Decidability of cutpoint isolation for letter-monotonic probabilistic finite automata

We show the surprising result that the cutpoint isolation problem is decidable for probabilistic finite automata where input words are taken from a letter-bounded context-free language. A context-free language $L$ is letter-bounded when $L \subseteq a_1^*a_2^* \cdots a_k^*$ for some finite $k > 0$ where each letter is distinct. A cutpoint is isolated when it cannot be approached arbitrarily closely. The decidability of this problem is in marked contrast to the situation for the (strict) emptiness problem for PFA which is undecidable under the even more severe restrictions of PFA with polynomial ambiguity, commutative matrices and input over a letter-bounded language as well as to the injectivity problem which is undecidable for PFA over letter-bounded languages. We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, which holds even when the PFA is exponentially ambiguous. We also show that the problem is at least NP-hard and use our decision procedure to solve several related problems

Polynomially Ambiguous Probabilistic Automata on Restricted Languages

We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for non-strict cut-points of polynomially ambiguous PFA remains undecidable even when the input word is over a bounded language and all PFA transition matrices are commutative. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automata which can be used to generate PFA of lower dimensions and of subexponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases

Towards Uniform Online Spherical Tessellations

The problem of uniformly placing N points onto a sphere finds applications in many areas. For example, points on the sphere correspond to unit quaternions as well as to the group of rotations SO(3) and the online version of generating uniform rotations (known as “incremental generation”) plays a crucial role in a large number of engineering applications ranging from robotics and aeronautics to computer graphics. An online version of this problem was recently studied with respect to the gap ratio as a measure of uniformity. The first online algorithm of Chen et al. was upper-bounded by 5.99 and later improved to 3.69, which is achieved by considering a circumscribed dodecahedron followed by a recursive decomposition of each face. In this paper we provide a more efficient tessellation technique based on the regular icosahedron, which improves the upper-bound for the online version of this problem, decreasing it to approximately 2.84. Moreover, we show that the lower bound for the gap ratio of placing at least three points is 1.618 and for at least four points is no less than 1.726

Exploring the current landscape of intravenous infusion practices and errors (ECLIPSE): protocol for a mixedmethods observational study

Introduction: Intravenous medication is essential for many hospital inpatients. However, providing intravenous therapy is complex and errors are common. ‘Smart pumps’ incorporating dose error reduction software have been widely advocated to reduce error. However, little is known about their effect on patient safety, how they are used or their likely impact. This study will explore the landscape of intravenous medication infusion practices and errors in English hospitals and how smart pumps may relate to the prevalence of medication administration errors. Methods and analysis: This is a mixed-methods study involving an observational quantitative point prevalence study to determine the frequency and types of errors that occur in the infusion of intravenous medication, and qualitative interviews with hospital staff to better understand infusion practices and the contexts in which errors occur. The study will involve 5 clinical areas (critical care, general medicine, general surgery, paediatrics and oncology), across 14 purposively sampled acute hospitals and 2 paediatric hospitals to cover a range of intravenous infusion practices. Data collectors will compare each infusion running at the time of data collection against the patient’s medication orders to identify any discrepancies. The potential clinical importance of errors will be assessed. Quantitative data will be analysed descriptively; interviews will be analysed using thematic analysis. Ethics and dissemination: Ethical approval has been obtained from an NHS Research Ethics Committee (14/SC/0290); local approvals will be sought from each participating organisation. Findings will be published in peer-reviewed journals and presented at conferences for academic and health professional audiences. Results will also be fed back to participating organisations to inform local policy, training and procurement. Aggregated findings will inform the debate on costs and benefits of the NHS investing in smart pump technology, and what other changes may need to be made to ensure effectiveness of such an investment

Scalar Ambiguity and Freeness in Matrix Semigroups over Bounded Languages

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, mainly related to the dimensions of the generator matrices and the semiring over which the matrices are defined. A recent paper has also investigated freeness properties of matrices within a bounded language of matrices, which are of the form M1M2 · · · Mk ⊆ F n×n for some semiring F [9]. Most freeness problems have been shown to be undecidable starting from dimension three, even for upper-triangular matrices over the natural numbers. There are many open problems still remaining in dimension two. We introduce a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρ TMτ |M ∈ S}, where ρ, τ ∈ F n are vectors and S is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of uniqueness of factorizations leading to each scalar. We show various undecidability results

