2,773 research outputs found
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
Locality and topology with fat link overlap actions
We study the locality and topological properties of fat link clover overlap
(FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1
step of HYP) already results in greatly improved properties compared to the
Wilson overlap (WO). We present a detailed study of the localisation of the FCO
and its connection to the density of low modes of . In contrast to
the Wilson overlap, on quenched gauge backgrounds we do not find any dependence
of the localization of the FCO on the gauge coupling. This suggests that the
FCO remains local in the continuum limit. The FCO also faithfully reproduces
the zero mode wave functions of typical lattice instantons, not like the Wilson
overlap. After a general discussion of different lattice definitions of the
topological charge we also show that the FCO together with the Boulder charge
are likely to satisfy the index theorem in the continuum limit. Finally, we
present a high statistics computation of the quenched topological
susceptibility with the FCO action.Comment: 19 pages, LaTe
Topology and chiral symmetry breaking in SU(N) gauge theories
We study the low-lying eigenmodes of the lattice overlap Dirac operator for
SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic
topological charge from the zero-modes of this operator and show that, as N
grows, any disagreement with the topological charge obtained by cooling the
fields, becomes rapidly less likely. By examining the fields where there is a
disagreement, we are able to show that the Dirac operator does not resolve
instantons below a critical size of about rho = 2.5 a, but resolves the larger,
more physical instantons. We investigate the local chirality of the near-zero
modes and how it changes as we go to larger N. We observe that the local
chirality of these modes, which is prominent for SU(2) and SU(3), becomes
rapidly weaker for larger N and is consistent with disappearing entirely in the
limit of N -> infinity. We find that this is not due to the observed
disappearance of small instantons at larger N.Comment: 41 pages, 12 figures, RevTe
A Simplex-Based Extension of Fourier-Motzkin for Solving Linear Integer Arithmetic
International audienceThis paper describes a novel decision procedure for quantifier-free linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g. Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaustive search for a model with bounds inference. These bounds are computed provided an oracle capable of finding constant positive linear combinations of affine forms. We also show how to design an efficient oracle based on the Simplex procedure. Our algorithm is proved sound, complete, and terminating and is implemented in the Alt-Ergo theorem prover. Experimental results are promising and show that our approach is competitive with state-of-the-art SMT solvers
Effect of vessel wettability on the foamability of "ideal" surfactants and "real-world" beer heads
The ability to tailor the foaming properties of a solution by controlling its chemical composition is highly desirable and has been the subject of extensive research driven by a range of applications. However, the control of foams by varying the wettability of the foaming vessel has been less widely reported. This work investigates the effect of the wettability of the side walls of vessels used for the in situ generation of foam by shaking aqueous solutions of three different types of model surfactant systems (non-ionic, anionic and cationic surfactants) along with four different beers (Guinness Original, Banks’s Bitter, Bass No 1 and Harvest Pale). We found that hydrophilic vials increased the foamability only for the three model systems but increased foam stability for all foams except the model cationic system. We then compared stability of beer foams produced by shaking and pouring and demonstrated weak qualitative agreement between both foam methods. We also showed how wettability of the glass controls bubble nucleation for beers and champagne and used this effect to control exactly where bubbles form using simple wettability patterns
Prospects for Probing the Spacetime of Sgr A* with Pulsars
The discovery of radio pulsars in compact orbits around Sgr A* would allow an
unprecedented and detailed investigation of the spacetime of the supermassive
black hole. This paper shows that pulsar timing, including that of a single
pulsar, has the potential to provide novel tests of general relativity, in
particular its cosmic censorship conjecture and no-hair theorem for rotating
black holes. These experiments can be performed by timing observations with 100
micro-second precision, achievable with the Square Kilometre Array for a normal
pulsar at frequency above 15 GHz. Based on the standard pulsar timing
technique, we develop a method that allows the determination of the mass, spin,
and quadrupole moment of Sgr A*, and provides a consistent covariance analysis
of the measurement errors. Furthermore, we test this method in detailed mock
data simulations. It seems likely that only for orbital periods below ~0.3 yr
is there the possibility of having negligible external perturbations. For such
orbits we expect a ~10^-3 test of the frame dragging and a ~10^-2 test of the
no-hair theorem within 5 years, if Sgr A* is spinning rapidly. Our method is
also capable of identifying perturbations caused by distributed mass around Sgr
A*, thus providing high confidence in these gravity tests. Our analysis is not
affected by uncertainties in our knowledge of the distance to the Galactic
center, R0. A combination of pulsar timing with the astrometric results of
stellar orbits would greatly improve the measurement precision of R0.Comment: 12 pages, 10 Figures, accepted for publication in Ap
Linear Momentum Density in Quasistatic Electromagnetic Systems
We discuss a couple of simple quasistatic electromagnetic systems in which
the density of electromagnetic linear momentum can be easily computed. The
examples are also used to illustrate how the total electromagnetic linear
momentum, which may also be calculated by using the vector potential, can be
understood as a consequence of the violation of the action-reaction principle,
because a non-null external force is required to maintain constant the
mechanical linear momentum. We show how one can avoid the divergence in the
interaction linear electromagnetic momentum of a system composed by an
idealization often used in textbooks (an infinite straight current) and a point
charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy
Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition
We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour
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