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Designing cable harnesses can be time-consuming and complex due to many design and manufacturing aspects and rules. Automating the design process can help to fulfil these rules, speed up the process, and optimize the design. To accommodate this, we formulate a harness routing optimization problem to minimize cable lengths, maximize bundling by rewarding shared paths, and optimize the cables' spatial location with respect to case-specific information of the routing environment, e.g., zones to avoid. A deterministic and computationally effective cable harness routing algorithm has been developed to solve the routing problem and is used to generate a set of cable harness topology candidates and approximate the Pareto front. Our approach was tested against a stochastic and an exact solver and our routing algorithm generated objective function values better than the stochastic approach and close to the exact solver. Our algorithm was able to find solutions, some of them being proven to be near-optimal, for three industrial-sized 3D cases within reasonable time (in magnitude of seconds to minutes) and the computation times were comparable to those of the stochastic approach.

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A technique that allows a formation-enforcing control (FEC) derived from graph rigidity theory to interface with a realistic relative localization system onboard lightweight Unmanned Aerial Vehicles (UAVs) is proposed in this paper. The proposed methodology enables reliable real-world deployment of UAVs in tight formation using real relative localization systems burdened by non-negligible sensory noise, which is typically not fully taken into account in FEC algorithms. The proposed solution is based on decomposition of the gradient descent-based FEC command into interpretable elements, and then modifying these individually based on the estimated distribution of sensory noise, such that the resulting action limits the probability of overshooting the desired formation. The behavior of the system has been analyzed and the practicality of the proposed solution has been compared to pure gradient-descent in real-world experiments where it presented significantly better performance in terms of oscillations, deviation from the desired state and convergence time.

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather restrictive modelling assumptions or involve intricate algorithms for posterior inference, thus preventing their widespread use. In response to these challenges, we present a flexible, versatile, and computationally tractable model for density regression based on a single-weights dependent Dirichlet process mixture of normal distributions model for univariate continuous responses. We assume an additive structure for the mean of each mixture component and incorporate the effects of continuous covariates through smooth nonlinear functions. The key components of our modelling approach are penalised B-splines and their bivariate tensor product extension. Our proposed method also seamlessly accommodates parametric effects of categorical covariates, linear effects of continuous covariates, interactions between categorical and/or continuous covariates, varying coefficient terms, and random effects, which is why we refer our model as a Dirichlet process mixture of normal structured additive regression models. A noteworthy feature of our method is its efficiency in posterior simulation through Gibbs sampling, as closed-form full conditional distributions for all model parameters are available. Results from a simulation study demonstrate that our approach successfully recovers true conditional densities and other regression functionals in various challenging scenarios. Applications to a toxicology, disease diagnosis, and agricultural study are provided and further underpin the broad applicability of our modelling framework. An R package, \texttt{DDPstar}, implementing the proposed method is publicly available at \url{//bitbucket.org/mxrodriguez/ddpstar}.

Memory constraint of always-on devices is one of the major concerns when deploying speech processing models on these devices. While larger models trained with sufficiently large amount of data generally perform better, making them fit in the device memory is a demanding challenge. In this paper, we aim to reduce model size by reparameterizing model weights across Transformer encoder layers and assuming a special weight composition and structure. More specifically, inspired by ResNet and the more recent LoRA work, we propose an approach named ResidualTransformer, where each weight matrix in a Transformer layer comprises 1) a shared full-rank component with its adjacent layers, and 2) a unique low-rank component to itself. The low-rank matrices only account for a small amount of model size increase. In addition, we add diagonal weight matrices to improve modeling capacity of the low-rank matrices. Experiments of our 10k-hour speech recognition and speech translation tasks show that the Transformer encoder size can be reduced by ~3X with very slight performance degradation.

Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data-driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to estimation of inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the Discrete Cosine Transform (DCT) is proposed. The method is implemented in the R package vstdct that accompanies the paper.

