arXiv subjects

Johannes Müller

Publications and source records attributed to Johannes Müller.

65 records · Page 4Linked to original sources

arXiv2019

A Trust Management and Misbehaviour Detection Mechanism for Multi-Agent Systems and its Application to Intelligent Transportation Systems

Cooperative information shared among a multi-agent system (MAS) can be useful to agents to efficiently fulfill their missions. Relying on wrong information, however, can have severe consequences. While classical approaches only consider measurement uncertainty, reliability information on the incoming data can be useful for decision making. In this work, a subjective logic based mechanism is proposed that amends reliability information to the data shared among the MAS. If multiple agents report the same event, their information is fused. In order to maintain high reliability, the mechanism detects and isolates misbehaving agents. Therefore, an attacker model is specified that includes faulty as well as malicious agents. The mechanism is applied to Intelligent Transportation Systems (ITS) and it is shown in simulation that the approach scales well with the size of the MAS and that it is able to efficiently detected and isolated misbehaving agents. Keywords: Multi-agent systems, Fault Detection, Sensor/data fusion, Control Applications

eess.SP↗

arXiv2019

Homogeneous and Heterogeneous Response of Quorum-Sensing Bacteria in an Evolutionary Context

To explain the stability of cooperation is a central task of evolutionary theory. We investigate this question in the case of quorum sensing (QS) bacteria, which regulate cooperative traits in response to population density. Cooperation is modeled by the prisoner's dilemma, where individuals produce a costly public good (PG) that equally benefits all members of a community divided into multiple, distinct patches (multilevel selection). Cost and benefit are non-linear functions of the PG production. The analysis of evolutionary stability yields an optimization problem for the expression of PG in dependency on the number of QS individuals within a colony. We find that the optimal total PG production of the QS population mainly depends on the shape of the benefit. A graded and a switch-like response is possible, in accordance with earlier results. Interestingly, at the level of the individual cell, the QS response is determined by the shape of the costs. All QS individuals respond either homogeneously if cost are a convex function of the PG production rate, or they respond heterogeneously with distinct ON/OFF responses if the costs are concave. The latter finding is consistent with recent experimental findings, and contradicts the usual interpretation of QS as a mechanism to establish a uniform, synchronized response of a bacterial population.

q-bio.PE↗

arXiv2019

Are the better cooperators dormant or quiescent?

Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role, though these are often ignored. We consider here species such as bacteria, fungi, invertebrates and plants which exhibit resting stages in the form of a quiescent state or a seedbank. When quiescent, individuals are inactive and reproduce upon activation, while under seed bank parents produce offspring remaining dormant for different amount of time. We assume weak frequency-dependent selection modeled using game-theory and the prisoners dilemma (cooperation/defect) as payoff matrix. The cooperators and defectors are allowed to evolve different quiescence or dormancy times. By means of singular perturbation theory we reduce the model to a one-dimensional equation resembling the well known replicator equation, where the gain functions are scaled with lumped parameters reflecting the time scale of the resting state of the cooperators and defectors. If both time scales are identical cooperation cannot persist in a homogeneous population. If, however, the time scale of the cooperator is distinctively different from that of the defector, cooperation may become a locally asymptotically stable strategy. Interestingly enough, in the seedbank case the cooperator needs to be faster than the defector, while in the quiescent case the cooperator has to be slower. We use adaptive dynamics to identify situations where cooperation may evolve and form a convergent stable ESS. We conclude by highlighting the relevance fo these results for many non-model species and the maintenance of cooperation in microbial, invertebrate or plant populations.

q-bio.PE↗

arXiv2018

Global stability properties of renewal epidemic models

We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected removal rates are arbitrary functions of the infection age, $τ$, and use the direct Lyapunov method to establish the global asymptotic stability of the equilibrium solutions. In particular, we show that the basic reproduction number, $R_0$, represents a sharp threshold parameter such that for $R_0\leq 1$, the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when $R_0 > 1$, i.e. when it exists.

q-bio.PE↗

arXiv2018

Do voters choose rationally, irrationally or at random? Data and theory for proportional elections

Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported before. We first show this correlation in results from recent elections in Germany, France and republican primaries in the USA. However the mechanism generating such feature remains so far unexplained. We develop a mathematical model of voter grouping that is only based on the word of mouth and not on political contents. The model is close to the infinite allele model and the Ewens sampling formula that are well known in population genetics. Strikingly, the model generates output agreeing very well with the observed election data. We further identify a cannibalism effect in Germany, whereby parties above the 5% threshold withdraw votes from parties just below the threshold. We demonstrate that the number of parties present in the parliament can be predicted given the number of parties standing for election. Finally, the steady loss of big-tent parties in Germany in the last 20 years relates to the increasing number of parties since 1975. We discuss the interpretation and consequences of these findings for modern democracies and the rationality or lack thereof of voters' choices.

