Solving Linear Constraints in Elementary Abelian p-Groups of Symmetries

Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of symmetries that can be huge, and the problem of their very existence is NP-hard. We formulate such an existence problem as a constraint problem on one variable (the symmetry to be used) ranging over a group, and try to find restrictions that may be solved in polynomial time. By considering a simple form of constraints (restricted by a cardinality k) and the class of groups that have the structure of Fp-vector spaces, we propose a partial algorithm based on linear algebra. This polynomial algorithm always applies when k=p=2, but may fail otherwise as we prove the problem to be NP-hard for all other values of k and p. Experiments show that this approach though restricted should allow for an efficient use of at least some groups of symmetries. We conclude with a few directions to be explored to efficiently solve this problem on the general case.Comment: 18 page

Putting the genome on the map

The maps of our everyday lives are much more than just linear lists of place names. Instead, their colours, symbols, contours and grid lines seek to describe different types of landscape, and to depict the spatial relationships between structural and functional landmarks of the environment (Fig. 1). It was the combination of photography and aviation that revolutionized mapmaking in the early part of this century. In much the same way, it is fluorescence microscopy and digital imaging (Box 1) in combination with molecular genetics that is driving our emerging view of the genome in space and time

Evidence of Activity-Specific, Radial Organization of Mitotic Chromosomes in Drosophila

A fluorescently labeled protein specifically binding to genes was reproducibly found at the periphery of condensed mitotic fruit fly chromosomes, illustrating preservation of a radial structure between consecutive divisions

3D-CLEM reveals that a major portion of mitotic chromosomes is not Chromatin

Recent studies have revealed the importance of Ki-67 and the chromosome periphery in chromosome structure and segregation, but little is known about this elusive chromosome compartment. Here we used correlative light and serial block-face scanning electron microscopy, which we term 3D-CLEM, to model the entire mitotic chromosome complement at ultra-structural resolution. Prophase chromosomes exhibit a highly irregular surface appearance with a volume smaller than metaphase chromosomes. This may be because of the absence of the periphery, which associates with chromosomes only after nucleolar disassembly later in prophase. Indeed, the nucleolar volume almost entirely accounts for the extra volume found in metaphase chromosomes. Analysis of wild-type and Ki-67-depleted chromosomes reveals that the periphery comprises 30%-47% of the entire chromosome volume and more than 33% of the protein mass of isolated mitotic chromosomes determined by quantitative proteomics. Thus, chromatin makes up a surprisingly small percentage of the total mass of metaphase chromosomes

True Parallel Graph Transformations: an Algebraic Approach Based on Weak Spans

21 pages, 5 figuresWe address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the form $L\xleftarrow{l}K \xleftarrow{i} I \xrightarrow{r} R$, called weak spans. A parallel coherent transformation is introduced and shown to be a conservative extension of the interleaving semantics of parallel independent direct transformations. A categorical construction of finitely attributed structures is proposed, in which parallel coherent transformations can be built in a natural way. These notions are introduced and illustrated on detailed examples

Monographs, a Category of Graph Structures

International audienceDoes a graph necessarily have nodes? May an edge be adjacent to itself and be a self-loop? These questions arise in the study of graph structures, i.e., monadic many-sorted signatures and the corresponding algebras. A simple notion of monograph is proposed that generalizes the standard notion of directed graph and can be drawn consistently with them. It is shown that monadic many-sorted signatures can be represented by monographs, and that the corresponding algebras are isomorphic to the monographs typed by the corresponding signature monograph. Monographs therefore provide a simple unifying framework for working with monadic algebras. Their simplicity is illustrated by deducing some of their categorial properties from those of sets