1,851 research outputs found
Machine-Checked Proofs For Realizability Checking Algorithms
Virtual integration techniques focus on building architectural models of
systems that can be analyzed early in the design cycle to try to lower cost,
reduce risk, and improve quality of complex embedded systems. Given appropriate
architectural descriptions, assume/guarantee contracts, and compositional
reasoning rules, these techniques can be used to prove important safety
properties about the architecture prior to system construction. For these
proofs to be meaningful, each leaf-level component contract must be realizable;
i.e., it is possible to construct a component such that for any input allowed
by the contract assumptions, there is some output value that the component can
produce that satisfies the contract guarantees. We have recently proposed (in
[1]) a contract-based realizability checking algorithm for assume/guarantee
contracts over infinite theories supported by SMT solvers such as linear
integer/real arithmetic and uninterpreted functions. In that work, we used an
SMT solver and an algorithm similar to k-induction to establish the
realizability of a contract, and justified our approach via a hand proof. Given
the central importance of realizability to our virtual integration approach, we
wanted additional confidence that our approach was sound. This paper describes
a complete formalization of the approach in the Coq proof and specification
language. During formalization, we found several small mistakes and missing
assumptions in our reasoning. Although these did not compromise the correctness
of the algorithm used in the checking tools, they point to the value of
machine-checked formalization. In addition, we believe this is the first
machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur
The Effects of Foam Rolling on Hamstring Flexibility, Muscle Soreness and Power
Click the PDF icon to download the abstract
The Magnetic Field Geometry of Small Solar Wind Flux Ropes Inferred from their Twist Distribution
This work extends recent efforts on the force-free modeling of large flux
rope-type structures (magnetic clouds, MCs) to much smaller spatial scales. We
first select small flux ropes (SFRs) by eye whose duration is unambiguous and
which were observed by the Solar Terrestrial Relations Observatory (STEREO) or
Wind spacecraft during solar maximum years. We inquire into which analytical
technique is physically most appropriate. We consider three models: (i) linear
force-free field ( B = B) with a
specific, prescribed constant (Lundquist solution), and (ii) with
as a free constant parameter (Lundquist-alpha solution), (iii) uniform
twist field (Gold-Hoyle solution). We retain only those cases where the impact
parameter is less than one-half the FR radius, , so the results should be
robust (29 cases). The SFR radii lie in the range [ 0.003, 0.059] AU.
Comparing results, we find that the Lundquist-alpha and uniform twist solutions
yielded comparable and small normalized values in most cases. We then
use Grad-Shafranov (GS) reconstruction to analyze these events further. We then
considered the twist per unit length, , both its profile through the FR
and its absolute value. We find to lie in the range [5.6, 34] turns/AU.
The GH model-derived values are comparable to those obtained from GS
reconstruction. We find that twist unit length () is inversely proportional
to , as . We combine MC and SFR results on and
give a relation which is approximately valid for both sets. The axial and
azimuthal fluxes, and , vary as Mx and Mx/AU. The
relative helicity per unit length,
Mx/AU.Comment: abstract shortened for arxiv, 31 pages, 15 Figures, in press at Solar
Physic
Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach
We consider goodness-of-fit tests of symmetric stable distributions based on
weighted integrals of the squared distance between the empirical characteristic
function of the standardized data and the characteristic function of the
standard symmetric stable distribution with the characteristic exponent
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that is
fixed. For estimation of parameters and the standardization of data we use
maximum likelihood estimator (MLE) and an equivariant integrated squared error
estimator (EISE) which minimizes the weighted integral. We derive the
asymptotic covariance function of the characteristic function process with
parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of
the covariance function are numerically evaluated and asymptotic distribution
of the test statistic is obtained using complex integration. Simulation studies
show that the asymptotic distribution of the test statistics is very accurate.
We also present a formula of the asymptotic covariance function of the
characteristic function process with parameters estimated by an efficient
estimator for general distributions
Spectrum occupancy measurement: a case for cognitive radio network in lagos, Nigeria
The proliferation in technologies and with the recent introduction of new paradigm for wireless communication, the demand for wireless devices has increased drastically in recent years. This therefore, posed a major threat on the available frequency spectrum and as a result, an efficient method for the utilisation of the limited frequency spectrum is required. As the scarcity of frequency spectrum is a major problem in the telecommunication field, cognitive radio technology has been identified as a promising solution to this problem. Cognitive radio allows the opportunistic access of licensed bands by unlicensed users without causing harmful interference to the licensed user. There is a need to evaluate the utilisation level of the licensed bands in order to identify which frequency bands can be used for cognitive radio implementation. Nevertheless, spectrum measurement campaigns have been conducted mostly in USA and a few other locations around the world. In this paper, the results of the measurement campaign conducted in Ikeja, the capital city of Lagos, Nigeria covering the range of frequency 700 MHz up to 2.2 GHz is presented. The measurement results are analysed and compared to the frequency allocation table published by the Nigerian Communications Commission. The results obtained show that the frequency spectrum is underutilised and therefore a significant amount of spectrum is available for the future implementation of cognitive radio networks
Formalising Mathematics in Simple Type Theory
Despite the considerable interest in new dependent type theories, simple type
theory (which dates from 1940) is sufficient to formalise serious topics in
mathematics. This point is seen by examining formal proofs of a theorem about
stereographic projections. A formalisation using the HOL Light proof assistant
is contrasted with one using Isabelle/HOL. Harrison's technique for formalising
Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic
type classes. However, every formal system can be outgrown, and mathematics
should be formalised with a view that it will eventually migrate to a new
formalism
Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach
This paper studies the decay of a large, closed domain wall in a closed
universe. Such walls can form in the presence of a broken, discrete symmetry.
We study a novel process of quantum decay for such a wall, in which the vacuum
fluctuates from one discrete state to another throughout one half of the
universe, so that the wall decays into pure field energy. Equivalently, the
fluctuation can be thought of as the nucleation of a second closed domain wall
of zero size, followed by its growth by quantum tunnelling and its collision
with the first wall, annihilating both. We therefore study the 2-wall system
coupled to a spherically symmetric gravitational field. We derive a simple form
of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function
for annihilation, find from it the barrier factor for this quantum tunneling,
and thereby get the decay probability. This is the second paper of a series.Comment: 27 pages LaTeX, using revtex and psfig. 3 figure
Computing Volume Bounds of Inclusions by EIT Measurements
The size estimates approach for Electrical Impedance Tomography (EIT) allows
for estimating the size (area or volume) of an unknown inclusion in an
electrical conductor by means of one pair of boundary measurements of voltage
and current. In this paper we show by numerical simulations how to obtain such
bounds for practical application of the method. The computations are carried
out both in a 2D and a 3D setting.Comment: 20 pages with figure
- …