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Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq. This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps. Moreover, we design a special mechanism which automatically introduces an appropriate representation of a polyhedron or a face, depending on the context of the proof. We demonstrate the usability of this approach by establishing some of the most important combinatorial properties of faces, namely that they constitute a family of graded atomistic and coatomistic lattices closed under interval sublattices. We also prove a theorem due to Balinski on the $d$-connectedness of the adjacency graph of polytopes of dimension $d$.

Since frequent severe droughts are lengthening the dry season in the Amazon Rainforest, it is important to detect wildfires promptly and forecast possible spread for effective suppression response. Current wildfire detection models are not versatile enough for the low-technology conditions of South American hot spots. This deep learning study first trains a Fully Convolutional Neural Network on Landsat 8 images of Ecuador and the Galapagos, using Green and Short-wave Infrared bands to predict pixel-level binary fire masks. This model achieves a 0.962 validation F2 score and a 0.932 F2 score on test data from Guyana and Suriname. Afterward, image segmentation is conducted on the Cirrus band using K-Means Clustering to simplify continuous pixel values into three discrete classes representing differing degrees of cirrus cloud contamination. Three additional Convolutional Neural Networks are trained to conduct a sensitivity analysis measuring the effect of simplified features on model accuracy and train time. The Experimental model trained on the segmented cirrus images provides a statistically significant decrease in train time compared to the Control model trained on raw cirrus images, without compromising binary accuracy. This proof of concept reveals that feature engineering can improve the performance of wildfire detection models by lowering computational expense.

Background: Transrectal ultrasound guided systematic biopsies of the prostate is a routine procedure to establish a prostate cancer diagnosis. However, the 10-12 prostate core biopsies only sample a relatively small volume of the prostate, and tumour lesions in regions between biopsy cores can be missed, leading to a well-known low sensitivity to detect clinically relevant cancer. As a proof-of-principle, we developed and validated a deep convolutional neural network model to distinguish between morphological patterns in benign prostate biopsy whole slide images from men with and without established cancer. Methods: This study included 14,354 hematoxylin and eosin stained whole slide images from benign prostate biopsies from 1,508 men in two groups: men without an established prostate cancer (PCa) diagnosis and men with at least one core biopsy diagnosed with PCa. 80% of the participants were assigned as training data and used for model optimization (1,211 men), and the remaining 20% (297 men) as a held-out test set used to evaluate model performance. An ensemble of 10 deep convolutional neural network models was optimized for classification of biopsies from men with and without established cancer. Hyperparameter optimization and model selection was performed by cross-validation in the training data . Results: Area under the receiver operating characteristic curve (ROC-AUC) was estimated as 0.727 (bootstrap 95% CI: 0.708-0.745) on biopsy level and 0.738 (bootstrap 95% CI: 0.682 - 0.796) on man level. At a specificity of 0.9 the model had an estimated sensitivity of 0.348. Conclusion: The developed model has the ability to detect men with risk of missed PCa due to under-sampling of the prostate. The proposed model has the potential to reduce the number of false negative cases in routine systematic prostate biopsies and to indicate men who could benefit from MRI-guided re-biopsy.

While utilization of digital agents to support crucial decision making is increasing, trust in suggestions made by these agents is hard to achieve. However, it is essential to profit from their application, resulting in a need for explanations for both the decision making process and the model. For many systems, such as common black-box models, achieving at least some explainability requires complex post-processing, while other systems profit from being, to a reasonable extent, inherently interpretable. We propose a rule-based learning system specifically conceptualised and, thus, especially suited for these scenarios. Its models are inherently transparent and easily interpretable by design. One key innovation of our system is that the rules' conditions and which rules compose a problem's solution are evolved separately. We utilise independent rule fitnesses which allows users to specifically tailor their model structure to fit the given requirements for explainability.

Online news and social media have been the de facto mediums to disseminate information globally from the beginning of the last decade. However, bias in content and purpose of intentions are not regulated, and managing bias is the responsibility of content consumers. In this regard, understanding the stances and biases of news sources towards specific entities becomes important. To address this problem, we use pretrained language models, which have been shown to bring about good results with no task-specific training or few-shot training. In this work, we approach the problem of characterizing Named Entities and Tweets as an open-ended text classification and open-ended fact probing problem.We evaluate the zero-shot language model capabilities of Generative Pretrained Transformer 2 (GPT-2) to characterize Entities and Tweets subjectively with human psychology-inspired and logical conditional prefixes and contexts. First, we fine-tune the GPT-2 model on a sufficiently large news corpus and evaluate subjective characterization of popular entities in the corpus by priming with prefixes. Second, we fine-tune GPT-2 with a Tweets corpus from a few popular hashtags and evaluate characterizing tweets by priming the language model with prefixes, questions, and contextual synopsis prompts. Entity characterization results were positive across measures and human evaluation.

