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This paper deals with left star, star, and core partial orders for complex matrices. For each partial order, we present an order-isomorphism between the down-set of a fixed matrix B and a certain set (depending on the partial order) of orthogonal projectors whose matrix sizes can be considerably smaller than that of the matrix B. We study the lattice structure and we give properties of the down-sets. We prove that the down-set of B ordered by the core partial order and by the star partial order are sublattices of the down-set ordered by the left star partial order. We analize the existence of supremum and infimum of two given matrices and we give characterizations of these operations (whenever they exist). Some of the results given in the paper are already known in the literature but we present a different proof based on the previously established order-isomorphism. [ABSTRACT FROM AUTHOR]

In this paper we extend the definition of BT inverse of square complex matrices to rectangular matrices. This new generalized inverse (called the W -weighted BT inverse) always exists and is unique. We investigate several characterizations of the W -weighted BT inverse. We give two representations of the W -weighted BT inverse; the first one uses the weighted core EP decomposition and the second one is given in terms of a singular value decomposition. In addition, we derive some properties of the W -weighted BT inverse and its relationship with others well-known inverses. [ABSTRACT FROM AUTHOR]

In this paper, we present several representations of the W-weighted WG inverse. These representations are expressed in terms of matrix powers as well as in terms of matrix products involving only the Moore–Penrose inverse. In addition, a new characterization of the W-weighted WG inverse is presented by using a rank equation. [ABSTRACT FROM AUTHOR]

This paper introduces and investigates a new class of generalized inverses, called GDMP-inverses (and their duals), as a generalization of DMP-inverses. GDMP-inverses are defined from G-Drazin inverses and the Moore-Penrose inverse of a complex square matrix. In contrast to most other generalized inverses, GDMP-inverses are not only outer inverses but also inner inverses. Characterizations and representations of GDMP-inverses are obtained by means of the core-nilpotent and the Hartwig-Spindelböck decompositions. [ABSTRACT FROM AUTHOR]

In this paper, we present necessary and sufficient conditions for the k-commutative equality A k X = X A k , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations. [ABSTRACT FROM AUTHOR]

In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra62(3) (2014), 792-802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses. [ABSTRACT FROM AUTHOR]

In this paper, {1}-inverses of a nilpotent matrix as well as matrices above a given nilpotent matrix under the minus partial order are characterized. [ABSTRACT FROM AUTHOR]

This paper deals with singular systems of index. Our main goal is to find a state-feedback such that the closed-loop system satisfies the regularity condition and it is nonnegative and stable. In order to do that, the core-nilpotent decomposition of a square matrix is applied to the singular matrix of the system. Moreover, if the Drazin projector of this matrix is nonnegative, then the previous decomposition allows us to write the core-part of the matrix in a specific block form. In addition, an algorithm to study this kind of systems via a state-feedback is designed. [ABSTRACT FROM AUTHOR]

The problem of characterizing all situations in which aA + bB is an idempotent matrix when A2 = A, Bk + 1 = B, AB ≠ BA, and a, b are nonzero complex numbers is studied. [ABSTRACT FROM AUTHOR]

This paper deals with autonomous linear systems and the sharp partial order. Given an autonomous linear system, we find another system, which is related to the first one by means of the sharp partial order. This relation can be interpreted in different ways: as a perturbation or as a projection of the initial system. Both points of view allow us to work with a new system with some previously selected behaviour. The solutions of the two systems are related via a matrix that gives the gap between them. We design some algorithms and analize their performance with numerical examples. [ABSTRACT FROM AUTHOR]

This paper derives some further results on recent generalized inverses studied in the literature, namely core EP, DMP, and CMP inverses. Our main aim is to develop maximal classes of matrices for which their representations remain valid. [ABSTRACT FROM AUTHOR]

