1,380 research outputs found
Classification of minimal actions of a compact Kac algebra with amenable dual
We show the uniqueness of minimal actions of a compact Kac algebra with
amenable dual on the AFD factor of type II. This particularly implies the
uniqueness of minimal actions of a compact group. Our main tools are a Rohlin
type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type
intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction
Extracting the Groupwise Core Structural Connectivity Network: Bridging Statistical and Graph-Theoretical Approaches
Finding the common structural brain connectivity network for a given
population is an open problem, crucial for current neuro-science. Recent
evidence suggests there's a tightly connected network shared between humans.
Obtaining this network will, among many advantages , allow us to focus
cognitive and clinical analyses on common connections, thus increasing their
statistical power. In turn, knowledge about the common network will facilitate
novel analyses to understand the structure-function relationship in the brain.
In this work, we present a new algorithm for computing the core structural
connectivity network of a subject sample combining graph theory and statistics.
Our algorithm works in accordance with novel evidence on brain topology. We
analyze the problem theoretically and prove its complexity. Using 309 subjects,
we show its advantages when used as a feature selection for connectivity
analysis on populations, outperforming the current approaches
Lattice dynamics and structural stability of ordered Fe3Ni, Fe3Pd and Fe3Pt alloys
We investigate the binding surface along the Bain path and phonon dispersion
relations for the cubic phase of the ferromagnetic binary alloys Fe3X (X = Ni,
Pd, Pt) for L12 and DO22 ordered phases from first principles by means of
density functional theory. The phonon dispersion relations exhibit a softening
of the transverse acoustic mode at the M-point in the L12-phase in accordance
with experiments for ordered Fe3Pt. This instability can be associated with a
rotational movement of the Fe-atoms around the Ni-group element in the
neighboring layers and is accompanied by an extensive reconstruction of the
Fermi surface. In addition, we find an incomplete softening in [111] direction
which is strongest for Fe3 Ni. We conclude that besides the valence electron
density also the specific Fe-content and the masses of the alloying partners
should be considered as parameters for the design of Fe-based functional
magnetic materials.Comment: Revised version, accepted for publication in Physical Review
Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II
In the first part, we have constructed several families of interacting
wedge-local nets of von Neumann algebras. In particular, there has been
discovered a family of models based on the endomorphisms of the U(1)-current
algebra of Longo-Witten.
In this second part, we further investigate endomorphisms and interacting
models. The key ingredient is the free massless fermionic net, which contains
the U(1)-current net as the fixed point subnet with respect to the U(1) gauge
action. Through the restriction to the subnet, we construct a new family of
Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting
wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the
structure of particle numbers and the S-matrices of the models constructed here
do mix the spaces with different particle numbers of the bosonic Fock space.Comment: 33 pages, 1 tikz figure. The final version is available under Open
Access. CC-B
Ground state representations of loop algebras
Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in
S^1 and identifying the real line with the punctured circle, we consider the
subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the
translation-invariant 2-cocycles on Sg. We show that the ground state
representation of Sg is unique for each cocycle. These ground states correspond
precisely to the vacuum representations of Lg.Comment: 22 pages, no figur
On the Structure of the Fusion Ideal
We prove that there is a finite level-independent bound on the number of
relations defining the fusion ring of positive energy representations of the
loop group of a simple, simply connected Lie group. As an illustration, we
compute the fusion ring of at all levels
Portable simulation framework for diffusion MRI
The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite element discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite element discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite element software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.La Caixa 201
Suicide and suicide prevention in Asia
Access the book via http://www.who.int/mental_health/resources/suicide_prevention_asia.pd
Dynamic changes in spatial representation within the posterior parietal cortex in response to visuomotor adaptation
From conformal embeddings to quantum symmetries: an exceptional SU(4) example
We briefly discuss several algebraic tools that are used to describe the
quantum symmetries of Boundary Conformal Field Theories on a torus. The
starting point is a fusion category, together with an action on another
category described by a quantum graph. For known examples, the corresponding
modular invariant partition function, which is sometimes associated with a
conformal embedding, provides enough information to recover the whole
structure. We illustrate these notions with the example of the conformal
embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the
exceptional quantum graph E4(SU(4)).Comment: 22 pages, 3 color figures. Version 2: We changed the color of figures
(ps files) in such a way that they are still understood when converted to
gray levels. Version 3: Several references have been adde
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