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Infinite sums of Brooks quasimorphisms and cup products in bounded cohomology
(2020)arXivWe study a class of quasimorphisms of the free group that can be expressed as infinite sums of Brooks quasimorphisms with some nice properties. We then review Heuer's framework of decompositions developed in arXiv:1710.03193, and put these quasimorphisms in that context. This allows us to prove triviality of a number of cup products in the bounded cohomology of the free group with trivial real coefficients. Finally, we introduce free ...Working Paper -
Nonclassical Temporal Correlations Enhance the Performance of Ticking Clocks
(2020)arXivWe investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario. We show that the problem of optimal models for ticking clocks is related to the violation of Leggett-Garg-type temporal inequalities formulated in terms of, possibly invasive, sequential measurements, but on a system with a bounded memory capacity. Moreover, the idea of ticking clocks inspires the ...Working Paper -
Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities
(2020)arXivThe Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel tool for this task by deriving a quantitative lower bound on the Lyapunov exponent in terms of a matrix sum which is efficiently computable in ergodic situations. Our approach combines ...Working Paper -
On the Continuum Limit of Benincasa-Dowker-Glaser Causal Set Action
(2020)arXivWe study the continuum limit of the Benincasa-Dowker-Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of arbitrary curvature in various spacetime dimensions. In the continuum limit, we show that the action admits a finite limit. More importantly, the limit is composed by an Einstein-Hilbert bulk term as predicted ...Working Paper -
Autonomous Ticking Clocks from Axiomatic Principles
(2020)arXivThere are many different types of time keeping devices. We coin the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this manuscript is to introduce a new ticking clock model from axiomatic ...Working Paper -
Chromosome-scale de novo diploid assembly of the apple cultivar ‘Gala Galaxy’
(2020)Working Paper -
Conventional NK cells and tissue-resident ILC1s join forces to control liver metastasis
(2020)bioRxivThe liver is a major metastatic target organ, and little is known about the role of immunity in controlling hepatic metastases. Here, we discovered that the concerted and non-redundant action of two innate lymphocyte subpopulations, conventional NK cells (cNKs) and tissue-resident type I Innate Lymphoid Cells (trILC1s), is essential for anti-metastatic defense. Using different preclinical models for liver metastasis, we found that trILC1 ...Working Paper -
Electron Scattering in Liquid Water and Amorphous Ice: A Striking Resemblance
(2020)The lack of accurate low-energy electron scattering cross sections for liquid water is a substantial source of uncertainty in the modelling of radiation chemistry and biology. The use of existing amorphous ice scattering cross sections for lack of liquid data has been discussed controversially over decades. Here, we compare experimental photoemission data of liquid water with corresponding predictions using amorphous ice cross sections, ...Working Paper -
ARNOLD HARTLEY GIBSON: Hydraulics professor and textbook author
(2022)The United Kingdom was the leading nation in the 19th century, then the British Empire. Despite this fact, hydraulic engineering was not a main concern. Scientists rather worked in maritime hydraulics and naval architecture. In all the above three topics, textbooks were not really available, because both engineers and scientists rather published their works in scientific journals. Gibson, an indirect successor of Osborne Reynolds at the ...Working Paper