welcome to reykjavik! - uzh

Welcome to Reykjavik!

The organisers of NDES 2016 are delighted to welcome you to this intimate edition of Nonlinear Dynamics of Electronic Systems. We hope that the extra time allowed in this year’s format will stimulate exchange of ideas in our small group, and lively discussion long into the summer solstice twilight.

NDES will return in August 2017 to the standard format and central location in Swiss alps, in conjunction with CRP Lavin 2017.

Magnus S. Magnusson and Gudberg K. JonssonUniversity of Iceland

Sigurdur I. Erlingsson University of Reykjavik

Ruedi Stoop University and ETH Zurich

Pre-conference welcome drinks

Sunday 19th June, 7:00 PM to 9:00 PM

in the “Stúdentakjallarinn” bar, located in the basement of the University Centre (see map, next page) on the Main University Campus of the University of Iceland.

How to get to the conference venue

The conference will be held on the Main University Campus of the University of Iceland, in the “Oddi” building (Sturlugata 3,101 Reykjavík - see map, next page). All talks will be on the second floor in Room 202.

Room 2022nd Floor“Oddi” building

A Háskólasvæðið Main University Campus

C Stakkahlíð E Laugarvatn

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Norræna húsiðThe Nordic House

ÞjóðminjasafniðThe National Museum

ÞjóðarbókhlaðanThe National Libray

1 Aðalbygging Main Building Miðlæg stjórn - sýsla Central Adminis-tration. Hugvísindsvið School of Humanities

2 Stapi Heilbrigðisvísindasvið School of Health Sciences

3 Háskólatorg University Centre Þjónusta við nemendur Student Services. Fyrirlestra salir Lecture halls

4 Lögberg Félagsvísinda-svið School of Social Sciences

5 Nýi-Garður Hugvísinda-svið School of Humanities

6 Oddi Félagsvísindasvið School of Social Sciences Heilbrigðisvísindasvið School of Health Sciences

7 Gimli Félagsvísindasvið School of Social Sciences

8 Árnagarður Hugvísinda-svið School of Hu-manities. Stofnun Árna Magnússonar í íslenskum fræðum The Árni Magnús son Institute for Icelandic Studies

9 Íþróttahús University Sport Centre

10 Askja Verkfræði- og nátt úruvísindasvið School of Engineering and Natural Sciences

11 Sturlugata 8 Verkfræði- og náttúruvísindasvið School og Engineering and Natural Sciences. Heilbrigðisvísindasvið School of Health Sciences

12 Aragata 9 Kennslu mið-stöð Centre for teaching and learning

13 Aragata 14 Heilbrigðisvísindasvið School og Health Sciences

14 VR-III Verkfræði- og nátt-úruvísindasvið School of Engineering and Natural Sciences

15 VR-I Verkfræði- og nátt-úru vísindasvið School of Engineering and Natural Sciences

16 VR-II Verkfræði- og nátt-úruvísindasvið School of Engineering and Natural Sciences

17 Tæknigarður Verkfræði- og náttúruvísindasvið School of Engineering and Natural Sciences

18 Smyrilsvegur Verkfræði- og náttúruvísindasvið School of Engineering and Natural Sciences

19 Endurmenntun Continuing Education

20 Raunvísindastofnun Science Institute

21 Háskólabíó Fyrirlestra salir Lecture halls

22 Neshagi 16 Stofnun Árna Magnússonar í íslenskum fræðum The Árni Magnússon Institute for Icelandic Studies

23 Hagi School of Health Sciences

24 Læknagarður School of Health Sciences

25 Eirberg School of Health Sciences

26 Stakkahlíð School of Education

27 Bolholt 6 School of Education

28 Skipholt 37 School of Education

29 Skólabygging School of Education

30 Íþróttahús og sundlaug School of Education

31 Íþróttamiðstöð School of Education

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Háskóli Íslands er starfræktur á fimm svæðum The University of Iceland is located in five campuses

conferencetalks

welcome drinks

Monday 20th June

9:00 AM Registration

9:30 AM Conference opening and welcome

Plenary talks session 1

10:00 AM Plenary talk 1: Arkady PikovskyCollective dynamics of oscillator populations: Multifrequency ensembles and chimera states

