Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Attitudes towards the use and acceptance of eHealth technologies : a case study of older adults living with chronic pain and implications for rural healthcare

Acknowledgements The research described here is supported by the award made by the RCUK Digital Economy programme to the dot.rural Digital Economy Hub; award reference: EP/G066051/1. MC’s time writing the paper is funded by the Scottish Government’s Rural and Environmental Science and Analytical Services Division (RESAS) under Theme 8 ‘Vibrant Rural Communities’ of the Food, Land and People Programme (2011–2016). MC is also an Honorary Research Fellow at the Division of Applied Health Sciences, University of Aberdeen. The input of other members of the TOPS research team, Alastair Mort, Fiona Williams, Sophie Corbett, Phil Wilson and Paul MacNamee who contributed to be wider study and discussed preliminary findings reported here with the authors of the paper is acknowledged. We acknowledge the feedback on earlier versions of this paper provided by members of the Trans-Atlantic Rural Research Network, especially Stefanie Doebler and Carmen Hubbard. We also thank Deb Roberts for her comments.Peer reviewedPublisher PD

Simplicity, one‑shot hypotheses and paleobiological explanation

This is the final version. Available on open access from Springer via the DOI in this recordPaleobiologists (and other historical scientists) often provide simple narratives to explain complex, contingent episodes. These narratives are sometimes ‘one-shot hypotheses’ which are treated as being mutually exclusive with other possible explanations of the target episode, and are thus extended to accommodate as much about the episode as possible. I argue that a provisional preference for such hypotheses provides two kinds of productive scaffolding. First, they generate ‘hypothetical difference-makers’: one-shot hypotheses highlight and isolate empirically tractable dependencies between variables. Second, investigations of hypothetical difference-makers provision explanatory resources, the ‘raw materials’ for constructing more complex—and likely more adequate—explanations. Provisional preferences for simple, one-shot hypotheses in historical science, then, is defeasibly justified on indirect—strategic—grounds. My argument is made in reference to recent developments regarding the K-Pg extinction.John Templeton Foundatio

Epistemic Optimism, Speculation, and the Historical Sciences

This is the final version. Available from Michigan Publishing via the DOI in this record.I summarize the central ideas and arguments of Rock, Bone and Ruin: An Optimist’s Guide to the Historical Sciences, before responding to criticisms from Leonard Finkelman, Joyce Havstad, Derek Turner and Alison Wylie. These cover whether, and to what extent, we can establish optimism about the historical sciences, the distinctions between ‘trace-based’ and ‘non-trace’ evidence, and between experiments and models, and the purpose and limits of speculation in scientific reasoning.John Templeton Foundatio

The Mystery of the Triceratops’s Mother: How to be a Realist About the Species Category

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Can we be realists about a general category but pluralists about concepts relating to that category? I argue that paleobiological methods of delineating species are not affected by differing species concepts, and that this underwrites an argument that species concept pluralists should be species category realists. First, the criteria by which paleobiologists delineate species are ‘indifferent’ to the species category. That is, their method for identifying species applies equally to any species concept. To identify a new species, paleobiologists show that interspecies processes, such as phenotypic plasticity (including pathology), sexual dimorphism, or ontogenetic diversity, are a worse explanation of the variance between specimens than intraspecies processes. As opposed to operating under a single or plurality of species concepts, then, paleobiologists use abductive inferences, which would be required regardless of any particular species concept. Second, paleobiologists are frequently interested in large-scale, long-term morphological patterns in the fossil record, and resolving the fine-grained differences which result from different species concepts is irrelevant at those scales. I argue that this claim about paleobiological practice supports what I call ‘indifference realism’ about the species category. The indifference realist argues that when legitimate investigation is indifferent to a plurality of concepts, we should be realists about the category those concepts pertain to

Big Dragons on Small Islands: generality and particularity in science.

Angela Potochnik’s Idealization and the Aims of Science (Chicago) defends an ambitious and systematic account of scientific knowledge: ultimately science pursues human understanding rather than truth. Potochnik argues that idealization is rampant and unchecked in science. Further, given that idealizations involve departures from truth, this suggests science is not primarily about truth. I explore the relationship between truths about causal patterns and scientific understanding in light of this, and suggest that Potochnik underestimates the importance and power of highly particular narrative explanations

Mass Extinctions as Major Transitions

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Both paleobiology and investigations of ‘major evolutionary transitions’ are intimately concerned with the macroevolutionary shape of life. It is surprising, then, how little paleontological perspectives and evidence inform studies of major transitions. I argue that this disconnect is partially justified because paleobiological investigation is typically ‘phenomena-led’, while investigations of major transitions (at least as commonly understood) are ‘theory-led’. The distinction turns on evidential relevance: in the former case, evidence is relevant in virtue of its relationship to some phenomena or hypotheses that concern those phenomena; in the latter, evidence is relevant in virtue of providing insights into, or tests of, an abstract body of theory. Because paleobiological data is by-and-large irrelevant to the theory which underwrites the traditional conception of major transitions, it is of limited use to that research program. I suggest that although the traditional conception of major transitions is neither ad-hoc or problematically incomplete, its promise of providing unificatory explanations of the transitions is unlikely to be kept. Further, examining paleobiological investigations of mass extinctions and organogenesis, I further argue that (1) whether or not transitions in paleobiology count as ‘major’ turns on how we conceive of major transitions (that is, the notion is sensitive to investigative context); (2) although major transitions potentially have a unified theoretical basis, recent developments suggest that investigations are becoming increasingly phenomena-led; (3) adopting phenomenaled investigations maximizes the evidence available to paleobiologists.Templeton World Charity Foundatio

Geoengineering Tensions

There has been much discussion of the moral, legal and prudential implications of geoengineering, and of governance structures for both the research and deployment of such technologies. However, insufficient attention has been paid to how such measures might affect geoengineering in terms of the incentive structures which underwrite scientific progress. There is a tension between the features that make science productive, and the need to govern geoengineering research, which has thus far gone underappreciated. I emphasize how geoengineering research requires governance which reaches beyond science’s traditional boundaries, and moreover requires knowledge which itself reaches beyond what we traditionally expect scientists to know about. How we govern emerging technologies should be sensitive to the incentive structures which drive science

Mass Extinctions as Major Transitions

Both paleobiology and investigations of ‘major evolutionary transitions’ are intimately concerned with the macroevolutionary shape of life. It is surprising, then, how little paleontological perspectives and evidence inform studies of major transitions. I argue that this disconnect is partially justified because paleobiological investigation is typically ‘phenomena-led’, while investigations of major transitions (at least as commonly understood) are ‘theory-led’. The distinction turns on evidential relevance: in the former case, evidence is relevant in virtue of its relationship to some phenomena or hypotheses that concern those phenomena; in the latter, evidence is relevant in virtue of providing insights into, or tests of, an abstract body of theory. Because paleobiological data is by-and-large irrelevant to the theory which underwrites the traditional conception of major transitions, it is of limited use to that research program. I suggest that although the traditional conception of major transitions is neither ad-hoc or problematically incomplete, its promise of providing unificatory explanations of the transitions is unlikely to be kept. Further, examining paleobiological investigations of mass extinctions and organogenesis, I further argue that (1) whether or not transitions in paleobiology count as ‘major’ turns on how we conceive of major transitions (that is, the notion is sensitive to investigative context); (2) although major transitions potentially have a unified theoretical basis, recent developments suggest that investigations are becoming increasingly phenomena-led; (3) adopting phenomena-led investigations maximizes the evidence available to paleobiologists