Balinski-Tucker simplex tableaus : dimensions, degeneracy degrees, and interior points of optimal faces

This paper introduces a general, formal treatment of dynamic constraints, i.e., constraints on the state changes that are allowed in a given state space. Such dynamic constraints can be seen as representations of "real world" constraints in a managerial context. The notions of transition, reversible and irreversible transition, and transition relation will be introduced. The link with Kripke models (for modal logics) is also made explicit. Several (subtle) examples of dynamic constraints will be given. Some important classes of dynamic constraints in a database context will be identified, e.g. various forms of cumulativity, non-decreasing values, constraints on initial and final values, life cycles, changing life cycles, and transition and constant dependencies. Several properties of these dependencies will be treated. For instance, it turns out that functional dependencies can be considered as "degenerated" transition dependencies. Also, the distinction between primary keys and alternate keys is reexamined, from a dynamic point of view.

Degeneracy degrees of constraint collections

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

The data-correcting algorithm for supermodular functions, with applications to quadratic cost partition and simple plant location problems

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

From Junk to Function: LncRNAs in CNS Health and Disease

Recent advances in RNA sequencing technologies helped to uncover the existence of tens of thousands of long non-coding RNAs (lncRNAs) that arise from the dark matter of the genome. These lncRNAs were originally thought to be transcriptional noise but an increasing number of studies demonstrate that these transcripts can modulate protein-coding gene expression by a wide variety of transcriptional and post-transcriptional mechanisms. The spatiotemporal regulation of lncRNA expression is particularly evident in the central nervous system, suggesting that they may directly contribute to specific brain processes, including neurogenesis and cellular homeostasis. Not surprisingly, lncRNAs are therefore gaining attention as putative novel therapeutic targets for disorders of the brain. In this review, we summarize the recent insights into the functions of lncRNAs in the brain, their role in neuronal maintenance, and their potential contribution to disease. We conclude this review by postulating how these RNA molecules can be targeted for the treatment of yet incurable neurological disorders

microRNA-132 regulates gene expression programs involved in microglial homeostasis

microRNA-132 (miR-132), a known neuronal regulator, is one of the most robustly downregulated microRNAs (miRNAs) in the brain of Alzheimer's disease (AD) patients. Increasing miR-132 in AD mouse brain ameliorates amyloid and Tau pathologies, and also restores adult hippocampal neurogenesis and memory deficits. However, the functional pleiotropy of miRNAs requires in-depth analysis of the effects of miR-132 supplementation before it can be moved forward for AD therapy. We employ here miR-132 loss- and gain-of-function approaches using single-cell transcriptomics, proteomics, and in silico AGO-CLIP datasets to identify molecular pathways targeted by miR-132 in mouse hippocampus. We find that miR-132 modulation significantly affects the transition of microglia from a disease-associated to a homeostatic cell state. We confirm the regulatory role of miR-132 in shifting microglial cell states using human microglial cultures derived from induced pluripotent stem cells