11:00 AM Coffee break

11:30 AM Plenary talk 2: Tobias ReichenbachUnidirectional amplification: from low-frequency hearing to an active microphone

12:30 PM Lunch break

1:30 PM Plenary talk 3: Ruedi StoopThe ‘big data challenge’ approached from how humans process sound

Contributed talks session 1

2:30 PM L.V. Gambuzza et al.Onset of relay synchronization in complex networks

A. Buscarino et al.Control of imperfect uncertain dynamical systems

3:30 PM Coffee break

4:00 PM J. Held et al.Phytoplankton interaction at a critical state?

S. Glüge et al.Information-based identification of explanatory factors for enhanced sales forecasting

5:00 PM close of day 1

Tuesday 21st June


9:00 AM Plenary talk 4: Giorgio ManticaDynamical extreme value theory


10:30 AM Plenary talk 5: Arnar PalssonThe principles of regulatory evolution: transcriptional decay, cooption and network rewiring

11:30 AM Plenary talk 6: Troy ShinbrotSomething from nothing: self-charging of identical materials



1:30 PM K. Kanders et al.Spontaneous otoacoustic emissions from signal coupling between cochlear amplifiers

T. Lorimer et al.Toward nonparametric solutions to clustering problems in bioinformatics

Y. Uwate et al.Torus hub in two parameters space of coupled oscillators with transmission line model

3:00 PM Coffee break

3:30 PM E. LindbergOn the modified Barkhausen criterion

A. Buscarino et al.A new chaotic mechanical oscillator

4:30 PM close of day 2

7:30 PM CONFERENCE DINNER at restaurant “Höfnin”

Wednesday 22nd June


9:00 AM Plenary talk 7: Michael RosenblumReconstructing connectivity of oscillator networks from observations


10:30 AM Plenary talk 8: Magnus MagnussonSelf-similar repeated structured clustering in time and space: from space dust to DNA and neuronal and human interactions

11:30 AM Plenary talk 9: Carlo AlbertBayesian parameter inference of nonlinear stochastic differential equation models



1:30 PM S. Ulzega and C. AlbertFast Bayesian parameter inference in hydrological modeling using a Hamiltonian Monte Carlo approach with a stochastic rain model

S.F. HafsteinNumerical methods for the computation of Lyapunov functions for nonlinear systems

2:30 PM Closing address and Reykjavik city tour


Plenary talk 1: Monday 20th June, 10:00 AMArkady Pikovsky, University of Potsdam, Germany

Collective dynamics of oscillator populations: Multifrequency ensembles and chimera states

Ensembles of oscillator populations are a subject of hot interest mainly due to synchronization effects that can be viewed as a nonequilibrium order-disorder transition. Kuramoto model is a paradigmatic system in this field,similar to the Ising model for equilibrium phase transitions. In this talk, after introducing basic ideas, I focus on a method due to Watanabe, Strogatz, Ott, and Antonsen, allowing a closed description of the dynamics of the order parameter. This method is applied for two generalizations of the Kuramoto system. In the first case one skips the usual condition that frequencies of all oscillators are nearly equal, and considers multifrequency populations, having significantly different basic frequencies. In the second example, oscillators are arranged on a lattice, here one can describe chimera patches of coexisting synchrony and asynchrony as a pattern formation. In the third example, I show that in populations of identical oscillators with time delay chimera states, with some oscillators synchronized and some not, can exist.

Plenary talk 2: Monday 20th June, 11:30 AMTobias Reichenbach, Imperial College London, U.K.

