On Monge sequences in d-dimensional arrays

AbstractLet C be an n × m matrix. Then the sequence j:= ((i1, j1), (i2, j2), …, (inm, jnm)) of pairs of indices is called a Monge sequence with respect to the given matrix C if and only if, whenever (i, j) precedes both (i, s) and (r, j) in j, then c[i, j] + c[r, s] ≤ c[i, s] + c[r, j]. Monge sequences play an important role in greedily solvable transportation problems. Hoffman showed that the greedy algorithm which maximizes all variables along a sequence j in turn solves the classical Hitchcock transportation problem for all supply and demand vectors if and only if j is a Monge sequence with respect to the cost matrix C. In this paper we generalize Hoffman's approach to higher dimensions. We first introduce the concept of a d-dimensional Monge sequence. Then we show that the d-dimensional axial transportation problem is solved to optimality for arbitrary right-hand sides if and only if the sequence j applied in the greedy algorithm is a d-dimensional Monge sequence. Finally we present an algorithm for obtaining a d-dimensional Monge sequence which runs in polynomial time for fixed d

Recognition of d-dimensional Monge arrays

AbstractIt is known that the d-dimensional axial transportation (assignment) problem can easily be solved by a greedy algorithm if and only if the underlying cost array fulfills the d-dimensional Monge property. In this paper the following question is solved: Is it possible to find d permutations in such a way that the permuted array becomes a Monge array? Furthermore we give an algorithm which constructs such permutations in the affirmative case. If the cost array has the dimensions n1×n2×⋯×nd with n1⩽n2⩽⋯⩽nd, then the algorithm has time complexity O(d2n2⋯nd(n1+lognd)). By using this algorithm a wider class of d-dimensional axial transportation problems and in particular of the d-dimensional axial assignment problems can be solved efficiently

Weak Monge arrays in higher dimensions

AbstractAn n × n matrix C is called a weak Monge matrix if cii + crs ⩽is + cri for all 1 ⩽ i ⩽ r, s ⩽ n. It is well known that the classical linear assignment problem is optimally solved by the identity permutation if the underlying cost-matrix fulfills the weak Monge property.In this paper we introduce d-dimensional weak Monge arrays, (d ⩾ 2), and prove that d-dimensional axial assignment problems can be solved efficiently whenever the underlying cost-array fulfills the d-dimensional weak Monge property. Moreover, it is shown that all results also carry over into an abstract algebraic framework. Finally, the problem of testing whether or not a given array can be permuted to become a weak Monge array is investigated

Evaluation of semi-supervised learning using sparse labeling to segment cell nuclei

The analysis of microscopic images from cell cultures plays an important role in the development of drugs. The segmentation of such images is a basic step to extract the viable information on which further evaluation steps are build. Classical image processing pipelines often fail under heterogeneous conditions. In the recent years deep neuronal networks gained attention due to their great potentials in image segmentation. One main pitfall of deep learning is often seen in the amount of labeled data required for training such models. Especially for 3D images the process to generate such data is tedious and time consuming and thus seen as a possible reason for the lack of establishment of deep learning models for 3D data. Efforts have been made to minimize the time needed to create labeled training data or to reduce the amount of labels needed for training. In this paper we present a new semisupervised training method for image segmentation of microscopic cell recordings based on an iterative approach utilizing unlabeled data during training. This method helps to further reduce the amount of labels required to effectively train deep learning models for image segmentation. By labeling less than one percent of the training data, a performance of 90% compared to a full annotation with 342 nuclei can be achieved

Sweet Taste Is Complex: Signaling Cascades and Circuits Involved in Sweet Sensation

Sweetness is the preferred taste of humans and many animals, likely because sugars are a primary source of energy. In many mammals, sweet compounds are sensed in the tongue by the gustatory organ, the taste buds. Here, a group of taste bud cells expresses a canonical sweet taste receptor, whose activation induces Ca2+ rise, cell depolarization and ATP release to communicate with afferent gustatory nerves. The discovery of the sweet taste receptor, 20 years ago, was a milestone in the understanding of sweet signal transduction and is described here from a historical perspective. Our review briefly summarizes the major findings of the canonical sweet taste pathway, and then focuses on molecular details, about the related downstream signaling, that are still elusive or have been neglected. In this context, we discuss evidence supporting the existence of an alternative pathway, independent of the sweet taste receptor, to sense sugars and its proposed role in glucose homeostasis. Further, given that sweet taste receptor expression has been reported in many other organs, the physiological role of these extraoral receptors is addressed. Finally, and along these lines, we expand on the multiple direct and indirect effects of sugars on the brain. In summary, the review tries to stimulate a comprehensive understanding of how sweet compounds signal to the brain upon taste bud cells activation, and how this gustatory process is integrated with gastro-intestinal sugar sensing to create a hedonic and metabolic representation of sugars, which finally drives our behavior. Understanding of this is indeed a crucial step in developing new strategies to prevent obesity and associated diseases

A Novel Optical Tissue Clearing Protocol for Mouse Skeletal Muscle to Visualize Endplates in Their Tissue Context

Neuromuscular junctions (NMJs) mediate skeletal muscle contractions and play an important role in several neuromuscular disorders when their morphology and function are compromised. However, due to their small size and sparse distribution throughout the comparatively large, inherently opaque muscle tissue the analysis of NMJ morphology has been limited to teased fiber preparations, longitudinal muscle sections, and flat muscles. Consequently, whole mount analyses of NMJ morphology, numbers, their distribution, and assignment to a given muscle fiber have also been impossible to determine in muscle types that are frequently used in experimental paradigms. This impossibility is exacerbated by the lack of optical tissue clearing techniques that are compatible with clear and persistent NMJ stains. Here, we present MYOCLEAR, a novel and highly reproducible muscle tissue clearing protocol. Based on hydrogel-based tissue clearing methods, this protocol permits the labeling and detection of all NMJs in adult hindleg extensor digitorum longus muscles from wildtype and diseased mice. The method is also applicable to adult mouse diaphragm muscles and can be used for different staining agents, including toxins, lectins, antibodies, and nuclear dyes. It will be useful in understanding the distribution, morphological features, and muscle tissue context of NMJs in hindleg muscle whole mounts for biomedical and basic research

Motor Endplate—Anatomical, Functional, and Molecular Concepts in the Historical Perspective

By mediating voluntary muscle movement, vertebrate neuromuscular junctions (NMJ) play an extraordinarily important role in physiology. While the significance of the nerve-muscle connectivity was already conceived almost 2000 years back, the precise cell and molecular biology of the NMJ have been revealed in a series of fascinating research activities that started around 180 years ago and that continues. In all this time, NMJ research has led to fundamentally new concepts of cell biology, and has triggered groundbreaking advancements in technologies. This review tries to sketch major lines of thought and concepts on NMJ in their historical perspective, in particular with respect to anatomy, function, and molecular components. Furthermore, along these lines, it emphasizes the mutual benefit between science and technology, where one drives the other. Finally, we speculate on potential major future directions for studies on NMJ in these fields