physics.soc-ph↗

arXiv2017

Effects of population- and seed bank noise on neutral evolution and efficacy of natural selection

Population genetics models typically consider a fixed population size and a unique selection coefficient. However, population dynamics inherently generate noise in numbers of individuals and selection acts on various components of the individuals' fitness. In plant species with seed banks, the size of both the above- and below-ground compartments present noise depending on seed production and the state of the seed bank. We investigate if this noise has consequences on 1)~the rate of genetic drift, and 2)~the efficacy of selection. We consider four variants of two-allele Moran-type models defined by combinations of presence and absence of noise in above-ground and seed bank compartments. Time scale analysis and dimension reduction methods allow us to reduce the corresponding Fokker-Planck equation to a one-dimensional diffusion approximation of a Moran model. We first show that if the above-ground noise classically affects the rate of genetic drift, below-ground noise reduces the diversity storage effect of the seed bank. Second, we consider that selection can act on four different components of the plant fitness: plant or seed death rate, seed production or seed germination. Our striking result is that the efficacy of selection for seed death rate or germination rate is reduced by seed bank noise, whereas selection occurring on plant death rate or seed production is not affected. We derive the expected site-frequency spectrum reflecting this heterogeneity in selection efficacy between genes underpinning different plant fitness components. Our results highlight the importance to consider the effect of ecological noise to predict the impact of seed banks on neutral and selective evolution.

q-bio.PE↗

arXiv2017

Plasmid segregation and accumulation

The segregation of plasmids in a bacterial population is investigated. Hereby, a dynamical model is formulated in terms of a size-structured population using a hyperbolic partial differential equation incorporating non-local terms (the fragmentation equation). For a large class of parameter functions this PDE can be re-written as an infinite system of ordinary differential equations for the moments of its solution. We investigate the influence of different plasmid production modes, kinetic parameters, and plasmid segregation modes on the equilibrium plasmid distribution. In particular, at small plasmid numbers the distribution is strongly influenced by the production mode, while the kinetic parameters (cell growth rate resp. basic plasmid reproduction rate) influence the distribution mainly at large plasmid numbers. The plasmid transmission characteristics only gradually influence the distribution, but may become of importance for biologically relevant cases. We compare the theoretical findings with experimental results.

q-bio.PE↗

arXiv2016

The effect of delay on contact tracing

We consider a model for an infectious disease in the onset of an outbreak. We introduce contact tracing incorporating a tracing delay. The effect of randomness in the delay and the effect of the length of this delay in comparison to the infectious period of the disease respectively to a latency period on the effect of tracing, given e.g. by the change of the reproduction number, is analyzed. We focus particularly on the effect of randomness in the tracing delay.

math.DS↗

arXiv2016

Fisher-Wright model with deterministic seed bank and selection

Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation, which is a common issue in statistical physics. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached.

q-bio.PE↗

arXiv2014

Speeding up SOR Solvers for Constraint-based GUIs with a Warm-Start Strategy

Many computer programs have graphical user interfaces (GUIs), which need good layout to make efficient use of the available screen real estate. Most GUIs do not have a fixed layout, but are resizable and able to adapt themselves. Constraints are a powerful tool for specifying adaptable GUI layouts: they are used to specify a layout in a general form, and a constraint solver is used to find a satisfying concrete layout, e.g.\ for a specific GUI size. The constraint solver has to calculate a new layout every time a GUI is resized or changed, so it needs to be efficient to ensure a good user experience. One approach for constraint solvers is based on the Gauss-Seidel algorithm and successive over-relaxation (SOR). Our observation is that a solution after resizing or changing is similar in structure to a previous solution. Thus, our hypothesis is that we can increase the computational performance of an SOR-based constraint solver if we reuse the solution of a previous layout to warm-start the solving of a new layout. In this paper we report on experiments to test this hypothesis experimentally for three common use cases: big-step resizing, small-step resizing and constraint change. In our experiments, we measured the solving time for randomly generated GUI layout specifications of various sizes. For all three cases we found that the performance is improved if an existing solution is used as a starting solution for a new layout.

cs.HC↗

arXiv2013

Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method at the example of initial value uncertainties under deterministic dynamics and prove a consistency result. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations.

math.NA↗