Unidirectional amplification: from low-frequency hearing to an active microphone

Most sounds of interest consist of complex, time-dependent admixtures of tones of diverse frequencies and variable amplitudes. To detect and process these signals, the ear employs a highly nonlinear, adaptive, real-time spectral analyzer: the inner ear, or cochlea. Sound evokes a wave on the cochlear basilar membrane, an elastic band spiraling along the cochlea between two fluid-filled chambers. The oscillations of the basilar membrane deflect hair bundles, the mechanically sensitive organelles of the ear's sensory receptors, the hair cells. In addition to transducing mechanical inputs, hair cells amplify them by an active process. I present recent theoretical and experimental work on how this active process works in the low-frequency region of the cochlea, which is responsible for detecting the

low frequencies that are most relevant for speech. The scheme of unidirectional amplification which I propose can also serve to boost signal detection in engineering. I illustrate this by describing an active microphone that employs unidirectional amplification to achieve high sensitivity without distorting the incoming signal.

Plenary talk 3: Monday 20th June, 1:30 PMRuedi Stoop, UZH/ETHZ, Switzerland

The ‘big data challenge’ approached from how humans process sound

Biological sensors often deal with inputs across many orders of magnitude (expressed by a logarithmic stimulus scale, e.g., decibel or pH scales). They usually have the ability to strongly amplify weak inputs and to compress higher input levels. A very prominent manifestation of these characteristics is the hearing system with its “compressive nonlinearity”. Hearing sensors arguably deal with perhaps the most intricate signal among all recognized physical human sensors: a sound event may be any distribution along an excessively large frequency interval, with strengths that cover, in every-day life a dynamic range up to even more than one hundred dB. Sound is not only tied to the three dimensions of space, where it is often of great significance, from where sound arrives. In contrast to vision, sound intrinsically requires taking in space-time a whole temporal measurement chunk; due to its frequency characteristics, sound can also not be captured by making a snapshot in time. Correspondingly, it has taken much longer to get a coherent understanding of the physical sensor of sound provided by the mammalian (and other) constructions. Already Helmholtz profoundly addressed the question how the nonlinearity of the human hearing sensor, the cochlea, might shape human sound perception. At his time, research was, however, obstructed by the lack of experimental data regarding the amplification properties of the inner ear. In the meantime, accurate measuring methods permit the comparison of models of the hearing sensor with empirical data, leading to a strong revival of the interest into Helmholtz’s original research questions. In our paper, we describe some recent theoretical and modeling advances in the understanding of the nature of human pitch perception and beyond. We reveal a number of to date unexplained human auditory percept effects to be direct consequences of the nonlinear properties of the mammalian hearing sensor. Our insights also demonstrate, as a by-note, the limitations of the present reverse engineering approach towards cochlear implants. And most importantly, our approach and insights may provide a template or guideline for how to deal with signals of a very rich and intricate nature.


Onset of relay synchronization in complex networks

Lucia Valentina Gambuzza1, Mattia Frasca1, Luigi Fortuna1 and Stefano Boccaletti2,3

1Università degli Studi di Catania, Italy2CNR-Institute of Complex Systems, Italy3The Embassy of Italy in Tel Aviv, Israel

In the presence of heterogeneity in the node dynamics, chains of interacting oscillators may display a collective state, characterized by uncoupled dynamical units that synchronize through the action of mismatched inner nodes relaying the information but not synchronizing with them. This regime is known as relay synchronization and is here investigated in complex networks. We show that relay synchronization is not limited to simple motifs, but also emerge in larger and arbitrary topologies. We study the phenomenon in networks of chaotic systems (in particular, Roessler systems) under different conditions (fraction of mismatched units, topology of the networks, coupling strength) and its effect on lowering the synchronization threshold, thus favouring the onset of synchronization.

