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Frank Stephan

Publications and source records attributed to Frank Stephan.

At least 55 records · Page 3Linked to original sources
arXiv2018

Passive Ballistic Microbunching of Non-Ultrarelativistic Electron Bunches using Electromagnetic Wakefields in Dielectric-Lined Waveguides

Temporally-modulated electron beams have a wide array of applications ranging from the generation of coherently-enhanced electromagnetic radiation to the resonant excitation of electromagnetic wakefields in advanced-accelerator concepts. Likewise producing low-energy ultrashort microbunches could be useful for ultra-fast electron diffraction and new accelerator-based light-source concepts. In this Letter we propose and experimentally demonstrate a passive microbunching technique capable of forming a picosecond bunch train at $\sim 6$~MeV. The method relies on the excitation of electromagnetic wakefields as the beam propagates through a dielectric-lined waveguide. Owing to the non-ultrarelativistic nature of the beam, the induced energy modulation eventually converts into a density modulation as the beam travels in a following free-space drift. The modulated beam is further accelerated to $\sim20$~MeV while preserving the imparted density modulation.

physics.acc-ph↗
arXiv2018

Generation of quasi continuous-wave electron beams in an L-band normal conducting pulsed RF injector for laboratory astrophysics experiments

We report on an approach to produce quasi continuous-wave (cw) electron beams with an average beam current of milliamperes and a mean beam energy of a few MeV in a pulsed RF injector. Potential applications are in the planned laboratory astrophysics programs at DESY. The beam generation is based on field emission from a specially designed metallic field emitter. A quasi cw beam profile is formed over subsequent RF cycles at the resonance frequency of the gun cavity. This is realized by debunching in a cut disk structure accelerating cavity (booster) downstream of the gun. The peak and average beam currents can be tuned in beam dynamics simulations by adjusting operation conditions of the booster cavity. Optimization of the transverse beam size at specific positions (e.g., entrance of the plasma experiment) is performed by applying magnetic focusing fields provided by solenoids along the beam line. In this paper, the design of a microtip field emitter is introduced and characterized in electromagnetic field simulations in the gun cavity. A series of particle tracking simulations are conducted for multi-parametric optimization of the parameters of the produced quasi cw electron beams. The obtained results will be presented and discussed. In addition, measurements of the parasitic field emission (PFE) current (dark current) in the PITZ gun will be exemplarily shown to distinguish its order of magnitude from the produced beam current by the designed field emitter.

physics.acc-ph↗
arXiv2018

Algorithmic learning of probability distributions from random data in the limit

We study the problem of identifying a probability distribution for some given randomly sampled data in the limit, in the context of algorithmic learning theory as proposed recently by Vinanyi and Chater. We show that there exists a computable partial learner for the computable probability measures, while by Bienvenu, Monin and Shen it is known that there is no computable learner for the computable probability measures. Our main result is the characterization of the oracles that compute explanatory learners for the computable (continuous) probability measures as the high oracles. This provides an analogue of a well-known result of Adleman and Blum in the context of learning computable probability distributions. We also discuss related learning notions such as behaviorally correct learning and orther variations of explanatory learning, in the context of learning probability distributions from data.

cs.LG↗
arXiv2018

An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their data structure as a progress measure, allowing for a backward implementation instead of a complete unravelling of the game. To achieve this, a number of changes have to be made to their techniques, where the main one is to add power to the antagonistic player that allows for determining her rational move without changing the outcome of the game. We provide a first implementation for a quasi-polynomial algorithm, test it on small examples, and provide a number of side results, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al.

cs.LO↗
arXiv2017

Covering the recursive sets

We give solutions to two of the questions in a paper by Brendle, Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct constructions using martingales. At the same time, we introduce the concept of i.o. subuniformity and relate this concept to recursive measure theory. We prove that there are classes closed downwards under Turing reducibility that have recursive measure zero and that are not i.o. subuniform. This shows that there are examples of classes that cannot be covered with methods other than probabilistic ones. It is easily seen that every set of hyperimmune degree can cover the recursive sets. We prove that there are both examples of hyperimmune-free degree that can and that cannot compute such a cover.

math.LO↗
arXiv2017

Depth, Highness and DNR degrees

We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not order-deepC , that every many-one degree contains a set which is not O(1)-deepC , that O(1)-deepC sets and order-deepK sets have high or DNR Turing degree and that no K-trival set is O(1)-deepK.

cs.CC↗
arXiv2017

Closure of resource-bounded randomness notions under polynomial time permutations

An infinite bit sequence is called recursively random if no computable strategy betting along the sequence has unbounded capital. It is well-known that the property of recursive randomness is closed under computable permutations. We investigate analogous statements for randomness notions defined by betting strategies that are computable within resource bounds. Suppose that S is a polynomial time computable permutation of the set of strings over the unary alphabet (identified with N). If the inverse of S is not polynomially bounded, it is easy to build a polynomial time random bit sequence Z such that Z o S is not polynomial time random. So one should only consider permutations S satisfying the extra condition that the inverse is polynomially bounded. Now the closure depends on additional assumptions in complexity theory. Our first result shows that if BPP contains a superpolynomial deterministic time class then polynomial time randomness is not preserved by some permutation S such that in fact both S and its inverse are in P. Our second result shows that polynomial space randomness is preserved by polynomial time permutations with polynomially boun\-ded inverse, so if P=PSPACE then polynomial time randomness is preserved.

