298 research outputs found
Moduli spaces of coherent systems of small slope on algebraic curves
Let be an algebraic curve of genus . A coherent system on
consists of a pair , where is an algebraic vector bundle over of
rank and degree and is a subspace of dimension of the space of
sections of . The stability of the coherent system depends on a parameter
. We study the geometry of the moduli space of coherent systems for
. We show that these spaces are irreducible whenever they are
non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction
SO(p,q)-Higgs bundles and Higher Teichmuller components
Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2, q), with q >= 4)
Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions
Articles in Marketing and choice literatures have demonstrated the need for
incorporating person-level heterogeneity into behavioral models (e.g., logit
models for multiple binary outcomes as studied here). However, the logit
likelihood extended with a population distribution of heterogeneity doesn't
yield closed-form inferences, and therefore numerical integration techniques
are relied upon (e.g., MCMC methods).
We present here an alternative, closed-form Bayesian inferences for the logit
model, which we obtain by approximating the logit likelihood via a polynomial
expansion, and then positing a distribution of heterogeneity from a flexible
family that is now conjugate and integrable. For problems where the response
coefficients are independent, choosing the Gamma distribution leads to rapidly
convergent closed-form expansions; if there are correlations among the
coefficients one can still obtain rapidly convergent closed-form expansions by
positing a distribution of heterogeneity from a Multivariate Gamma
distribution. The solution then comes from the moment generating function of
the Multivariate Gamma distribution or in general from the multivariate
heterogeneity distribution assumed.
Closed-form Bayesian inferences, derivatives (useful for elasticity
calculations), population distribution parameter estimates (useful for
summarization) and starting values (useful for complicated algorithms) are
hence directly available. Two simulation studies demonstrate the efficacy of
our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative
Marketing and Economics vol 4 (2006), no. 2, 173--20
Supersymmetric Gauge Theories, Vortices and Equivariant Cohomology
We construct actions for (p,0)- and (p,1)- supersymmetric, 1 <= p <= 4,
two-dimensional gauge theories coupled to non-linear sigma model matter with a
Wess-Zumino term. We derive the scalar potential for a large class of these
models. We then show that the Euclidean actions of the (2,0) and
(4,0)-supersymmetric models without Wess-Zumino terms are bounded by
topological charges which involve the equivariant extensions of the Kahler
forms of the sigma model target spaces evaluated on the two-dimensional
spacetime. We give similar bounds for Euclidean actions of appropriate gauge
theories coupled to non-linear sigma model matter in higher spacetime
dimensions which now involve the equivariant extensions of the Kahler forms of
the sigma model target spaces and the second Chern character of gauge fields.
The BPS configurations are generalisations of abelian and non-abelian vortices.Comment: 45 pages, Late
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.
Small Horizons
All near horizon geometries of supersymmetric black holes in a N=2, D=5
higher-derivative supergravity theory are classified. Depending on the choice
of near-horizon data we find that either there are no regular horizons, or
horizons exist and the spatial cross-sections of the event horizons are
conformal to a squashed or round S^3, S^1 * S^2, or T^3. If the conformal
factor is constant then the solutions are maximally supersymmetric. If the
conformal factor is not constant, we find that it satisfies a non-linear vortex
equation, and the horizon may admit scalar hair.Comment: 21 pages, latex. Typos corrected and reference adde
Stability Walls in Heterotic Theories
We study the sub-structure of the heterotic Kahler moduli space due to the
presence of non-Abelian internal gauge fields from the perspective of the
four-dimensional effective theory. Internal gauge fields can be supersymmetric
in some regions of the Kahler moduli space but break supersymmetry in others.
In the context of the four-dimensional theory, we investigate what happens when
the Kahler moduli are changed from the supersymmetric to the non-supersymmetric
region. Our results provide a low-energy description of supersymmetry breaking
by internal gauge fields as well as a physical picture for the mathematical
notion of bundle stability. Specifically, we find that at the transition
between the two regions an additional anomalous U(1) symmetry appears under
which some of the states in the low-energy theory acquire charges. We compute
the associated D-term contribution to the four-dimensional potential which
contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from
the charged states. We show that this D-term correctly reproduces the expected
physics. Several mathematical conclusions concerning vector bundle stability
are drawn from our arguments. We also discuss possible physical applications of
our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure
Disequilibrium in development finance: the contested politics of institutional accountability and transparency at the World Bank inspection panel
This article examines the dynamic nature with which independent accountability mechanisms operate. Focusing on the World Bank, the authors argue that its Inspection Panel evolves according to internal and external pressures. In seeking to achieve equilibrium, and protect its authority and independence, the Panel has gone through several distinct phases: negotiation, emergence, protracted resistance, assertion of independence and authority, renewed tension, and contestation. The core novelty of the article is its application of concepts from outside the field of development studies â notably institutional accountability from the governance literature, and judicialization from the legal studies literature â to the topic of the Inspection Panel. Examining the Panel in this way demonstrates that accountability mechanisms represent a hybrid of transnational governance influenced by a range of actors including project-affected peoples, national governments, managers and development donors. Accountability in development finance is about competing interests as well as competing conceptions and expectations of accountability. In such a complex and multi-scalar system, the Panel is not only concerned with delivering well-researched investigation reports; it is also an entity seeking to ensure its own survival, as well as an arbiter of its own brand of legitimacy and accountability. © 2018 The Authors. Development and Change published by John Wiley & Sons Ltd on behalf of Institute of Social Studie
Recognizing Speech in a Novel Accent: The Motor Theory of Speech Perception Reframed
The motor theory of speech perception holds that we perceive the speech of
another in terms of a motor representation of that speech. However, when we
have learned to recognize a foreign accent, it seems plausible that recognition
of a word rarely involves reconstruction of the speech gestures of the speaker
rather than the listener. To better assess the motor theory and this
observation, we proceed in three stages. Part 1 places the motor theory of
speech perception in a larger framework based on our earlier models of the
adaptive formation of mirror neurons for grasping, and for viewing extensions
of that mirror system as part of a larger system for neuro-linguistic
processing, augmented by the present consideration of recognizing speech in a
novel accent. Part 2 then offers a novel computational model of how a listener
comes to understand the speech of someone speaking the listener's native
language with a foreign accent. The core tenet of the model is that the
listener uses hypotheses about the word the speaker is currently uttering to
update probabilities linking the sound produced by the speaker to phonemes in
the native language repertoire of the listener. This, on average, improves the
recognition of later words. This model is neutral regarding the nature of the
representations it uses (motor vs. auditory). It serve as a reference point for
the discussion in Part 3, which proposes a dual-stream neuro-linguistic
architecture to revisits claims for and against the motor theory of speech
perception and the relevance of mirror neurons, and extracts some implications
for the reframing of the motor theory
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