Deductive synthesis of recursive plans in linear logic

Linear logic has previously been shown to be suitable for describing and deductively solving planning problems involving conjunction and disjunction. We introduce a recursively defined datatype and a corresponding induction rule, thereby allowing recursive plans to be synthesised. In order to make explicit the relationship between proofs and plans, we enhance the linear logic deduction rules to handle plans as a form of proof term

Teleportation, Braid Group and Temperley--Lieb Algebra

We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley--Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version of the preprint, quant-ph/0601050, which includes details of calculation, more topics such as topological diagrammatical operations and entanglement swapping, and calls the Temperley--Lieb category for the collection of all the Temperley--Lieb algebra with physical operations like local unitary transformation

Quantum picturalism for topological cluster-state computing

Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of computing is a leading candidate for large-scale quantum computing. However, there has been a lack of sufficiently powerful high-level languages to describe computing in this form without resorting to single-qubit operations, which quickly become prohibitively complex as the system size increases. In this paper we apply the category-theoretic work of Abramsky and Coecke to the topological cluster-state model of quantum computing to give a high-level graphical language that enables direct translation between quantum processes and physical patterns of measurement in a computer - a "compiler language". We give the equivalence between the graphical and topological information flows, and show the applicable rewrite algebra for this computing model. We show that this gives us a native graphical language for the design and analysis of topological quantum algorithms, and finish by discussing the possibilities for automating this process on a large scale.Comment: 18 pages, 21 figures. Published in New J. Phys. special issue on topological quantum computin

Prevalence and Correlates of Common Mental Disorders among Mothers of Young Children in Kilimanjaro Region of Tanzania.

Although poor maternal mental health is a major public health problem, with detrimental effects on the individual, her children and society, information on its correlates in low-income countries is sparse. This study investigates the prevalence of common mental disorders (CMD) among at-risk mothers, and explores its associations with sociodemographic factors. This population-based survey of mothers of children aged 0-36 months used the 14-item Shona Symptom Questionnaire (SSQ). Mothers whose response was "yes" to 8 or more items on the scale were defined as "at risk of CMD." Of the 1,922 mothers (15-48 years), 28.8% were at risk of CMD. Risk of CMD was associated with verbal abuse, physical abuse, a partner who did not help with the care of the child, being in a polygamous relationship, a partner with low levels of education, and a partner who smoked cigarettes. Cohabiting appeared to be protective. Taken together, our results indicate the significance of the quality of relations with one's partner in shaping maternal mental health. The high proportion of mothers who are at risk of CMD emphasizes the importance of developing evidence-based mental health programmes as part of the care package aimed at improving maternal well-being in Tanzania and other similar settings

Seed Mucilage Improves Seedling Emergence of a Sand Desert Shrub

The success of seedling establishment of desert plants is determined by seedling emergence response to an unpredictable precipitation regime. Sand burial is a crucial and frequent environmental stress that impacts seedling establishment on sand dunes. However, little is known about the ecological role of seed mucilage in seedling emergence in arid sandy environments. We hypothesized that seed mucilage enhances seedling emergence in a low precipitation regime and under conditions of sand burial. In a greenhouse experiment, two types of Artemisia sphaerocephala achenes (intact and demucilaged) were exposed to different combinations of burial depth (0, 5, 10, 20, 40 and 60 mm) and irrigation regimes (low, medium and high, which simulated the precipitation amount and frequency in May, June and July in the natural habitat, respectively). Seedling emergence increased with increasing irrigation. It was highest at 5 mm sand burial depth and ceased at burial depths greater than 20 mm in all irrigation regimes. Mucilage significantly enhanced seedling emergence at 0, 5 and 10 mm burial depths in low irrigation, at 0 and 5 mm burial depths in medium irrigation and at 0 and 10 mm burial depths in high irrigation. Seed mucilage also reduced seedling mortality at the shallow sand burial depths. Moreover, mucilage significantly affected seedling emergence time and quiescence and dormancy percentages. Our findings suggest that seed mucilage plays an ecologically important role in successful seedling establishment of A. sphaerocephala by improving seedling emergence and reducing seedling mortality in stressful habitats of the sandy desert environment

The syntax and semantics of quantitative type theory

We present Quantitative Type Theory, a Type Theory that records usage information for each variable in a judgement, based on a previous system by McBride. The usage information is used to give a realizability semantics using a variant of Linear Combinatory Algebras, refining the usual realizability semantics of Type Theory by accurately tracking resource behaviour. We define the semantics in terms of Quantitative Categories with Families, a novel extension of Categories with Families for modelling resource sensitive type theories

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Determinants of Habitat Selection by Hatchling Australian Freshwater Crocodiles

Animals almost always use habitats non-randomly, but the costs and benefits of using specific habitat types remain unknown for many types of organisms. In a large lake in northwestern Australia (Lake Argyle), most hatchling (<12-month-old) freshwater crocodiles (Crocodylus johnstoni) are found in floating vegetation mats or grassy banks rather than the more widely available open banks. Mean body sizes of young crocodiles did not differ among the three habitat types. We tested four potential explanations for non-random habitat selection: proximity to nesting sites, thermal conditions, food availability, and exposure to predation. The three alternative habitat types did not differ in proximity to nesting sites, or in thermal conditions. Habitats with higher food availability harboured more hatchlings, and feeding rates (obtained by stomach-flushing of recently-captured crocodiles) were highest in such areas. Predation risk may also differ among habitats: we were twice as likely to capture a crocodile after seeing it in open-bank sites than in the other two habitat types. Thus, habitat selection of hatchling crocodiles in this system may be driven both by prey availability and by predation risk

Partial-order Boolean games: informational independence in a logic-based model of strategic interaction

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly (IF) logic