arXiv subjects

Frank Stephan

Publications and source records attributed to Frank Stephan.

At least 37 records · Page 2Linked to original sources

arXiv2022

Slice energy spread measurement in the low energy photoinjector

Slice energy spread is one of the key parameters in free electron laser optimizations, but its accurate measurement is not straightforward. Two recent studies from high energy ($>$100 MeV) photoinjectors at SwissFEL and European XFEL have reported much higher slice energy spread than expected at their XFEL working points (200 - 250 pC). In this paper, a new method for measuring slice energy spread at a lower beam energy ($\sim$20 MeV) is proposed and demonstrated at the PhotoInjector Test facility at DESY Zeuthen (PITZ), and the results for 250 pC and 500 pC are much lower than those measured at high energy injectors.

physics.acc-ph↗

arXiv2022

A Computation Model with Automatic Functions and Relations as Primitive Operations

Prior work of Hartmanis and Simon (Hartmanis and Simon, 1974) and Floyd and Knuth (Floyd and Knuth, 1990) investigated what happens if a device uses primitive steps more natural than single updates of a Turing tape. One finding was that in the numerical setting, addition, subtraction, comparisons and bit-wise Boolean operations of numbers preserve polynomial time while incorporating concatenation or multiplication allows to solve all PSPACE problems in polynomially many steps. Therefore we propose to use updates and comparisons with automatic functions as primitive operations and use constantly many registers; the resulting model covers all primitive operations of Hartmanis and Simon as well as Floyd and Knuth, but the model remains in polynomial time. The present work investigates in particular the deterministic complexity of various natural problems and also gives an overview on the nondeterministic complexity of this model.

cs.CC↗

arXiv2022

An Exact Algorithm for finding Maximum Induced Matching in Subcubic Graphs

The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this paper, we design an exact algorithm running in $O(1.2630^n)$ time and polynomial space to solve the Maximum Induced Matching problem for graphs where each vertex has degree at most 3. Prior work solved the problem by finding the Maximum Independent Set using polynomial space in the line graph $L(G^2)$; this method uses $O(1.3139^n)$ time.

cs.DS↗

arXiv2021

Improved Algorithms for the General Exact Satisfiability Problem

The Exact Satisfiability problem asks if we can find a satisfying assignment to each clause such that exactly one literal in each clause is assigned $1$, while the rest are all assigned $0$. We can generalise this problem further by defining that a $C^j$ clause is solved iff exactly $j$ of the literals in the clause are $1$ and all others are $0$. We now introduce the family of Generalised Exact Satisfiability problems called G$i$XSAT as the problem to check whether a given instance consisting of $C^j$ clauses with $j \in \{0,1,\ldots,i\}$ for each clause has a satisfying assignment. In this paper, we present faster exact polynomial space algorithms, using a nonstandard measure, to solve G$i$XSAT, for $i\in \{2,3,4\}$, in $O(1.3674^n)$ time, $O(1.5687^n)$ time and $O(1.6545^n)$ time, respectively, using polynomial space, where $n$ is the number of variables. This improves the current state of the art for polynomial space algorithms from $O(1.4203^n)$ time for G$2$XSAT by Zhou, Jiang and Yin and from $O(1.6202^n)$ time for G$3$XSAT by Dahllöf and from $O(1.6844^n)$ time for G$4$XSAT which was by Dahllöf as well. In addition, we present faster exact algorithms solving G$2$XSAT, G$3$XSAT and G$4$XSAT in $O(1.3188^n)$ time, $O(1.3407^n)$ time and $O(1.3536^n)$ time respectively at the expense of using exponential space.

cs.DS↗

arXiv2021

Learnability and Positive Equivalence Relations

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many equivalence classes. The present work investigates the infinite one-one numbered recursively enumerable (r.e.) families realised by such relations and asks how the choice of the equivalence relation impacts the learnability properties of these classes when studying learnability in the limit from positive examples, also known as learning from text. For all choices of such positive equivalence relations, for each of the following entries, there are one-one numbered r.e. families which satisfy it: (a) they are behaviourally correctly learnable but not vacillatorily learnable; (b) they are explanatorily learnable but not confidently learnable; (c) they are not behaviourally correctly learnable. Furthermore, there is a positive equivalence relation which enforces that (d) every vacillatorily learnable one-one numbered family of languages closed under this equivalence relation is already explanatorily learnable and cannot be confidently learnable.

