78,123 research outputs found
Stability of Influence Maximization
The present article serves as an erratum to our paper of the same title,
which was presented and published in the KDD 2014 conference. In that article,
we claimed falsely that the objective function defined in Section 1.4 is
non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean
Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example
to that claim.
Subsequent to becoming aware of the counter-example, we have shown that the
objective function is in fact NP-hard to approximate to within a factor of
for any .
In an attempt to fix the record, the present article combines the problem
motivation, models, and experimental results sections from the original
incorrect article with the new hardness result. We would like readers to only
cite and use this version (which will remain an unpublished note) instead of
the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was
presented and published in the KDD1
Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution
A general framework of evolutionary dynamics under heterogeneous populations
is presented. The framework allows continuously many types of heterogeneous
agents, heterogeneity both in payoff functions and in revision protocols and
the entire joint distribution of strategies and types to influence the payoffs
of agents. We clarify regularity conditions for the unique existence of a
solution trajectory and for the existence of equilibrium. We confirm that
equilibrium stationarity in general and equilibrium stability in potential
games are extended from the homogeneous setting to the heterogeneous setting.
In particular, a wide class of admissible dynamics share the same set of
locally stable equilibria in a potential game through local maximization of the
potential
Dynamics of Heterogeneous Congestion Tolerance in the Location Choices of U.S. Gulf of Mexico Shrimp Fishermen
Location choice is one of the most important short-run decisions made by commercial fishermen. Previous studies of location choice by commercial fishermen have focused primarily on site fidelity, profit-maximization behavior, and risk attitudes as factors influencing their location choice behavior. Although the recreational literature gives extensive consideration to the influence of congestion on site selection, few studies have considered the influence of congestion tolerance on site selection in the commercial fishing sector. This study uses a mixed logit model to analyze the heterogeneous congestion tolerance in location choice among U.S. Gulf of Mexico shrimp fishermen. The dynamics of fishermen responses to economic conditions are compared and contrasted for two periods; the first period coinciding with relative economic stability in the industry and the second period coinciding with deteriorating economic conditions. Results suggest that congestion externalities have significant influence on the location choice of shrimp fishermen, but that congestion tolerance level differs among them. A better understanding of heterogeneous congestion tolerance should aid the implementation of management tools such as area closures.location choice, congestion, mixed logit, shrimp fishery, Resource /Energy Economics and Policy,
Small gain theorems for large scale systems and construction of ISS Lyapunov functions
We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
Using a Maximum Entropy Production Principle (MEPP), we derive a new type of
relaxation equations for two-dimensional turbulent flows in the case where a
prior vorticity distribution is prescribed instead of the Casimir constraints
[Ellis, Haven, Turkington, Nonlin., 15, 239 (2002)]. The particular case of a
Gaussian prior is specifically treated in connection to minimum enstrophy
states and Fofonoff flows. These relaxation equations are compared with other
relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776
(1992)] and Chavanis [Physica D, 237, 1998 (2008)]. They can provide a
small-scale parametrization of 2D turbulence or serve as numerical algorithms
to compute maximum entropy states with appropriate constraints. We perform
numerical simulations of these relaxation equations in order to illustrate
geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure
Influence Maximization based on Simplicial Contagion Model in Hypergraph
In recent years, the issue of node centrality has been actively and
extensively explored due to its applications in product recommendations,
opinion propagation, disease spread, and other areas involving maximizing node
influence. This paper focuses on the problem of influence maximization on the
Simplicial Contagion Model, using the susceptible-infectedrecovered (SIR) model
as an example. To find practical solutions to this optimization problem, we
have developed a theoretical framework based on message passing processes and
conducted stability analysis of equilibrium solutions for the self-consistent
equations. Furthermore, we introduce a metric called collective influence and
propose an adaptive algorithm, known as the Collective Influence Adaptive
(CIA), to identify influential propagators in the spreading process. This
method has been validated on both synthetic hypergraphs and real hypergraphs,
outperforming other competing heuristic methods.Comment: 19 pages,16 figure
Coreness of Cooperative Games with Truncated Submodular Profit Functions
Coreness represents solution concepts related to core in cooperative games,
which captures the stability of players. Motivated by the scale effect in
social networks, economics and other scenario, we study the coreness of
cooperative game with truncated submodular profit functions. Specifically, the
profit function is defined by a truncation of a submodular function
: if and
otherwise, where is a given threshold. In this paper, we
study the core and three core-related concepts of truncated submodular profit
cooperative game. We first prove that whether core is empty can be decided in
polynomial time and an allocation in core also can be found in polynomial time
when core is not empty. When core is empty, we show hardness results and
approximation algorithms for computing other core-related concepts including
relative least-core value, absolute least-core value and least average
dissatisfaction value
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