On asymptotically hereditarily aspherical groups

We undertake a systematic study of asymptotically hereditarily aspherical (AHA) groups - the class of groups introduced by Tadeusz Januszkiewicz and the second author as a tool for exhibiting exotic properties of systolic groups. We provide many new examples of AHA groups, also in high dimensions. We relate AHA property with the topology at infinity of a group, and deduce in this way some new properties of (weakly) systolic groups. We also exhibit an interesting property of boundary at infinity for few classes of AHA groups.Comment: 36 pages, minor modifications to v

Shapes of Semiflexible Polymer Rings

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes depending on the flexibility of the polymer. For small perimeter to persistence length the fluctuating rings exhibit only planar, elliptical configurations. At higher flexibilities three dimensional, crumpled structures arise. Analytic calculations for tight polymer rings confirm an elliptical shape in the stiff regime.Comment: 4 pages, 3 figures, Version as published in Phys. Rev. Let

Operators on random hypergraphs and random simplicial complexes

Random hypergraphs and random simplicial complexes have potential applications in computer science and engineering. Various models of random hypergraphs and random simplicial complexes on n-points have been studied. Let L be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of L. By considering the minimal complex that a sub-hypergraph can be embedded in and the maximal complex that can be embedded in a sub-hypergraph, we define some operators on the space of probability functions on sub-hypergraphs of L. We study the compositions of these operators as well as their actions on the space of probability functions. As applications in computer science, we give algorithms generating large sparse random hypergraphs and large sparse random simplicial complexes.Comment: 22 page

The intracellular trafficking mechanism of Lipofectamine-based transfection reagents and its implication for gene delivery

Lipofectamine reagents are widely accepted as "gold-standard" for the safe delivery of exogenous DNA or RNA into cells. Despite this, a satisfactory mechanism-based explanation of their superior efficacy has remained mostly elusive thus far. Here we apply a straightforward combination of live cell imaging, single-particle tracking microscopy, and quantitative transfection-efficiency assays on live cells to unveil the intracellular trafficking mechanism of Lipofectamine/DNA complexes. We find that Lipofectamine, contrary to alternative formulations, is able to efficiently avoid active intracellular transport along microtubules, and the subsequent entrapment and degradation of the payload within acidic/digestive lysosomal compartments. This result is achieved by random Brownian motion of Lipofectamine-containing vesicles within the cytoplasm. We demonstrate here that Brownian diffusion is an efficient route for Lipofectamine/DNA complexes to avoid metabolic degradation, thus leading to optimal transfection. By contrast, active transport along microtubules results in DNA degradation and subsequent poor transfection. Intracellular trafficking, endosomal escape and lysosomal degradation appear therefore as highly interdependent phenomena, in such a way that they should be viewed as a single barrier on the route for efficient transfection. As a matter of fact, they should be evaluated in their entirety for the development of optimized non-viral gene delivery vectors

Large random simplicial complexes, II; the fundamental group

In our recent work we described conditions under which a multi-parameter random simplicial complex is connected and simply connected. We showed that the Betti numbers of multi-parameter random simplicial complexes in one specific dimension dominate significantly the Betti numbers in all other dimensions. In this paper we focus mainly on the properties of fundamental groups of multi-parameter random simplicial complexes, which can be viewed as a new class of random groups. We describe thresholds for nontrivially and hyperbolicity (in the sense of Gromov) for these groups. Besides, we find domains in the multi-parameter space where these groups have 2-torsion. We also prove that these groups have never odd-prime torsion and their geometric and cohomological dimensions are either 0,1, 2 or infinity. Another result presented in this paper states that aspherical 2-dimensional subcomplexes of random complexes satisfy the Whitehead Conjecture, i.e. all their subcomplexes are also aspherical (with probability tending to one).Comment: arXiv admin note: text overlap with arXiv:1312.1208, arXiv:1307.361

Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length

It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.Comment: v4: 41 pages, 6 figures rescaled at 120%; references updated, typos corrected, other minor corrections. v3: minor changes to the title, text and figures. v2: 41 pages, 6 figures; correction: Ore's conjecture was proved in 2008; 2 references added. v1: 40 pages, 6 figure