3,821 research outputs found
On the total variation regularized estimator over a class of tree graphs
We generalize to tree graphs obtained by connecting path graphs an oracle
result obtained for the Fused Lasso over the path graph. Moreover we show that
it is possible to substitute in the oracle inequality the minimum of the
distances between jumps by their harmonic mean. In doing so we prove a lower
bound on the compatibility constant for the total variation penalty. Our
analysis leverages insights obtained for the path graph with one branch to
understand the case of more general tree graphs.
As a side result, we get insights into the irrepresentable condition for such
tree graphs.Comment: 42 page
Consensus Control for Leader-follower Multi-agent Systems under Prescribed Performance Guarantees
This paper addresses the problem of distributed control for leader-follower
multi-agent systems under prescribed performance guarantees. Leader-follower is
meant in the sense that a group of agents with external inputs are selected as
leaders in order to drive the group of followers in a way that the entire
system can achieve consensus within certain prescribed performance transient
bounds. Under the assumption of tree graphs, a distributed control law is
proposed when the decay rate of the performance functions is within a
sufficient bound. Then, two classes of tree graphs that can have additional
followers are investigated. Finally, several simulation examples are given to
illustrate the results.Comment: 8 page
Labelled tree graphs, Feynman diagrams and disk integrals
In this note, we introduce and study a new class of "half integrands" in
Cachazo-He-Yuan (CHY) formula, which naturally generalize the so-called
Parke-Taylor factors; these are dubbed Cayley functions as each of them
corresponds to a labelled tree graph. The CHY formula with a Cayley function
squared gives a sum of Feynman diagrams, and we represent it by a combinatoric
polytope whose vertices correspond to Feynman diagrams. We provide a simple
graphic rule to derive the polytope from a labelled tree graph, and classify
such polytopes ranging from the associahedron to the permutohedron.
Furthermore, we study the linear space of such half integrands and find (1) a
nice formula reducing any Cayley function to a sum of Parke-Taylor factors in
the Kleiss-Kuijf basis (2) a set of Cayley functions as a new basis of the
space; each element has the remarkable property that its CHY formula with a
given Parke-Taylor factor gives either a single Feynman diagram or zero. We
also briefly discuss applications of Cayley functions and the new basis in
certain disk integrals of superstring theory.Comment: 30+8 pages, many figures;typos fixe
MHV Vertices And Tree Amplitudes In Gauge Theory
As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills
theory can be constructed from tree graphs in which the vertices are tree level
MHV scattering amplitudes, continued off shell in a particular fashion. The
formalism leads to new and relatively simple formulas for many amplitudes, and
can be heuristically derived from twistor space.Comment: 27 p
Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
We present examples of rooted tree graphs for which the Laplacian has
singular continuous spectral measures. For some of these examples we further
establish fractional Hausdorff dimensions. The singular continuous components,
in these models, have an interesting multiplicity structure. The results are
obtained via a decomposition of the Laplacian into a direct sum of Jacobi
matrices
On Volumes of Permutation Polytopes
This paper focuses on determining the volumes of permutation polytopes
associated to cyclic groups, dihedral groups, groups of automorphisms of tree
graphs, and Frobenius groups. We do this through the use of triangulations and
the calculation of Ehrhart polynomials. We also present results on the theta
body hierarchy of various permutation polytopes.Comment: 19 pages, 1 figur
- âŠ