Control of imperfect uncertain dynamical systems

Arturo Buscarino, Carlo Famoso, Luigi Fortuna and Mattia Frasca

Università degli Studi di Catania, Italy

In this paper, the new class of dynamical systems named as imperfect uncertain systems is introduced. As imperfect uncertain systems we will refer to large-scale electromechanical systems characterized by intermittent unmodeled dynamics and uncertain parameters. Due to their intrinsically imperfect structure, for this class of systems usual control techniques may often fail. In fact, in order to control such types of systems it is not convenient to consider classical control approach. On the contrary, the idea of our paper is to use only few actions in order to control the whole system by eliciting its intrinsic properties of self-organization stimulating the imperfect dynamics by using broadband chaotic signals. Therefore the control system will consist of a feedback loop generating the broad spectrum signal and stimulating the hidden dynamics of the system. The class of

considered systems is nonlinear and stochastic and includes parasitic dynamics that will help the system to be controlled. Indeed the control of such systems is particularly appealing when we consider couples of a large number of units making the system with an high number of state variables. Examples of high order vibration platforms on which a series of coils rotates through the interaction of magnetic devices will be reported to show the experimental suitability of the proposed control strategy.

Phytoplankton interaction at a critical state?

Jenny Held1, Carlo Albert1 and Ruedi Stoop2

1Eawag, Switzerland2UZH/ETHZ, Switzerland

Phytoplankton communities exhibit a rich repertoire of collective dynamical phenomena. Among the most prominent are phytoplankton blooms that may be related to cycles and chaotic behavior, but have defied predictability so far, due to the lack of a precise understanding of the underlying dynamical processes. For maintaining safe ecosystems, it is, however, essential to be able to understand, monitor, and predict blooms. Using automated flow cytometry measurements, individual phytoplankton trait information can now be collected in large quantities, but we are still lacking fast and reliable predictive tools. We approach this task from modeling the elements that contribute to these ecosystems on the individual level. By using our recently developed Rulkov neuron Hebbian learning clustering approach (RHLC), we raise the dynamical information obtained at this level to the group level. RHLC mimics unsupervised learning occurring in neuronal networks, by amplifying individual dynamical similarity between the neurons that code for the data items, until clusters can be identified as subnetworks of dynamically similar behavior. Due to the use of purely local similarity measures, shape biases that are intrinsic to standard clustering methods are avoided. We compare our clustering results with those of standard techniques and discuss first results of monitoring trait distributions in phytoplankton communities. Our analysis reveals scale-free characteristics in trait distributions, both at the species and at the community level. This hints at scale invariance of the cluster shapes and suggests that the systems might be operating in a critical state. We investigate this hypothesis using data collapse methods and inter-trait scaling relations.

Information-based identification of explanatory factors for enhanced sales forecasting Stefan Glüge1, Peter Kauf2 and Thomas Ott1 1Zurich University of Applied Sciences, Switzerland 1PrognosiX AG, Switzerland

A natural approach for the estimation of future values of a time series is the consideration of past values that occurred under comparable circumstances. Such comparable circumstances are defined by factors that represent the relevant information for the series. The focus on explanatory factors, particularly external ones, distinguishes our proposed forecasting method from conventional autoregressive models (ARIMA) and its derivatives. Consequently, the predictions do not primarily rely on the short term history of a sequence, but rather on those historic samples that most likely yield a reasonable prediction. The key issue in this process is the identification of factors that explain the observed time series. For this, we introduce a novel measure that involves the amount of information explained by a factor combination and the variance of the corresponding observed time series values. Our approach bears several advantages over regressive models. It provides an explanation for the prediction in terms of relevant variables. It is not influenced by missing historic values. The forecast horizon does not influence the prediction performance and it works with factorial variables like ‘month’ or ‘day of the week’. We evaluated on grocery sales data which are especially affected by external factors such as weather, promotions, etc. The proposed method could not only outperform the standard ARIMA approach in terms of prediction accuracy, but identify relevant variables that determine the amount of sales.


Plenary talk 4: Tuesday 21st June, 9:00 AMGiorgio Mantica, University of Insubria, Italy

Dynamical extreme value theory

The study of extreme events is a fundamental chapter in statistics and a pillar in its applications to natural phenomena. In recent years, this theory has been approached from a dynamical perspective: rather than arising from a stochastic process, extreme events occur along the deterministic evolution of a system, when motions approach a singular point in phase-space. I will discuss a generalization of this theory, in which singular points are located on a fractal set: this investigation reveals the dynamical role of objects of deep mathematical significance, like Minkowski dimension and content.

