12,789 research outputs found
On totally geodesic submanifolds in the Jacobian locus
We study submanifolds of A_g that are totally geodesic for the locally
symmetric metric and which are contained in the closure of the Jacobian locus
but not in its boundary. In the first section we recall a formula for the
second fundamental form of the period map due to Pirola, Tortora and the first
author. We show that this result can be stated quite neatly using a line bundle
over the product of the curve with itself. We give an upper bound for the
dimension of a germ of a totally geodesic submanifold passing through [C] in
M_g in terms of the gonality of C. This yields an upper bound for the dimension
of a germ of a totally geodesic submanifold contained in the Jacobian locus,
which only depends on the genus. We also study the submanifolds of A_g obtained
from cyclic covers of the projective line. These have been studied by various
authors. Moonen determined which of them are Shimura varieties using deep
results in positive characteristic. Using our methods we show that many of the
submanifolds which are not Shimura varieties are not even totally geodesic.Comment: To appear on International Journal of Mathematic
Boundary interpolation for slice hyperholomorphic Schur functions
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the
quaternionic setting. Given nonnegative real numbers , quaternions all of modulus , so that the
-spheres determined by each point do not intersect and for , and quaternions , we wish to find a slice
hyperholomorphic Schur function so that and
Our arguments relies on the theory of slice hyperholomorphic
functions and reproducing kernel Hilbert spaces
Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation
We revisit the problem of exact CMB likelihood and power spectrum estimation
with the goal of minimizing computational cost through linear compression. This
idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and
here we develop it into a fully working computational framework for large-scale
polarization analysis, adopting \WMAP\ as a worked example. We compare five
different linear bases (pixel space, harmonic space, noise covariance
eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise
covariance eigenvectors) in terms of compression efficiency, and find that the
computationally most efficient basis is the signal-to-noise eigenvector basis,
which is closely related to the Karhunen-Loeve and Principal Component
transforms, in agreement with previous suggestions. For this basis, the
information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a
smaller set of 3102 modes, with a maximum error increase of any single
multipole of 3.8\% at , and a maximum shift in the mean values of a
joint distribution of an amplitude--tilt model of 0.006. This
compression reduces the computational cost of a single likelihood evaluation by
a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust
likelihood by implicitly regularizing nearly degenerate modes. Finally, we use
the same compression framework to formulate a numerically stable and
computationally efficient variation of the Quadratic Maximum Likelihood
implementation that requires less than 3 GB of memory and 2 CPU minutes per
iteration for , rendering low- QML CMB power spectrum
analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ
On some differential-geometric aspects of the Torelli map
In this note we survey recent results on the extrinsic geometry of the
Jacobian locus inside . We describe the second fundamental form
of the Torelli map as a multiplication map, recall the relation between totally
geodesic subvarieties and Hodge loci and survey various results related to
totally geodesic subvarieties and the Jacobian locus.Comment: To appear on Boll. UMI, special volume in memory of Paolo de
Bartolomei
Eliciting public preferences for managing the public rights of way
Public Rights of Way (PROW) in England and Wales, provides a wide range of social and economic benefits to those other than owners of land. The protection and extension of PROW are an important way of encouraging people to engage in informal enjoyment of urban and rural areas, with beneficial consequences for health and welfare. In urban areas they provide networks of mobility and interaction for people at the community level, helping to reduce reliance on motorised transport. In the rural context they define access to the countryside, critically linked to recreation and tourism, as well as providing mobility networks for local residents. This study describes the use of a Choice Experiment (CE) to derive monetary estimates the social benefits of PROW in an English county.Choice Experiments, Public Rights of Way, Willingness to Pay, Land Economics/Use, Resource /Energy Economics and Policy,
Acquisitions of small high-tech firms as a mechanism for external knowledge sourcing: the integration-autonomy dilemma
Acquisitions of small high-tech firms by large incumbents are a prominent mechanism for external knowledge sourcing, whose success strictly depends on the choice of a wise post-acquisition implementation strategy. This paper theoretically discusses and empirically documents - on a sample of 458 deals in the 2001–2005 period - the antecedents of this choice by focusing on the integration-autonomy dilemma. Specifically, we jointly consider two main dimensions of the post-acquisition implementation: whether the acquiring firm absorbs the acquired one into its organization or keeps it separate as an autonomous subsidiary/business unit and whether the acquired CEO is replaced or retained. Separation with CEO retention corresponds to the minimum level of integration (and the maximum level of autonomy), whereas absorption with CEO replacement corresponds to the maximum level of integration (and the minimum level of autonomy.) We hypothesize that the acquiring firm chooses an implementation strategy with high level of integration when the acquired firm produces a component technology or operates in a related market. Indeed, in both cases, the interdependency between the two firms is high and thus the benefits of integration likely exceed the costs of the loss of autonomy. However, this positive association is weaker when the acquiring and acquired firms have common ground, originating from technological relatedness or prior alliances, which acts as a low-cost coordination mechanism. Results of econometric estimates largely confirm our hypotheses
Hyperbolic Balance Laws with a Non Local Source
This paper is devoted to hyperbolic systems of balance laws with non local
source terms. The existence, uniqueness and Lipschitz dependence proved here
comprise previous results in the literature and can be applied to physical
models, such as Euler system for a radiating gas and Rosenau regularization of
the Chapman-Enskog expansion.Comment: 26 page
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