This paper deals with weighted G-Drazin inverses, which is a new class of matrices introduced to extend (to the rectangular case) G-Drazin inverses recently considered by Wang and Liu for square matrices. First, we define and characterize weighted G-Drazin inverses. Next, we consider a new pre-order defined on complex rectangular matrices based on weighted G-Drazin inverses. Finally, we characterize this pre-order and relate it to the minus partial order and to the weighted Drazin pre-order. [ABSTRACT FROM AUTHOR]

Using the group inverse, an explicit solution to a symmetric singular system is described. The general explicit solution is derived when the symmetric singular system satisfies the regularity condition. Certain special properties of these singular systems are presented. Finally, a symmetric balanced realization is obtained from an equivalent standard control system. [Copyright &y& Elsevier]

Investigating the ecological context of microbial predator-prey interactions enables the identification of microorganisms, which produce multiple secondary metabolites to evade predation or to kill the predator. In addition, genome mining combined with molecular biology methods can be used to identify further biosynthetic gene clusters that yield new antimicrobials to fight the antimicrobial crisis. In contrast, classical screening-based approaches have limitations since they do not aim to unlock the entire biosynthetic potential of a given organism. Here, we describe the genomics-based identification of keanumycins A-C. These nonribosomal peptides enable bacteria of the genus Pseudomonas to evade amoebal predation. While being amoebicidal at a nanomolar level, these compounds also exhibit a strong antimycotic activity in particular against the devastating plant pathogen Botrytis cinerea and they drastically inhibit the infection of Hydrangea macrophylla leaves using only supernatants of Pseudomonas cultures. The structures of the keanumycins were fully elucidated through a combination of nuclear magnetic resonance, tandem mass spectrometry, and degradation experiments revealing an unprecedented terminal imine motif in keanumycin C extending the family of nonribosomal amino acids by a highly reactive building block. In addition, chemical synthesis unveiled the absolute configuration of the unusual dihydroxylated fatty acid of keanumycin A, which has not yet been reported for this lipodepsipeptide class. Finally, a detailed genome-wide microarray analysis of Candida albicans exposed to keanumycin A shed light on the mode-of-action of this potential natural product lead, which will aid the development of new pharmaceutical and agrochemical antifungals.

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic for Ecasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.

Objective: To study normative values of range of motion (ROM), strength, and functional performance and investigate changes over 1 year in adolescent female football players., Design: Cross-sectional., Participants: 418 adolescent female football players aged 12-17 years., Main Outcome Measures: The physical characteristic assessments included (1) ROM assessment of the trunk, hips, and ankles; (2) strength measures (maximal isometric and eccentric strength for the trunk, hips, and knees, and strength endurance for the neck, back, trunk and calves), and (3) functional performance (the one-leg long box jump test and the square hop test)., Results: Older players were stronger, but not when normalized to body weight. Only small differences in ROM regarding age were found. ROM increased over 1 year in most measurements with the largest change in hip external rotation, which increased by 6-7° (Cohen's d = 0.83-0.87). Hip (d = 0.28-1.07) and knee (d = 0.38-0.53) muscle strength and the square hop test (d = 0.71-0.99) improved over 1 year., Conclusions: Normative values for ROM and strength assessments of neck, back, trunk, hips, knees, calves and ankles are presented for adolescent female football players. Generally, fluctuations in ROM were small with little clinical meaning, whereas strength improved over 1 year., Competing Interests: Declaration of competing interest The authors affirm that they have no financial affiliation (including research funding) or involvement with any commercial organization that has a direct financial interest in any matter included in this manuscript., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Reliably quantifying the confidence of deep neural classifiers is a challenging yet fundamental requirement for deploying such models in safety-critical applications. In this paper, we introduce a novel target criterion for model confidence, namely the true class probability (TCP). We show that TCP offers better properties for confidence estimation than standard maximum class probability (MCP). Since the true class is by essence unknown at test time, we propose to learn TCP criterion from data with an auxiliary model, introducing a specific learning scheme adapted to this context. We evaluate our approach on the task of failure prediction and of self-training with pseudo-labels for domain adaptation, which both necessitate effective confidence estimates. Extensive experiments are conducted for validating the relevance of the proposed approach in each task. We study various network architectures and experiment with small and large datasets for image classification and semantic segmentation. In every tested benchmark, our approach outperforms strong baselines.

