1,744 research outputs found
A metadata-enhanced framework for high performance visual effects
This thesis is devoted to reducing the interactive latency of image processing computations in
visual effects. Film and television graphic artists depend upon low-latency feedback to receive
a visual response to changes in effect parameters. We tackle latency with a domain-specific optimising
compiler which leverages high-level program metadata to guide key computational and
memory hierarchy optimisations. This metadata encodes static and dynamic information about
data dependence and patterns of memory access in the algorithms constituting a visual effect –
features that are typically difficult to extract through program analysis – and presents it to the
compiler in an explicit form. By using domain-specific information as a substitute for program
analysis, our compiler is able to target a set of complex source-level optimisations that a vendor
compiler does not attempt, before passing the optimised source to the vendor compiler for
lower-level optimisation.
Three key metadata-supported optimisations are presented. The first is an adaptation of
space and schedule optimisation – based upon well-known compositions of the loop fusion and
array contraction transformations – to the dynamic working sets and schedules of a runtimeparameterised
visual effect. This adaptation sidesteps the costly solution of runtime code generation
by specialising static parameters in an offline process and exploiting dynamic metadata to
adapt the schedule and contracted working sets at runtime to user-tunable parameters. The second
optimisation comprises a set of transformations to generate SIMD ISA-augmented source code.
Our approach differs from autovectorisation by using static metadata to identify parallelism, in
place of data dependence analysis, and runtime metadata to tune the data layout to user-tunable
parameters for optimal aligned memory access. The third optimisation comprises a related set
of transformations to generate code for SIMT architectures, such as GPUs. Static dependence
metadata is exploited to guide large-scale parallelisation for tens of thousands of in-flight threads.
Optimal use of the alignment-sensitive, explicitly managed memory hierarchy is achieved by identifying
inter-thread and intra-core data sharing opportunities in memory access metadata.
A detailed performance analysis of these optimisations is presented for two industrially developed
visual effects. In our evaluation we demonstrate up to 8.1x speed-ups on Intel and AMD
multicore CPUs and up to 6.6x speed-ups on NVIDIA GPUs over our best hand-written implementations
of these two effects. Programmability is enhanced by automating the generation of
SIMD and SIMT implementations from a single programmer-managed scalar representation
Center vortices and confinement vs. screening
We study adjoint and fundamental Wilson loops in the center-vortex picture of
confinement, for gauge group SU(N) with general N. There are N-1 distinct
vortices, whose properties, including collective coordinates and actions, we
study. In d=2 we construct a center-vortex model by hand so that it has a
smooth large-N limit of fundamental-representation Wilson loops and find, as
expected, confinement. Extending an earlier work by the author, we construct
the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion
in powers of , where is the vortex density per unit area and M
is the vortex inverse size, and find, as expected, screening. The leading term
of the adjoint potential shows a roughly linear regime followed by string
breaking when the potential energy is about 2M. This leading potential is a
universal (N-independent at fixed fundamental string tension ) of the form
, where R is the spacelike dimension of a rectangular Wilson
loop. The linear-regime slope is not necessarily related to by Casimir
scaling. We show that in d=2 the dilute vortex model is essentially equivalent
to true d=2 QCD, but that this is not so for adjoint representations; arguments
to the contrary are based on illegal cumulant expansions which fail to
represent the necessary periodicity of the Wilson loop in the vortex flux. Most
of our arguments are expected to hold in d=3,4 also.Comment: 29 pages, LaTex, 1 figure. Minor changes; references added;
discussion of factorization sharpened. Major conclusions unchange
Center Vortices, Nexuses, and the Georgi-Glashow Model
In a gauge theory with no Higgs fields the mechanism for confinement is by
center vortices, but in theories with adjoint Higgs fields and generic symmetry
breaking, such as the Georgi-Glashow model, Polyakov showed that in d=3
confinement arises via a condensate of 't Hooft-Polyakov monopoles. We study
the connection in d=3 between pure-gauge theory and the theory with adjoint
Higgs by varying the Higgs VEV v. As one lowers v from the Polyakov semi-
classical regime v>>g (g is the gauge coupling) toward zero, where the unbroken
