6,580 research outputs found
On compatibility between isogenies and polarisations of abelian varieties
We discuss the notion of polarised isogenies of abelian varieties, that is,
isogenies which are compatible with given principal polarisations. This is
motivated by problems of unlikely intersections in Shimura varieties. Our aim
is to show that certain questions about polarised isogenies can be reduced to
questions about unpolarised isogenies or vice versa.
Our main theorem concerns abelian varieties B which are isogenous to a fixed
abelian variety A. It establishes the existence of a polarised isogeny A to B
whose degree is polynomially bounded in n, if there exist both an unpolarised
isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As
a further result, we prove that given any two principally polarised abelian
varieties related by an unpolarised isogeny, there exists a polarised isogeny
between their fourth powers.
The proofs of both theorems involve calculations in the endomorphism algebras
of the abelian varieties, using the Albert classification of these endomorphism
algebras and the classification of Hermitian forms over division algebras
Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space
This study provides sufficient conditions for the temporal monotonic decay of
enstrophy for two-dimensional perturbations traveling in the incompressible,
viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's
procedure (1938) to the initial-value problem allowed us to find the region of
the wavenumber-Reynolds number map where the enstrophy of any initial
disturbance cannot grow. This region is wider than the kinetic energy's one. We
also show that the parameters space is split in two regions with clearly
distinct propagation and dispersion properties
Jet Algorithms and Top Quark Mass Measurement
Mass measurements of objects that decay into hadronic jets, such as the top
quark, are shown to be improved by using a variant of the jet algorithm
in place of standard cone algorithms. The possibility and importance of better
estimating the neutrino component in tagged jets is demonstrated. These
techniques will also be useful in the search for Higgs boson .Comment: 35 pages, REVTeX, 14 figures (epsf) Final expanded version to appear
in Physical Review
Ethnographic perspectives on global mental health
The field of Global Mental Health (GMH) aims to influence mental health policy and practice worldwide, with a focus on human rights and access to care. There have been important achievements, but GMH has also been the focus of scholarly controversies arising from political, cultural and pragmatic critiques. These debates have become increasingly polarized, giving rise to a need for more dialogue and experience-near research to inform theorizing. Ethnography has much to offer in this respect. This paper frames and introduces five articles in the issue of Transcultural Psychiatry that illustrate the role of ethnographic methods in understanding the effects and implications of the field of global mental health on mental health policy and practice. The papers include ethnographies from South Africa, India and Tonga, that show the potential for ethnographic evidence to inform GMH projects. These studies provide nuanced conceptualizations of GMH’s varied manifestations across different settings, the diverse ways that GMH’s achievements can be evaluated, and the connections that can be drawn between locally observed experiences and wider historical, political and social phenomena. Ethnography can provide a basis for constructive dialogue between those engaged in developing and implementing GMH interventions and those critical of some of its approaches
Dislocation Free Island Formation in Heteroepitaxial Growth: An Equilibrium Study
We investigate the equilibrium properties of strained heteroepitaxial
systems, incorporating the formation and the growth of a wetting film,
dislocation free island formation, and ripening. The derived phase diagram
provides a detailed characterization of the possible growth modes in terms of
the island density, equilibrium island size, and wetting layer thickness.
Comparing our predictions with experimental results we discuss the growth
conditions that can lead to stable islands as well as ripening.Comment: 4 pages, LaTeX, 3 ps figure
The dynamics of matrix momentum
We analyse the matrix momentum algorithm, which provides an efficient approximation to on-line Newton's method, by extending a recent statistical mechanics framework to include second order algorithms. We study the efficacy of this method when the Hessian is available and also consider a practical implementation which uses a single example estimate of the Hessian. The method is shown to provide excellent asymptotic performance, although the single example implementation is sensitive to the choice of training parameters. We conjecture that matrix momentum could provide efficient matrix inversion for other second order algorithms
Phases of the one-dimensional Bose-Hubbard model
The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model
with nearest-neighbor interaction is investigated using the Density-Matrix
Renormalization Group. Recently normal phases without long-range order have
been conjectured between the charge density wave phase and the superfluid phase
in one-dimensional bosonic systems without disorder. Our calculations
demonstrate that there is no intermediate phase in the one-dimensional
Bose-Hubbard model but a simultaneous vanishing of crystalline order and
appearance of superfluid order. The complete phase diagrams with and without
nearest-neighbor interaction are obtained. Both phase diagrams show reentrance
from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure
Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation
Recent concerns about the very large next-to-leading logarithmic (NLL)
corrections to the BFKL equation are addressed by the introduction of a
physical rapidity-separation parameter . At the leading logarithm (LL)
this parameter enforces the constraint that successive emitted gluons have a
minimum separation in rapidity, . The most significant
effect is to reduce the BFKL Pomeron intercept from the standard result as
is increased from 0 (standard BFKL). At NLL this -dependence
is compensated by a modification of the BFKL kernel, such that the total
dependence on is formally next-to-next-to-leading logarithmic. In this
formulation, as long as (for ): (i) the NLL
BFKL pomeron intercept is stable with respect to variations of , and
(ii) the NLL correction is small compared to the LL result. Implications for
the applicability of the BFKL resummation to phenomenology are considered.Comment: 16 pages, 3 figures, Late
Dynamic Key-Value Memory Networks for Knowledge Tracing
Knowledge Tracing (KT) is a task of tracing evolving knowledge state of
students with respect to one or more concepts as they engage in a sequence of
learning activities. One important purpose of KT is to personalize the practice
sequence to help students learn knowledge concepts efficiently. However,
existing methods such as Bayesian Knowledge Tracing and Deep Knowledge Tracing
either model knowledge state for each predefined concept separately or fail to
pinpoint exactly which concepts a student is good at or unfamiliar with. To
solve these problems, this work introduces a new model called Dynamic Key-Value
Memory Networks (DKVMN) that can exploit the relationships between underlying
concepts and directly output a student's mastery level of each concept. Unlike
standard memory-augmented neural networks that facilitate a single memory
matrix or two static memory matrices, our model has one static matrix called
key, which stores the knowledge concepts and the other dynamic matrix called
value, which stores and updates the mastery levels of corresponding concepts.
Experiments show that our model consistently outperforms the state-of-the-art
model in a range of KT datasets. Moreover, the DKVMN model can automatically
discover underlying concepts of exercises typically performed by human
annotations and depict the changing knowledge state of a student.Comment: To appear in 26th International Conference on World Wide Web (WWW),
201
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