Purpose: Fully Convolutional neural Networks (FCNs) are the most popular models for medical image segmentation. However, they do not explicitly integrate spatial organ positions, which can be crucial for proper labeling in challenging contexts., Methods: In this work, we propose a method that combines a model representing prior probabilities of an organ position in 3D with visual FCN predictions by means of a generalized prior-driven prediction function. The prior is also used in a self-labeling process to handle low-data regimes, in order to improve the quality of the pseudo-label selection., Results: Experiments carried out on CT scans from the public TCIA pancreas segmentation dataset reveal that the resulting STIPPLE model can significantly increase performances compared to the FCN baseline, especially with few training images. We also show that STIPPLE outperforms state-of-the-art semi-supervised segmentation methods by leveraging the spatial prior information., Conclusions: STIPPLE provides a segmentation method effective with few labeled examples, which is crucial in the medical domain. It offers an intuitive way to incorporate absolute position information by mimicking expert annotators., (© 2021. CARS.)

Training deep ConvNets requires large labeled datasets. However, collecting pixel-level labels for medical image segmentation is very expensive and requires a high level of expertise. In addition, most existing segmentation masks provided by clinical experts focus on specific anatomical structures. In this paper, we propose a method dedicated to handle such partially labeled medical image datasets. We propose a strategy to identify pixels for which labels are correct, and to train Fully Convolutional Neural Networks with a multi-label loss adapted to this context. In addition, we introduce an iterative confidence self-training approach inspired by curriculum learning to relabel missing pixel labels, which relies on selecting the most confident prediction with a specifically designed confidence network that learns an uncertainty measure which is leveraged in our relabeling process. Our approach, INERRANT for Iterative coNfidencE Relabeling of paRtial ANnoTations, is thoroughly evaluated on two public datasets (TCAI and LITS), and one internal dataset with seven abdominal organ classes. We show that INERRANT robustly deals with partial labels, performing similarly to a model trained on all labels even for large missing label proportions. We also highlight the importance of our iterative learning scheme and the proposed confidence measure for optimal performance. Finally we show a practical use case where a limited number of completely labeled data are enriched by publicly available but partially labeled data., (Copyright © 2021. Published by Elsevier Ltd.)

The preparation of well diffracting crystals and their handling before their X-ray analysis are two critical steps of biocrystallographic studies. We describe a versatile microfluidic chip that enables the production of crystals by the efficient method of counter-diffusion. The convection-free environment provided by the microfluidic channels is ideal for crystal growth and useful to diffuse a substrate into the active site of the crystalline enzyme. Here we applied this approach to the CCA-adding enzyme of the psychrophilic bacterium Planococcus halocryophilus in the presented example. After crystallization and substrate diffusion/soaking, the crystal structure of the enzyme:substrate complex was determined at room temperature by serial crystallography and the analysis of multiple crystals directly inside the chip. The whole procedure preserves the genuine diffraction properties of the samples because it requires no crystal handling.

The abundance of image-level labels and the lack of large scale detailed annotations (e.g. bounding boxes, segmentation masks) promotes the development of weakly supervised learning (WSL) models. In this work, we propose a novel framework for WSL of deep convolutional neural networks dedicated to learn localized features from global image-level annotations. The core of the approach is a new latent structured output model equipped with a pooling function which explicitly models negative evidence, e.g. a cow detector should strongly penalize the prediction of the bedroom class. We show that our model can be trained end-to-end for different visual recognition tasks: multi-class and multi-label classification, and also structured average precision (AP) ranking. Extensive experiments highlight the relevance of the proposed method: our model outperforms state-of-the art results on six datasets. We also show that our framework can be used to improve the performance of state-of-the-art deep models for large scale image classification on ImageNet. Finally, we evaluate our model for weakly supervised tasks: in particular, a direct adaptation for weakly supervised segmentation provides a very competitive model.

