3,328 research outputs found
Tiling groupoids and Bratteli diagrams II: structure of the orbit equivalence relation
In this second paper, we study the case of substitution tilings of R^d. The
substitution on tiles induces substitutions on the faces of the tiles of all
dimensions j=0, ..., d-1. We reconstruct the tiling's equivalence relation in a
purely combinatorial way using the AF-relations given by the lower dimensional
substitutions. We define a Bratteli multi-diagram B which is made of the
Bratteli diagrams B^j, j=0, ..., d, of all those substitutions. The set of
infinite paths in B^d is identified with the canonical transversal Xi of the
tiling. Any such path has a "border", which is a set of tails in B^j for some j
less than or equal to d, and this corresponds to a natural notion of border for
its associated tiling. We define an etale equivalence relation R_B on B by
saying that two infinite paths are equivalent if they have borders which are
tail equivalent in B^j for some j less than or equal to d. We show that R_B is
homeomorphic to the tiling's equivalence relation R_Xi.Comment: 34 pages, 14 figure
Linear Multifractional Stable Motion: fine path properties
Linear Multifractional Stable Motion (LMSM), denoted by ,
has been introduced by Stoev and Taqqu in 2004-2005, by substituting to the
constant Hurst parameter of a classical Linear Fractional Stable Motion (LFSM),
a deterministic function depending on the time variable ; we
always suppose to be continuous and with values in (1/\al,1),
also, in general we restrict its range to a compact interval. The main goal of
our article is to make a comprehensive study of the local and asymptotic
behavior of ; to this end, one needs to derive fine path
properties of , the field
generating the latter process (i.e. one has for all ).
This leads us to introduce random wavelet series representations of as well as of all its pathwise partial
derivatives of any order with respect to . Then our strategy consists in
using wavelet methods. Among other things, we solve a conjecture of Stoev and
Taqqu, concerning the existence for LMSM of a modification with almost surely
continuous paths; moreover we provides some bounds for the local H\"older
exponent of LMSM: namely, we obtain a quasi-optimal global modulus of
continuity for it, and also an optimal local one. It is worth noticing that,
even in the quite classical case of LFSM, the latter optimal local modulus of
continuity provides a new result which was unknown so far
On the noncommutative geometry of tilings
This is a chapter in an incoming book on aperiodic order. We review results
about the topology, the dynamics, and the combinatorics of aperiodically
ordered tilings obtained with the tools of noncommutative geometry
Complexity and cohomology for cut and projection tilings
29 pages.We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of certain groups which appear in the construction. We give bounds for \alpha. These computations apply to some well known tilings, such as the octagonal tilings, or tilings associated with billiard sequences. A link is made between the exponent of the complexity, and the fact that the cohomology of the associated tiling space is finitely generated over \Q. We show that such a link cannot be established for more general tilings, and we present a counter-example in dimension one
Entrepreneurship in biotechnology: The case of four start-ups in the Upper-Rhine Biovalley.
This paper explores entrepreneurship in biotech through the in depth analysis of four new ventures located in the Upper-Rhine Biovalley. One of the strengths of this paper is the presence of both successful cases of entrepreneurship and of cases of failures. This gives the opportunity to discuss the role of several factors on the performance of a new biotech venture. Three points particularly comes out of this study: The importance of public science, without which new biotech firms could hardly exist; the role of the patent system, the importance of which we link to the business model adopted by the firm; and the importance of collaborations, which we study through the concept of distributed entrepreneurship.Intellectual property rights, patents, science, distributed entrepreneurship, collective invention.
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