cs.LO↗

arXiv2021

Ordered Semiautomatic Rings with Applications to Geometry

The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a countable dense subring of the real numbers and additions and comparisons and multiplications with constants need to be automatic. It is shown that the ring can be selected such that equilateral triangles can be represented and rotations by 30 degrees are possible, while the standard representation of the b-adic rationals does not allow this.

cs.FL↗

arXiv2020

Randomness and initial segment complexity for probability measures

We study algorithmic randomness properties for probability measures on Cantor space. We say that a measure $μ$ on the space of infinite bit sequences is ML absolutely continuous if the non-ML-random bit sequences form a null set with respect to~$μ$. We think of this as a weak randomness notion for measures. We begin with examples, and provide a robustness property related to Solovay tests. Our main work connects our weak randomness notion to the growth of the initial segment complexity for measures~$μ$; the latter is defined as a $μ$-average over the complexity of strings of the same length. We show that a maximal growth implies our weak randomness property, but also that both implications of the Levin-Schnorr theorem fail. We discuss $C$-triviality and $K$-triviality for measures and relate these two notions with each other. Here triviality means that the growth of initial segment complexity is as slow as possible. We show that full Martin-Löf randomness of a measure implies ML absolute continuity; the converse fails because only the latter property is compatible with having atoms. In a final section we consider weak randomness relative to a general ergodic computable measure. We seek appropriate effective versions of the Shannon-McMillan-Breiman theorem and the Brudno theorem where the bit sequences are replaced by measures. We conclude with several open questions.

math.LO↗

arXiv2020

members of thin $Π_1^0$ classes and generic degrees

A $Π^{0}_{1}$ class $P$ is thin if every $Π^{0}_{1}$ subclass $Q$ of $P$ is the intersection of $P$ with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the study of Turing degrees of members of thin $Π^{0}_{1}$ classes, and proved that degrees containing no members of thin $Π^{0}_{1}$ classes can be recursively enumerable, and can be minimal degree below {\bf 0}$'$. In this paper, we work on this topic in terms of genericity, and prove that all 2-generic degrees contain no members of thin $Π^{0}_{1}$ classes. In contrast to this, we show that all 1-generic degrees below {\bf 0}$'$ contain members of thin $Π^{0}_{1}$ classes.

math.LO↗

arXiv2020

A Faster Exact Algorithm to Count X3SAT Solutions

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are set to 0. If we restrict the length of each clause to be at most 3 literals, then it is known as the X3SAT problem. In this paper, we consider the problem of counting the number of satisfying assignments to the X3SAT problem, which is also known as #X3SAT. The current state of the art exact algorithm to solve #X3SAT is given by Dahllöf, Jonsson and Beigel and runs in $O(1.1487^n)$, where $n$ is the number of variables in the formula. In this paper, we propose an exact algorithm for the #X3SAT problem that runs in $O(1.1120^n)$ with very few branching cases to consider, by using a result from Monien and Preis to give us a bisection width for graphs with at most degree 3.

cs.DS↗

arXiv2020

Subrecursive Approximations of Irrational Numbers by Variable Base Sums

There are numerous ways to represent real numbers. We may use, e.g., Cauchy sequences, Dedekind cuts, numerical base-10 expansions, numerical base-2 expansions and continued fractions. If we work with full Turing computability, all these representations yield the same class of real numbers. If we work with some restricted notion of computability, e.g., polynomial time computability or primitive recursiveness, they do not. Irrational numbers can be represented by infinite sums of certain forms. We prove some results related to representation of irrational numbers by infinite sums.

math.LO↗

arXiv2020

Single shot cathode transverse momentum imaging in high brightness photoinjectors

In state of the art photoinjector electron sources, thermal emittance from photoemission dominates the final injector emittance. Therefore, low thermal emittance cathode developments and diagnostics are very important. Conventional thermal emittance measurements for the high gradient gun are time-consuming and thus thermal emittance is not measured as frequently as quantum efficiency during the lifetime of photocathodes, although both are important properties for the photoinjector optimizations. In this paper, a single shot measurement of photoemission transverse momentum, i.e., thermal emittance per rms laser spot size, is proposed for photocathode RF guns. By tuning the gun solenoid focusing, the electrons transverse momenta at the cathode are imaged to a downstream screen, which enables a single shot measurement of both the rms value and the detailed spectra of the photoelectrons transverse momenta. Both simulations and proof of principle experiments are reported.

