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We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters controlling the smoothness and the correlation length of the Gaussian random field. The proposed numerical method relies on the Balakrishnan integral representation of the solution and does not require the approximation of eigenpairs. Rather, it consists of a sinc quadrature coupled with a standard surface finite element method. We provide a complete error analysis of the method and illustrate its performances by several numerical experiments.

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Split Learning (SL) is a promising Distributed Learning approach in electromyography (EMG) based prosthetic control, due to its applicability within resource-constrained environments. Other learning approaches, such as Deep Learning and Federated Learning (FL), provide suboptimal solutions, since prosthetic devices are extremely limited in terms of processing power and battery life. The viability of implementing SL in such scenarios is caused by its inherent model partitioning, with clients executing the smaller model segment. However, selecting an inadequate cut layer hinders the training process in SL systems. This paper presents an algorithm for optimal cut layer selection in terms of maximizing the convergence rate of the model. The performance evaluation demonstrates that the proposed algorithm substantially accelerates the convergence in an EMG pattern recognition task for improving prosthetic device control.

Though a core element of the digital age, numerical difference algorithms struggle with noise susceptibility. This stems from a key disconnect between the infinitesimal quantities in continuous differentiation and the finite intervals in its discrete counterpart. This disconnect violates the fundamental definition of differentiation (Leibniz and Cauchy). To bridge this gap, we build a novel general difference (Tao General Difference, TGD). Departing from derivative-by-integration, TGD generalizes differentiation to finite intervals in continuous domains through three key constraints. This allows us to calculate the general difference of a sequence in discrete domain via the continuous step function constructed from the sequence. Two construction methods, the rotational construction and the orthogonal construction, are proposed to construct the operators of TGD. The construction TGD operators take same convolution mode in calculation for continuous functions, discrete sequences, and arrays across any dimension. Our analysis with example operations showcases TGD's capability in both continuous and discrete domains, paving the way for accurate and noise-resistant differentiation in the digital era.

In black-box optimization, noise in the objective function is inevitable. Noise disrupts the ranking of candidate solutions in comparison-based optimization, possibly deteriorating the search performance compared with a noiseless scenario. Explicit averaging takes the sample average of noisy objective function values and is widely used as a simple and versatile noise-handling technique. Although it is suitable for various applications, it is ineffective if the mean is not finite. We theoretically reveal that explicit averaging has a negative effect on the estimation of ground-truth rankings when assuming stably distributed noise without a finite mean. Alternatively, sign averaging is proposed as a simple but robust noise-handling technique. We theoretically prove that the sign averaging estimates the order of the medians of the noisy objective function values of a pair of points with arbitrarily high probability as the number of samples increases. Its advantages over explicit averaging and its robustness are also confirmed through numerical experiments.

Soft electrohydraulic actuators known as HASEL actuators have attracted widespread research interest due to their outstanding dynamic performance and high output power. However, the displacement of electrohydraulic actuators usually declines with time under constant DC voltage, which hampers its prospective application. A mathematical model is firstly established to not only explain the decrease in displacement under DC voltage but also predict the relatively stable displacement with oscillation under AC square wave voltage. The mathematical model is validated since the actual displacement confirms the trend observed by our model. To smooth the displacement oscillation introduced by AC voltage, a serial elastic component is incorporated to form a SE-HASEL actuator. A feedback control with a proportion-integration algorithm enables the SE-HASEL actuator to eliminate the obstinate displacement hysteresis. Our results revealed that, through our methodology, the SE-HASEL actuator can give stable and smooth displacement and is capable of absorbing external impact disturbance simultaneously. A rotary joint based on the SE-HASEL actuator is developed to reflect its possibility to generate a common rotary motion for wide robotic applications. More importantly, this paper also proposes a highly accurate needle biopsy robot that can be utilized in MRI-guide surgical procedures. Overall, we have achieved AC-driven series elastic electrohydraulic actuators that can exhibit stable and smooth displacement output.

Mechanical metamaterial is a synthetic material that can possess extraordinary physical characteristics, such as abnormal elasticity, stiffness, and stability, by carefully designing its internal structure. To make metamaterials contain delicate local structures with unique mechanical properties, it is a potential method to represent them through high-resolution voxels. However, it brings a substantial computational burden. To this end, this paper proposes a fast inverse design method, whose core is an advanced deep generative AI algorithm, to generate voxel-based mechanical metamaterials. Specifically, we use the self-conditioned diffusion model, capable of generating a microstructure with a resolution of $128^3$ to approach the specified homogenized tensor matrix in just 3 seconds. Accordingly, this rapid reverse design tool facilitates the exploration of extreme metamaterials, the sequence interpolation in metamaterials, and the generation of diverse microstructures for multi-scale design. This flexible and adaptive generative tool is of great value in structural engineering or other mechanical systems and can stimulate more subsequent research.

