Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices and edges of the graph on the surface (avoiding the obstacles) to remove all crossings; in other words, whether the drawing is homotopic to an embedding. While the problem boils down to planarity testing when the surface is the sphere or the disk (or equivalently the plane without any obstacle), the other cases have never been studied before, except when the input graph is a cycle, in an abundant literature in topology and more recently by Despr\'e and Lazarus [SoCG 2017, J. ACM 2019]. Our algorithm runs in O(m + poly(g+b) n log n) time, where g >= 0 and b >= 0 are the genus and the number of boundary components of the input orientable surface S, and n is the size of the input graph drawing, lying on some fixed graph of size m cellularly embedded on S. We use various techniques from two-dimensional computational topology and from the theory of hyperbolic surfaces. Most notably, we introduce reducing triangulations, a novel discrete analog of hyperbolic surfaces in the spirit of systems of quads by Lazarus and Rivaud [FOCS 2012] and Erickson and Whittlesey [SODA 2013], which have the additional benefit that reduced paths are unique and stable upon reversal; they are likely of independent interest. Tailored data structures are needed to achieve certain homotopy tests efficiently on these triangulations. As a key subroutine, we rely on an algorithm to test the weak simplicity of a graph drawn on a surface by Akitaya, Fulek, and T\'oth [SODA 2018, TALG 2019].

In this paper, we study the problem of gossiping with interference constraint in radio ring networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and algorithms that attain this makespan. We focus on the case where the transmission network is a ring network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We also suppose that, during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover communication is subject to interference constraints. We use a primary node interference model where, if a node receives a message from one of its neighbors, its other neighbor cannot send at the same time. With these assumptions we completely solve the problem for ring networks. We first show lower bounds and then give gossiping algorithms which meet these lower bounds and so are optimal. The number of rounds depends on the congruences of n modulo 12.

Surveillance imaging of patients with chronic aortic diseases, such as aneurysms and dissections, relies on obtaining and comparing cross-sectional diameter measurements along the aorta at predefined aortic landmarks, over time. The orientation of the cross-sectional measuring planes at each landmark is currently defined manually by highly trained operators. Centerline-based approaches are unreliable in patients with chronic aortic dissection, because of the asymmetric flow channels, differences in contrast opacification, and presence of mural thrombus, making centerline computations or measurements difficult to generate and reproduce. In this work, we present three alternative approaches – INS, MCDS, MCDbS – based on convolutional neural networks and uncertainty quantification methods to predict the orientation (ϕ,θ) of such cross-sectional planes. For the monitoring of chronic aortic dissections, we show how a dataset of 162 CTA volumes with overall 3273 imperfect manual annotations routinely collected in a clinic can be efficiently used to accomplish this task, despite the presence of non-negligible interoperator variabilities in terms of mean absolute error (MAE) and 95% limits of agreement (LOA). We show how, despite the large limits of agreement in the training data, the trained model provides faster and more reproducible results than either an expert user or a centerline method. The remaining disagreement lies within the variability produced by three independent expert annotators and matches the current state of the art, providing a similar error, but in a fraction of the time.

Cranial implants are commonly used for surgical repair of craniectomy-induced skull defects. These implants are usually generated offline and may require days to weeks to be available. An automated implant design process combined with onsite manufacturing facilities can guarantee immediate implant availability and avoid secondary intervention. To address this need, the AutoImplant II challenge was organized in conjunction with MICCAI 2021, catering for the unmet clinical and computational requirements of automatic cranial implant design. The first edition of AutoImplant (AutoImplant I, 2020) demonstrated the general capabilities and effectiveness of data-driven approaches, including deep learning, for a skull shape completion task on synthetic defects. The second AutoImplant challenge (i.e., AutoImplant II, 2021) built upon the first by adding real clinical craniectomy cases as well as additional synthetic imaging data. The AutoImplant II challenge consisted of three tracks. Tracks 1 and 3 used skull images with synthetic defects to evaluate the ability of submitted approaches to generate implants that recreate the original skull shape. Track 3 consisted of the data from the first challenge (i.e., 100 cases for training, and 110 for evaluation), and Track 1 provided 570 training and 100 validation cases aimed at evaluating skull shape completion algorithms at diverse defect patterns. Track 2 also made progress over the first challenge by providing 11 clinically defective skulls and evaluating the submitted implant designs on these clinical cases. The submitted designs were evaluated quantitatively against imaging data from post-craniectomy as well as by an experienced neurosurgeon. Submissions to these challenge tasks made substantial progress in addressing issues such as generalizability, computational efficiency, data augmentation, and implant refinement. This paper serves as a comprehensive summary and comparison of the submissions to the AutoImplant II challenge. Codes and models are available at https://github.com/Jianningli/Autoimplant_II.