physics.acc-ph↗

arXiv2019

A note on the experiment parameters for the non-resonant streaming instability: competition between left and right circularly polarized modes

A non-resonant streaming instability driven by cosmic-ray currents, also called Bell's instability, is proposed as a candidate for providing the required magnetic turbulence of efficient diffusive shock accelerations. To demonstrate the saturation level and mechanism of the non-resonant streaming instability in a laboratory environment, we attempt to develop an experiment at the Photo Injector Test Facility at DESY, Zeuthen site (PITZ). As an electron beam is used to replace the proton beam to carry the cosmic-ray current in our experiment, the polarization of the non-resonant streaming instability will be modified from the left-handed (LH) mode to the right-handed (RH) mode. The theoretical instability analysis shows that the growth rate of this RH non-resonant mode may be smaller than it of the LH resonant mode. However the LH resonant mode can be ignored in our experiment while the expected wavelength is longer than the used plasma cell. The results of PIC simulations will also support this contention and the occurrence of non-resonant streaming instability in our experiment.

physics.plasm-ph↗

arXiv2019

A Fast Exponential Time Algorithm for Max Hamming Distance X3SAT

X3SAT is the problem of whether one can satisfy a given set of clauses with up to three literals such that in every clause, exactly one literal is true and the others are false. A related question is to determine the maximal Hamming distance between two solutions of the instance. Dahllöf provided an algorithm for Maximum Hamming Distance XSAT, which is more complicated than the same problem for X3SAT, with a runtime of $O(1.8348^n)$; Fu, Zhou and Yin considered Maximum Hamming Distance for X3SAT and found for this problem an algorithm with runtime $O(1.6760^n)$. In this paper, we propose an algorithm in $O(1.3298^n)$ time to solve the Max Hamming Distance X3SAT problem; the algorithm actually counts for each $k$ the number of pairs of solutions which have Hamming Distance $k$.

cs.CC↗

arXiv2019

The isomorphism problem for tree-automatic ordinals with addition

This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such that their elements are coded by finite trees for which the linear order relation of the ordinal and the ordinal addition operation can be determined by tree automata. We describe an algorithm that, given two tree-automatic ordinals with the ordinal addition operation, decides if the ordinals are isomorphic.

cs.FL↗

arXiv2019

On the order dimension of locally countable partial orderings

We show that the order dimension of the partial order of all finite subsets of $κ$ under set inclusion is ${\log}_{2}({\log}_{2}(κ))$ whenever $κ$ is an infinite cardinal. We also show that the order dimension of any locally countable partial ordering $(P, <)$ of size $κ^+$, for any $κ$ of uncountable cofinality, is at most $κ$. In particular, this implies that it is consistent with ZFC that the dimension of the Turing degrees under partial ordering can be strictly less than the continuum.

math.LO↗

arXiv2019

Random Subgroups of Rationals

This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of $(G,+)$; second, what learnability properties can one extract from $G$ and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of $(G,+)$ coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for $G$ with respect to any generating sequence for $G$ is not even semi-decidable, one can build a generating sequence $β$ such that the word problem for $G$ with respect to $β$ is co-recursively enumerable (assuming that the set of generators of $G$ is limit-recursive). In regard to the second question, it is proven that there is a generating sequence $β$ for $G$ such that every non-trivial finitely generated subgroup of $G$ is recursively enumerable and the class of all such subgroups of $G$ is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of $G$ is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of $G$ cannot be syntactically identified in the limit with respect to any generating sequence for $G$. The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.

cs.LO↗

arXiv2018

Equivalences between learning of data and probability distributions, and their applications

Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by [Vitanyi and Chater, 2017] and [Bienvenu et al., 2014] has adapted this framework to the study of learnability of effective probability distributions from random data. We prove that for certain families of probability measures that are parametrized by reals, learnability of a subclass of probability measures is equivalent to learnability of the class of the corresponding real parameters. This equivalence allows to transfer results from classical algorithmic theory to learning theory of probability measures. We present a number of such applications, providing many new results regarding EX and BC learnability of classes of measures, thus drawing parallels between the two learning theories.

math.LO↗

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↗