studies. The primary contribution of this paper is our proposal of a novel vignette study design: “SMART vignettes.” Our design has two notable features: the first is its use of sequential randomization, which conceptually originates from the sequential multiple assignment randomization trial (SMART) design developed by Murphy (2004). The second feature is adaptive allocation. These new features in vignette studies offer unique advantages not offered by traditional vignettes: (1) valid causal inferences on the conditional distributions of the primary outcome of interest, given other factors, (2) balanced allocations across groups, and (3) a greater degree of interactivity for the survey respondent. We illustrate the utility of our method using a case example of a vignette study used to probe physicians’ attitudes toward an AI-embedded clinical system. In this example, a SMART vignette was used to randomize hypothetical scenarios to gain a better understanding of the causal impact of physician attitudes, given emerging evidence that a range of factors including previous decisions, play a role in influencing clinical decisions. We simulated hypothetical vignette studies under both SMART and conventional (i.e. single randomization at baseline) designs. We varied the number of factors for each study and fixed each factor to have two levels. Relative loss was used to compare the degree of imbalance between groups. Both designs had smaller relative losses with larger sample sizes. The SMART study design had lower loss than its conventional counterpart for all values of [Formula: see text] for all studies, indicating better balance. As demonstrated by the relative loss in our simulations, our proposed SMART vignette design has an advantage over the conventional design. This method holds promise in generating new knowledge in decision making scenarios occurring over multiple and discrete time points.

Model Predictive Control for Trajectory Planning Considering Constraints on Vertical Load Variation

To address the issue of centrifugal force affecting the vertical load during the stability and trajectory planning of autonomous vehicles during high-speed cornering and obstacle avoidance, a model predictive control of trajectory planning and tracking is proposed that considers the roll factor using only a two-degrees-of-freedom vehicle dynamics model. Firstly, a trajectory planning controller is designed. As a predictive model, a dual-track two-degrees-of-freedom vehicle dynamics model is established. This model describes the relationship between tire lateral forces and vertical loads using a quadratic nonlinear tire model. To reflect the actual dynamic state of the vehicle, the controller incorporates a nonlinear constraint that considers vertical load variations. The nonlinear optimization problem is transformed into a simplified quadratic programming problem by using the Jacobian matrix method to linearize the constraints. By fitting a fourth-degree polynomial curve to the discrete points calculated by the replanning algorithm, an optimal collision-free trajectory is obtained. Secondly, an MPC trajectory tracking controller is designed to control the vehicle in real time along the optimal trajectory from the planning, incorporating control quantity constraints, control increment constraints, and lateral angle constraints to maintain the vehicle’s motion state. We transform the trajectory tracking control problem into a quadratic programming problem, solving for the optimal control sequence for the autonomous vehicle to track the trajectory, achieving an optimized solution and rolling time domain control. Finally, the effectiveness of the vehicle’s obstacle avoidance planning and tracking under high-speed double-lane-change maneuver conditions is validated using the Simulink simulation platform. The results indicate that the designed planning and tracking controllers effectively improve the obstacle avoidance planning and tracking control for high-speed autonomous vehicles.

On the data assimilation of initial distribution for 2-dimensionalshallow-water equation model

Abstract The utilization of data assimilation (DA) techniques is prevalent in marine meteorology for the purpose of estimating the complete state of the system. This is done to address the practical limitations associated with measurement data, which can only be specified at finite number of discrete points within a limited domain. We develop an efficient DA algorithm to reconstruct the initial state of the shallow-water equations (SWE) within a 2-dimensional rectangular domain using sparse spatial measurement data. Our algorithm takes into account both the complete Coriolis force and the ocean bottom topography in the SWE model, resulting in accurate recovery of the initial status. After establishing the uniqueness of the solution to the nonlinear SWE with appropriate boundary conditions, we proceed to establish the conservation laws for the suitably defined energy quantity for this traveling wave system. This generalization of the known conservation laws for the simplified SWE system, which ignores the Coriolis force and topography, allows us to reveal the influence of nonconstant sea floor topography on wave propagation. In order to restore the initial state through the minimization of a cost functional using DA techniques, we proceed by deriving the adjoint problem for our iteration process. Additionally, we establish a discrete scheme for the governing equations in the Arakawa C-grid framework, from which we rigorously derive the error associated with energy conservation in discrete form. The numerical implementations are also provided to validate our proposed scheme through the verification of energy conservation and the reconstruction effect of the initial state for various configurations.