The aorta is the largest vessel of the human body and its pathological degenerations, such as dissections and aneurysms, can be life threatening. An automatic and fast segmentation of the aorta can therefore be a helpful tool to quickly identify an abnormal anatomy. The segmentation of the aortic vessel tree (AVT) typically requires extensive manual labor, but, in recent years, progress in deep learning techniques made the automation of this process viable. For this purpose, we tested different deep learning networks to segment the aortic vessel tree from computed tomography angiography (CTA) scans with a deep neural network consisting of an encoder-decoder architecture with skip connections and an optional self-attention block. The networks were trained on a dataset of 56 CTA scans from three different sources and resulted in Dice score similarities between 0.043−0.897. Generally, the classical U-Nets performed better than the ones containing a self-attention block, indicating that they might diminish performance for AVT segmentation. The quality of the resulting segmentations was highly dependent on the CTA image quality, especially on the contrast between the aorta and the surrounding tissues. However, the trained deep neural network can segment CTA scans well with limited computational resources and training data.

Data management systems are increasingly used in industrial processes. However, data collected as part of industrial process operations, such as sensor or measurement instruments data, contain various sources of errors that can hamper process analysis and decision-making. Therefore, in order to take full advantage of collected and stored data and to increase data quality, an operating regime-based data-processing framework for industrial process decision-making is proposed in this paper. This systematic and structured approach includes the following stages: (1) scope of the analysis, (2) data management and (3) operating regime detection and identification. All steps are based on the combination of process knowledge and data-driven approaches. The proposed framework is applied to data from a brownstock washing department of a dissolving pulp mill, and employed in a case study presented in Part II of this publication, where, considering an activity-based costing analysis, the optimal way to operate the department is identified.

Given a boolean predicate $\Pi$ on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for $\Pi$ is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying $\Pi$. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size $n$ of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of $O(\log \log n)$ bits per node in any $n$-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use $\Omega(\log \log n)$-bit per node registers in some $n$-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms.

AbstractFor medical applications, trustworthiness, interpretability, and robustness are necessary properties of (deep) neural networks. For generative models, one approach towards this could be analyzing and structuring the latent space representation. In this context, the term disentanglement is often used, but still not uniquely defined. In 2022, we organized the first workshop about Medical Applications with Disentanglements (MAD) at the MICCAI conference in Singapore (https://mad.ikim.nrw/). The workshop had a general call for disentanglement papers in the medical field and the submitted papers are published in a Springer challenge proceedings. The aim of the introduction paper of this proceeding is to present the necessary background information for them. Thus, we give a short overview of this field and how challenges for deep learning in healthcare could be addressed with the help of disentanglement.KeywordsDisentanglementGenerative modelsDeep learningMAD WorkshopMICCAI

We present a methodology to automatically parallelize outlier detection ensemble models using directed acyclic graphs embedding the MapReduce paradigm. The DAGs are built implicitly such that naive sequential computations can be transformed into efficient parallel computations without changing the underlying implementation. We show that the proposed parallelization approach is an effective strategy to combat the computational complexity inherent to ensemble learning models, leading to a near-optimal speedup in a theoretical setting, and a substantial speedup in a practical setting.

For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. For fast-slow systems, truncated ODEs describe the fast dynamics. We define compatibility classes as subsets of the state space, obtained by equating the conservation laws to constants. A set of conservation laws is complete when the corresponding compatibility classes contain a finite number of steady states. Complete sets of conservation laws can be used for model order reduction and for studying the multistationarity of the model. We provide algorithmic methods for computing linear, monomial, and polynomial conservation laws of polynomial ODE models and for testing their completeness. The resulting conservation laws and their completeness are either independent or dependent on the parameters. In the latter case, we provide parametric case distinctions. In particular, we propose a new method to compute polynomial conservation laws by comprehensive Gr\"obner systems and syzygies. Keywords: First integrals, chemical reaction networks, polynomial conservation laws, syzygies, comprehensive Gr\"obner systems.