Plenary talk 5: Tuesday 21st June, 10:30 AMArnar Palsson, University of Iceland, Iceland

The principles of regulatory evolution: transcriptional decay, cooption and network rewiring

The development and function of organisms and cells relies on complex regulatory systems, involving information stored in motifs in DNA, RNA and proteins. A large fraction of the gene content and energy budget of cells is devoted to regulation of gene expression and cellular functions. This enables both hardwired unfoldings of programs (such as development of multicellular organisms) but also dynamic expression of phenotypes and functions in response to external stimuli (like environment or infection). We use regulatory DNA and trans-factors to study the principles of regulatory function and evolution. The same genes have been redeployed for multiple functions during evolution, as is evident from comparisons of metazoan genomes and development. Natural selection preserves core functions of the cell but also gives rise to novel adaptations or improvements of existing systems. Gene regulation is shaped by biochemical, genetic and evolutionary principles. We outline these principles and argue that they and the fact stabilizing selection acts on gene expression leads to evolutionary flexibility of regulatory systems, which can manifest as turnover of regulatory motifs in DNA, entire regulatory modules, Trans-factor inputs and alterations in the topology of gene regulatory networks. Finally we elaborate on factors

that may predict the turnover of connections in regulatory networks, including cooption of genes, decay of existing connections and the side effects of strong selection on these system. The principles implicated here could potentially apply to other regulatory systems, for instance networks of cellular, metabolic and protein components. The project addresses both questions of proximal mechanisms and about the role of necessity and chance in cellular functions.

Plenary talk 6: Tuesday 21st June, 11:30 AMTroy Shinbrot, Rutgers University, USA

Something from nothing: self-charging of identical materials

Recent experiments have demonstrated that identical material samples can produce complex charged patterns after being brought into symmetric contact. The mechanism for this charging is not known. In this talk, I overview what is currently known of this phenomenon and describe both a discrete element and a Turing model that appear to account for many observed features. The models predict a rich variety of complex spatiotemporal patterns that have implications for fields as diverse as crack propagation and sandstorm dynamics.


Spontaneous otoacoustic emissions from signal coupling between cochlear amplifiers

Karlis Kanders, Tom Lorimer and Ruedi StoopUZH/ETHZ, Switzerland

The sounds emitted by the ear in the absence of an external stimulus, spontaneous otoacoustic emissions, are commonly argued to arise from a loss of stability through a Hopf bifurcation in the dynamics of the outer hair cells. This phenomenon has been conjectured to arise due to local cochlear irregularities, but the evidence is insufficient. Here we propose a novel mechanism for the generation of spontaneous otoacoustic emissions based on a recent finding that Hopf systems, individually below bifurcation, can undergo a collective bifurcation when coupled by their signals. We show that our mesoscopic model of the cochlea, that reproduces all salient phenomena of hearing, can be modified by introducing a weak feed-back signal coupling between the cochlear amplifiers to also produce spontaneous emissions. The qualitative and quantitative features of the model emissions are similar to the experimental observations in humans.

Toward nonparametric solutions to clustering problems in bioinformatics

Tom Lorimer1, Jenny Held2, Carlo Albert2 and Ruedi Stoop1

1UZH/ETHZ, Switzerland2Eawag, Switzerland

Clustering in bioinformatics is a fundamental process involving computational issues that are far from being resolved. In our work, we reveal that even some of the most recent popular approaches to this task can not deal with simple convex-concave sets, introducing artificial divisions in synthetic data test cases. We show that our own clustering approach overcomes these problems in synthetic data, but produces systematically different results from other popular approaches on a real-world data set. This raises questions about how a ‘gold standard’ should be defined for benchmarking clustering algorithms against real-world bioinformatics data.

