The present work determines the exact nature of {em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time notions permit f
ull learnability for learning in the limit of automatic classes (families of languages which are uniformly recognised by a finite automaton). In particular it is shown that a function is automatic iff there is a one-tape Turing machine with a left end which computes the function in linear time where the input before the computation and the output after the computation both start at the left end. It is known that learners realised as automatic update functions are restrictive for learning. In the present work it is shown that one can overcome the problem by providing work tapes additional to a resource-bounded base tape while keeping the update-time to be linear in the length of the largest datum seen so far. In this model, one additional such work tape provides additional learning power over the automatic learner model and two additional work tapes give full learning power. Furthermore, one can also consider additional queues or additional stacks in place of additional work tapes and for these devices, one queue or two stacks are sufficient for full learning power while one stack is insufficient.
We briefly describe the energy loss processes of ultrahigh energy protons, heavier nuclei and gamma rays in interactions with the universal photon fields of the Universe. We then discuss the modification of the accelerated cosmic ray energy spectrum
in propagation by the energy loss processes and the charged cosmic ray scattering in the extragalactic magnetic fields. The energy lost by the ultrahigh energy cosmic rays goes into gamma rays and neutrinos that carry additional information about the sources of highest energy particles. The new experimental results of the HiRes and the Auger collaborations are discussed in view of the predictions from propagation calculations.
We discuss the anisotropic arrival directions of the ultra high energy cosmic rays detected by Auger which I consider one of the biggest discoverie in astrophysics during the last year.
We discuss the main results that were recently published by the Auger Collaboration and their impact on our knowledge of the ultra high energy cosmic rays and neutrinos.
We discuss the basic difficulties in understanding the origin of the highest energy particles in the Universe - the ultrahigh energy cosmic rays (UHECR). It is difficult to imagine the sources they are accelerated in. Because of the strong attenuatio
n of UHECR on their propagation from the sources to us these sources should be at cosmologically short distance from us but are currently not identified. We also give information of the most recent experimental results including the ones reported at this conference and compare them to models of the UHECR origin.
We use all-electrical methods to inject, transport, and detect spin-polarized electrons vertically through a 350-micron-thick undoped single-crystal silicon wafer. Spin precession measurements in a perpendicular magnetic field at different accelerati
ng electric fields reveal high spin coherence with at least 13pi precession angles. The magnetic-field spacing of precession extrema are used to determine the injector-to-detector electron transit time. These transit time values are associated with output magnetocurrent changes (from in-plane spin-valve measurements), which are proportional to final spin polarization. Fitting the results to a simple exponential spin-decay model yields a conduction electron spin lifetime (T1) lower bound in silicon of over 500ns at 60K.
A longitudinal electric field is used to control the transit time (through an undoped silicon vertical channel) of spin-polarized electrons precessing in a perpendicular magnetic field. Since an applied voltage determines the final spin direction at
the spin detector and hence the output collector current, this comprises a spin field-effect transistor. An improved hot-electron spin injector providing ~115% magnetocurrent, corresponding to at least ~38% electron current spin polarization after transport through 10 microns undoped single-crystal silicon, is used for maximum current modulation.
