5,741 research outputs found
Cut Size Statistics of Graph Bisection Heuristics
We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin
Non-Markovian data-driven modeling of single-cell motility
Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by thenon-Markovian version of the Langevin equation that includes an arbitrary memory function. When averagedover cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterizedby Gaussian velocity distributions. Accordingly, the data are described by a linear memory model whichincludes different random walk models that were previously used to account for various aspects of cell motilitysuch as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memoryfunction is extracted from the trajectory data without restrictions or assumptions, thus making our approachtruly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayedsingle-exponential negative friction, which clearly distinguishes cell motion from the simple persistent randomwalk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extractedmemory function we formulate a generalized exactly solvable cell migration model which indicates thatnegative friction generates cell persistence over long timescales. The nonequilibrium character of cell motionis investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model thatinvolves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process
The non-Abelian tensor multiplet in loop space
We introduce a non-Abelian tensor multiplet directly in the loop space
associated with flat six-dimensional Minkowski space-time, and derive the
supersymmetry variations for on-shell supersymmetry.Comment: 11 pages, v2: cleaner presentation, mistakes are corrected (and an
erroneous section was removed
Stable Non-Supersymmetric Supergravity Solutions from Deformations of the Maldacena-Nunez Background
We study a deformation of the type IIB Maldacena-Nunez background which
arises as the near-horizon limit of NS5 branes wrapped on a two-cycle. This
background is dual to a "little string theory" compactified on a two-sphere, a
theory which at low energies includes four-dimensional N = 1 super Yang-Mills
theory. The deformation we study corresponds to a mass term for some of the
scalar fields in this theory, and it breaks supersymmetry completely. In the
language of seven-dimensional SO(4) gauged supergravity the deformation
involves (at leading order) giving a VEV, depending only on the radial
coordinate, to a particular scalar field. We explicitly construct the
corresponding solution at leading order in the deformation, both in
seven-dimensional and in ten-dimensional supergravity, and we verify that it
completely breaks supersymmetry. Since the original background had a mass gap
and we are performing a small deformation, the deformed background is
guaranteed to be stable even though it is not supersymmetric.Comment: 1+31 pages, one figure. v2: minor clarifications, refs adde
- …