2,595 research outputs found
Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
Contrary to what is often stated, a fundamental spacetime discreteness need
not contradict Lorentz invariance. A causal set's discreteness is in fact
locally Lorentz invariant, and we recall the reasons why. For illustration, we
introduce a phenomenological model of massive particles propagating in a
Minkowski spacetime which arises from an underlying causal set. The particles
undergo a Lorentz invariant diffusion in phase space, and we speculate on
whether this could have any bearing on the origin of high energy cosmic rays.Comment: 13 pages. Replaced version with corrected fundamental solution,
missing m's (mass) and c's (speed of light) added and reference on diffusion
on the three sphere changed. Note with additional references added and
addresses updated, as in published versio
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
A Bell Inequality Analog in Quantum Measure Theory
One obtains Bell's inequalities if one posits a hypothetical joint
probability distribution, or {\it measure}, whose marginals yield the
probabilities produced by the spin measurements in question. The existence of a
joint measure is in turn equivalent to a certain causality condition known as
``screening off''. We show that if one assumes, more generally, a joint {\it
quantal measure}, or ``decoherence functional'', one obtains instead an
analogous inequality weaker by a factor of . The proof of this
``Tsirel'son inequality'' is geometrical and rests on the possibility of
associating a Hilbert space to any strongly positive quantal measure. These
results lead both to a {\it question}: ``Does a joint measure follow from some
quantal analog of `screening off'?'', and to the {\it observation} that
non-contextual hidden variables are viable in histories-based quantum
mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the
meaning more clearly. Minor rewording and extra acknowledgements, now closer
to published versio
Substance-Abusing Mothers and fathers\u27 Willingness to Allow Their Children to Receive Mental Health Treatment
The purpose of this study was to examine attitudes of substance-abusing mothers and fathers entering outpatient treatment toward allowing their children to participate in individual- or family-based interventions. Data were collected from a brief anonymous survey completed by adults at intake into a large substance abuse treatment program in western New York. Only one-third of parents reported that they would be willing to allow their children to participate in any form of mental health treatment. Results of chi-square analyses revealed that a significantly greater proportion of mothers reported that they would allow their children to participate in mental health treatment (41%) compared to fathers (28%). Results of logistic regression analyses revealed even after controlling for child age, mothers were more likely than fathers to indicate their willingness to allow their children to receive mental health treatment; however, type of substance abuse (alcohol versus drug abuse) was not associated with parents\u27 willingness to allow their children to receive treatment. Parental reluctance to allow their children to receive individual or family-based treatment is a significant barrier in efforts to intervene with these at-risk children
Kinetics of the γ–δ phase transition in energetic nitramine-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine
The solid, secondary explosive nitramine-octahydro-1,3,5,7-tetranitro-1,3,5,7 or HMX has four different stable polymorphs which have different molecular conformations, crystalline structures, and densities, making structural phase transitions between these nontrivial. Previous studies of the kinetics of the β–δ HMX structural transition found this to happen by a nucleation and growth mechanism, where growth was governed by the heat of fusion, or melting, even though the phase transition temperature is more than 100 K below the melting point. A theory known as virtual melting could easily justify this since the large volume difference in the two phases creates a strain at their interface that can lower the melting point to the phase transition temperature through a relaxation of the elastic energy. To learn more about structural phase transitions in organic crystalline solids and virtual melting, here we use time-resolved X-ray diffraction to study another structural phase transition in HMX, γ–δ. Again, second order kinetics are observed which fit to the same nucleation and growth model associated with growth by melting even though the volume change in this transition is too small to lower the melting point by interfacial strain. To account for this, we present a more general model illustrating that melting over a very thin layer at the interface between the two phases reduces the total interfacial energy and is therefore thermodynamically favorable and can drive the structural phase transition in the absence of large volume changes. Our work supports the idea that virtual melting may be a more generally applicable mechanism for structural phase transitions in organic crystalline solids
Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
We present a computational tool that can be used to obtain the "spatial"
homology groups of a causal set. Localisation in the causal set is seeded by an
inextendible antichain, which is the analog of a spacelike hypersurface, and a
one parameter family of nerve simplicial complexes is constructed by
"thickening" this antichain. The associated homology groups can then be
calculated using existing homology software, and their behaviour studied as a
function of the thickening parameter. Earlier analytical work showed that for
an inextendible antichain in a causal set which can be approximated by a
globally hyperbolic spacetime region, there is a one parameter sub-family of
these simplicial complexes which are homological to the continuum, provided the
antichain satisfies certain conditions. Using causal sets that are approximated
by a set of 2d spacetimes our numerical analysis suggests that these conditions
are generically satisfied by inextendible antichains. In both 2d and 3d
simulations, as the thickening parameter is increased, the continuum homology
groups tend to appear as the first region in which the homology is constant, or
"stable" above the discreteness scale. Below this scale, the homology groups
fluctuate rapidly as a function of the thickening parameter. This provides a
necessary though not sufficient criterion to test for manifoldlikeness of a
causal set.Comment: Latex, 46 pages, 43 .eps figures, v2 numerous changes to content and
presentatio
The moduli space of isometry classes of globally hyperbolic spacetimes
This is the last article in a series of three initiated by the second author.
We elaborate on the concepts and theorems constructed in the previous articles.
In particular, we prove that the GH and the GGH uniformities previously
introduced on the moduli space of isometry classes of globally hyperbolic
spacetimes are different, but the Cauchy sequences which give rise to
well-defined limit spaces coincide. We then examine properties of the strong
metric introduced earlier on each spacetime, and answer some questions
concerning causality of limit spaces. Progress is made towards a general
definition of causality, and it is proven that the GGH limit of a Cauchy
sequence of , path metric Lorentz spaces is again a
, path metric Lorentz space. Finally, we give a
necessary and sufficient condition, similar to the one of Gromov for the
Riemannian case, for a class of Lorentz spaces to be precompact.Comment: 29 pages, 9 figures, submitted to Class. Quant. Gra
Simulating causal collapse models
We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of
probability distribution of labellings correcte
Fast Optimal Transport Averaging of Neuroimaging Data
Knowing how the Human brain is anatomically and functionally organized at the
level of a group of healthy individuals or patients is the primary goal of
neuroimaging research. Yet computing an average of brain imaging data defined
over a voxel grid or a triangulation remains a challenge. Data are large, the
geometry of the brain is complex and the between subjects variability leads to
spatially or temporally non-overlapping effects of interest. To address the
problem of variability, data are commonly smoothed before group linear
averaging. In this work we build on ideas originally introduced by Kantorovich
to propose a new algorithm that can average efficiently non-normalized data
defined over arbitrary discrete domains using transportation metrics. We show
how Kantorovich means can be linked to Wasserstein barycenters in order to take
advantage of an entropic smoothing approach. It leads to a smooth convex
optimization problem and an algorithm with strong convergence guarantees. We
illustrate the versatility of this tool and its empirical behavior on
functional neuroimaging data, functional MRI and magnetoencephalography (MEG)
source estimates, defined on voxel grids and triangulations of the folded
cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of
Skye, United Kingdom. Springer, 201
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