Cycle-Level Products in Equivariant Cohomology of Toric Varieties

In this paper, we define an action of the group of equivariant Cartier divisors on a toric variety X on the equivariant cycle groups of X, arising naturally from a choice of complement map on the underlying lattice. If X is nonsingular, this gives a lifting of the multiplication in equivariant cohomology to the level of equivariant cycles. As a consequence, one naturally obtains an equivariant cycle representative of the equivariant Todd class of any toric variety. These results extend to equivariant cohomology the results of Thomas and Pommersheim. In the case of a complement map arising from an inner product, we show that the equivariant cycle Todd class obtained from our construction is identical to the result of the inductive, combinatorial construction of Berline-Vergne. In the case of arbitrary complement maps, we show that our Todd class formula yields the local Euler-Maclarurin formula introduced in Garoufalidis-Pommersheim.Comment: 15 pages, to be published in Michigan Mathematical Journal; LaTe

BASEL - The base language for an extensible language facility

Basic language for extensible language facilit

VR/Urban: spread.gun - design process and challenges in developing a shared encounter for media façades

Designing novel interaction concepts for urban environments is not only a technical challenge in terms of scale, safety, portability and deployment, but also a challenge of designing for social configurations and spatial settings. To outline what it takes to create a consistent and interactive experience in urban space, we describe the concept and multidisciplinary design process of VR/Urban's media intervention tool called Spread.gun, which was created for the Media Façade Festival 2008 in Berlin. Main design aims were the anticipation of urban space, situational system configuration and embodied interaction. This case study also reflects on the specific technical, organizational and infrastructural challenges encountered when developing media façade installations

The nonrelativistic limit of Dirac-Fock codes: the role of Brillouin configurations

We solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method (MCDF). We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We show that only large scale calculations that include all single excitations, even those obeying the Brillouin's theorem have the correct limit. We reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED. We obtain the correct non-relativistic limit not only for fine structure but also for level energies and show that RMBPT calculations are not immune to this problem.Comment: AUgust 9th, 2004 Second version Nov. 18th, 200

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

On Combining Lensing Shear Information from Multiple Filters

We consider the possible gain in the measurement of lensing shear from imaging data in multiple filters. Galaxy shapes may differ significantly across filters, so that the same galaxy offers multiple samples of the shear. On the other extreme, if galaxy shapes are identical in different filters, one can combine them to improve the signal-to-noise and thus increase the effective number density of faint, high redshift galaxies. We use the GOODS dataset to test these scenarios by calculating the covariance matrix of galaxy ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are highly correlated, and estimate the gain in galaxy number density by combining their shapes.Comment: 8 pages, no figures, submitted to JCA

On the Structure of Equilibria in Basic Network Formation

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by Alon et al. (2010), in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest $k$-vicinity (defined as the the set of vertices within distance $k$ from a vertex), for any $k \geq 1$ and in terms of the number of edges, thus settling positively a conjecture of Alon et al. in the cases of graphs of large $k$-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.Comment: 11 pages, 4 figure

Free-induction decay and envelope modulations in a narrowed nuclear spin bath

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure

On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups

We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. The problem for non-cubic groups was studied in previous papers by D. Bochis and the second author (Discrete Comput. Geom. 25:3 (2001), 419-444, and Beitr. Algebra Geom., 47:1 (2006), 89-120). This paper deals with ''full'' cubic groups, while ''quarter'' cubic groups are left for a subsequent paper. Here, ''full'' and ''quarter'' refers to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston (math.MG/9911185, Beitr. Algebra Geom. 42.2 (2001), 475-507). Our main result in this paper is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also find stereohedra with 17 facets for one of these groups.Comment: 28 pages, 12 figures. Changes from v1: apart of some editing (mostly at the end of the introduction) and addition of references, an appendix has been added, which analyzes the case where the base point does not have trivial stabilize