8,595 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
3D billiards: visualization of regular structures and trapping of chaotic trajectories
The dynamics in three-dimensional billiards leads, using a Poincar\'e
section, to a four-dimensional map which is challenging to visualize. By means
of the recently introduced 3D phase-space slices an intuitive representation of
the organization of the mixed phase space with regular and chaotic dynamics is
obtained. Of particular interest for applications are constraints to classical
transport between different regions of phase space which manifest in the
statistics of Poincar\'e recurrence times. For a 3D paraboloid billiard we
observe a slow power-law decay caused by long-trapped trajectories which we
analyze in phase space and in frequency space. Consistent with previous results
for 4D maps we find that: (i) Trapping takes place close to regular structures
outside the Arnold web. (ii) Trapping is not due to a generalized
island-around-island hierarchy. (iii) The dynamics of sticky orbits is governed
by resonance channels which extend far into the chaotic sea. We find clear
signatures of partial transport barriers. Moreover, we visualize the geometry
of stochastic layers in resonance channels explored by sticky orbits.Comment: 20 pages, 11 figures. For videos of 3D phase-space slices and
time-resolved animations see http://www.comp-phys.tu-dresden.de/supp
On the impossibility of effectively using likely-invariants for software attestation purposes
Invariants monitoring is a software attestation technique that aims at proving the integrity of a running application by checking likely-invariants, which are statistically significant predicates inferred on variablesâ values. Being very promising, according to the software protection literature, we developed a technique to remotely monitor invariants. This paper presents the analysis we have performed to assess the effectiveness of our technique and the effectiveness of likely-invariants for software attestation purposes. Moreover, it illustrates the identified limitations and our studies to improve the detection abilities of this technique. Our results suggest that, despite further studies and future results may increase the efficacy and reduce the side effects, software attestation based on likely-invariants is not yet ready for the real world. Software developers should be warned of these limitations, if they could be tempted by adopting this technique, and companies developing software protections should not invest in development without also investing in further research
- âŠ