Slowly synchronizing automata and digraphs

We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure

Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

Understanding decision quality through satisfaction

"PAAMS 2014 International Workshops, Salamanca, Spain, June 4-6, 2014. Proceedings"One of the most important factors to determine the success of an or-ganization is the quality of decisions made. In order to improve the decisions taken and to strengthen the competitiveness of organizations, systems such as Group Decision Support Systems (GDSSs) have been strongly developed and studied in recent decades. The amount of GDSSs incorporating automatic nego-tiation mechanisms, such as argumentation, is increasing nowadays. The evalu-ation of these mechanisms and the understanding of their real benefits for the organizations is still a hard challenge. In this article, we propose a model that allows a GDSS to measure the participant’s satisfaction with the decision, con-sidering aspects such as problem evaluation, personality, emotions and expecta-tions. This model is intended to enable the understanding of the decision’s qual-ity achieved with an argumentation system and to evaluate its capability to po-tentiate the decision’s quality. The proposed model validates all the assump-tions found in the literature regarding the participant’s satisfaction.This work is supported by FEDER Funds through the “Programa Operacional Fac-tores de Competitividade - COMPETE” program and by National Funds through FCT “Fundação para a Ciência e a Tecnologia” under the project: FCOMP-01-0124-FEDER-PEst-OE/EEI/UI0760/2011 and SFRH/BD/89697/2012

Transverse phase-locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps

We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the $IV$ curve with voltage noise, Lyapunov exponents and Poincar\'e sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model.Comment: 12 pages, 11 figure

Professionalism, Golf Coaching and a Master of Science Degree: A commentary

As a point of reference I congratulate Simon Jenkins on tackling the issue of professionalism in coaching. As he points out coaching is not a profession, but this does not mean that coaching would not benefit from going through a professionalization process. As things stand I find that the stimulus article unpacks some critically important issues of professionalism, broadly within the context of golf coaching. However, I am not sure enough is made of understanding what professional (golf) coaching actually is nor how the development of a professional golf coach can be facilitated by a Master of Science Degree (M.Sc.). I will focus my commentary on these two issues

Interleukin-6 Receptor Antagonists in Critically Ill Patients with Covid-19.

BACKGROUND: The efficacy of interleukin-6 receptor antagonists in critically ill patients with coronavirus disease 2019 (Covid-19) is unclear. METHODS: We evaluated tocilizumab and sarilumab in an ongoing international, multifactorial, adaptive platform trial. Adult patients with Covid-19, within 24 hours after starting organ support in the intensive care unit (ICU), were randomly assigned to receive tocilizumab (8 mg per kilogram of body weight), sarilumab (400 mg), or standard care (control). The primary outcome was respiratory and cardiovascular organ support-free days, on an ordinal scale combining in-hospital death (assigned a value of -1) and days free of organ support to day 21. The trial uses a Bayesian statistical model with predefined criteria for superiority, efficacy, equivalence, or futility. An odds ratio greater than 1 represented improved survival, more organ support-free days, or both. RESULTS: Both tocilizumab and sarilumab met the predefined criteria for efficacy. At that time, 353 patients had been assigned to tocilizumab, 48 to sarilumab, and 402 to control. The median number of organ support-free days was 10 (interquartile range, -1 to 16) in the tocilizumab group, 11 (interquartile range, 0 to 16) in the sarilumab group, and 0 (interquartile range, -1 to 15) in the control group. The median adjusted cumulative odds ratios were 1.64 (95% credible interval, 1.25 to 2.14) for tocilizumab and 1.76 (95% credible interval, 1.17 to 2.91) for sarilumab as compared with control, yielding posterior probabilities of superiority to control of more than 99.9% and of 99.5%, respectively. An analysis of 90-day survival showed improved survival in the pooled interleukin-6 receptor antagonist groups, yielding a hazard ratio for the comparison with the control group of 1.61 (95% credible interval, 1.25 to 2.08) and a posterior probability of superiority of more than 99.9%. All secondary analyses supported efficacy of these interleukin-6 receptor antagonists. CONCLUSIONS: In critically ill patients with Covid-19 receiving organ support in ICUs, treatment with the interleukin-6 receptor antagonists tocilizumab and sarilumab improved outcomes, including survival. (REMAP-CAP ClinicalTrials.gov number, NCT02735707.)

The Origin, Early Evolution and Predictability of Solar Eruptions

Coronal mass ejections (CMEs) were discovered in the early 1970s when space-borne coronagraphs revealed that eruptions of plasma are ejected from the Sun. Today, it is known that the Sun produces eruptive flares, filament eruptions, coronal mass ejections and failed eruptions; all thought to be due to a release of energy stored in the coronal magnetic field during its drastic reconfiguration. This review discusses the observations and physical mechanisms behind this eruptive activity, with a view to making an assessment of the current capability of forecasting these events for space weather risk and impact mitigation. Whilst a wealth of observations exist, and detailed models have been developed, there still exists a need to draw these approaches together. In particular more realistic models are encouraged in order to asses the full range of complexity of the solar atmosphere and the criteria for which an eruption is formed. From the observational side, a more detailed understanding of the role of photospheric flows and reconnection is needed in order to identify the evolutionary path that ultimately means a magnetic structure will erupt