Dendroidal sets as models for connective spectra

Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant objects given by fully Kan dendroidal sets. Moreover we show that the resulting homotopy theory is equivalent to the homotopy theory of connective spectra.Comment: 27 pages, final version, accepted for publication in Journal of K-theor

The maximal energy of classes of integral circulant graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count $n$ and a set $\cal D$ of divisors of $n$ in such a way that they have vertex set $\mathbb{Z}_n$ and edge set ${{a,b}: a,b\in\mathbb{Z}_n, \gcd(a-b,n)\in {\cal D}}$. For a fixed prime power $n=p^s$ and a fixed divisor set size $|{\cal D}| =r$, we analyze the maximal energy among all matching integral circulant graphs. Let $p^{a_1} < p^{a_2} < ... < p^{a_r}$ be the elements of ${\cal D}$. It turns out that the differences $d_i=a_{i+1}-a_{i}$ between the exponents of an energy maximal divisor set must satisfy certain balance conditions: (i) either all $d_i$ equal $q:=\frac{s-1}{r-1}$, or at most the two differences $[q]$ and $[q+1]$ may occur; %(for a certain $d$ depending on $r$ and $s$) (ii) there are rules governing the sequence $d_1,...,d_{r-1}$ of consecutive differences. For particular choices of $s$ and $r$ these conditions already guarantee maximal energy and its value can be computed explicitly.Comment: Discrete Applied Mathematics (2012

Koštana pregradnja pomoću osteoklasta: što smo naučili iz ispitivanja knockout gena?

Osteopetroses are disorders of bone remodeling resulting in increased bone mass. Osteopetrosis abnormalities can include changes in osteoclast lineage, bone marrow microenvironment, or both. Little is known about the mechanisms that regulate the activity of different bone cell types. Various agents act on bone in a complicated web of interactions, with either synergistic or diverse effects. Advances in molecular biology have enabled studies in knockout or transgenic animals, providing an insight into the mechanism of bone remodeling.Osteopetroze su poremećaji pregradnje kostiju koji dovode do povećanja koštane mase. Osteopetrotične abnormalnosti mogu obuhvaćati promjene u staničnoj liniji osteoklasta, u mikrookolišu koštane srži ili oboje. Malo se zna o mehanizmima koji reguliraju aktivnost različitih vrsta koštanih stanica. Različiti čimbenici utječu na kost kroz čitav splet međusobnih aktivnosti sa sinergističnim ili raznovrsnim učincima. Napredak u molekularnoj biologiji omogućio je ispitivanja na knockout ili transgenskim životinjama, pružajući uvid u mehanizme koštane pregradnje