Background and purpose: The unanticipated detection by magnetic resonance imaging (MRI) in the brain of asymptomatic subjects of white matter lesions suggestive of multiple sclerosis (MS) has been named radiologically isolated syndrome (RIS). As the difference between early MS [i.e. clinically isolated syndrome (CIS)] and RIS is the occurrence of a clinical event, it is logical to improve detection of the subclinical form without interfering with MRI as there are radiological diagnostic criteria for that. Our objective was to use machine-learning classification methods to identify morphometric measures that help to discriminate patients with RIS from those with CIS. Methods: We used a multimodal 3-T MRI approach by combining MRI biomarkers (cortical thickness, cortical and subcortical grey matter volume, and white matter integrity) of a cohort of 17 patients with RIS and 17 patients with CIS for single-subject level classification. Results: The best proposed models to predict the diagnosis of CIS and RIS were based on the Naive Bayes, Bagging and Multilayer Perceptron classifiers using only three features: the left rostral middle frontal gyrus volume and the fractional anisotropy values in the right amygdala and right lingual gyrus. The Naive Bayes obtained the highest accuracy [overall classification, 0.765; area under the receiver operating characteristic (AUROC), 0.782]. Conclusions: A machine-learning approach applied to multimodal MRI data may differentiate between the earliest clinical expressions of MS (CIS and RIS) with an accuracy of 78%. Keywords: Bagging; Multilayer Perceptron; Naive Bayes classifier; clinically isolated syndrome; diffusion tensor imaging; machine-learning; magnetic resonance imaging; multiple sclerosis; radiologically isolated syndrome.

Mobile crowdsourcing refers to systems where the completion of tasks necessarily requires physical movement of crowdworkers in an on-demand workforce. Evidence suggests that in such systems, tasks often get assigned to crowdworkers who struggle to complete those tasks successfully, resulting in high failure rates and low service quality. A promising solution to ensure higher quality of service is to continuously adapt the assignment and respond to failure-causing events by transferring tasks to better-suited workers who use different routes or vehicles. However, implementing task transfers in mobile crowdsourcing is difficult because workers are autonomous and may reject transfer requests. Moreover, task outcomes are uncertain and need to be predicted. In this paper, we propose different mechanisms to achieve outcome prediction and task coordination in mobile crowdsourcing. First, we analyze different data stream learning approaches for the prediction of task outcomes. Second, based on the suggested prediction model, we propose and evaluate two different approaches for task coordination with different degrees of autonomy: an opportunistic approach for crowdshipping with collaborative, but non-autonomous workers, and a market-based model with autonomous workers for crowdsensing.

NeRF's high-quality scene synthesis capability was quickly accepted by scholars in the years after it was proposed, and significant progress has been made in 3D scene representation and synthesis. However, the high computational cost limits intuitive and efficient editing of scenes, making NeRF's development in the scene editing field facing many challenges. This paper reviews the preliminary explorations of scholars on NeRF in the scene or object editing field in recent years, mainly changing the shape and texture of scenes or objects in new synthesized scenes; through the combination of residual models such as GaN and Transformer with NeRF, the generalization ability of NeRF scene editing has been further expanded, including realizing real-time new perspective editing feedback, multimodal editing of text synthesized 3D scenes, 4D synthesis performance, and in-depth exploration in light and shadow editing, initially achieving optimization of indirect touch editing and detail representation in complex scenes. Currently, most NeRF editing methods focus on the touch points and materials of indirect points, but when dealing with more complex or larger 3D scenes, it is difficult to balance accuracy, breadth, efficiency, and quality. Overcoming these challenges may become the direction of future NeRF 3D scene editing technology.

When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to overcome this problem. Often, time periods with constant values even have been counted as times of monotone increase. To overcome this, a new approach is proposed: it explicitly allows for ties and, hence, considers more patterns than before. Ties are no longer seen as nuisance, but to carry valuable information. Limit theorems in the new framework are provided, both, for a single time series and for the dependence between two time series. The methods are used on hydrological data sets. It is common to distinguish five flood classes (plus 'absence of flood'). Considering data vectors of these classes at a certain gauge in a river basin, one will usually encounter several ties. Co-monotonic behavior between the data sets of two gauges (increasing, constant, decreasing) can be detected by the method as well as spatial patterns. Thus, it helps to analyze the strength of dependence between different gauges in an intuitive way. This knowledge can be used to asses risk and to plan future construction projects.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

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