Using Regular Languages to Explore the Representational Capacity of Recurrent Neural Architectures

The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these state-of-the-art architectures, there is growing need for rich benchmarking datasets. However, one of the drawbacks of existing datasets is the lack of experimental control with regards to the presence and/or degree of LDDs. This lack of control limits the analysis of model performance in relation to the specific challenge posed by LDDs. One way to address this is to use synthetic data having the properties of subregular languages. The degree of LDDs within the generated data can be controlled through the k parameter, length of the generated strings, and by choosing appropriate forbidden strings. In this paper, we explore the capacity of different RNN extensions to model LDDs, by evaluating these models on a sequence of SPk synthesized datasets, where each subsequent dataset exhibits a longer degree of LDD. Even though SPk are simple languages, the presence of LDDs does have significant impact on the performance of recurrent neural architectures, thus making them prime candidate in benchmarking tasks.Comment: International Conference of Artificial Neural Networks (ICANN) 201

Proof Relevant Corecursive Resolution

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the role of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on non-terminating type class resolution problems.Comment: 23 pages, with appendices in FLOPS 201

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

Misaligned spin and orbital axes cause the anomalous precession of DI Herculis

The orbits of binary stars precess as a result of general relativistic effects, forces arising from the asphericity of the stars, and forces from additional stars or planets in the system. For most binaries, the theoretical and observed precession rates are in agreement. One system, however -- DI Herculis -- has resisted explanation for 30 years. The observed precession rate is a factor of four slower than the theoretical rate, a disagreement that once was interpreted as evidence for a failure of general relativity. Among the contemporary explanations are the existence of a circumbinary planet and a large tilt of the stellar spin axes with respect to the orbit. Here we report that both stars of DI Herculis rotate with their spin axes nearly perpendicular to the orbital axis (contrary to the usual assumption for close binary stars). The rotationally induced stellar oblateness causes precession in the direction opposite to that of relativistic precession, thereby reconciling the theoretical and observed rates.Comment: Nature, in press [11 pg

Quantum Storage of Photonic Entanglement in a Crystal

Entanglement is the fundamental characteristic of quantum physics. Large experimental efforts are devoted to harness entanglement between various physical systems. In particular, entanglement between light and material systems is interesting due to their prospective roles as "flying" and stationary qubits in future quantum information technologies, such as quantum repeaters and quantum networks. Here we report the first demonstration of entanglement between a photon at telecommunication wavelength and a single collective atomic excitation stored in a crystal. One photon from an energy-time entangled pair is mapped onto a crystal and then released into a well-defined spatial mode after a predetermined storage time. The other photon is at telecommunication wavelength and is sent directly through a 50 m fiber link to an analyzer. Successful transfer of entanglement to the crystal and back is proven by a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by almost three standard deviations (S=2.64+/-0.23). These results represent an important step towards quantum communication technologies based on solid-state devices. In particular, our resources pave the way for building efficient multiplexed quantum repeaters for long-distance quantum networks.Comment: 5 pages, 3 figures + supplementary information; fixed typo in ref. [36

Heralded quantum entanglement between two crystals

Quantum networks require the crucial ability to entangle quantum nodes. A prominent example is the quantum repeater which allows overcoming the distance barrier of direct transmission of single photons, provided remote quantum memories can be entangled in a heralded fashion. Here we report the observation of heralded entanglement between two ensembles of rare-earth-ions doped into separate crystals. A heralded single photon is sent through a 50/50 beamsplitter, creating a single-photon entangled state delocalized between two spatial modes. The quantum state of each mode is subsequently mapped onto a crystal, leading to an entangled state consisting of a single collective excitation delocalized between two crystals. This entanglement is revealed by mapping it back to optical modes and by estimating the concurrence of the retrieved light state. Our results highlight the potential of rare-earth-ions doped crystals for entangled quantum nodes and bring quantum networks based on solid-state resources one step closer.Comment: 10 pages, 5 figure

