µ-Charts and Z: Examples and extensions

μ-Charts are a way of specifying reactive systems, i.e. systems which are in some environment to which they have to react, based on the well-established formalism Statecharts. This paper gives (very abbreviated) examples of translating μ-charts to Z, which is itself a well-established language for specifying computational systems with tried and tested methods and support tools which guide its effective use in systems development. We undertake this translation in order that investigation of the modelled system can be performed before expensive and lengthy implementation is considered. We also present an extension of the μ-charts and the related Z to deal with a simple command language, local variables and integer-valued signals

An Exercise in Invariant-based Programming with Interactive and Automatic Theorem Prover Support

Invariant-Based Programming (IBP) is a diagram-based correct-by-construction programming methodology in which the program is structured around the invariants, which are additionally formulated before the actual code. Socos is a program construction and verification environment built specifically to support IBP. The front-end to Socos is a graphical diagram editor, allowing the programmer to construct invariant-based programs and check their correctness. The back-end component of Socos, the program checker, computes the verification conditions of the program and tries to prove them automatically. It uses the theorem prover PVS and the SMT solver Yices to discharge as many of the verification conditions as possible without user interaction. In this paper, we first describe the Socos environment from a user and systems level perspective; we then exemplify the IBP workflow by building a verified implementation of heapsort in Socos. The case study highlights the role of both automatic and interactive theorem proving in three sequential stages of the IBP workflow: developing the background theory, formulating the program specification and invariants, and proving the correctness of the final implementation.Comment: In Proceedings THedu'11, arXiv:1202.453

How many dark energy parameters?

For exploring the physics behind the accelerating universe a crucial question is how much we can learn about the dynamics through next generation cosmological experiments. For example, in defining the dark energy behavior through an effective equation of state, how many parameters can we realistically expect to tightly constrain? Through both general and specific examples (including new parametrizations and principal component analysis) we argue that the answer is 42 - no, wait, two. Cosmological parameter analyses involving a measure of the equation of state value at some epoch (e.g. w_0) and a measure of the change in equation of state (e.g. w') are therefore realistic in projecting dark energy parameter constraints. More elaborate parametrizations could have some uses (e.g. testing for bias or comparison with model features), but do not lead to accurately measured dark energy parameters.Comment: 10 pages, 1 figur

Dark Before Light: Testing the Cosmic Expansion History through the Cosmic Microwave Background

The cosmic expansion history proceeds in broad terms from a radiation dominated epoch to matter domination to an accelerated, dark energy dominated epoch. We investigate whether intermittent periods of acceleration are possible in the early universe -- between Big Bang nucleosynthesis (BBN) and recombination and beyond. We establish that the standard picture is remarkably robust: observations of anisotropies in the cosmic microwave background exclude any extra period of accelerated expansion between 1 \leq z \lesssim 10^5 (corresponding to 5\times10^{-4}\ {\rm eV} \leq T \lesssim 25\ {\rm eV}).Comment: 7 pages, 5 figure

Experimental constraints on the polarizabilities of the 6s^2 1S0 and 6s6p 3P0 states of Yb

We utilize accurate experimental data available in the literature to yield bounds on the polarizabilities of the ground and first excited states of atomic Yb. For the 6s^2 1S0 ground state, we find the polarizability alpha to be constrained to 134.4<alpha<144.2 in atomic units, while for the 6s6p 3P0 excited state we find 280.1<alpha<289.9. The uncertainty in each of these values is 1.0. These constraints provide a valuable check for ab initio and semi-empirical methods used to compute polarizabilities and other related properties in Yb.Comment: 7 pages, 1 figur

Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the maximizer adopts a myopic strategy. This game is shown to admit a saddle point whose structure is characterized by applying and extending results presented earlier in [1] for static least-squares estimation. The resulting minimax filter takes the form of a risk-sensitive filter with a time varying risk sensitivity parameter, which depends on the tolerance bound applied to the model dynamics and observations at the corresponding time index. The least-favorable model is constructed and used to evaluate the performance of alternative filters. Simulations comparing the proposed risk-sensitive filter to a standard Kalman filter show a significant performance advantage when applied to the least-favorable model, and only a small performance loss for the nominal model

A kinematical approach to dark energy studies

We present and employ a new kinematical approach to cosmological `dark energy' studies. We construct models in terms of the dimensionless second and third derivatives of the scale factor a(t) with respect to cosmic time t, namely the present-day value of the deceleration parameter q_0 and the cosmic jerk parameter, j(t). An elegant feature of this parameterization is that all LCDM models have j(t)=1 (constant), which facilitates simple tests for departures from the LCDM paradigm. Applying our model to the three best available sets of redshift-independent distance measurements, from type Ia supernovae and X-ray cluster gas mass fraction measurements, we obtain clear statistical evidence for a late time transition from a decelerating to an accelerating phase. For a flat model with constant jerk, j(t)=j, we measure q_0=-0.81+-0.14 and j=2.16+0.81-0.75, results that are consistent with LCDM at about the 1sigma confidence level. A standard `dynamical' analysis of the same data, employing the Friedmann equations and modeling the dark energy as a fluid with an equation of state parameter, w (constant), gives Omega_m=0.306+0.042-0.040 and w=-1.15+0.14-0.18, also consistent with LCDM at about the 1sigma level. In comparison to dynamical analyses, the kinematical approach uses a different model set and employs a minimum of prior information, being independent of any particular gravity theory. The results obtained with this new approach therefore provide important additional information and we argue that both kinematical and dynamical techniques should be employed in future dark energy studies, where possible. Our results provide further interesting support for the concordance LCDM paradigm.Comment: 12 pages, 5 figures, 2 tables. Accepted for publication in MNRA