A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and insert a pair of non-crossing segments, while keeping the same vertex degrees. The goal of this paper is to devise efficient strategies to flip the segments in order to obtain crossing-free segments after a small number of flips. Linear and near-linear bounds on the number of flips were only known for segments with endpoints in convex position. We generalize these results, proving linear and near-linear bounds for cases with endpoints that are not in convex position. Our results are proved in a general setting that applies to multiple problems, using multigraphs and the distinction between removal and insertion choices when performing a flip.
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For a fixed finite set of finite tournaments ${\mathcal F}$, the ${\mathcal F}$-free orientation problem asks whether a given finite undirected graph $G$ has an $\mathcal F$-free orientation, i.e., whether the edges of $G$ can be oriented so that the resulting digraph does not embed any of the tournaments from ${\mathcal F}$. We prove that for every ${\mathcal F}$, this problem is in P or NP-complete. Our proof reduces the classification task to a complete complexity classification of the orientation completion problem for ${\mathcal F}$, which is the variant of the problem above where the input is a directed graph instead of an undirected graph, introduced by Bang-Jensen, Huang, and Zhu (2017). Our proof uses results from the theory of constraint satisfaction, and a result of Agarwal and Kompatscher (2018) about infinite permutation groups and transformation monoids.
Under missing-not-at-random (MNAR) sample selection bias, the performance of a prediction model is often degraded. This paper focuses on one classic instance of MNAR sample selection bias where a subset of samples have non-randomly missing outcomes. The Heckman selection model and its variants have commonly been used to handle this type of sample selection bias. The Heckman model uses two separate equations to model the prediction and selection of samples, where the selection features include all prediction features. When using the Heckman model, the prediction features must be properly chosen from the set of selection features. However, choosing the proper prediction features is a challenging task for the Heckman model. This is especially the case when the number of selection features is large. Existing approaches that use the Heckman model often provide a manually chosen set of prediction features. In this paper, we propose Heckman-FA as a novel data-driven framework for obtaining prediction features for the Heckman model. Heckman-FA first trains an assignment function that determines whether or not a selection feature is assigned as a prediction feature. Using the parameters of the trained function, the framework extracts a suitable set of prediction features based on the goodness-of-fit of the prediction model given the chosen prediction features and the correlation between noise terms of the prediction and selection equations. Experimental results on real-world datasets show that Heckman-FA produces a robust regression model under MNAR sample selection bias.
The aim of this work is to improve musculoskeletal-based models of the upper-limb Wrench Feasible Set i.e. the set of achievable maximal wrenches at the hand for applications in collaborative robotics and computer aided ergonomics. In particular, a recent method performing wrench capacity evaluation called the Iterative Convex Hull Method is upgraded in order to integrate non dislocation and compression limitation constraints at the glenohumeral joint not taken into account in the available models. Their effects on the amplitude of the force capacities at the hand, glenohumeral joint reaction forces and upper-limb muscles coordination in comparison to the original iterative convex hull method are investigated in silico. The results highlight the glenohumeral potential dislocation for the majority of elements of the wrench feasible set with the original Iterative Convex Hull method and the fact that the modifications satisfy correctly stability constraints at the glenohumeral joint. Also, the induced muscles coordination pattern favors the action of stabilizing muscles, in particular the rotator-cuff muscles, and lowers that of known potential destabilizing ones according to the literature.
Achieving success in agricultural activities heavily relies on precise navigation in row crop fields. Recently, segmentation-based navigation has emerged as a reliable technique when GPS-based localization is unavailable or higher accuracy is needed due to vegetation or unfavorable weather conditions. It also comes in handy when plants are growing rapidly and require an online adaptation of the navigation algorithm. This work applies a segmentation-based visual agnostic navigation algorithm to lavender fields, considering both simulation and real-world scenarios. The effectiveness of this approach is validated through a wide set of experimental tests, which show the capability of the proposed solution to generalize over different scenarios and provide highly-reliable results.
Perfect paradefinite algebras are De Morgan algebras expanded with a perfection (or classicality) operation. They form a variety that is term-equivalent to the variety of involutive Stone algebras. Their associated multiple-conclusion (Set-Set) and single-conclusion (Set-Fmla) order-preserving logics are non-algebraizable self-extensional logics of formal inconsistency and undeterminedness determined by a six-valued matrix, studied in depth by Gomes et al. (2022) from both the algebraic and the proof-theoretical perspectives. We continue hereby that study by investigating directions for conservatively expanding these logics with an implication connective (essentially, one that admits the deduction-detachment theorem). We first consider logics given by very simple and manageable non-deterministic semantics whose implication (in isolation) is classical. These, nevertheless, fail to be self-extensional. We then consider the implication realized by the relative pseudo-complement over the six-valued perfect paradefinite algebra. Our strategy is to expand such algebra with this connective and study the (self-extensional) Set-Set and Set-Fmla order-preserving logics, as well as the T-assertional logics of the variety induced by the new algebra. We provide axiomatizations for such new variety and for such logics, drawing parallels with the class of symmetric Heyting algebras and with Moisil's `symmetric modal logic'. For the Set-Set logic, in particular, the axiomatization we obtain is analytic. We close by studying interpolation properties for these logics and concluding that the new variety has the Maehara amalgamation property.
The recent Facebook rebranding to Meta has drawn renewed attention to the metaverse. Technology giants, amongst others, are increasingly embracing the vision and opportunities of a hybrid social experience that mixes physical and virtual interactions. As the metaverse gains in traction, it is expected that everyday objects may soon connect more closely with virtual elements. However, discovering this "hidden" virtual world will be a crucial first step to interacting with it in this new augmented world. In this paper, we address the problem of connecting physical objects with their virtual counterparts, especially through connections built upon visual markers. We propose a unified recognition framework that guides approaches to the metaverse access points. We illustrate the use of the framework through experimental studies under different conditions, in which an interactive and visually attractive decoration pattern, an Artcode, is used as the approach to enable the connection. This paper will be of interest to, amongst others, researchers working in Interaction Design or Augmented Reality who are seeking techniques or guidelines for augmenting physical objects in an unobtrusive, complementary manner.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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