arXiv subjects

Sebastian Müller

Publications and source records attributed to Sebastian Müller.

At least 55 records · Page 3Linked to original sources

arXiv2021

On asymptotic fairness in voting with greedy sampling

The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have the same weight. We study voting protocols for heterogeneous weights with respect to fairness. A voting protocol is fair if the influence on the eventual outcome of a given participant is linear in its weight. Previous work used sampling with replacement to construct a fair voting scheme. However, it was shown that using greedy sampling, i.e., sampling with replacement until a given number of distinct elements is chosen, turns out to be more robust and performant. In this paper, we study fairness of voting protocols with greedy sampling and propose a voting scheme that is asymptotically fair for a broad class of weight distributions. We complement our theoretical findings with numerical results and present several open questions and conjectures.

math.PR↗

arXiv2020

On Fairness in Voting Consensus Protocols

Voting algorithms have been widely used as consensus protocols in the realization of fault-tolerant systems. These algorithms are best suited for distributed systems of nodes with low computational power or heterogeneous networks, where different nodes may have different levels of reputation or weight. Our main contribution is the construction of a fair voting protocol in the sense that the influence of the eventual outcome of a given participant is linear in its weight. Specifically, the fairness property guarantees that any node can actively participate in the consensus finding even with low resources or weight. We investigate effects that may arise from weighted voting, such as loss of anonymity, centralization, scalability, and discuss their relevance to protocol design and implementation.

cs.DC↗

arXiv2020

On transience of frogs on Galton-Watson trees

We consider a random interacting particle system, known as the frog model, on infinite Galton-Watson trees allowing offspring zero and one. The system starts with one awake particle (frog) at the root of the tree and a random number of sleeping particles at the other vertices. Awake frogs move according to simple random walk on the tree and as soon as they encounter sleeping frogs, those will wake up and move independently according to simple random walk. The frog model is called transient, if there are almost surely only finitely many particles returning to the root. In this paper we prove a zero-one law for transience of the frog model and show the existence of a transient phase for certain classes of Galton-Watson trees.

math.PR↗

arXiv2020

Bet and Run for Test Case Generation

Anyone working in the technology sector is probably familiar with the question: "Have you tried turning it off and on again?", as this is usually the default question asked by tech support. Similarly, it is known in search based testing that metaheuristics might get trapped in a plateau during a search. As a human, one can look at the gradient of the fitness curve and decide to restart the search, so as to hopefully improve the results of the optimization with the next run. Trying to automate such a restart, it has to be programmatically decided whether the metaheuristic has encountered a plateau yet, which is an inherently difficult problem. To mitigate this problem in the context of theoretical search problems, the Bet and Run strategy was developed, where multiple algorithm instances are started concurrently, and after some time all but the single most promising instance in terms of fitness values are killed. In this paper, we adopt and evaluate the Bet and Run strategy for the problem of test case generation. Our work indicates that use of this restart strategy does not generally lead to gains in the quality metrics, when instantiated with the best parameters found in the literature.

cs.SE↗

arXiv2020

Fast Probabilistic Consensus with Weighted Votes

The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficient in Byzantine infrastructure. We propose an adaption of the FPC to a setting where the voting power is proportional to the nodes reputations. We model the reputation using a Zipf law and show using simulations that the performance of the protocol in Byzantine infrastructure increases with the Zipf exponent. Moreover, we propose several improvements of the FPC that decrease the failure rates significantly and allow the protocol to withstand adversaries with higher weight. We distinguish between cautious and berserk strategies of the adversaries and propose an efficient method to detect the more harmful berserk strategies. Our study refers at several points to a specific implementation of the IOTA protocol, but the principal results hold for general implementations of reputation models.

cs.DC↗

arXiv2020

A Survey on Human Machine Interaction in Industry 4.0

Industry 4.0 or Industrial IoT both describe new paradigms for seamless interaction between humans and machines. Both concepts rely on intelligent, inter-connected cyber-physical production systems that are able to control the process flow of industrial production. As those machines take many decisions autonomously and further interact with production and manufacturing planning systems, the integration of human users requires new paradigms. In this paper, we provide an analysis of the current state-of-the-art in human-machine interaction in the Industry 4.0 domain.We focus on new paradigms that integrate the application of augmented and virtual reality technology. Based on our analysis, we further provide a discussion of research challenges.

