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The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting hierarchical Bayesian models have been shown to be very effective in the recovery of almost piecewise constant solutions in linear inverse problems. We demonstrate that by exploiting linear algebraic considerations it is possible to organize the calculation for the Bayesian solution of the nonlinear EIT inverse problem via finite element methods with sparsity promoting priors in a computationally efficient manner. The proposed approach uses the Iterative Alternating Sequential (IAS) algorithm for the solution of the linearized problems. Within the IAS algorithm, a substantial reduction in computational complexity is attained by exploiting the low dimensionality of the data space and an adjoint formulation of the Tikhonov regularized solution that constitutes part of the iterative updating scheme. Numerical tests illustrate the computational efficiency of the proposed algorithm. The paper sheds light also on the convexity properties of the objective function of the maximum a posteriori (MAP) estimation problem.

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With the development of deep learning technology, the detection and classification of distracted driving behaviour requires higher accuracy. Existing deep learning-based methods are computationally intensive and parameter redundant, limiting the efficiency and accuracy in practical applications. To solve this problem, this study proposes an improved YOLOv8 detection method based on the original YOLOv8 model by integrating the BoTNet module, GAM attention mechanism and EIoU loss function. By optimising the feature extraction and multi-scale feature fusion strategies, the training and inference processes are simplified, and the detection accuracy and efficiency are significantly improved. Experimental results show that the improved model performs well in both detection speed and accuracy, with an accuracy rate of 99.4%, and the model is smaller and easy to deploy, which is able to identify and classify distracted driving behaviours in real time, provide timely warnings, and enhance driving safety.

We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:2105.06173 for discontinuous Galerkin (DG) volume discretizations. We show that the conditions that $kh/p$ be sufficiently small and that $\log(k) / p$ be bounded imply quasi-optimality of both conforming and DG-method, where $k$ is the wavenumber, $h$ the mesh size, and $p$ the approximation order. The analysis relies on a $k$-explicit regularity theory for a three-field coupling formulation.

Due to the effective performance of multi-scale feature fusion, Path Aggregation FPN (PAFPN) is widely employed in YOLO detectors. However, it cannot efficiently and adaptively integrate high-level semantic information with low-level spatial information simultaneously. We propose a new model named MAF-YOLO in this paper, which is a novel object detection framework with a versatile neck named Multi-Branch Auxiliary FPN (MAFPN). Within MAFPN, the Superficial Assisted Fusion (SAF) module is designed to combine the output of the backbone with the neck, preserving an optimal level of shallow information to facilitate subsequent learning. Meanwhile, the Advanced Assisted Fusion (AAF) module deeply embedded within the neck conveys a more diverse range of gradient information to the output layer. Furthermore, our proposed Re-parameterized Heterogeneous Efficient Layer Aggregation Network (RepHELAN) module ensures that both the overall model architecture and convolutional design embrace the utilization of heterogeneous large convolution kernels. Therefore, this guarantees the preservation of information related to small targets while simultaneously achieving the multi-scale receptive field. Finally, taking the nano version of MAF-YOLO for example, it can achieve 42.4% AP on COCO with only 3.76M learnable parameters and 10.51G FLOPs, and approximately outperforms YOLOv8n by about 5.1%. The source code of this work is available at: //github.com/yang-0201/MAF-YOLO.

Implicit visual knowledge in a large latent diffusion model (LLDM) pre-trained on natural images is rich and hypothetically universal to natural and medical images. To test this hypothesis from a practical perspective, we propose a novel framework for undersampled MRI Reconstruction by Prompting a large latent Diffusion model (MRPD). While the existing methods trained on MRI datasets are typically of limited generalizability toward diverse data acquisition scenarios, MRPD supports unsupervised and universally adaptive MRI reconstruction. For unsupervised reconstruction, MRSampler guides LLDM with a random-phase-modulated hard-to-soft control. With any single- or multiple-source MRI dataset, MRPD's performance is boosted universally by a lightweight MRAdapter that only finetunes the LLDM's autoencoder. Experiments on FastMRI and IXI show that MRPD is the only model that supports both MRI database-free and database-available scenarios and attains the best generalizability towards out-of-domain (OOD) samplings, contrasts, and organs among compared unsupervised, supervised, and MRI diffusion methods. To our knowledge, MRPD is the first method that empirically shows the universal prowess of an LLDM pre-trained on vast natural images for MRI. Our official implementation is at //github.com/Z7Gao/MRPD.

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a single-exponential running time. Previously only a doubly-exponential algorithm was known. As an application, we provide a conversion from context-free session types to simple grammars whose valuation is linear in the size of the type. In this way, we provide the first polynomial-time algorithm for deciding context-free session type equivalence.

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be $O(\varepsilon^2)$ when using $N \lesssim \log (1/\varepsilon)$ many JKO steps ($N$ Residual Blocks in the flow) where $\varepsilon $ is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of the JKO-type $W_2$-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest. The analysis framework can extend to other first-order Wasserstein optimization schemes applied to flow-based generative models.

In order to be deployed safely, Large Language Models (LLMs) must be capable of dynamically adapting their behavior based on their level of knowledge and uncertainty associated with specific topics. This adaptive behavior, which we refer to as self-restraint, is non-trivial to teach since it depends on the internal knowledge of an LLM. By default, LLMs are trained to maximize the next token likelihood, which does not teach the model to modulate its answer based on its level of uncertainty. In order to learn self-restraint, we devise a utility function that can encourage the model to produce responses only when it is confident in them. This utility function can be used to score generation of different length and abstention. To optimize this function, we introduce ReSearch, a process of "self-reflection" consisting of iterative self-prompting and self-evaluation. We use the ReSearch algorithm to generate synthetic data on which we finetune our models. Compared to their original versions, our resulting models generate fewer \emph{hallucinations} overall at no additional inference cost, for both known and unknown topics, as the model learns to selectively restrain itself. In addition, our method elegantly incorporates the ability to abstain by augmenting the samples generated by the model during the search procedure with an answer expressing abstention.

Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modelling of extremes has to take into account that feature. In addition, environmental processes are often attached with an angle, e.g., wind speed and direction or extreme snowfall and time of occurrence in year. This article proposes a Bayesian hierarchical model with a conditional independence assumption that aims at modelling simultaneously spatial extremes and an angular component. The proposed model relies on the extreme value theory as well as recent developments for handling directional statistics over a continuous domain. Working within a Bayesian setting, a Gibbs sampler is introduced whose performances are analysed through a simulation study. The paper ends with an application on extreme wind speed in France. Results show that extreme wind events in France are mainly coming from West apart from the Mediterranean part of France and the Alps.

A Variable Parameter (VP) analysis aims to give precise time complexity expressions of algorithms with exponents appearing solely in terms of variable parameters. A variable parameter is the number of objects with specific properties. Here we describe two VP-algorithms, an implicit enumeration and a polynomial-time approximation scheme for a strongly $NP$-hard problem of scheduling $n$ independent jobs with release and due times on one machine to minimize the maximum job completion time $C_{\max}$. Our variable parameters are the amounts of some specially defined types of jobs. A partial solution without these jobs is constructed in a low degree polynomial time, and an exponential time procedure (in the number of variable parameters) is carried out to augment it to a complete optimal solution. In the alternative time complexity expressions, the exponential dependence is solely on the some job parameters. Applying the fixed parameter analysis to these estimations, a polynomial-time dependence is achieved. Both, the intuitive probabilistic estimations and our extensive experimental study support our conjecture that the total number of the variable parameters is far less than $n$ and its ratio to $n$ converges to 0 asymptotically.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

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