19 research outputs found
Free vacuum for loop quantum gravity
We linearize extended ADM-gravity around the flat torus, and use the
associated Fock vacuum to construct a state that could play the role of a free
vacuum in loop quantum gravity. The state we obtain is an element of the
gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a
natural consequence of the momentum cutoff of the original Fock state. It has
the form of a Gaussian superposition of spin networks. We show that the peak of
the Gaussian lies at weave-like states and derive a relation between the
coloring of the weaves and the cutoff scale. Our analysis indicates that the
peak weaves become independent of the cutoff length when the latter is much
smaller than the Planck length. By the same method, we also construct
multiple-graviton states. We discuss the possible use of these states for
deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde
Space as a low-temperature regime of graphs
I define a statistical model of graphs in which 2-dimensional spaces arise at
low temperature. The configurations are given by graphs with a fixed number of
edges and the Hamiltonian is a simple, local function of the graphs.
Simulations show that there is a transition between a low-temperature regime in
which the graphs form triangulations of 2-dimensional surfaces and a
high-temperature regime, where the surfaces disappear. I use data for the
specific heat and other observables to discuss whether this is a phase
transition. The surface states are analyzed with regard to topology and
defects.Comment: 22 pages, 12 figures; v3: published version; J.Stat.Phys. 201
Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
Loop Quantum Gravity defines the quantum states of space geometry as spin
networks and describes their evolution in time. We reformulate spin networks in
terms of harmonic oscillators and show how the holographic degrees of freedom
of the theory are described as matrix models. This allow us to make a link with
non-commutative geometry and to look at the issue of the semi-classical limit
of LQG from a new perspective. This work is thought as part of a bigger project
of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure
Realizing Wardrop Equilbria with Real-Time Traffic Information
A Wardrop equilibrium for multiple routes requires equal travel time on each
path used. With real-time traffic data regarding travel times, it is important
to analyze how to use the information provided. In particular, can a Wardrop
equilibrium be realized? Simulations using the three-phase model on a two-route
example are presented to answer this question. One route (the main line) is a
two-lane highway with a stalled vehicle in the right lane and the other route
is a low-speed bypass. For a critical incoming flow, a phase transition between
free flow and congested flow near the stalled vehicle is observed, making this
a challenging example. In the first scenario, drivers choose routes selfishly
on the basis of current travel times. The result is strong oscillations in
travel time because of the inherent delay in the information provided. The
second scenario involves a hypothetical control system that limits the number
of vehicles on the main line to prevent the free-flow to congested-flow phase
transition by diverting sufficient flow to the bypass. The resulting steady
state is neither a Wardrop equilibrium nor a system optimum, but an
intermediate state in which the main-line travel time is less than on the
bypass but the average for all vehicles is close to a minimum. In a third
scenario, anticipation is used as a driver-advice system to provide a fair
indicator of which route to take. Prediction is based on real-time data
comparing the number of vehicles on the main line at the time a vehicle leaves
the origin to the actual travel time when it reaches the destination. Steady
states that approximate Wardrop equilbria, or close to them, are obtained.Comment: 50 pages, 24 figure
Recursive Definitions of Monadic Functions
Using standard domain-theoretic fixed-points, we present an approach for
defining recursive functions that are formulated in monadic style. The method
works both in the simple option monad and the state-exception monad of
Isabelle/HOL's imperative programming extension, which results in a convenient
definition principle for imperative programs, which were previously hard to
define.
For such monadic functions, the recursion equation can always be derived
without preconditions, even if the function is partial. The construction is
easy to automate, and convenient induction principles can be derived
automatically.Comment: In Proceedings PAR 2010, arXiv:1012.455
Spin foams with timelike surfaces
Spin foams of 4d gravity were recently extended from complexes with purely
spacelike surfaces to complexes that also contain timelike surfaces. In this
article, we express the associated partition function in terms of vertex
amplitudes and integrals over coherent states. The coherent states are
characterized by unit 3--vectors which represent normals to surfaces and lie
either in the 2--sphere or the 2d hyperboloids. In the case of timelike
surfaces, a new type of coherent state is used and the associated completeness
relation is derived. It is also shown that the quantum simplicity constraints
can be deduced by three different methods: by weak imposition of the
constraints, by restriction of coherent state bases and by the master
constraint.Comment: 22 pages, no figures; v2: remarks on operator formalism added in
discussion; correction: the spin 1/2 irrep of the discrete series does not
appear in the Plancherel decompositio
A spin foam model for general Lorentzian 4-geometries
We derive simplicity constraints for the quantization of general Lorentzian
4-geometries. Our method is based on the correspondence between coherent states
and classical bivectors and the minimization of associated uncertainties. For
spacelike geometries, this scheme agrees with the master constraint method of
the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to
general Lorentzian geometries, we obtain new constraints that include the EPRL
constraints as a special case. They imply a discrete area spectrum for both
spacelike and timelike surfaces. We use these constraints to define a spin foam
model for general Lorentzian 4-geometries.Comment: 27 pages, 1 figure; v4: published versio
Analyzing program termination and complexity automatically with AProVE
In this system description, we present the tool AProVE for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and rewrite systems. In addition to classical term rewrite systems (TRSs), AProVE also supports rewrite systems containing built-in integers (int-TRSs). To analyze programs in high-level languages, AProVE automatically converts them to (int-)TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting rewrite systems. The generated proofs can be exported to check their correctness using automatic certifiers. To use AProVE in software construction, we present a corresponding plug-in for the popular Eclipse software development environment
Tumor-derived GDF-15 blocks LFA-1 dependent T cell recruitment and suppresses responses to anti-PD-1 treatment
Immune checkpoint blockade therapy is beneficial and even curative for some cancer patients. However, the majority don't respond to immune therapy. Across different tumor types, pre-existing T cell infiltrates predict response to checkpoint-based immunotherapy. Based on in vitro pharmacological studies, mouse models and analyses of human melanoma patients, we show that the cytokine GDF-15 impairs LFA-1/β2-integrin-mediated adhesion of T cells to activated endothelial cells, which is a pre-requisite of T cell extravasation. In melanoma patients, GDF-15 serum levels strongly correlate with failure of PD-1-based immune checkpoint blockade therapy. Neutralization of GDF-15 improves both T cell trafficking and therapy efficiency in murine tumor models. Thus GDF-15, beside its known role in cancer-related anorexia and cachexia, emerges as a regulator of T cell extravasation into the tumor microenvironment, which provides an even stronger rationale for therapeutic anti-GDF-15 antibody development