We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of ...

We prove the computational intractability of rotating and placing n square tiles into a 1×n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NP-hard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying the...

We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NPhard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying th...

current innovative lateral load carrying systems for tall buildings are those in which the lateral drift is limited to an allowable value without considerable influence on economy. this aim is achieved by using special systems capable of using maximum stiffness and strength capacity of individual structural elements. an effective structural solution in this respect is the use of outrigger brace...

Gene tagging facilitates systematic genomic and proteomic analyses but chromosomal tagging typically disrupts gene regulatory sequences. Here we describe a seamless gene tagging approach that preserves endogenous gene regulation and is potentially applicable in any species with efficient DNA double-strand break repair by homologous recombination. We implement seamless tagging in Saccharomyces c...

the chechen republic (commonly referred to as chechnya) is a part of vast territory of russian federation that has been a source of contention since collapse of the soviet :union:. identity elements and tattered cultural bonds have strained ties between two nations of chechnya and russia. various aspects of crisis in chechnya have been addressed by many theoretical approaches of international r...

We present a generic transformation that allows us to use a large class of pairing-based signatures to construct schemes for signing group elements in a structure preserving way. As a result of our transformation we obtain a new efficient signature scheme for signing a vector of group elements that is based only on the well established decisional linear assumption (DLIN). Moreover, the public k...