Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.If F is a polynomial automorphism over a finite field Fq in dimension n, then it induces a permutation pqr(F) of (Fqr)n for every r О N*. We say that F can be "mimicked" by elements of a certain group of automorphisms G if there are gr О G such that pqr(gr) = pqr(F). Derksen's theorem in characteristic zero states that the tame automorphisms in dimension n і 3 are generated by the affine maps and the one map (x1+x22, x2,ј, xn). We show that Derksen's theorem is not true in characteristic p in general. However, we prove a modified, weaker version of Derksen's theorem over finite fields: we introduce the Derksen group DAn(Fq), n і 3, which is generated by the affine maps and one well-chosen nonlinear map, and show that DAn(Fq) mimicks any element of TAn(Fq). Also, we do give an infinite set E of non-affine maps which, together with the affine maps, generate the tame automorphisms in dimension 3 and up. We conjecture that such a set E cannot be finite. We consider the subgroups GLINn(k) and GTAMn(k). We prove that for k a finite field, these groups are equal if and only if k\not = F2. The latter result provides a tool to show that a map is not linearizable

Fast and robust bootstrap for multivariate inference: the R package FRB

We present the FRB package for R, which implements the fast and robust bootstrap. This method constitutes an alternative to ordinary bootstrap or asymptotic inference procedures when using robust estimators such as S-, MM- or GS-estimators. The package considers three multivariate settings: principal components analysis, Hotelling tests and multivariate regression. It provides both the robust point estimates and uncertainty measures based on the fast and robust bootstrap. In this paper we give some background on the method, discuss the implementation and provide various examples

Samen vooruit

Wie denkt aan pathologie, denkt aan microscopie.Dankzij de microscoop ging een wereld voor ons open. Dit leidde tot inzicht in het ontstaan en het beter classificeren van ziekten, en leerde ons op abstracter niveau ook een belangrijk principe: dat samenwerking loont.Pathologie is een verbindend specialisme zowel binnen de patiëntenzorg als het onderzoek, alsook daartussen. Aan deze rol dankt de pathologie haar positie, haar kracht, maar ook haar identiteit: alleen door deze verbinding kan de pathologie bestaan. We hebben niet alleen geleerd dat samenwerken noodzakelijk is, het brengt ons ook verder. De grootste vooruitgang binnen ons vak zoals op het gebied van de digitale en moleculaire pathologie komt juist door kruisbestuiving met andere domeinen.SamenwerkenHet vereist moed om muren tussen domeinen te laten zakken, over eigen grenzen heen te reiken en ook toestaan dat anderen dat bij jou doen. Dat geldt voor zowel samenwerkingen binnen verschillende diagnostische disciplines, alsook netwerksamenwerkingen tussen verschillende ziekenhuizen. Hier liggen niet alleen kansen. Het is ook noodzakelijk om de academische pathologie levendig te houden, de best mogelijke diagnostiek te leveren en de zorg betaalbaar te houden.Onderwijs en opleiding spelen een cruciale rol in deze transitie. Niet alleen zijn zij essentieel voor de verdere integratie van kennis op het gebied van IT, digitalisering en automatisering binnen de opleiding tot arts en patholoog. Maar nog belangrijker: ze leidt op tot een patholoog die leert kijken vanuit de ander, met een breder, integraler perspectief, gestoeld op een nieuwe vorm van leiderschap. Minder ik, meer wij. Alleen samen komen we vooruit

Optical inter-site spin transfer probed by energy and spin-resolved transient absorption spectroscopy

Optically driven spin transport is the fastest and most efficient process to manipulate macroscopic magnetization as it does not rely on secondary mechanisms to dissipate angular momentum. In the present work, we show that such an optical inter-site spin transfer (OISTR) from Pt to Co emerges as a dominant mechanism governing the ultrafast magnetization dynamics of a CoPt alloy. To demonstrate this, we perform a joint theoretical and experimental investigation to determine the transient changes of the helicity dependent absorption in the extreme ultraviolet spectral range. We show that the helicity dependent absorption is directly related to changes of the transient spin-split density of states, allowing us to link the origin of OISTR to the available minority states above the Fermi level. This makes OISTR a general phenomenon in optical manipulation of multi-component magnetic systems. Optically driven spin transfer is the fastest process to manipulate magnetism. Here, the authors show that this process emerges as the dominant mechanism in femtosecond spin dynamics enabling to the engineering of functional magnetic systems for future all optical technologies

Overview and Reassessment of Noise Budget of Starshade Exoplanet Imaging

High-contrast imaging enabled by a starshade in formation flight with a space telescope can provide a near-term pathway to search for and characterize temperate and small planets of nearby stars. NASA’s Starshade Technology Development Activity to TRL5 (S5) is rapidly maturing the required technologies to the point at which starshades could be integrated into potential future missions. Here we reappraise the noise budget of starshade-enabled exoplanet imaging to incorporate the experimentally demonstrated optical performance of the starshade and its optical edge. Our analyses of stray light sources – including the leakage through micrometeoroid damage and the reflection of bright celestial bodies – indicate that sunlight scattered by the optical edge (i.e., the solar glint) is by far the dominant stray light. With telescope and observation parameter that approximately correspond to Starshade Rendezvous with Roman and HabEx, we find that the dominating noise source would be exozodiacal light for characterizing a temperate and Earth-sized planet around Sun-like and earlier stars and the solar glint for later-type stars. Further reducing the brightness of solar glint by a factor of 10 with a coating would prevent it from becoming the dominant noise for both Roman and HabEx. With an instrument contrast of 10⁻¹⁰, the residual starlight is not a dominant noise; and increasing the contrast level by a factor 10 would not lead to any appreciable change in the expected science performance. If unbiased calibration of the background to the photon-noise limit can be achieved, Starshade Rendezvous with Roman could provide nearly photon-limited spectroscopy of temperate and Earth-sized planets of F, G, and K stars < 4 parsecs away, and HabEx could extend this capability to many more stars < 8 parsecs. Larger rocky planets around stars < 8 parsecs would be within the reach of Roman. To achieve these capabilities, the exozodiacal light may need to be calibrated to a precision better than 2% and the solar glint better than 5%. Our analysis shows that the expected temporal variability of the solar glint is unlikely to hinder the calibration, and the main challenge for background calibration likely comes from the unsmooth spatial distribution of exozodiacal dust in some stars. Taken together, these results validate the optical noise budget and technology milestones adopted by S5 against key science objectives and inform the priorities of future technology developments and science and industry community partnerships

Multi-Color Imaging of Magnetic Co/Pt Multilayers

We demonstrate for the first time the realization of a spatial resolved two color, element-specific imaging experiment at the free-electron laser facility FERMI. Coherent imaging using Fourier transform holography was used to achieve direct real space access to the nanometer length scale of magnetic domains of Co/Pt heterostructures via the element-specific magnetic dichroism in the extreme ultraviolet spectral range. As a first step to implement this technique for studies of ultrafast phenomena we present the spatially resolved response of magnetic domains upon femtosecond laser excitation