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Due to its computational complexity, graph cuts for cluster detection and identification are used mostly in the form of convex relaxations. We propose to utilize the original graph cuts such as Ratio, Normalized or Cheeger Cut in order to detect clusters in weighted undirected graphs by restricting the graph cut minimization to the subset of $st$-MinCut partitions. Incorporating a vertex selection technique and restricting optimization to tightly connected clusters, we therefore combine the efficient computability of $st$-MinCuts and the intrinsic properties of Gomory-Hu trees with the cut quality of the original graph cuts, leading to linear runtime in the number of vertices and quadratic in the number of edges. Already in simple scenarios, the resulting algorithm Xist is able to approximate graph cut values better empirically than spectral clustering or comparable algorithms, even for large network datasets. We showcase its applicability by segmenting images from cell biology and provide empirical studies of runtime and classification rate.

This paper introduces a rigorous approach to establish the sharp minimax optimalities of both LASSO and SLOPE within the framework of double sparse structures, notably without relying on RIP-type conditions. Crucially, our findings illuminate that the achievement of these optimalities is fundamentally anchored in a sparse group normalization condition, complemented by several novel sparse group restricted eigenvalue (RE)-type conditions introduced in this study. We further provide a comprehensive comparative analysis of these eigenvalue conditions. Furthermore, we demonstrate that these conditions hold with high probability across a wide range of random matrices. Our exploration extends to encompass the random design, where we prove the random design properties and optimal sample complexity under both weak moment distribution and sub-Gaussian distribution.

In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of AM for traditional and new business models enforces the need for efficient planning procedures for AM facilities. In this area, the assignment and sequencing of components to be built by an AM machine, also called a 3D printer, is a complex problem joining the nesting and scheduling of parts to be printed. This paper proposes a new branch-and-cut algorithm for integrated planning for unrelated parallel machines. The algorithm is based on combinatorial Benders decomposition: The scheduling problem is considered in the master problem, while the feasibility of a solution is checked in the sub-problem. Current state-of-the-art techniques are extended to solve the orthogonal packing with rotation to speed up the solution of the sub-problem. Extensive computational tests on existing instances and a new benchmark instance set show the algorithm's superior performance compared to an existing integrated mixed-integer programming model.

This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed proximal-point iteration that admits two complementary interpretations. For models that are smooth or regularised by Moreau-Yosida smoothing, the algorithm is equivalent to an implicit midpoint discretisation of an overdamped Langevin diffusion targeting the posterior distribution of interest. This discretisation is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is $\kappa$-strongly log-concave (i.e., requiring in the order of $\sqrt{\kappa}$ iterations to converge, similarly to accelerated optimisation schemes), comparing favorably to [M. Pereyra, L. Vargas Mieles, K.C. Zygalakis, SIAM J. Imaging Sciences, 13, 2 (2020), pp. 905-935] which is only provably accelerated for Gaussian targets and has bias. For models that are not smooth, the algorithm is equivalent to a Leimkuhler-Matthews discretisation of a Langevin diffusion targeting a Moreau-Yosida approximation of the posterior distribution of interest, and hence achieves a significantly lower bias than conventional unadjusted Langevin strategies based on the Euler-Maruyama discretisation. For targets that are $\kappa$-strongly log-concave, the provided non-asymptotic convergence analysis also identifies the optimal time step which maximizes the convergence speed. The proposed methodology is demonstrated through a range of experiments related to image deconvolution with Gaussian and Poisson noise, with assumption-driven and data-driven convex priors.

The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it through first order optimality conditions. Furthermore, we systematically develop a priori as well as a posteriori error estimates. Our proposed method can be applied to a wide range of constrained optimal control problems subject to, e.g., scalar second-order PDEs and the Stokes equations. Numerical experiments that illustrate our theoretical findings are presented.

The stripe noise existing in remote sensing images badly degrades the visual quality and restricts the precision of data analysis. Therefore, many destriping models have been proposed in recent years. In contrast to these existing models, in this paper, we propose a nonconvex model with a DC function (i.e., the difference of convex functions) structure to remove the strip noise. To solve this model, we make use of the DC structure and apply an inexact proximal majorization-minimization algorithm with each inner subproblem solved by the alternating direction method of multipliers. It deserves mentioning that we design an implementable stopping criterion for the inner subproblem, while the convergence can still be guaranteed. Numerical experiments demonstrate the superiority of the proposed model and algorithm.

We propose a method named AudioFormer,which learns audio feature representations through the acquisition of discrete acoustic codes and subsequently fine-tunes them for audio classification tasks. Initially,we introduce a novel perspective by considering the audio classification task as a form of natural language understanding (NLU). Leveraging an existing neural audio codec model,we generate discrete acoustic codes and utilize them to train a masked language model (MLM),thereby obtaining audio feature representations. Furthermore,we pioneer the integration of a Multi-Positive sample Contrastive (MPC) learning approach. This method enables the learning of joint representations among multiple discrete acoustic codes within the same audio input. In our experiments,we treat discrete acoustic codes as textual data and train a masked language model using a cloze-like methodology,ultimately deriving high-quality audio representations. Notably,the MPC learning technique effectively captures collaborative representations among distinct positive samples. Our research outcomes demonstrate that AudioFormer attains significantly improved performance compared to prevailing monomodal audio classification models across multiple datasets,and even outperforms audio-visual multimodal classification models on select datasets. Specifically,our approach achieves remarkable results on datasets including AudioSet (2M,20K),and FSD50K,with performance scores of 53.9,45.1,and 65.6,respectively. We have openly shared both the code and models: //github.com/LZH-0225/AudioFormer.git.

Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

We propose an end-to-end Automatic Speech Recognition (ASR) system that can be trained on transcribed speech data, text-only data, or a mixture of both. The proposed model uses an integrated auxiliary block for text-based training. This block combines a non-autoregressive multi-speaker text-to-mel-spectrogram generator with a GAN-based enhancer to improve the spectrogram quality. The proposed system can generate a mel-spectrogram dynamically during training. It can be used to adapt the ASR model to a new domain by using text-only data from this domain. We demonstrate that the proposed training method significantly improves ASR accuracy compared to the system trained on transcribed speech only. It also surpasses cascade TTS systems with the vocoder in the adaptation quality and training speed.

Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numerical solution. In detail, the larger the number of matched terms between modified equations for initialisation and bulk methods, the smoother the obtained numerical solution. This is particularly manifest for numerical dissipation. Starting from the constraints to achieve time smoothness, which can quickly become prohibitive for they have to take the parasitic modes into consideration, we explain how the distinct lack of observability for certain lattice Boltzmann schemes -- seen as dynamical systems on a commutative ring -- can yield rather simple conditions and be easily studied as far as their initialisation is concerned. This comes from the reduced number of initialisation schemes at the fully discrete level. These theoretical results are successfully assessed on several lattice Boltzmann methods.