Dynamic stability and control of vortex induced oscillations of tension leg platform tethers

Dynamic stability and control of sway oscillations of Tension Leg Platform (TLP) tether under regular vortex shedding are investigated. The TLP is modelled as a single degree of freedom simply supported uniform beam under pretension, assuming transverse oscillation to take place only in its fundamental natural mode. The tether is subjected to parametric excitation due to the heave motion of the TLP. The incremental harmonic balance (IHB) method is employed to investigate the period-1 and period-2 responses of the TLP as a function of the detuning parameter. The same system is then investigated under time-delayed state feedback control. Suitable control parameters are selected from the analysis of the local stability of the system equilibrium. The stability of solutions is analyzed by the semidiscretization method with the modified Floquet theory. The stable and periodic responses obtained by the IHB method are verified by directly integrating the equation of motion using the fifth-order Runge-Kutta algorithm at discrete points. Finally, the efficacy of the control scheme has been investigated in the plane of response amplitude versus excitation amplitude. The results show that appropriate selections of control parameters can effectively reduce the response amplitude to a great extent with the improved measure of stability.

Demonstrating a new evaluation method on ReLU based Neural Networks for classification problems

Deep neural networks, which have proven to be effective methods to solve complex problems, can even be applied in decision systems controlling critical processes. However, in such applications the outcomes of the neural network must be checked if it we have a clear understanding regarding the operation of network at given input intervals. The most straightforward, though often computationally expensive approach for this checking process evaluates the network at discrete input points and estimates the expected outputs at the given interval. The present research aims to develop a novel approach that can identify in the case of specific input intervals whether the operation process and the output of a neural network can be considered as known or unknown. During the presented case study, we investigated the ReLU (Rectified Linear Unit) and Sigmoid activation functions, using the double moon and the Banknote Authentication classification problems for demonstration.Our method can be applied to identify certain input intervals where the given neural network cannot support critical decisions. The evaluation is performed based on a nonlinear system of equations and inequalities built on arbitrary continuous activation functions. To define the critical intervals of the input variables (i.e. where the decision-making system should not be relied on), those input variable combinations are identified which result in a non-expected output value. This inverse logic is intended to identify intervals of the input variables where the response of the system and the correct decision are not identical. The presented demonstration examples supported our assumption that the number of the neurons and the dimension of the decision space have a significant impact on the complexity of the evaluation process.

Emergent Properties in Chemistry - Relating Molecular Properties to Bulk Behavior.

Certain properties of an object only emerge when a sufficient number of those objects are present in a definite arrangement. For example, one or two water molecules cannot said to be in a liquid state, but a drop of water can be. This concept of emergence has been studied extensively, but only occasionally discussed explicitly in the context of chemistry. In this paper, we aim to show the fruitfulness of the concept of emergence for chemical inquiry by considering four case studies of emergent chemical properties, i. e., the liquidity and freezing of water, structural properties of crystals, thermodynamical phase transitions and quantum mechanical phenomena. We show that some of these properties emerge gradually, some at discrete points, and some should be taken to emerge only when the number of constituents tends to infinity. We argue that studying the way in which chemical properties emerge presents a useful avenue for research that promises greater insight into the nature of those properties.

Joint extension speed dictates bio-inspired morphing trajectories for optimal longitudinal flight dynamics.

Avian wing morphing allows dynamic, active control of complex flight manoeuvres. Previous linear time-invariant (LTI) models have quantified the effect of varying fixed wing configurations but the time-dependent effects of morphing between different configurations is not well understood. To fill this gap, I implemented a linear parameter-varying (LPV) model for morphing wing gull flight. This approach models the wing joint angles as scheduled parameters and accounts for nonlinear kinematic and gravitational effects while interpolating between LTI models at discrete trim points. With the resulting model, I investigated the longitudinal response associated with various joint extension trajectories. By optimizing the extension trajectory for four independent objectives (speed and pitch angle overshoot, speed rise time and pitch angle settling time), I found that the extension trajectory inherent to the gull wing does not guarantee an optimal response but may provide a sufficient response with a simpler mechanical implementation. Furthermore, the results indicated that gulls likely require extension speed feedback. This morphing LPV model provides insights into underlying control mechanisms, which may allow for avian-like flight in future highly manoeuvrable uncrewed aerial vehicles.