theory lies, one encounters effects associated with the unbroken theory at a
finite value v\sim g, where dynamical mass generation of a gauge-symmetric
gauge- boson mass m\sim g^2 takes place, in addition to the Higgs-generated
non-symmetric mass M\sim vg. This dynamical mass generation is forced by the
infrared instability (in both 3 and 4 dimensions) of the pure-gauge theory. We
construct solitonic configurations of the theory with both m,M non-zero which
are generically closed loops consisting of nexuses (a class of soliton recently
studied for the pure-gauge theory), each paired with an antinexus, sitting like
beads on a string of center vortices with vortex fields always pointing into
(out of) a nexus (antinexus); the vortex magnetic fields extend a transverse
distance 1/m. An isolated nexus with vortices is continuously deformable from
the 't Hooft-Polyakov (m=0) monopole to the pure-gauge nexus-vortex complex
(M=0). In the pure-gauge M=0 limit the homotopy (or its
analog for SU(N)) of the 't Hooft monopoles is no longer applicable, and is
replaced by the center-vortex homotopy .Comment: 27 pages, LaTeX, 3 .eps figure
Nexus solitons in the center vortex picture of QCD
It is very plausible that confinement in QCD comes from linking of Wilson
loops to finite-thickness vortices with magnetic fluxes corresponding to the
center of the gauge group. The vortices are solitons of a gauge-invariant QCD
action representing the generation of gluon mass. There are a number of other
solitonic states of this action. We discuss here what we call nexus solitons,
in which for gauge group SU(N), up to N vortices meet a a center, or nexus,
provided that the total flux of the vortices adds to zero (mod N). There are
fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as
composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by
the flux condition; and fully non-Abelian, resembling a deformed sphaleron.
Analytic solutions are available for the quasi-Abelian case, and we discuss
variational estimates of the action of the fully non-Abelian nexus solitons in
SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge
in four dimensions). Their presence does not change the fundamentals of
confinement in the center-vortex picture, but they may lead to a modified
picture of the QCD vacuum.Comment: LateX, 24 pages, 2 .eps figure
Center Vortices, Nexuses, and Fractional Topological Charge
It has been remarked in several previous works that the combination of center
vortices and nexuses (a nexus is a monopole-like soliton whose world line
mediates certain allowed changes of field strengths on vortex surfaces) carry
topological charge quantized in units of 1/N for gauge group SU(N). These
fractional charges arise from the interpretation of the standard topological
charge integral as a sum of (integral) intersection numbers weighted by certain
(fractional) traces. We show that without nexuses the sum of intersection
numbers gives vanishing topological charge (since vortex surfaces are closed
and compact). With nexuses living as world lines on vortices, the contributions
to the total intersection number are weighted by different trace factors, and
yield a picture of the total topological charge as a linking of a closed nexus
world line with a vortex surface; this linking gives rise to a non-vanishing
but integral topological charge. This reflects the standard 2\pi periodicity of
the theta angle. We argue that the Witten-Veneziano relation, naively violating
2\pi periodicity, scales properly with N at large N without requiring 2\pi N
periodicity. This reflects the underlying composition of localized fractional
topological charge, which are in general widely separated. Some simple models
are given of this behavior. Nexuses lead to non-standard vortex surfaces for
all SU(N) and to surfaces which are not manifolds for N>2. We generalize
previously-introduced nexuses to all SU(N) in terms of a set of fundamental
nexuses, which can be distorted into a configuration resembling the 't
Hooft-Polyakov monopole with no strings. The existence of localized but
widely-separated fractional topological charges, adding to integers only on
long distance scales, has implications for chiral symmetry breakdown.Comment: 15 pages, revtex, 6 .eps figure
Baryon number non-conservation and phase transitions at preheating
Certain inflation models undergo pre-heating, in which inflaton oscillations
can drive parametric resonance instabilities. We discuss several phenomena
stemming from such instabilities, especially in weak-scale models; generically,
these involve energizing a resonant system so that it can evade tunneling by
crossing barriers classically. One possibility is a spontaneous change of phase
from a lower-energy vacuum state to one of higher energy, as exemplified by an
asymmetric double-well potential with different masses in each well. If the
lower well is in resonance with oscillations of the potential, a system can be