cs.HC↗

arXiv2019

The giant outburst of 4U 0115+634 in 2011 with Suzaku and RXTE

We present an analysis of X-ray spectra of the high mass X-ray binary 4U 0115+634 as observed with Suzaku and RXTE in 2011 July, during the fading phase of a giant X-ray outburst. We used a continuum model consisting of an absorbed cutoff power-law and an ad-hoc Gaussian emission feature centered around 8.5 keV, which we discuss to be due to cyclotron emission. Our results are consistent with a fundamental cyclotron absorption line centered at ${\sim}10.2$ keV for all observed flux ranges. At the same time we rule out significant influence of the 8.5 kev Gaussian on the CRSF parameters, which are not consistent with the cyclotron line energies and depths of previously reported flux-dependent descriptions. We also show that some continuum models can lead to artificial line-like residuals in the analyzed spectra, which are then misinterpreted as unphysically strong cyclotron lines. Specifically, our results do not support the existence of a previously claimed additional cyclotron feature at ${\sim}15$ keV. Apart from these features, we find for the first time evidence for a He-like Fe XXV emission line at ${\sim}6.7$ keV and weak H-like Fe XXVI emission close to ${\sim}7.0$ keV.

astro-ph.HE↗

arXiv2018

Einstein relation for random walk in a one-dimensional percolation model

We consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. In a companion paper, we have shown that if the random walk is pulled to the right by a positive bias $λ> 0$, then its asymptotic linear speed $\overline{\mathrm{v}}$ is continuous in the variable $λ> 0$ and differentiable for all sufficiently small $λ> 0$. In the paper at hand, we complement this result by proving that $\overline{\mathrm{v}}$ is differentiable at $λ= 0$. Further, we show the Einstein relation for the model, i.e., that the derivative of the speed at $λ= 0$ equals the diffusivity of the unbiased walk.

math.PR↗

arXiv2018

Semiclassical calculation of spectral correlation functions of chaotic systems

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and therefore provide constructive interference. We calculate explicitly the first correlation functions, to leading orders in their energy arguments, for both unitary and orthogonal symmetry classes. The results agree with corresponding predictions from random matrix theory, thereby giving solid support to the conjecture of universality.

nlin.CD↗

arXiv2018

Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We obtain to all orders in perturbation theory the non-oscillatory parts of all correlation functions, showing that the off-diagonal contributions to these correlation functions cancel and the conjectured universailty holds. The innovation that allows this calculation to be performed is the introduction of an auxiliary matrix model which is governed by the same diagrammatic rules as the semiclassical approach and which can be exactly solved.

nlin.CD↗

arXiv2018

On Elo based prediction models for the FIFA Worldcup 2018

We propose an approach for the analysis and prediction of a football championship. It is based on Poisson regression models that include the Elo points of the teams as covariates and incorporates differences of team-specific effects. These models for the prediction of the FIFA World Cup 2018 are fitted on all football games on neutral ground of the participating teams since 2010. Based on the model estimates for single matches Monte-Carlo simulations are used to estimate probabilities for reaching the different stages in the FIFA World Cup 2018 for all teams. We propose two score functions for ordinal random variables that serve together with the rank probability score for the validation of our models with the results of the FIFA World Cups 2010 and 2014. All models favor Germany as the new FIFA World Champion. All possible courses of the tournament and their probabilities are visualized using a single Sankey diagram.

stat.AP↗

arXiv2017

A precessing Be disk as a possible model for occultation events in GX 304-1

We report on the RXTE detection of a sudden increase in the absorption column density, $N_\mathrm{H}$, during the 2011 May outburst of GX 304-1. The $N_\mathrm{H}$ increased up to ${\sim}16\times 10^{22}$ atoms cm$^{-2}$, which is a factor of 3-4 larger than what is usually measured during the outbursts of GX 304-1 as covered by RXTE. Additionally, an increase in the variability of the hardness ratio as calculated from the energy resolved RXTE-PCA light curves is measured during this time range. We interpret these facts as an occultation event of the neutron star by material in the line of sight. Using a simple 3D model of an inclined and precessing Be disk around the Be type companion, we are able to qualitatively explain the $N_\mathrm{H}$ evolution over time. We are able to constrain the Be-disk density to be on the order of $10^{-11}$ g cm$^{-3}$. Our model strengthens the idea of inclined Be disks as origin of double-peaked outbursts as the derived geometry allows accretion twice per orbit under certain conditions.