Torus hub in two parameters space of coupled oscillators with transmission line model

Yoko Uwate, Yuichi Tanji and Yoshifumi NishioTokushima University, Japan

Synchronization phenomena in coupled oscillators and chaotic circuits systems have been studied in various fields. It is important to investigate the fundaments of synchronization in coupled oscillatory systems, for future engineering applications such as chaotic communication and chaotic cryptography. In high-speed VLSI, the internal wiring must be realized in transmission technology, because the structure of high-speed VLSI is complex and is tightly packed with many components. Despite of the importance of these phenomena, there are still not many discussions regarding the synchronization of coupled oscillatory systems in a transmission line implementation. Previously, we have investigated synchronization phenomena in two van der Pol oscillators coupled by a transmission line, where we modeled a lossless transmission line using a ladder of circuits of inductors and capacitors. In our computer simulations, depending on the chosen circuit parameters, several types of synchronization states such as coexistence in-phase and anti-phase have been observed. In this study, we investigate how the obtained solutions and synchronization states change under variation of the transmission line length. In particular, a torus region in two parameters space can be observed if the transmission line length exceeds a length of 10. We investigate the construction mechanism underlying the creation of the torus region in detail.

On the modified Barkhausen criterion

Erik LindbergTechnical University of Denmark, Denmark

Oscillators are normally designed according to the Modified Barkhausen Criterion i.e. the complex pole pair is moved out in RHP so that the linear circuit becomes unstable. By means of the Mancini Phaseshift Oscillator it is demonstrated that the distortion of the oscillator may be minimized by introducing a nonlinear ”Hewlett Resistor” so that the complex pole-pair is in the RHP for small signals and in the LHP for large signals i.e. the complex pole pair of the instant linearized small signal model is moving around the imaginary axis in the complex frequency plane.

A new chaotic mechanical oscillator

Arturo Buscarino, Carlo Famoso, Luigi Fortuna, Mattia FrascaUniversità degli Studi di Catania, Italy

In this research we present theoretical and experimental results regarding a new electromechanical oscillator able to exhibit a wide range of dynamical behaviors, including chaos. The classical reference example for chaotic mechanical/electromechanical oscillator is the Duffing system. Recently a new electromechanical chaotic oscillator has been introduced. Starting from a similar setup, the results included in this paper deal with a very simple electromechanical system: it consists of a coil rotating over two trails, through which a voltage is supplied, thanks to the magnetic interaction with a magnet fixed below the trails. The voltage supply consists of a continuous voltage signal with a superposed discontinuous signal, switching at a given frequency. A numerical analysis of the system leads to nontrivial bifurcation diagrams in terms both of amplitude and frequency. Several windows of chaotic oscillations in the parameter space can be found for the angular speed of the rotating coils. The experimental analysis of the real setup has been made taking in consideration the angular speed of the coil, collected by means of a simple optoelectronic device. The results obtained allowed us to observe a good matching with the mathematical model. The peculiarity of the proposed device is the simplicity, the possibility of realizing easily the system and the related quite identical agreement between numerical and experimental trends. Realizing simple circuits with very complex behavior give use the possibility of introducing a new class of mechanical chaotic generators realized also with few components and with very low power supply.


Plenary talk 7: Wednesday 22nd June, 9:00 AMMichael Rosenblum, University of Potsdam, Germany

Reconstructing connectivity of oscillator networks from observations

We discuss recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The technique is relevant, e.g., for addressing the brain connectivity problem. We start with the case of two interacting units and discuss in detail reconstruction of the phase coupling function. We apply the method to obtain the coupling functions describing cardio-respiratory interactions and the phase response curve of 17 healthy humans. Furthermore, we extract the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators – in this case heartbeat and respiration – in its natural environment and under free-running conditions. Next, we consider networks of several oscillators. The main idea here is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.

