2,049 research outputs found
The gauge structure of generalised diffeomorphisms
We investigate the generalised diffeomorphisms in M-theory, which are gauge
transformations unifying diffeomorphisms and tensor gauge transformations.
After giving an En(n)-covariant description of the gauge transformations and
their commutators, we show that the gauge algebra is infinitely reducible,
i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised
diffeomorphisms gives such a reducibility transformation. We give a concrete
description of the ghost structure, and demonstrate that the infinite sums give
the correct (regularised) number of degrees of freedom. The ghost towers belong
to the sequences of rep- resentations previously observed appearing in tensor
hierarchies and Borcherds algebras. All calculations rely on the section
condition, which we reformulate as a linear condition on the cotangent
directions. The analysis holds for n < 8. At n = 8, where the dual gravity
field becomes relevant, the natural guess for the gauge parameter and its
reducibility still yields the correct counting of gauge parameters.Comment: 24 pp., plain tex, 1 figure. v2: minor changes, including a few added
ref
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
A group model for stable multi-subject ICA on fMRI datasets
Spatial Independent Component Analysis (ICA) is an increasingly used
data-driven method to analyze functional Magnetic Resonance Imaging (fMRI)
data. To date, it has been used to extract sets of mutually correlated brain
regions without prior information on the time course of these regions. Some of
these sets of regions, interpreted as functional networks, have recently been
used to provide markers of brain diseases and open the road to paradigm-free
population comparisons. Such group studies raise the question of modeling
subject variability within ICA: how can the patterns representative of a group
be modeled and estimated via ICA for reliable inter-group comparisons? In this
paper, we propose a hierarchical model for patterns in multi-subject fMRI
datasets, akin to mixed-effect group models used in linear-model-based
analysis. We introduce an estimation procedure, CanICA (Canonical ICA), based
on i) probabilistic dimension reduction of the individual data, ii) canonical
correlation analysis to identify a data subspace common to the group iii)
ICA-based pattern extraction. In addition, we introduce a procedure based on
cross-validation to quantify the stability of ICA patterns at the level of the
group. We compare our method with state-of-the-art multi-subject fMRI ICA
methods and show that the features extracted using our procedure are more
reproducible at the group level on two datasets of 12 healthy controls: a
resting-state and a functional localizer study
Pure type I supergravity and DE(10)
We establish a dynamical equivalence between the bosonic part of pure type I
supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset
space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we
make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our
analysis also deals partly with the fermionic fields of the supergravity theory
and we define corresponding representations of the generalized spatial Lorentz
group K(DE(10)).Comment: 28 page
An E9 multiplet of BPS states
We construct an infinite E9 multiplet of BPS states for 11D supergravity. For
each positive real root of E9 we obtain a BPS solution of 11D supergravity, or
of its exotic counterparts, depending on two non-compact transverse space
variables. All these solutions are related by U-dualities realised via E9 Weyl
transformations in the regular embedding of E9 in E10, E10 in E11. In this way
we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5
brane and the KK6-monopole, as well as other solutions admitting eight
longitudinal space dimensions. A novel technique of combining Weyl reflexions
with compensating transformations allows the construction of many new BPS
solutions, each of which can be mapped to a solution of a dual effective action
of gravity coupled to a certain higher rank tensor field. For real roots of E10
which are not roots of E9, we obtain additional BPS solutions transcending 11D
supergravity (as exemplified by the lowest level solution corresponding to the
M9 brane). The relation between the dual formulation and the one in terms of
the original 11D supergravity fields has significance beyond the realm of BPS
solutions. We establish the link with the Geroch group of general relativity,
and explain how the E9 duality transformations generalize the standard Hodge
dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure
Spatially Invariant Coding of Numerical Information in Functionally Defined Subregions of Human Parietal Cortex
Macaque electrophysiology has revealed neurons responsive to number in lateral (LIP) and ventral (VIP) intraparietal areas. Recently, fMRI pattern recognition revealed information discriminative of individual numbers in human parietal cortex but without precisely localizing the relevant sites or testing for subregions with different response profiles. Here, we defined the human functional equivalents of LIP (feLIP) and VIP (feVIP) using neurophysiologically motivated localizers. We applied multivariate pattern recognition to investigate whether both regions represent numerical information and whether number codes are position specific or invariant. In a delayed number comparison paradigm with laterally presented numerosities, parietal cortex discriminated between numerosities better than early visual cortex, and discrimination generalized across hemifields in parietal, but not early visual cortex. Activation patterns in the 2 parietal regions of interest did not differ in the coding of position-specific or position-independent number information, but in the expression of a numerical distance effect which was more pronounced in feLIP. Thus, the representation of number in parietal cortex is at least partially position invariant. Both feLIP and feVIP contain information about individual numerosities in humans, but feLIP hosts a coarser representation of numerosity than feVIP, compatible with either broader tuning or a summation cod
Effects of nature of cooling surface on radiator performance
This report discusses the effects of roughness, smoothness, and cleanness of cooling surfaces on the performance of aeronautic radiators, as shown by experimental work, with different conditions of surface, on (1) heat transfer from a single brass tube and from a radiator; (2) pressure drop in an air stream in a single brass tube and in a radiator; (3) head resistance of a radiator; and (4) flow of air through a radiator. It is shown that while smooth surfaces are better than rough, the surfaces usually found in commercial radiators do not differ enough to show marked effect on performance, provided the surfaces are kept clean
Head Resistance Due to Radiators
Part 1 deals with the head resistance of a number of common types of radiator cores at different speeds in free air, as measured in the wind tunnel at the bureau of standards. This work was undertaken to determine the characteristics of various types of radiator cores, and in particular to develop the best type of radiator for airplanes. Some 25 specimens of core were tested, including practically all the general types now in use, except the flat plate type. Part 2 gives the results of wind tunnel tests of resistance on a model fuselage with a nose radiator. Part 3 presents the results of preliminary tests of head resistance of a radiator enclosed in a streamlined casing. Special attention is given to the value of wing radiator and of the radiator located in the open, especially when it is provided with a properly designed streamlined casing
Gradient Representations and Affine Structures in AE(n)
We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of
Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and
their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}.
The interplay between these two subalgebras is used, for n=3, to determine the
commutation relations of the `gradient generators' within AE(3). The low level
truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is
shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear
sigma-model resulting from the reduction Einstein's equations in (n+1)
dimensions to (1+1) dimensions. A further truncation to diagonal solutions can
be exploited to define a one-to-one correspondence between such solutions, and
null geodesic trajectories on the infinite-dimensional coset space H/K(H),
where H is the (extended) Heisenberg group, and K(H) its maximal compact
subgroup. We clarify the relation between H and the corresponding subgroup of
the Geroch group.Comment: 43 page
K(E10), Supergravity and Fermions
We study the fermionic extension of the E10/K(E10) coset model and its
relation to eleven-dimensional supergravity. Finite-dimensional spinor
representations of the compact subgroup K(E10) of E(10,R) are studied and the
supergravity equations are rewritten using the resulting algebraic variables.
The canonical bosonic and fermionic constraints are also analysed in this way,
and the compatibility of supersymmetry with local K(E10) is investigated. We
find that all structures involving A9 levels 0,1 and 2 nicely agree with
expectations, and provide many non-trivial consistency checks of the existence
of a supersymmetric extension of the E10/K(E10) coset model, as well as a new
derivation of the `bosonic dictionary' between supergravity and coset
variables. However, there are also definite discrepancies in some terms
involving level 3, which suggest the need for an extension of the model to
infinite-dimensional faithful representations of the fermionic degrees of
freedom.Comment: 50 page
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