Inter-organizational business processes involve multiple independent organizations collaborating to achieve mutual interests. Process mining techniques have the potential to allow these organizations to enhance operational efficiency, improve performance, and deepen the understanding of their business based on the recorded process event data. However, inter-organizational process mining faces substantial challenges, including topical secrecy concerns: The involved organizations may not be willing to expose their own data to run mining algorithms jointly with their counterparts or third parties. In this paper, we introduce CONFINE, a novel approach that unlocks process mining on multiple actors' process event data while safeguarding the secrecy and integrity of the original records in an inter-organizational business setting. To ensure that the phases of the presented interaction protocol are secure and that the processed information is hidden from involved and external actors alike, our approach resorts to a decentralized architecture comprised of trusted applications running in Trusted Execution Environments (TEEs). We show the feasibility of our solution by showcasing its application to a healthcare scenario and evaluating our implementation in terms of memory usage and scalability on real-world event logs.

Quasiperiodic systems, related to irrational numbers, are space-filling structures without decay nor translation invariance. How to accurately recover these systems, especially for non-smooth cases, presents a big challenge in numerical computation. In this paper, we propose a new algorithm, finite points recovery (FPR) method, which is available for both smooth and non-smooth cases, to address this challenge. The FPR method first establishes a homomorphism between the lower-dimensional definition domain of the quasiperiodic function and the higher-dimensional torus, then recovers the global quasiperiodic system by employing interpolation technique with finite points in the definition domain without dimensional lifting. Furthermore, we develop accurate and efficient strategies of selecting finite points according to the arithmetic properties of irrational numbers. The corresponding mathematical theory, convergence analysis, and computational complexity analysis on choosing finite points are presented. Numerical experiments demonstrate the effectiveness and superiority of FPR approach in recovering both smooth quasiperiodic functions and piecewise constant Fibonacci quasicrystals. While existing spectral methods encounter difficulties in accurately recovering non-smooth quasiperiodic functions.

The present work is devoted to strong approximations of a generalized Ait-Sahalia model arising from mathematical finance. The numerical study of the considered model faces essential difficulties caused by a drift that blows up at the origin, highly nonlinear drift and diffusion coefficients and positivity-preserving requirement. In this paper, a novel explicit Euler-type scheme is proposed, which is easily implementable and able to preserve positivity of the original model unconditionally, i.e., for any time step-size h>0. A mean-square convergence rate of order 0.5 is also obtained for the proposed scheme in both non-critical and general critical cases. Our work is motivated by the need to justify the multi-level Monte Carlo (MLMC) simulations for the underlying model, where the rate of mean-square convergence is required and the preservation of positivity is desirable particularly for large discretization time steps. To the best of our knowledge, this is the first paper to propose an unconditionally positivity preserving explicit scheme with order 1/2 of mean-square convergence for the model. Numerical experiments are finally provided to confirm the theoretical findings.

This study aims to acquire knowledge for creating very large language models that are immune to hallucinations. Hallucinations in contemporary large language models are often attributed to a misunderstanding of real-world social relationships. Therefore, I hypothesize that very large language models capable of thoroughly grasping all these relationships will be free from hallucinations. Additionally, I propose that certain types of equivariant language models are adept at learning and understanding these relationships. Building on this, I have developed a specialized cross-entropy error function to create a hallucination scale for language models, which measures their extent of equivariance acquisition. Utilizing this scale, I tested language models for their ability to acquire character-level equivariance. In particular, I introduce and employ a novel technique based on T5 (Text To Text Transfer Transformer) that efficiently understands permuted input texts without the need for explicit dictionaries to convert token IDs (integers) to texts (strings). This T5 model demonstrated a moderate ability to acquire character-level equivariance. Additionally, I discovered scale laws that can aid in developing hallucination-free language models at the character level. This methodology can be extended to assess equivariance acquisition at the word level, paving the way for very large language models that can comprehensively understand relationships and, consequently, avoid hallucinations.

Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.

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