59,026 research outputs found
Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
We consider the Edwards-Anderson Ising spin glass model on the half-plane with zero external field and a wide range of choices, including
mean zero Gaussian, for the common distribution of the collection J of i.i.d.
nearest neighbor couplings. The infinite-volume joint distribution
of couplings J and ground state pairs with periodic
(respectively, free) boundary conditions in the horizontal (respectively,
vertical) coordinate is shown to exist without need for subsequence limits. Our
main result is that for almost every J, the conditional distribution
is supported on a single ground state pair.Comment: 20 pages, 3 figure
Doing the Public a Disservice: Behavioral Economics and Maintaining the Status Quo
When deciding whether to grant a preliminary injunction or a stay pending appeal, courts consider, among other factors, whether granting the preliminary injunction or stay would disserve the public interest. In the context of individual-rights cases, courts often experience pressure to remedy the alleged constitutional harms immediately. However, behavioral-economic concepts demonstrate that such quick action can negatively affect society as a whole. Specifically, granting a right and then taking it away, as happens when a lower court grants a right and is reversed on appeal, results in a net loss to society. Using the recent same-sex marriage litigation, this analysis demonstrates that to avoid disserving the public interest, courts should consider the behavioral-economic effects of loss aversion and the endowment effect within the public-interest factor of the tests for preliminary relief and should attempt to maintain the status quo until the decisions are final
Component sizes in networks with arbitrary degree distributions
We give an exact solution for the complete distribution of component sizes in
random networks with arbitrary degree distributions. The solution tells us the
probability that a randomly chosen node belongs to a component of size s, for
any s. We apply our results to networks with the three most commonly studied
degree distributions -- Poisson, exponential, and power-law -- as well as to
the calculation of cluster sizes for bond percolation on networks, which
correspond to the sizes of outbreaks of SIR epidemic processes on the same
networks. For the particular case of the power-law degree distribution, we show
that the component size distribution itself follows a power law everywhere
below the phase transition at which a giant component forms, but takes an
exponential form when a giant component is present.Comment: 5 pages, 1 figur
Stations, trains and small-world networks
The clustering coefficient, path length and average vertex degree of two
urban train line networks have been calculated. The results are compared with
theoretical predictions for appropriate random bipartite graphs. They have also
been compared with one another to investigate the effect of architecture on the
small-world properties.Comment: 6 pages, prepared in RevTe
Results of a zonally truncated three-dimensional model of the Venus middle atmosphere
Although the equatorial rotational speed of the solid surface of Venus is only 4 m s(exp-1), the atmospheric rotational speed reaches a maximum of approximately 100 m s(exp-1) near the equatorial cloud top level (65 to 70 km). This phenomenon, known as superrotation, is the central dynamical problem of the Venus atmosphere. We report here the results of numerical simulations aimed at clarifying the mechanism for maintaining the equatorial cloud top rotation. Maintenance of an equatorial rotational speed maximum above the surface requires waves or eddies that systematically transport angular momentum against its zonal mean gradient. The zonally symmetric Hadley circulation is driven thermally and acts to reduce the rotational speed at the equatorial cloud top level; thus wave or eddy transport must counter this tendency as well as friction. Planetary waves arising from horizontal shear instability of the zonal flow (barotropic instability) could maintain the equatorial rotation by transporting angular momentum horizontally from midlatitudes toward the equator. Alternatively, vertically propagating waves could provide the required momentum source. The relative motion between the rotating atmosphere and the pattern of solar heating, which as a maximum where solar radiation is absorbed near the cloud tops, drives diurnal and semidiurnal thermal tides that propagate vertically away from the cloud top level. The effect of this wave propagation is to transport momentum toward the cloud top level at low latitudes and accelerate the mean zonal flow there. We employ a semispectral primitive equation model with a zonal mean flow and zonal wavenumbers 1 and 2. These waves correspond to the diurnal and semidiurnal tides, but they can also be excited by barotropic or baroclinic instability. Waves of higher wavenumbers and interactions between the waves are neglected. Symmetry about the equator is assumed, so the model applies to one hemisphere and covers the altitude range 30 to 110 km. Horizontal resolution is 1.5 deg latitude, and vertical resolution is 1.5 km. Solar and thermal infrared heating, based on Venus observations and calculations drive the model flow. Dissipation is accomplished mainly by Rayleigh friction, chosen to produce strong dissipation above 85 km in order to absorb upward propagating waves and limit extreme flow velocities there, yet to give very weak Rayleigh friction below 70 km; results in the cloud layer do not appear to be sensitive to the Rayleigh friction. The model also has weak vertical diffusion, and very weak horizontal diffusion, which has a smoothing effect on the flow only at the two grid points nearest the pole
Large-scale structure of time evolving citation networks
In this paper we examine a number of methods for probing and understanding
the large-scale structure of networks that evolve over time. We focus in
particular on citation networks, networks of references between documents such
as papers, patents, or court cases. We describe three different methods of
analysis, one based on an expectation-maximization algorithm, one based on
modularity optimization, and one based on eigenvector centrality. Using the
network of citations between opinions of the United States Supreme Court as an
example, we demonstrate how each of these methods can reveal significant
structural divisions in the network, and how, ultimately, the combination of
all three can help us develop a coherent overall picture of the network's
shape.Comment: 10 pages, 6 figures; journal names for 4 references fixe
Optimization in Gradient Networks
Gradient networks can be used to model the dominant structure of complex
networks. Previous works have focused on random gradient networks. Here we
study gradient networks that minimize jamming on substrate networks with
scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural
correlations and strongly reduce congestion occurring on the network by using a
Monte Carlo optimization scheme. This optimization alters the degree
distribution and other structural properties of the resulting gradient
networks. These results are expected to be relevant for transport and other
dynamical processes in real network systems.Comment: 5 pages, 4 figure
Community detection and graph partitioning
Many methods have been proposed for community detection in networks. Some of
the most promising are methods based on statistical inference, which rest on
solid mathematical foundations and return excellent results in practice. In
this paper we show that two of the most widely used inference methods can be
mapped directly onto versions of the standard minimum-cut graph partitioning
problem, which allows us to apply any of the many well-understood partitioning
algorithms to the solution of community detection problems. We illustrate the
approach by adapting the Laplacian spectral partitioning method to perform
community inference, testing the resulting algorithm on a range of examples,
including computer-generated and real-world networks. Both the quality of the
results and the running time rival the best previous methods.Comment: 5 pages, 2 figure
- …