This paper explores Null Island, a fictional place located at 0$^\circ$ latitude and 0$^\circ$ longitude in the WGS84 geographic coordinate system. Null Island is erroneously associated with large amounts of geographic data in a wide variety of location-based services, place databases, social media and web-based maps. While it was originally considered a joke within the geospatial community, this article will demonstrate implications of its existence, both technological and social in nature, promoting Null Island as a fundamental issue of geographic information that requires more widespread awareness. The article summarizes error sources that lead to data being associated with Null Island. We identify four evolutionary phases which help explain how this fictional place evolved and established itself as an entity reaching beyond the geospatial profession to the point of being discovered by the visual arts and the general population. After providing an accurate account of data that can be found at (0, 0), geospatial, technological and social implications of Null Island are discussed. Guidelines to avoid misplacing data to Null Island are provided. Since data will likely continue to appear at this location, our contribution is aimed at both GIScientists and the general population to promote awareness of this error source.

This paper studies the application of reconfigurable intelligent surface (RIS) to cooperative non-orthogonal multiple access (C-NOMA) networks with simultaneous wireless information and power transfer (SWIPT). We aim for maximizing the rate of the strong user with guaranteed weak user's quality of service (QoS) by jointly optimizing power splitting factors, beamforming coefficients, and RIS reflection coefficients in two transmission phases. The formulated problem is difficult to solve due to its complex and non-convex constraints. To tackle this challenging problem, we first use alternating optimization (AO) framework to transform it into three subproblems, and then use the penalty-based arithmetic-geometric mean approximation (PBAGM) algorithm and the successive convex approximation (SCA)-based method to solve them. Numerical results verify the superiority of the proposed algorithm over the baseline schemes.

Bearing fault identification and analysis is an important research area in the field of machinery fault diagnosis. Aiming at the common faults of rolling bearings, we propose a data-driven diagnostic algorithm based on the characteristics of bearing vibrations called multi-size kernel based adaptive convolutional neural network (MSKACNN). Using raw bearing vibration signals as the inputs, MSKACNN provides vibration feature learning and signal classification capabilities to identify and analyze bearing faults. Ball mixing is a ball bearing production quality problem that is difficult to identify using traditional frequency domain analysis methods since it requires high frequency resolutions of the measurement signals and results in a long analyzing time. The proposed MSKACNN is shown to improve the efficiency and accuracy of ball mixing diagnosis. To further demonstrate the effectiveness of MSKACNN in bearing fault identification, a bearing vibration data acquisition system was developed, and vibration signal acquisition was performed on rolling bearings under five different fault conditions including ball mixing. The resulting datasets were used to analyze the performance of our proposed model. To validate the adaptive ability of MSKACNN, fault test data from the Case Western Reserve University Bearing Data Center were also used. Test results show that MSKACNN can identify the different bearing conditions with high accuracy with high generalization ability. We presented an implementation of the MSKACNN as a lightweight module for a real-time bearing fault diagnosis system that is suitable for production.

Refractive freeform components are becoming increasingly relevant for generating controlled patterns of light, because of their capability to spatially-modulate optical signals with high efficiency and low background. However, the use of these devices is still limited by difficulties in manufacturing macroscopic elements with complex, 3-dimensional (3D) surface reliefs. Here, 3D-printed and stretchable magic windows generating light patterns by refraction are introduced. The shape and, consequently, the light texture achieved can be changed through controlled device strain. Cryptographic magic windows are demonstrated through exemplary light patterns, including micro-QR-codes, that are correctly projected and recognized upon strain gating while remaining cryptic for as-produced devices. The light pattern of micro-QR-codes can also be projected by two coupled magic windows, with one of them acting as the decryption key. Such novel, freeform elements with 3D shape and tailored functionalities is relevant for applications in illumination design, smart labels, anti-counterfeiting systems, and cryptographic communication.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.