Tensor-restriction categories

Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are partially defined with respect to this spatial structure. We introduce a construction that turns a firm monoidal category into a restriction category and axiomatise the monoidal restriction categories that arise this way, called tensor-restriction categories.Comment: 31 page

Decomposition spaces and restriction species

We show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce directed restriction species that subsume Schmitt’s restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finite sets and injections, directed restriction species are presheaves on the category of finite posets and convex maps. We also introduce the notion of monoidal (directed) restriction species, which induce monoidal decomposition spaces and hence bialgebras, most often Hopf algebras. Examples of this notion include rooted forests, directed graphs, posets, double posets, and many related structures. A prominent instance of a resulting incidence bialgebra is the Butcher–Connes–Kreimer Hopf algebra of rooted trees. Both ordinary and directed restriction species are shown to be examples of a construction of decomposition spaces from certain cocartesian fibrations over the category of finite ordinals that are also cartesian over convex maps. The proofs rely on some beautiful simplicial combinatorics, where the notion of convexity plays a key role. The methods developed are of independent interest as techniques for constructing decomposition spacesPeer ReviewedPostprint (author's final draft

Witt vectors as a polynomial functor

For every commutative ring $A$, one has a functorial commutative ring $W(A)$ of $p$-typical Witt vectors of $A$, an iterated extension of $A$ by itself. If $A$ is not commutative, it has been known since the pioneering work of L. Hesselholt that $W(A)$ is only an abelian group, not a ring, and it is an iterated extension of the Hochschild homology group $HH_0(A)$ by itself. It is natural to expect that this construction generalizes to higher degrees and arbitrary coefficients, so that one can define "Hochschild-Witt homology" $WHH_*(A,M)$ for any bimodule $M$ over an associative algebra $A$ over a field $k$. Moreover, if one want the resulting theory to be a trace theory in the sense of arXiv:1308.3743, then it suffices to define it for $A=k$. This is what we do in this paper, for a perfect field $k$ of positive characteristic $p$. Namely, we construct a sequence of polynomial functors $W_m$, $m \geq 1$ from $k$-vector spaces to abelian groups, related by restriction maps, we prove their basic properties such as the existence of Frobenius and Verschiebung maps, and we show that $W_m$ are trace functors in the sense of arXiv:1308.3743. The construction is very simple, and it only depends on elementary properties of finite cyclic groups.Comment: LaTeX2e, 49 pages. Final version -- corrected some typo

A physical map of human Alu repeats cleavage by restriction endonucleases

<p>Abstract</p> <p>Background</p> <p>Alu repetitive elements are the abundant sequences in human genome. Diversity of DNA sequences of these elements makes difficult the construction of theoretical patterns of Alu repeats cleavage by restriction endonucleases. We have proposed a method of restriction analysis of Alu repeats sequences <it>in silico</it>.</p> <p>Results</p> <p>Simple software to analyze Alu repeats database has been suggested and Alu repeats digestion patterns for several restriction enzymes' recognition sites have been constructed. Restriction maps of Alu repeats cleavage for corresponding restriction enzymes have been calculated and plotted. Theoretical data have been compared with experimental results on DNA hydrolysis with restriction enzymes, which we obtained earlier.</p> <p>Conclusion</p> <p>Alu repeats digestions provide the main contribution to the patterns of human chromosomal DNA cleavage. This corresponds to the experimental data on total human DNA hydrolysis with restriction enzymes.</p

Automatic construction of restriction site maps by computer

Thesis (B.S.) in Liberal Arts and Sciences--University of Illinois at Urbana-Champaign, 1984.Bibliography: leaf 51.Microfiche of typescript. [Urbana, Ill.] : Photographic Services, University of Illinois, U of I Library, [1987]. 2 microfiches (62 frames) negative ; 11 x 15 cm

Full Length Research Paper LTR-retrotransposons-based molecular markers in cultivated Egyptian cottons G. barbadense L.

Long terminal repeat (LTR)-retrotransposons are mobile genetic elements that are ubiquitous in plants and constitute a major portion of their nuclear genomes. LTR-retrotransposons possess unique properties that make them appropriate for investigating relationships between closely related species and populations. The aim of the current study was to employ Ty1-copia group retrotransposons as molecular markers in cultivated Egyptian cottons, G. barbadense L. Restriction site analysis of PCRamplified Ty1-copia RT domain promoted the construction of a restriction map for each Egyptian cultivar. These maps display distinctive patterns of restriction site variation. Furthermore, these patterns are capable of differentiating even between cultivars that appear to have diverged only in the past 50 years. These results demonstrate that retrotransposon-based molecular markers are particularly valuable tools for plant molecular phylogenetic and population genetic studie