Decision questions for probabilistic automata on small alphabets

We study the emptiness and λ-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its alphabet. Our main result is that emptiness and λ-reachability are solvable in EXPTIME for polynomially ambiguous unary PFA and if, in addition, the transition matrix is over {0, 1}, we show they are in NP. In contrast to the Skolem-hardness of the λ-reachability and emptiness problems for exponentially ambiguous unary PFA, we show that these problems are NP-hard even for finitely ambiguous unary PFA. We also show that the value of a polynomially ambiguous PFA can be computed in EXPTIME. For binary polynomially ambiguous PFA with commuting transition matrices, we prove NP-hardness of the λ-reachability (dimension 9), nonstrict emptiness (dimension 37) and strict emptiness (dimension 40) problems

Decision Questions for Probabilistic Automata on Small Alphabets

We study the emptiness and λ-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its alphabet. Our main result is that emptiness and λ-reachability are solvable in EXPTIME for polynomially ambiguous unary PFA and if, in addition, the transition matrix is over {0, 1}, we show they are in NP. In contrast to the Skolem-hardness of the λ-reachability and emptiness problems for exponentially ambiguous unary PFA, we show that these problems are NP-hard even for finitely ambiguous unary PFA. For binary polynomially ambiguous PFA with commuting transition matrices, we prove NP-hardness of the λ-reachability (dimension 9), nonstrict emptiness (dimension 37) and strict emptiness (dimension 40) problems

Stellar Disk Truncations: Where do we stand ?

In the light of several recent developments we revisit the phenomenon of galactic stellar disk truncations. Even 25 years since the first paper on outer breaks in the radial light profiles of spiral galaxies, their origin is still unclear. The two most promising explanations are that these 'outer edges' either trace the maximum angular momentum during the galaxy formation epoch, or are associated with global star formation thresholds. Depending on their true physical nature, these outer edges may represent an improved size characteristic (e.g., as compared to D_25) and might contain fossil evidence imprinted by the galaxy formation and evolutionary history. We will address several observational aspects of disk truncations: their existence, not only in normal HSB galaxies, but also in LSB and even dwarf galaxies; their detailed shape, not sharp cut-offs as thought before, but in fact demarcating the start of a region with a steeper exponential distribution of starlight; their possible association with bars; as well as problems related to the line-of-sight integration for edge-on galaxies (the main targets for truncation searches so far). Taken together, these observations currently favour the star-formation threshold model, but more work is necessary to implement the truncations as adequate parameters characterising galactic disks.Comment: LaTeX, 10 pages, 6 figures, presented at the "Penetrating Bars through Masks of Cosmic Dust" conference in South Africa, proceedings published by Kluwer, and edited by Block, D.L., Freeman, K.C., Puerari, I., & Groess, R; v3 to match published versio

Unique Decipherability in Formal Languages

We consider several language-theoretic aspects of various notions of unique decipherability (or unique factorization) in formal languages. Given a language L at some position within the Chomsky hierarchy, we investigate the language of words UD(L) in L^* that have unique factorization over L. We also consider similar notions for weaker forms of unique decipherability, such as numerically decipherable words ND(L), multiset decipherable words MSD(L) and set decipherable words SD(L). Although these notions of unique factorization have been considered before, it appears that the languages of words having these properties have not been positioned in the Chomsky hierarchy up until now. We show that UF(L), ND(L), MSD(L) and SD(L) need not be context-free if L is context-free. In fact ND(L) and MSD(L) need not be context-free even if L is finite, although UD(L) and SD(L) are regular in this case. We show that if L is context-sensitive, then so are UD(L), ND(L), MSD(L) and SD(L). We also prove that the membership problem (resp., emptiness problem) for these classes is PSPACE-complete (resp., undecidable). We finally determine upper and lower bounds on the length of the shortest word of L^* not having the various forms of unique decipherability into elements of L

Marked long-term decline in ambient CO mixing ratio in SE England, 1997–2014:Evidence of policy success in improving air quality

Atmospheric CO at Egham in SE England has shown a marked and progressive decline since 1997, following adoption of strict controls on emissions. The Egham site is uniquely positioned to allow both assessment and comparison of ‘clean Atlantic background’ air and CO-enriched air downwind from the London conurbation. The decline is strongest (approximately 50ppb per year) in the 1997–2003 period but continues post 2003. A ‘local CO increment’ can be identified as the residual after subtraction of contemporary background Atlantic CO mixing ratios from measured values at Egham. This increment, which is primarily from regional sources (during anticyclonic or northerly winds) or from the European continent (with easterly air mass origins), has significant seasonality, but overall has declined steadily since 1997. On many days of the year CO measured at Egham is now not far above Atlantic background levels measured at Mace Head (Ireland). The results are consistent with MOPITT satellite observations and ‘bottom-up’ inventory results. Comparison with urban and regional background CO mixing ratios in Hong Kong demonstrates the importance of regional, as opposed to local reduction of CO emission. The Egham record implies that controls on emissions subsequent to legislation have been extremely successful in the UK