1,301 research outputs found
On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
We derive the Euler-Lagrange equations for minimizers of causal variational
principles in the non-compact setting with constraints, possibly prescribing
symmetries. Considering first variations, we show that the minimizing measure
is supported on the intersection of a hyperplane with a level set of a function
which is homogeneous of degree two. Moreover, we perform second variations to
obtain that the compact operator representing the quadratic part of the action
is positive semi-definite. The key ingredient for the proof is a subtle
adaptation of the Lagrange multiplier method to variational principles on
convex sets.Comment: 24 pages, LaTeX, 2 figures, minor improvements (published version
The Econometrics of Social Networks
In a social network, agents have their own reference group that may influence their behavior. In turn, the agents' attributes and their behavior affect the formation and the structure of the social network. We survey the econometric literature on both aspects of social networks and discuss the identification and estimation issues they raise.Social network, peer effects, identification, network formation, pair-wise regressions, separability, mutual consent
Concentration-compactness and finite-time singularities for Chen's flow
Chen's flow is a fourth-order curvature flow motivated by the spectral
decomposition of immersions, a program classically pushed by B.-Y. Chen since
the 1970s. In curvature flow terms the flow sits at the critical level of
scaling together with the most popular extrinsic fourth-order curvature flow,
the Willmore and surface diffusion flows. Unlike them however the famous Chen
conjecture indicates that there should be no stationary nonminimal data, and so
in particular the flow should drive all closed submanifolds to singularities.
We investigate this idea, proving that (1) closed data becomes extinct in
finite time in all dimensions and for any codimension; (2) singularities are
characterised by concentration of curvature in for intrinsic dimension and any codimension (a Lifespan Theorem); and (3) for and
in one codimension only, there exists an explicit small constant
such that if the norm of the tracefree curvature is
initially smaller than , the flow remains smooth until it
shrinks to a point, and that the blowup of that point is an embedded smooth
round sphere.Comment: 48 page
Identification of Peer Effects through Social Networks
We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where each individual has his own specific reference group. Interactions are thus structured through a social network. We assume that correlated unobservables are either absent, or treated as fixed effects at the component level. In both cases, we provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. Monte Carlo simulations provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of social effects. Our approach generalizes a number of previous results due to Manski (1993), Moffitt (2001), and Lee (2006).Social networks, Peer effects, identification, reflection problem
Generalization of the Van Cittert--Zernike theorem: observers moving with respect to sources
The use of the Van Cittert--Zernike theorem for the formulation of the
visibility function in satellite-based Earth observation with passive
radiometers does not take into account the relative motion of the observer (the
satellite antenna) with respect to sources of the electro-magnetic fields at
the surface of the Earth. The motion of the observer leads on the one hand to a
more complex signal due to a pixel-dependent Doppler shift that is neglected in
the standard derivation of the Van Cittert--Zernike theorem, but on the other
hand one may hope that it could be employed for a temporal aperture synthesis,
where virtual baselines are created through the motion of the satellite. Here,
we generalize the formulation of the aperture synthesis concept to the case of
observers moving with respect to the sources, and to the correlation of fields
measured at times that differ by the travel time of the observer along a
virtual baseline. Our derivation is based on first principles, starting with
the wave propagation in the Earth reference frame of electro-magnetic fields
arising from incoherent current sources, and Lorentz transforming the fields
into the reference frame of the satellite. Our detailed study leads to the
remarkable conclusion that the delay time due to observer motion cancels
exactly the Doppler effect. This justifies the neglect of the Doppler effect in
existing imaging systems based on the standard Van Cittert--Zernike theorem.Comment: 13 pages in IOP MST forma
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