Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

Cosmic censorship of smooth structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde

Experimental demonstration of a measurement-based realisation of a quantum channel

We introduce and experimentally demonstrate a method for realising a quantum channel using the measurement-based model. Using a photonic setup and modifying the bases of single-qubit measurements on a four-qubit entangled cluster state, representative channels are realised for the case of a single qubit in the form of amplitude and phase damping channels. The experimental results match the theoretical model well, demonstrating the successful performance of the channels. We also show how other types of quantum channels can be realised using our approach. This work highlights the potential of the measurement-based model for realising quantum channels which may serve as building blocks for simulations of realistic open quantum systems.Comment: 8 pages, 4 figure

Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Long-term health outcomes after exposure to repeated concussion in elite level: rugby union players

Background: There is continuing concern about effects of concussion in athletes, including risk of the neurodegenerative disease chronic traumatic encephalopathy. However, information on long-term health and wellbeing in former athletes is limited. Method: Outcome after exposure to repeated brain injury was investigated in 52 retired male Scottish international rugby players (RIRP) and 29 male controls who were similar in age and social deprivation. Assessment included history of playing rugby and traumatic brain injury, general and mental health, life stress, concussion symptoms, cognitive function, disability and markers of chronic stress (allostatic load). Results: The estimated number of concussions in RIRP averaged 14 (median=7; IQR 5-40). Performance was poorer in RIRP than controls on a test of verbal learning (p=0.022) and of fine co-ordination of the dominant hand (p=0.038) and not significantly different on other cognitive tests (p>0.05). There were no significant associations between number of concussions and performance on cognitive tests. Other than a higher incidence of cardiovascular disease in controls, no group differences were detected in general or mental health or estimates of allostatic load. In RIRP, persisting symptoms attributed to concussion were more common if reporting more than nine concussions (p=0.028), although these symptoms were not perceived to affect social or work functioning. Conclusions: Despite a high number of concussions in RIRP, differences in mental health, social or work functioning were not found late after injury. Subtle group differences were detected on two cognitive tests, the cause of which is uncertain. Prospective group comparison studies on representative cohorts are required

Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D ±J\pm J Ising Spin Glass

The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When $L$ is even, almost all domain walls have energy $E_{dw}$ = 0 or 4. When $L$ is odd, most domain walls have $E_{dw}$ = 2. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. When $E_{dw} = 0$, the probability distribution of $|S_{dw}|$ is approximately exponential. The variance of this distribution is proportional to $L$, in agreement with the results of Saul and Kardar. For $E_{dw} = k > 0$ the distribution of $S_{dw}$ is not symmetric about zero. In these cases the variance still appears to be linear in $L$, but the average of $S_{dw}$ grows faster than $\sqrt{L}$. This suggests a one-parameter scaling form for the $L$-dependence of the distributions of $S_{dw}$ for $k > 0$.Comment: 13 page

Experimentally exploring compressed sensing quantum tomography

In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross-validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.Comment: 12 pages, 5 figure

Assessment of vitamin E status in patients with systemic inflammatory response syndrome: plasma, plasma corrected for lipids or red blood cell measurements?

<b>Background:</b> There is some evidence that the plasma vitamin E status is perturbed as part of systemic inflammatory response and correcting this with other plasma markers may not lead to reliable results. The aim of the present study was to examine the longitudinal inter-relationships between plasma and red blood cell vitamin α-tocopherol in patients with systemic inflammatory response syndrome. <b>Methods:</b> α-tocopherol concentrations were measured, by HPLC, in plasma and red blood cells in normal subjects (n = 67) and in critically ill patients with systemic inflammatory response syndrome (n = 82) on admission and on follow-up. <b>Results:</b> Plasma α-tocopherol was significantly lower in the critically ill patients compared with the controls (all p < 0.001) with 41% of patients having concentrations below the 95% confidence interval. In contrast, when corrected for cholesterol, α-tocopherol concentrations were significantly higher in the critically ill patients compared with the control group (p < 0.001, 27% above the 95% confidence interval) and when corrected for triglycerides, α-tocopherol concentrations were significantly lower in the critically ill patients compared with the control group (p < 0.001). Red blood cell α-tocopherol corrected for haemoglobin was similar (p = 0.852) in the critically ill patients compared with control subjects. The longitudinal measurements (n = 53) gave similar results. <b>Conclusions:</b> These results indicate that there is a discrepancy between vitamin E measurements in plasma, in plasma corrected for lipids and in red blood cells. Although the value of correcting vitamin E concentrations by lipids is well established in population studies, the present study indicates that such correction is unreliable in the presence of systemic inflammatory response syndrome and that vitamin E status should be assessed using red blood cell α-tocopherol measurement

On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page

Two-photon interference between disparate sources for quantum networking

Quantum networks involve entanglement sharing between multiple users. Ideally, any two users would be able to connect regardless of the type of photon source they employ, provided they fulfill the requirements for two-photon interference. From a theoretical perspective, photons coming from different origins can interfere with a perfect visibility, provided they are made indistinguishable in all degrees of freedom. Previous experimental demonstrations of such a scenario have been limited to photon wavelengths below 900 nm, unsuitable for long distance communication, and suffered from low interference visibility. We report two-photon interference using two disparate heralded single photon sources, which involve different nonlinear effects, operating in the telecom wavelength range. The measured visibility of the two-photon interference is 80+/-4%, which paves the way to hybrid universal quantum networks