Mild exercise expedites joint clearance and slows joint degradation in a joint instability model of osteoarthritis in male rats

ObjectiveExercise remains a hallmark treatment for post-traumatic osteoarthritis (PTOA) and may maintain joint homeostasis in part by clearing inflammatory cytokines, cells, and particles. It remains largely unknown whether exercise-induced joint clearance can provide therapeutic relief of PTOA. In this study, we hypothesized that exercise could slow progression of preclinical PTOA in part by enhancing knee joint clearance. DesignSurgical medial meniscal transection was used to induce PTOA in 3-month-old male Lewis rats. A sham surgery was used as a control. Mild treadmill walking was introduced 3 weeks post-surgery and maintained to 6 weeks post-surgery. Gait and isometric muscle torque were measured at the study endpoint. Near-infrared imaging tracked how exercise altered lymphatic and venous knee joint clearance during discrete time points of PTOA progression. ResultsExercise mitigated joint degradation associated with PTOA by preserving glycosaminoglycan content and reducing osteophyte volume (effect size (95% CI); 1.74 (0.71-2.26). PTOA increased hind step widths (0.57 (0.18-0.95) cm), but exercise corrected this gait dysfunction (0.54 (0.16-0.93) cm), potentially indicating pain relief. Venous, but not lymphatic, clearance was quicker 1-, 3-, and 6-weeks post-surgery compared to baseline. The mild treadmill walking protocol expedited lymphatic clearance rate in moderate PTOA (3.39 (0.20-6.59) hrs), suggesting exercise may play a critical role in restoring joint homeostasis. ConclusionsWe conclude that mild exercise has the potential to slow disease progression in part by expediting joint clearance in moderate PTOA.

EVALUATION OF DIFFERENT INTERPOLATION METHODS VIA ArcGIS, APPLIED TO SATELLITE DATA OF SEA SURFACE TEMPERATURE SST, CASE OF THE ALBORAN SEA

In various fields such as Oceanography, interpolation methods are pivotal in generating continuous surface data from discrete point data. This research endeavors to conduct a comprehensive comparison and evaluation of deterministic interpolation techniques, including Radial Basis Function (RBF), Inverse Distance Weighting (IDW), and geostatistical methods like Kriging Universal (KU) and Kriging Ordinary (KO), in the context of mapping sea surface temperature (SST) within the Alboran Sea. Among these methods, the KO interpolation method emerges as particularly promising, boasting a Root Mean Square Error (RMSE) of 0.035 and an impressive coefficient of determination (R²) approaching unity (0.999). Furthermore, the cross-validation results reveal that the KO method not only provides the most accurate estimates but exhibits minimal bias, as evidenced by a mean error close to zero. These findings not only contribute to the field of SST mapping but also have broader implications for the interpolation of other climate parameters.

Flow prediction of heterogeneous nanoporous media based on physical information neural network

The simulation and prediction of fluid flow in porous media play a profoundly significant role in today's scientific and engineering domains, particularly in gaining a deeper understanding of phenomena such as the migration and fluid flow in underground rock formations and the enhancement of oil recovery rates. The flow of fluids in nanoscale porous media requires consideration of the effects of microscale phenomena, which are challenging to accurately describe using traditional physical models. Currently, research in deep learning for porous media predominantly focuses on conventional porous media, and there is an urgent need for investigations into heterogeneous nanoporous media. Simultaneously, there is a necessity to overcome the limitations of traditional data-driven models lacking physical prior knowledge. Therefore, the integration of physics-informed neural networks, which combine deep learning with physical principles, becomes essential for inferring relatively accurate results from sparse data. In this work, based on the heterogeneity of porous media in shale, we have introduced a deep learning model that couples physical information to predict the flow in heterogeneous nanoscale porous media. In the Physical Information Neural Network model, we utilize point clouds and couple them with deep residual networks. Discrete sampling points are used as inputs, and a multi-level residual connection, along with dimension concatenation, is employed to fuse feature information. The network, through backpropagation, takes into account the Navier-Stokes equations and wall conditions in heterogeneous nanoscale porous media. The results indicate that the apparent permeability and pressure field accuracy are over 90% and 95%, respectively. The Physical Information Neural Network demonstrates promising prospects for predicting flow in nanoscale porous media. Future work will extend to the multiphase complex flow in three-dimensional porous media.

A novel technique for minimizing energy functional using neural networks

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system’s energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system’s energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN’s effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Moreover, the paper explores the minimization of the elastic bending energy with an area constraint.