72 research outputs found

### Technological Devices in the Archives: A Policy Analysis

Doing research in the archive is the cornerstone of humanities scholarship.
Various archives institute policies regarding the use of technological
devices, such as mobile phones, laptops, and cameras in their reading rooms.
Such policies directly affect the scholars as the devices mediate the nature of
their interaction with the source materials in terms of capturing, organizing,
note taking, and record keeping for future use of found materials. In this paper,
we present our analysis of the policies of thirty archives regarding the use of
technology in their reading rooms. This policy analysis, along with data from
interviews of scholars and archivists, is intended to serve as a basis for developing
mobile applications for assisting scholars in their research activities. In this
paper we introduce an early prototype of such a mobile application—
AMTracker.Informatio

### Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex
algebras, which are variants of topological vertex operator algebras studied
recently by Lian and Zuckerman. As an application, we obtain a conceptual and
geometric construction of the Batalin-Vilkovisky algebraic structure (or the
Gerstenhaber algebra structure) on the cohomology of a topological vertex
algebra (or of a weak topological vertex algebra) by combining this operadic
formulation with a theorem of Getzler (or of Cohen) which formulates
Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology
of the framed little disk operad (or of the little disk operad).Comment: 42 page

### An Inquiry into the Practice of Proving in Low-Dimensional Topology

The aim of this article is to investigate speciﬁc aspects connected with visualization in the practice of a mathematical subﬁeld: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justiﬁcations can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect diﬀerent pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a speciﬁc practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology

### Virtually abelian K\"ahler and projective groups

We characterise the virtually abelian groups which are fundamental groups of
compact K\"ahler manifolds and of smooth projective varieties. We show that a
virtually abelian group is K\"ahler if and only if it is projective. In
particular, this allows to describe the K\"ahler condition for such groups in
terms of integral symplectic representations

### Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems

In this paper we study a class of dynamical systems defined by Pfaffian maps. It is a sub-class of o-minimal dynamical systems which capture rich
continuous dynamics and yet can be studied using finite bisimulations.
The existence of finite bisimulations for o-minimal dynamical and hybrid systems has been shown by several authors; see e.g. Brihaye et al (2004), Davoren (1999), Lafferriere et al (2000).
The next natural question to investigate is how the sizes of such bisimulations can be bounded. The first step in this direction was done by Korovina et al (2004) where a double exponential upper bound was shown for Pfaffian dynamical and hybrid systems. In the present paper we improve this bound to a single exponential upper bound. Moreover we show that this bound is tight in general, by exhibiting a parameterized class of systems on which the exponential bound is attained.
The bounds provide a basis for designing efficient algorithms for computing
bisimulations, solving reachability and motion planning problems

### A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m,
which often happens for 2m<3n+4, then no concrete complete description of
embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint
unions of spheres. Let N be a closed connected orientable 3-manifold. Our main
result is the following description of the set Emb^6(N) of embeddings N\to R^6
up to isotopy.
The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in
H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where
d(u) is the divisibility of the projection of u to the free part of H_1(N;Z).
The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on
Emb^6(N) by embedded connected sum. It was proved that the orbit space of this
action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's
smoothing theory). The new part of our classification result is determination
of the orbits of the action. E. g. for N=RP^3 the action is free, while for
N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that
for each knot l:S^3\to R^6 the embedding f#l is isotopic to f.
Our proof uses new approaches involving the Kreck modified surgery theory or
the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in
Math. Zei

### Computing pseudotriangulations via branched coverings

We describe an efficient algorithm to compute a pseudotriangulation of a
finite planar family of pairwise disjoint convex bodies presented by its
chirotope. The design of the algorithm relies on a deepening of the theory of
visibility complexes and on the extension of that theory to the setting of
branched coverings. The problem of computing a pseudotriangulation that
contains a given set of bitangent line segments is also examined.Comment: 66 pages, 39 figure

### Chirality and Symmetry Breaking in a discrete internal Space

In previous papers the permutation group S_4 has been suggested as an
ordering scheme for elementary particles, and the appearance of this finite
symmetry group was taken as indication for the existence of a discrete inner
symmetry space underlying elementary particle interactions. Here it is pointed
out that a more suitable choice than the tetrahedral group S_4 is the
pyritohedral group A_4 x Z_2 because its vibrational spectrum exhibits exactly
the mass multiplet structure of the 3 fermion generations. Furthermore it is
noted that the same structure can also be obtained from a primordial symmetry
breaking S_4 --> A_4. Since A_4 is a chiral group, while S_4 is achiral, an
argument can be given why the chirality of the inner pyritohedral symmetry
leads to parity violation of the weak interactions.Comment: 42 pages, 3 table

- …