Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

"Medicine is still against Black people": Mapping and visualising intersections of social inequalities, community mistrust, and vaccine hesitancy in online and physical spaces in the UK and US

Funded by the British Academy, this report is part of a research project entitled “Mapping and visualising intersections of social inequalities, community mistrust, and vaccine hesitancy in online and physical spaces in the UK and US”. The report investigates social, cultural, and political factors underlying vaccine hesitant beliefs and ideas among minoritised communities in the United Kingdom (UK) and the United States of America (US). The data is collected through interviews and focus groups with vaccine-hesitant individuals within various religiously, ethnically, and racially minoritised communities, interviews with medical practitioners, and through thematic analysis of vaccine communication in Twitter and Telegram during the COVID-19 pandemic

A psychoanalytic concept illustrated: Will, must, may, can — revisiting the survival function of primitive omnipotence

The author explores the linear thread connecting the theory of Freud and Klein, in terms of the central significance of the duality of the life and death instinct and the capacity of the ego to tolerate contact with internal and external reality. Theoretical questions raised by later authors, informed by clinical work with children who have suffered deprivation and trauma in infancy, are then considered. Theoretical ideas are illustrated with reference to observational material of a little boy who suffered deprivation and trauma in infancy. He was first observed in the middle of his first year of life while he was living in foster care, and then later at the age of two years and three months, when he had been living with his adoptive parents for more than a year

Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning

We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in [Devetak and Winter, Proc. of the Roy. Soc. of London Series A, 461, 207 (2005); Kraus, Gisin and Renner, Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, d and d+1 mutually unbiased bases where d is a prime, and show that for the protocols with 2 and d+1 MUBs the optimal attack is an optimal cloner, but for the protocols with d MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the BB84 protocol or the 6-state protocol

Principles for applying optogenetic tools derived from direct comparative analysis of microbial opsins

Diverse optogenetic tools have allowed versatile control over neural activity. Many depolarizing and hyperpolarizing tools have now been developed in multiple laboratories and tested across different preparations, presenting opportunities but also making it difficult to draw direct comparisons. This challenge has been compounded by the dependence of performance on parameters such as vector, promoter, expression time, illumination, cell type and many other variables. As a result, it has become increasingly complicated for end users to select the optimal reagents for their experimental needs. For a rapidly growing field, critical figures of merit should be formalized both to establish a framework for further development and so that end users can readily understand how these standardized parameters translate into performance. Here we systematically compared microbial opsins under matched experimental conditions to extract essential principles and identify key parameters for the conduct, design and interpretation of experiments involving optogenetic techniques