astro-ph.HE↗

arXiv2016

First Study of Combined Blazar Light Curves with FACT and HAWC

For studying variable sources like blazars, it is crucial to achieve unbiased monitoring, either with dedicated telescopes in pointing mode or survey instruments. At TeV energies, the High Altitude Water Cherenkov (HAWC) observatory monitors approximately two thirds of the sky every day. It uses the water Cherenkov technique, which provides an excellent duty cycle independent of weather and season. The First G-APD Cherenkov Telescope (FACT) monitors a small sample of sources with better sensitivity, using the imaging air Cherenkov technique. Thanks to its camera with silicon-based photosensors, FACT features an excellent detector performance and stability and extends its observations to times with strong moonlight, increasing the duty cycle compared to other imaging air Cherenkov telescopes. As FACT and HAWC have overlapping energy ranges, a joint study can exploit the longer daily coverage given that the observatories' locations are offset by 5.3 hours. Furthermore, the better sensitivity of FACT adds a finer resolution of features on hour-long time scales, while the continuous duty cycle of HAWC ensures evenly sampled long-term coverage. Thus, the two instruments complement each other to provide a more complete picture of blazar variability. In this presentation, the first joint study of light curves from the two instruments will be shown, correlating long-term measurements with daily sampling between air and water Cherenkov telescopes. The presented results focus on the study of the variability of the bright blazars Mrk 421 and Mrk 501 during the last two years featuring various flaring activities.

astro-ph.HE↗

arXiv2016

Simultaneous fits in ISIS on the example of GRO J1008-57

Parallel computing and steadily increasing computation speed have led to a new tool for analyzing multiple datasets and datatypes: fitting several datasets simultaneously. With this technique, physically connected parameters of individual data can be treated as a single parameter by implementing this connection into the fit directly. We discuss the terminology, implementation, and possible issues of simultaneous fits based on the X-ray data analysis tool Interactive Spectral Interpretation System (ISIS). While all data modeling tools in X-ray astronomy allow in principle fitting data from multiple data sets individually, the syntax used in these tools is not often well suited for this task. Applying simultaneous fits to the transient X-ray binary GRO J1008-57, we find that the spectral shape is only dependent on X-ray flux. We determine time independent parameters such as, e.g., the folding energy E_fold, with unprecedented precision.

astro-ph.HE↗

arXiv2016

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups

In this article we prove existence of the asymptotic entropy for isotropic random walks on regular Fuchsian buildings. Moreover, we give formulae for the asymptotic entropy, and prove that it is equal to the rate of escape of the random walk with respect to the Green distance. When the building arises from a Fuchsian Kac-Moody group our results imply results for random walks induced by bi-invariant measures on these groups, however our results are proven in the general setting without the assumption of any group acting on the building. The main idea is to consider the retraction of the isotropic random walk onto an apartment of the building, to prove existence of the asymptotic entropy for this retracted walk, and to `lift' this in order to deduce the existence of the entropy for the random walk on the building.

math.PR↗

arXiv2016

Spectral statistics of chaotic many-body systems

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross-Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose-Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner-Dyson ensembles of random matrix theory. The conditions for Wigner-Dyson statistics involve a gap in the spectrum of the Frobenius-Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.

nlin.CD↗

arXiv2015

The Transient Accereting X-Ray Pulsar XTE J1946+274: Stability of the X-Ray Properties at Low Flux and Updated Orbital Solution

We present a timing and spectral analysis of the X-ray pulsar XTE J1946+274 observed with Suzaku during an outburst decline in 2010 October and compare with previous results. XTE J1946+274 is a transient X-ray binary consisting of a Be-type star and a neutron star with a 15.75 s pulse period in a 172 d orbit with 2-3 outbursts per orbit during phases of activity. We improve the orbital solution using data from multiple instruments. The X-ray spectrum can be described by an absorbed Fermi-Dirac cutoff power law model along with a narrow Fe K line at 6.4 keV and a weak Cyclotron Resonance Scattering Feature (CRSF) at ~35 keV. The Suzaku data are consistent with the previously observed continuum flux versus iron line flux correlation expected from fluorescence emission along the line of sight. However, the observed iron line flux is slightly higher, indicating the possibility of a higher iron abundance or the presence of non-uniform material. We argue that the source most likely has only been observed in the subcritical (non-radiation dominated) state since its pulse profile is stable over all observed luminosities and the energy of the CRSF is approximately the same at the highest (~$5 \times 10^{37} $erg s$^{-1}$) and lowest (~$5 \times 10^{36} $erg s$^{-1}$) observed 3-60 keV luminosities.

astro-ph.HE↗

arXiv2015

Counting self-avoiding walks on free products of graphs

The connective constant $μ(G)$ of a graph $G$ is the asymptotic growth rate of the number $σ_{n}$ of self-avoiding walks of length $n$ in $G$ from a given vertex. We prove a formula for the connective constant for free products of quasi-transitive graphs and show that $σ_{n}\sim A_{G} μ(G)^{n}$ for some constant $A_{G}$ that depends on $G$. In the case of finite products $μ(G)$ can be calculated explicitly and is shown to be an algebraic number.

math.CO↗