Designing powerful models able to handle weakly labeled data are a crucial problem in machine learning. In this paper, we propose a new multiple instance learning (MIL) framework. Examples are represented as bags of instances, but we depart from standard MIL assumptions by introducing a symmetric strategy (SyMIL) that seeks discriminative instances in positive and negative bags. The idea is to use the instance the most distant from the hyper-plan to classify the bag. We provide a theoretical analysis featuring the generalization properties of our model. We derive a large margin formulation of our problem, which is cast as a difference of convex functions, and optimized using concave-convex procedure. We provide a primal version optimizing with stochastic subgradient descent and a dual version optimizing with one-slack cutting-plane. Successful experimental results are reported on standard MIL and weakly supervised object detection data sets: SyMIL significantly outperforms competitive methods (mi/MI/Latent-SVM), and gives very competitive performance compared to state-of-the-art works. We also analyze the selected instances of symmetric and asymmetric approaches on weakly supervised object detection and text classification tasks. Finally, we show complementarity of SyMIL with recent works on learning with label proportions on standard MIL data sets.

In this chapter, we examine the demographics and risk factors in the population diagnosed with head and neck cancer (HNC), what challenges these patients face post-treatment and what the role of psychosocial support through clinical social work is in managing these stressors. While many forms of head and neck cancer found in the early stages have a high cure rate, the side effects of treatment for these cancers have major life-altering effects. Previously, the majority of those diagnosed with head and neck cancers were those who used excessive alcohol and tobacco, but the numbers are changing to include the human papillomavirus (HPV) as a major risk factor. Due to the behavioral risk factors that are often causes of head and neck cancers and the effects of treatment that often lend to psychosocial distress, the role of psychosocial intervention at time of diagnosis throughout the disease trajectory is essential for compliance with treatment and healthy coping post-treatment. Clinical social workers play an essential role within the multidisciplinary team of assessment and interventions for managing patient's psychosocial distress.

In this paper, we propose a hybrid architecture that combines the image modeling strengths of the bag of words framework with the representational power and adaptability of learning deep architectures. Local gradient-based descriptors, such as SIFT, are encoded via a hierarchical coding scheme composed of spatial aggregating restricted Boltzmann machines (RBM). For each coding layer, we regularize the RBM by encouraging representations to fit both sparse and selective distributions. Supervised fine-tuning is used to enhance the quality of the visual representation for the categorization task. We performed a thorough experimental evaluation using three image categorization data sets. The hierarchical coding scheme achieved competitive categorization accuracies of 79.7% and 86.4% on the Caltech-101 and 15-Scenes data sets, respectively. The visual representations learned are compact and the model's inference is fast, as compared with sparse coding methods. The low-level representations of descriptors that were learned using this method result in generic features that we empirically found to be transferrable between different image data sets. Further analysis reveal the significance of supervised fine-tuning when the architecture has two layers of representations as opposed to a single layer.

This paper presents an extension of the HMAX model, a neural network model for image classification. The HMAX model can be described as a four-level architecture, with the first level consisting of multiscale and multiorientation local filters. We introduce two main contributions to this model. First, we improve the way the local filters at the first level are integrated into more complex filters at the last level, providing a flexible description of object regions and combining local information of multiple scales and orientations. These new filters are discriminative and yet invariant, two key aspects of visual classification. We evaluate their discriminative power and their level of invariance to geometrical transformations on a synthetic image set. Second, we introduce a multiresolution spatial pooling. This pooling encodes both local and global spatial information to produce discriminative image signatures. Classification results are reported on three image data sets: Caltech101, Caltech256, and fifteen scenes. We show significant improvements over previous architectures using a similar framework.