driven resonantly to the upper well and stay there (except for tunneling) if
the upper well is not resonant. Another example occurs in hybrid inflation
models where the Higgs field is resonant; the Higgs oscillations can be
transferred to electroweak (EW) gauge potentials, leading to rapid transitions
over sphaleron barriers and consequent B+L violation. Given an appropriate
CP-violating seed, we find that preheating can drive a time-varying condensate
of Chern-Simons number over large spatial scales; this condensate evolves by
oscillation as well as decay into modes with shorter spatial gradients,
eventually ending up as a condensate of sphalerons. We study these examples
numerically and to some extent analytically. The emphasis in the present paper
is on the generic mechanisms, and not on specific preheating models; these will
be discussed in a later paper.Comment: 10 pages, 7 figures included, revtex, epsf, references adde
On the connection between the pinch technique and the background field method
The connection between the pinch technique and the background field method is
further explored. We show by explicit calculations that the application of the
pinch technique in the framework of the background field method gives rise to
exactly the same results as in the linear renormalizable gauges. The general
method for extending the pinch technique to the case of Green's functions with
off-shell fermions as incoming particles is presented. As an example, the
one-loop gauge independent quark self-energy is constructed. We briefly discuss
the possibility that the gluonic Green's functions, obtained by either method,
correspond to physical quantities.Comment: 13 pages and 3 figures, all included in a uuencoded file, to appear
in Physical Review
Two-dimensional quasineutral description of particles and fields above discrete auroral arcs
Stationary hot and cool particle distributions in the auroral magnetosphere are modelled using adiabatic assumptions of particle motion in the presence of broad-scale electrostatic potential structure. The study has identified geometrical restrictions on the type of broadscale potential structure which can be supported by a multispecies plasma having specified sources and energies. Without energization of cool thermal ionospheric electrons, a substantial parallel potential drop cannot be supported down to altitudes of 2000 km or less. Observed upward-directed field-aligned currents must be closed by return currents along field lines which support little net potential drop. In such regions the plasma density appears significantly enhanced. Model details agree well with recent broad-scale implications of satellite observations
On the structures and mapping of auroral electrostatic potentials
The mapping of magnetospheric and ionospheric electric fields in a kinetic model of magnetospheric-ionospheric electrodynamic coupling proposed for the aurora is examined. One feature is the generalization of the kinetic current-potential relationship to the return current region (identified as a region where the parallel drop from magnetosphere to ionosphere is positive); such a return current always exists unless the ionosphere is electrically charged to grossly unphysical values. A coherent phenomenological picture of both the low energy return current and the high energy precipitation of an inverted-V is given. The mapping between magnetospheric and ionospheric electric fields is phrased in terms of a Green's function which acts as a filter, emphasizing magnetospheric latitudinal spatial scales of order (when mapped to the ionosphere) 50 to 150 km. This same length, when multiplied by electric fields just above the ionosphere, sets the scale for potential drops between the ionosphere and equatorial magnetosphere
Positivity issues for the pinch-technique gluon propagator and their resolution
Although gauge-boson propagators in asymptotically-free gauge theories
satisfy a dispersion relation, they do not satisfy the K\"allen-Lehmann (KL)
representation because the spectral function changes sign. We argue that this
is a simple consequence of asymptotic freedom. On the basis of the QED-like
Ward identities of the pinch technique (PT) we claim that the product of the
coupling and the scalar part of the PT propagator, which
is both gauge invariant and renormalization-group invariant, can be factored
into the product of the running charge and a term
both of which satisfy the KL representation although their
product does not. We show that this behavior is consistent with some simple
analytic models that mimic the gauge-invariant PT Schwinger-Dyson equations
(SDE) provided that the dynamic gauge boson mass is sufficiently large. The PT
SDEs do not depend directly on the PT propagator through but only
through .Comment: 13 pages, revtex4. Same physics, shortened; version accepted for
publication in Phys. Rev.
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