Plenary talk 8: Wednesday 22nd June, 10:30 AMMagnus Magnusson, University of Iceland, Iceland

Self-similar repeated structured clustering in time and space: from space dust to DNA and neuronal and human interactions

This talk is essentially all about one mathematical/statistical pattern type, called a T-pattern, its origins in human ethological interaction research more than 35 years ago (Magnusson, 1978, 1981), its defining characteristics and its application and statistical and external validation through the use of the T-pattern detection algorithm and software (Theme) in numerous research areas, from human behavior and interactions to neuronal interactions in living brains and even in DNA/protein analysis. In an attempt to understand the possibility of such general applicability, the universality of self-similarity and structured hierarchical clustering is also highlighted by reference to

modern astrophysics and the recently discovered fractal structure of the known universe. It now seems possible to classify the T-pattern as a particular kind of repeated statistical pseudo-fractal (statistically self-similar) objects characterized by statistical (significant) translation symmetry over its occurrences, while the occurrences of each T-pattern occurrence may look very different. The T-pattern with the first detection algorithms were developed after available multivariate statistical methods turned out to be inadequate for the detecting recurrent interaction sequences in ethological studies of children‘s interactions as complex relations between multiple (occurrence) time point series. The acceptance of T-pattern Analysis has been gradual but increasing with a university research network created around it in 1995 in Paris leading to many publications (see Anolli et al eds. 2005) and in the last one or two years with a comprehensive review published in Neuroscience Methods (Maurizio et al, 2015) and a new edited book published by Springer in its Neuroscience series (Magnusson et al eds., 2016) and in the last few weeks a T-pattern Analysis (TPA) paper on neuronal interactions in the olfactory lobe of rat brains (Nicol et al, 2015) was selected by World Biomedical Frontiers for inclusion in their next issue. The concepts of self-similarity and symmetry, still uncommon in behavioral research, together with insights into Cell City, the city of proteins, where all the citizens are brainless, inspire a fresh view of all its descendants such as insect and human societies and especially regarding social behavioral phenomena such as religion (Magnusson, 2009).

Plenary talk 9: Wednesday 22nd June, 11:30 AMCarlo Albert, Eawag, Switzerland

Bayesian parameter inference of nonlinear stochastic differential equation models

Bayesian parameter inference is a fundamental problem in data-driven modeling. Given observed data, which is believed to be a realization of some parameterized model, the aim is to find a distribution of likely parameter values that are able to explain the observed data. This so-called posterior distribution expresses the probability of a given parameter to be the "true" one, and can be used for making probabilistic predictions. For truly stochastic models this posterior distribution is typically extremely expensive to evaluate. We propose a novel, exact and very efficient, approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is

inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, whose dynamics is confined by both the model and the measurements. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.


Fast Bayesian parameter inference in hydrological modeling using a Hamiltonian Monte Carlo approach with a stochastic rain model

Simone Ulzega and Carlo AlbertEawag, Switzerland

Conceptual models of the rainfall-runoff behavior of both natural and urban catchments have proven to be useful tools for flood prediction. For making reliable probabilistic predictions, parameters of such models need to be calibrated to measured data and their uncertainty needs to be quantified. Bayesian statistics allows us to express knowledge about model parameters through probability distributions and learning from data through an update rule. One of the dominant sources of uncertainty in rainfall-runoff modeling is the true rainfall over the catchment, which typically needs to be inferred from a few rain-gauge and runoff measurements. Modeling this uncertainty naturally leads to nonlinear stochastic differential equation models, which render Bayesian parameter inference computationally very expensive. For this reason, in hydrology and other applied fields of research, people usually resort to over-simplified error models or use inconsistent inference methods. By means of a case study from urban hydrology we demonstrate that our newly developed Hamiltonian Monte Carlo based inference algorithm makes many of the stochastic prediction models used in hydrology amenable to a consistent Bayesian parameter inference.

Numerical methods for the computation of Lyapunov functions for nonlinear systems

Sigurdur Freyr HafsteinReykjavik University, Iceland

A Lyapunov function for a dynamical system delivers important information on its qualitative behavior like its attractors' domains of attraction. Thus, if a Lyapunov function for a system is known, a lot is known about how its solutions will behave. In this talk some numerical methods for the computation of Lyapunov functions for nonlinear systems are presented. Especially, we discuss a method that uses linear optimization to parameterize true Lyapunov functions. This method can also be used to very Lyapunov function candidates computed by other means.

welcome to reykjavik! - uzh

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