Unitary nn-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.Comment: This is a new and extended version of the Supplementary material presented in arXiv:1709.05060v1, rewritten as a companion paper. Version accepted to Phys. Rev. A. Minus sign corrected in Eq (5

Uniformly Positive Entropy of Induced Transformations

Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does the induced system (\cM(X),\wt{T}) on the space of Borel probability measures endowed with the weak$^*$ topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.Comment: To apper in ETD

Towards a codification of practical knowledge

International audienceAs practical knowledge seems to have a central place in organisational issues, we focus on possibilities to study and formalize it. From an unusual theoretical perspective, we view practical knowledge as embodied knowing which only is only manifest through action in a particular situation. Although this knowledge is largely implicit, we try to make what is 'articulable' explicit. After highlighting the stakes involved in the codification of practices, we review the ontological and epistemological assumptions underlying the method developed. It is founded on participant observation, a video recording of a situated subjective perspective and an ex post interview using this perspective to aid an actor to make part of his/her practical knowledge explicit. We present its implementation within research on polar expeditions in order to understand how an experienced actor deals with risks. In conclusion, we point out (1) the importance of this kind of data in knowledge management, (2) some lines of further research

Efficacy of alemtuzumab over 6 years in relapsing–remitting multiple sclerosis patients who relapsed between courses 1 and 2: Post hoc analysis of the CARE-MS studies

Background: Alemtuzumab is administered as two annual courses for relapsing–remitting multiple sclerosis (MS). Patients may relapse before completing the two-course regimen. Objective: The objective was to evaluate 6-year outcomes in patients who relapsed between alemtuzumab Courses 1 and 2 (early relapsers). Methods: Post hoc analysis of patients from the Comparison of Alemtuzumab and Rebif® Efficacy in Multiple Sclerosis (CARE-MS) studies who enrolled in the extension. Results: Early relapsers (CARE-MS I: 15%; CARE-MS II: 24%) had more relapses in 1–2 years pre-alemtuzumab and higher mean baseline Expanded Disability Status Scale score than patients without relapse. Their annualized relapse rate declined from Year 1 (CARE-MS I: 1.3; CARE-MS II: 1.2) to Year 2 following Course 2 (0.3; 0.5) and remained low thereafter. Over 6 years, 60% remained free of 6-month confirmed disability worsening; 24% (CARE-MS I) and 34% (CARE-MS II) achieved 6-month confirmed disability improvement. During Year 6, 69% (CARE-MS I) and 68% (CARE-MS II) were free of magnetic resonance imaging (MRI) disease activity. Median percent yearly brain volume loss (Year 1: −0.67% (CARE-MS I); −0.47% (CARE-MS II)) declined after Course 2 (Year 6: −0.24%; −0.13%). Conclusion: Early relapsers’ outcomes improved after completing the second alemtuzumab course. These findings support administering the approved two-course regimen to maximize clinical benefit. ClinicalTrials.gov registration numbers: CARE-MS I, II, extension: NCT00530348, NCT00548405, NCT00930553