Modeling the effects of combining diverse software fault detection techniques

The software engineering literature contains many studies of the efficacy of fault finding techniques. Few of these, however, consider what happens when several different techniques are used together. We show that the effectiveness of such multitechnique approaches depends upon quite subtle interplay between their individual efficacies and dependence between them. The modelling tool we use to study this problem is closely related to earlier work on software design diversity. The earliest of these results showed that, under quite plausible assumptions, it would be unreasonable even to expect software versions that were developed ‘truly independently’ to fail independently of one another. The key idea here was a ‘difficulty function’ over the input space. Later work extended these ideas to introduce a notion of ‘forced’ diversity, in which it became possible to obtain system failure behaviour better even than could be expected if the versions failed independently. In this paper we show that many of these results for design diversity have counterparts in diverse fault detection in a single software version. We define measures of fault finding effectiveness, and of diversity, and show how these might be used to give guidance for the optimal application of different fault finding procedures to a particular program. We show that the effects upon reliability of repeated applications of a particular fault finding procedure are not statistically independent - in fact such an incorrect assumption of independence will always give results that are too optimistic. For diverse fault finding procedures, on the other hand, things are different: here it is possible for effectiveness to be even greater than it would be under an assumption of statistical independence. We show that diversity of fault finding procedures is, in a precisely defined way, ‘a good thing’, and should be applied as widely as possible. The new model and its results are illustrated using some data from an experimental investigation into diverse fault finding on a railway signalling application

Amplitude-mode dynamics of polariton condensates

We study the stability of collective amplitude excitations in non-equilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wavevectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.Comment: 4 pages, 2 figure

Non-equilibrium quantum condensation in an incoherently pumped dissipative system

We study spontaneous quantum coherence in an out of equilibrium system, coupled to multiple baths describing pumping and decay. For a range of parameters describing coupling to, and occupation of the baths, a stable steady-state condensed solution exists. The presence of pumping and decay significantly modifies the spectra of phase fluctuations, leading to correlation functions that differ both from an isolated condensate and from a laser.Comment: 5 pages, 2 eps figure

Ferrodistortive instability at the (001) surface of half-metallic manganites

We present the structure of the fully relaxed (001) surface of the half-metallic manganite La0.7Sr0.3MnO3, calculated using density functional theory within the generalized gradient approximation (GGA). Two relevant ferroelastic order parameters are identified and characterized: The tilting of the oxygen octahedra, which is present in the bulk phase, oscillates and decreases towards the surface, and an additional ferrodistortive Mn off-centering, triggered by the surface, decays monotonically into the bulk. The narrow d-like energy band that is characteristic of unrelaxed manganite surfaces is shifted down in energy by these structural distortions, retaining its uppermost layer localization. The magnitude of the zero-temperature magnetization is unchanged from its bulk value, but the effective spin-spin interactions are reduced at the surface.Comment: 4 pages, 2 figure

Sliding Density-Wave in Sr_{14}Cu_{24}O_{41} Ladder Compounds

We used transport and Raman scattering measurements to identify the insulating state of self-doped spin 1/2 two-leg ladders of Sr_{14}Cu_{24}O_{41} as a weakly pinned, sliding density wave with non-linear conductivity and a giant dielectric response that persists to remarkably high temperatures

Density and spin response functions in ultracold fermionic atom gases

We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the density response function signals the transition between a BEC and a BCS regimes, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC to BCS crossover. Also, we predict spin rotational symmetry-breaking in this system

Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their (trivial) mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the (quantum) anharmonic oscillator. The photon statistics at the crossover are different in the high- and low- temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects.Comment: 12 pages, 5 figures. v2: Revised version with minor corrections (typos, added reference, correction in argument following Eq. 25). v3: further typos correcte

Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence

The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent on the size of the perturbation.Comment: Corrected typo in the title and statement of Lemma 3.