Cracking in asphalt materials

This chapter provides a comprehensive review of both laboratory characterization and modelling of bulk material fracture in asphalt mixtures. For the purpose of organization, this chapter is divided into a section on laboratory tests and a section on models. The laboratory characterization section is further subdivided on the basis of predominant loading conditions (monotonic vs. cyclic). The section on constitutive models is subdivided into two sections, the first one containing fracture mechanics based models for crack initiation and propagation that do not include material degradation due to cyclic loading conditions. The second section discusses phenomenological models that have been developed for crack growth through the use of dissipated energy and damage accumulation concepts. These latter models have the capability to simulate degradation of material capacity upon exceeding a threshold number of loading cycles.Peer ReviewedPostprint (author's final draft

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

A study of general practitioners' perspectives on electronic medical records systems in NHS Scotland

<b>Background</b> Primary care doctors in NHSScotland have been using electronic medical records within their practices routinely for many years. The Scottish Health Executive eHealth strategy (2008-2011) has recently brought radical changes to the primary care computing landscape in Scotland: an information system (GPASS) which was provided free-of-charge by NHSScotland to a majority of GP practices has now been replaced by systems provided by two approved commercial providers. The transition to new electronic medical records had to be completed nationally across all health-boards by March 2012. <p></p><b> Methods</b> We carried out 25 in-depth semi-structured interviews with primary care doctors to elucidate GPs' perspectives on their practice information systems and collect more general information on management processes in the patient surgical pathway in NHSScotland. We undertook a thematic analysis of interviewees' responses, using Normalisation Process Theory as the underpinning conceptual framework. <p></p> <b>Results</b> The majority of GPs' interviewed considered that electronic medical records are an integral and essential element of their work during the consultation, playing a key role in facilitating integrated and continuity of care for patients and making clinical information more accessible. However, GPs expressed a number of reservations about various system functionalities - for example: in relation to usability, system navigation and information visualisation. <b>Conclusion </b>Our study highlights that while electronic information systems are perceived as having important benefits, there remains substantial scope to improve GPs' interaction and overall satisfaction with these systems. Iterative user-centred improvements combined with additional training in the use of technology would promote an increased understanding, familiarity and command of the range of functionalities of electronic medical records among primary care doctors

Subclinical thyroid dysfunction and cognitive decline in old age

<p>Background: Subclinical thyroid dysfunction has been implicated as a risk factor for cognitive decline in old age, but results are inconsistent. We investigated the association between subclinical thyroid dysfunction and cognitive decline in the PROspective Study of Pravastatin in the Elderly at Risk (PROSPER).</p> <p>Methods: Prospective longitudinal study of men and women aged 70–82 years with pre-existing vascular disease or more than one risk factor to develop this condition (N = 5,154). Participants taking antithyroid medications, thyroid hormone supplementation and/or amiodarone were excluded. Thyroid function was measured at baseline: subclinical hyper- and hypothyroidism were defined as thyroid stimulating hormones (TSH) <0.45 mU/L or >4.50 mU/L respectively, with normal levels of free thyroxine (FT4). Cognitive performance was tested at baseline and at four subsequent time points during a mean follow-up of 3 years, using five neuropsychological performance tests.</p> <p>Results: Subclinical hyperthyroidism and hypothyroidism were found in 65 and 161 participants, respectively. We found no consistent association of subclinical hyper- or hypothyroidism with altered cognitive performance compared to euthyroid participants on the individual cognitive tests. Similarly, there was no association with rate of cognitive decline during follow-up.</p> <p>Conclusion: We found no consistent evidence that subclinical hyper- or hypothyroidism contribute to cognitive impairment or decline in old age. Although our data are not in support of treatment of subclinical thyroid dysfunction to prevent cognitive dysfunction in later life, only large randomized controlled trials can provide definitive evidence.</p&gt