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We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are modeled by an undirected graph $G$, in which compatible jobs are represented by adjacent vertices. We show that several subproblems are polynomial. We propose some exact polynomial algorithms to solve these subproblems. To solve the general case, we propose a mixed-integer linear programming (MILP) formulation alongside with heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods.

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoretical and applied points of view.

Recent architectural developments have enabled recurrent neural networks (RNNs) to reach and even surpass the performance of Transformers on certain sequence modeling tasks. These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers. By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers. Our findings highlight the importance of multiplicative interactions in neural networks and suggest that certain RNNs might be unexpectedly implementing attention under the hood.

We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general port-Hamiltonian systems with possibly state-dependent system matrices. We prove well-posedness of these systems and characterize optimal controls by the first-order optimality system, which is the starting point for the derivation of an adjoint-based gradient descent algorithm. Our theoretical analysis is complemented by a proof of concept, where we apply the proposed algorithm to static minimum cost flow problems and dynamic minimum cost flow problems on a simple directed acyclic graph. We present numerical results to validate the approach.

Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression under a multivariate Gaussian prior distribution. Adapting more general derivations in Anceschi et al. (2023), we show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine having a per-iteration cost that scales linearly in the number of covariates. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.

Distributed averaging is among the most relevant cooperative control problems, with applications in sensor and robotic networks, distributed signal processing, data fusion, and load balancing. Consensus and gossip algorithms have been investigated and successfully deployed in multi-agent systems to perform distributed averaging in synchronous and asynchronous settings. This study proposes a heuristic approach to estimate the convergence rate of averaging algorithms in a distributed manner, relying on the computation and propagation of local graph metrics while entailing simple data elaboration and small message passing. The protocol enables nodes to predict the time (or the number of interactions) needed to estimate the global average with the desired accuracy. Consequently, nodes can make informed decisions on their use of measured and estimated data while gaining awareness of the global structure of the network, as well as their role in it. The study presents relevant applications to outliers identification and performance evaluation in switching topologies.

Timely response of Network Intrusion Detection Systems (NIDS) is constrained by the flow generation process which requires accumulation of network packets. This paper introduces Multivariate Time Series (MTS) early detection into NIDS to identify malicious flows prior to their arrival at target systems. With this in mind, we first propose a novel feature extractor, Time Series Network Flow Meter (TS-NFM), that represents network flow as MTS with explainable features, and a new benchmark dataset is created using TS-NFM and the meta-data of CICIDS2017, called SCVIC-TS-2022. Additionally, a new deep learning-based early detection model called Multi-Domain Transformer (MDT) is proposed, which incorporates the frequency domain into Transformer. This work further proposes a Multi-Domain Multi-Head Attention (MD-MHA) mechanism to improve the ability of MDT to extract better features. Based on the experimental results, the proposed methodology improves the earliness of the conventional NIDS (i.e., percentage of packets that are used for classification) by 5x10^4 times and duration-based earliness (i.e., percentage of duration of the classified packets of a flow) by a factor of 60, resulting in a 84.1% macro F1 score (31% higher than Transformer) on SCVIC-TS-2022. Additionally, the proposed MDT outperforms the state-of-the-art early detection methods by 5% and 6% on ECG and Wafer datasets, respectively.

This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential equations (PDEs) are reformulated into boundary integral equations and are then solved with the matrix-free generalized minimal residual (GMRES) method. The evaluation of boundary integrals is performed by solving equivalent and simple interface problems with finite difference methods, allowing the use of fast PDE solvers, such as fast Fourier transform (FFT) and geometric multigrid methods. The interface curve is evolved utilizing the $\theta-L$ variables instead of the more commonly used $x-y$ variables. This choice simplifies the preservation of mesh quality during the interface evolution. In addition, the $\theta-L$ approach enables the design of efficient and stable time-stepping schemes to remove the stiffness that arises from the curvature term. Ample numerical examples, including simulations of complex viscous fingering and dendritic solidification problems, are presented to showcase the capability of the proposed method to handle challenging moving interface problems.

Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of data where multiple classification tasks are presented sequentially. This scenario, known as Continual Learning (CL) poses challenges to standard learning algorithms which struggle to maintain knowledge of old tasks while learning new ones. This stability-plasticity dilemma remains central to CL and multiple metrics have been proposed to adequately measure stability and plasticity separately. However, none considers the increasing difficulty of the classification task, which inherently results in performance loss for any model. In that sense, we analyze some limitations of current metrics and identify the presence of setup-induced forgetting. Therefore, we propose new metrics that account for the task's increasing difficulty. Through experiments on benchmark datasets, we demonstrate that our proposed metrics can provide new insights into the stability-plasticity trade-off achieved by models in the continual learning environment.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.