820 research outputs found
Covariant hamiltonian dynamics
We discuss the covariant formulation of the dynamics of particles with
abelian and non-abelian gauge charges in external fields. Using this
formulation we develop an algorithm for the construction of constants of
motion, which makes use of a generalization of the concept of Killing vectors
and tensors in differential geometry. We apply the formalism to the motion of
classical charges in abelian and non-abelian monopole fieldsComment: 15 pages, no figure
Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off
Bundling of graph edges (node-to-node connections) is a common technique to
enhance visibility of overall trends in the edge structure of a large graph
layout, and a large variety of bundling algorithms have been proposed. However,
with strong bundling, it becomes hard to identify origins and destinations of
individual edges. We propose a solution: we optimize edge coloring to
differentiate bundled edges. We quantify strength of bundling in a flexible
pairwise fashion between edges, and among bundled edges, we quantify how
dissimilar their colors should be by dissimilarity of their origins and
destinations. We solve the resulting nonlinear optimization, which is also
interpretable as a novel dimensionality reduction task. In large graphs the
necessary compromise is whether to differentiate colors sharply between locally
occurring strongly bundled edges ("local bundles"), or also between the weakly
bundled edges occurring globally over the graph ("global bundles"); we allow a
user-set global-local tradeoff. We call the technique "peacock bundles".
Experiments show the coloring clearly enhances comprehensibility of graph
layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Examples of D=11 S-supersymmetric actions for point-like dynamical systems
A non standard super extensions of the Poincare algebra (S-algebra [1,2]),
which seems to be relevant for construction of various D=11 models, are
studied. We present two examples of actions for point-like dynamical systems,
which are invariant under off-shell closed realization of the S-algebra as well
as under local fermionic -symmetry. On this ground, an explicit form of
the S-algebra is advocated.Comment: 18 pages, LaTex fil
Green-Schwarz type formulation of D=11 S - invariant superstring and superparticle actions
A manifestly Poincare invariant formulations for and SO(2,9)
superstring actions are proposed. The actions are invariant under a local
fermionic -symmetry as well as under a number of global symmetries,
which turn out to be on-shell realization of the known ``new supersymmetry``
S-algebra. Canonical quantization of the theory is performed and relation of
the quantum state spectrum with that of type IIA Green-Schwarz superstring is
discussed. Besides, a mechanical model is constructed, which is a zero tension
limit of the D=11 superstring and which incorporates all essential features of
the latter. A corresponding action invariant under off-shell closed realization
of the S-algebra is obtained.Comment: Revised version, in particular, discussion of SO(2,9) case is
included. To be published in Int. J. Mod. Phys.
Scalability considerations for multivariate graph visualization
Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations
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