math.LO↗
arXiv2016

How to verify computation with a rational network

The present paper introduces a practical protocol for provably secure, outsourced computation. Our protocol minimizes overhead for verification by requiring solutions to withstand an interactive game between a prover and challenger. For optimization problems, the best or nearly best of all submitted solutions is expected to be accepted by this approach. Financial incentives and deposits are used in order to overcome the problem of fake participants.

cs.GT↗
arXiv2016

Partial functions and domination

The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. Here a set A is called pdominant iff there is a partial A-recursive function ψ such that for every partial recursive function ϕ and almost every x in the domain of ϕ there is a y in the domain of ψ with y<= x and ψ(y) > ϕ(x). While there is a full π01-class of nonrecursive sets where no set is pdominant, there is no π01-class containing only pdominant sets. No weakly 2-generic set is pdominant while there are pdominant 1-generic sets below K. The halves of Chaitin's Ω are pdominant. No set which is low for Martin-Löf random is pdominant. There is a low r.e. set which is pdominant and a high r.e. set which is not pdominant.

cs.LO↗
arXiv2015

Combining Models of Approximation with Partial Learning

In Gold's framework of inductive inference, the model of partial learning requires the learner to output exactly one correct index for the target object and only the target object infinitely often. Since infinitely many of the learner's hypotheses may be incorrect, it is not obvious whether a partial learner can be modifed to "approximate" the target object. Fulk and Jain (Approximate inference and scientific method. Information and Computation 114(2):179--191, 1994) introduced a model of approximate learning of recursive functions. The present work extends their research and solves an open problem of Fulk and Jain by showing that there is a learner which approximates and partially identifies every recursive function by outputting a sequence of hypotheses which, in addition, are also almost all finite variants of the target function. The subsequent study is dedicated to the question how these findings generalise to the learning of r.e. languages from positive data. Here three variants of approximate learning will be introduced and investigated with respect to the question whether they can be combined with partial learning. Following the line of Fulk and Jain's research, further investigations provide conditions under which partial language learners can eventually output only finite variants of the target language. The combinabilities of other partial learning criteria will also be briefly studied.

cs.LG↗
arXiv2014

Higher Kurtz randomness

A real $x$ is $Δ^1_1$-Kurtz random ($Π^1_1$-Kurtz random) if it is in no closed null $Δ^1_1$ set ($Π^1_1$ set). We show that there is a cone of $Π^1_1$-Kurtz random hyperdegrees. We characterize lowness for $Δ^1_1$-Kurtz randomness as being $Δ^1_1$-dominated and $Δ^1_1$-semi-traceable.

math.LO↗
arXiv2014

Arithmetic complexity via effective names for random sequences

We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-Löf, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-Löf randoms and Kurtz non-randoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals.

math.LO↗
arXiv2014

Kolmogorov complexity and the Recursion Theorem

Several classes of DNR functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wtt-compute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of the initial segments of A. Furthermore, A can Turing compute a DNR function iff there is a nontrivial A-recursive lower bound on the Kolmogorov complexity of the initial segements of A. A is PA-complete, that is, A can compute a {0,1}-valued DNR function, iff A can compute a function F such that F(n) is a string of length n and maximal C-complexity among the strings of length n. A solves the halting problem iff A can compute a function F such that F(n) is a string of length n and maximal H-complexity among the strings of length n. Further characterizations for these classes are given. The existence of a DNR function in a Turing degree is equivalent to the failure of the Recursion Theorem for this degree; thus the provided results characterize those Turing degrees in terms of Kolmogorov complexity which do no longer permit the usage of the Recursion Theorem.

math.LO↗
arXiv2014

On Martin's Pointed Tree Theorem

We investigate the reverse mathematics strength of Martin's pointed tree theorem (MPT) and one of its variants, weak Martin's pointed tree theorem (wMPT).

math.LO↗
arXiv2014

Things that can be made into themselves

One says that a property $P$ of sets of natural numbers can be made into itself iff there is a numbering $α_0,α_1,\ldots$ of all left-r.e. sets such that the index set $\{e: α_e$ satisfies $P\}$ has the property $P$ as well. For example, the property of being Martin-Löf random can be made into itself. Herein we characterize those singleton properties which can be made into themselves. A second direction of the present work is the investigation of the structure of left-r.e. sets under inclusion modulo a finite set. In contrast to the corresponding structure for r.e. sets, which has only maximal but no minimal members, both minimal and maximal left-r.e. sets exist. Moreover, our construction of minimal and maximal left-r.e. sets greatly differs from Friedberg's classical construction of maximal r.e. sets. Finally, we investigate whether the properties of minimal and maximal left-r.e. sets can be made into themselves.

cs.LO↗
arXiv2014

Algorithmic aspects of Lipschitz functions

We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a real z is Schnorr random if and only if every Lipschitz function with $L_1$-computable derivative is differentiable at z.

math.LO↗
arXiv2013

Automatic functions, linear time and learning

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 full 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.

cs.FL↗