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June 101112, 2013 Workshop on Probabilistic Cellular Automata: Theory, Applications and Future Perspectives
SUMMARY The workshop aims at exploring Probabilistic Cellular Automata (PCA) from the point of view of Statistical Mechanics, Probability Theory, Computational Biology, Computer Science and Discrete Dynamical Systems. PCA revealed to be a fruitful tool in those fields nevertheless many challenges remain open. There is a recent growing interest from these different fields and agreement on the emergency of a turning point: interactions has to be strengthened. This workshop will give an opportunity for the different communities to interact. We welcome contributed talks and posters. Doctoral and postdoctoral researchers are invited to participate. Interested advanced Master students will benefit from the creative interdisciplinary atmosphere we want to promote. The aim of the workshop is to explore the Probabilistic Cellular Automata field from different point of view. Cellular Automata (CA) are discrete dynamical systems consisting of simple elementary elements interacting according to some local rules. Simple update rules may produce extremely complex behaviour. They have been used to model a wide range of physical phenomena including traffic flow, disease epidemics, invasion of populations, and dynamics of stock markets. PCA build a bridge among different scientific disciplines such as Probability Theory, Statistical Mechanics, Theoretical Computer Science, Complex Systems and Computational Life Sciences, and more. Indeed, in recent years there have been active research efforts on the following briefly outlined three directions: ● Computer Science and Discrete Dynamical Systems e.g. robustness of PCA when going from synchronous to asynchronous updating scheme, deterministic CA with random initial condition, density classification, synchronous / asynchronous updating. ● Probability and Statistical Mechanics, e.g. PCA as discretetime interacting particle system, nonequilibrium statistical mechanics, metastability, cutoff phenomena and abrupt convergence, phase transitions, Gibbs/NonGibbs transitions, PCA and stochastic algorithms ● Applications mainly in computational (cell) biology e.g. Cellular Potts Model and stability of emerging patterns, time to stationarity in simulation algorithms, transient regimes
ORGANISERS
LIST OF SPEAKERS
Each day, an opening talk will give an introductory lecture (40 minutes) intended to present to a broad audience the chosen days perspectives. There will be long talk of 40 minutes and short ones of 20 minutes. Relatively long breaks will give to the participants the opportunity for discussions. Poster sessions create the opportunity to explore each others work. These sessions prove to be a great success
MONDAY JUNE 10
TUESDAY JUNE 11
WEDNESDAY JUNE 12
n.b. All abstracts are included in the BOOKLET, which has been printed for all participants.ABSTRACTSPablo Arrighi Stochastic Cellular Automata: Correlations, Decidability and Simulations We introduce a simple formalism for dealing with
deterministic, non deterministic and stochastic cellular automata in an unified
and composable manner. This formalism allows for local probabilistic
correlations, a feature which is not present in usual definitions. We show that
this feature allows for strictly more behaviors (for instance, number conserving
stochastic cellular automata require these local probabilistic correlations). We
also show that several problems which are deceptively simple in the usual
definitions, become undecidable when we allow for local probabilistic
correlations, even in dimension one. Armed with this formalism, we extend the
notion of intrinsic simulation between deterministic cellular automata, to the
nondeterministic and stochas tic settings. Although the intrinsic simulation
relation is shown to become undecidable in dimension two and higher, we provide
explicit tools to prove or disprove the existence of such a simulation between
any two given stochastic cellular automata. Those tools rely upon a
characterization of equality of stochastic global maps, shown to be equivalent
to the existence of a stochastic coupling between the random sources. We apply
them to prove that there is no universal stochastic cellular automaton. Yet we
provide stochastic cellular automata achieving optimal partial universality, as
well as a universal nondeterministic cellular automaton. Franco Bagnoli Topological phase transitions in cellular automata Cellular automata are successful modeling tools, but in many cases the classical regular lattice is not adequate to the problem under investigation. By changing the topology of the lattice, several interesting phenomena occurs. We illustrate an example of a phase transition that can be induced by a change in parameters or in the topology of the lattice. We show also how one can map the change in the topology onto the change in the parameters.
Jean Bricmont Phase transitions: from equilibrium models to PCA I will review some of the techniques used to prove the
existence of phase transitions in equilibrium models and the problems that one
encounters if one tries to extend those techniques to PCA.
Emilio Cirillo Metastable behavior of reversible Probabilistic Cellular Automata Metastability is a relevant phenomenon in many different
applied sciences. Its full mathematical description is quite recent and still
incomplete. In this framework Probabilistic Celluar Automata pose changelling
problems and show unexpected behaviors. In this talk some results will be
reviewd. Paolo Dai Pra Strategic interaction in trenddriven dynamics We propose a stochastic dynamics in which N agents update their state simultaneously but not independently. At each time step agents aim at maximizing their individual payoff, depending on their action, on the global trend of the system and on a random noise. In the limit of infinitely many agents, a law of large numbers is obtained; the limit dynamics consist in an implicit dynamical system, possibly multiple valued. For a special model, we determine the phase diagram for the long time behavior of these limit dynamics and we show the existence of a phase, where a locally stable fixed point coexists with a locally stable periodic orbit.
Andreas Deutsch (cancelled) Analyzing emergent behaviour in cellular automaton models of cancer invasion
While molecular biology methods are required for a better characterization and identification of individual cancer cells, mathematical modelling and computer simulation is needed for investigating collective effects of cancer invasion. Here, we demonstrate how latticegas cellular automaton (LGCA) models allow for an adequate description of individual cancer cell behaviour [1]. We will then show how analysis of the LGCA models allows for prediction of emerging properties (in particular of the invasion speed) [2]. Furthermore, we propose that the transition to invasive phenotypes can be explained on the basis of the microscopic ‘Go or Grow’ mechanism (migration/proliferation dichotomy) and oxygen shortage, i.e. hypoxia, in the environment of a growing tumour. We test this hypothesis again with the help of a latticegas cellular automaton. Finally, we use our LGCA models for the interpretation of data from in vitro glioma cancer cell invasion assays [3]. References: [1] A. Deutsch, S. Dormann: Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis Birkhäuser, Boston, 2005 [2] H. Hatzikirou, D. Basanta, M. Simon, K. Schaller, A. Deutsch: ‘Go or Grow’: the key to the emergence of invasion in tumour progression?
Math. Med. Biol., 29, 1, 4965, 2012 [3] M. Tektonidis, H. Hatzikirou, A. Chauviere, M. Simon, K. Schaller, A. Deutsch: Identification of intrinsic mechanisms for glioma invasion J. Theor. Biol., 287, 131147, 2011
Aernout van Enter Anisotropic bootstrap percolation Bootstrap percolation models
are Cellular Automata with probabilistic initial conditions. We discuss some
results and open problems on the influence of anisotropy on properties of
bootstrap percolation models in two and three dimensions. In particular we
discuss finitesize scaling behaviour and sharp thresholds.
Nazim Fatès Modeling natural phenomena or computing, do we need to choose ? On the landscape of randomness in cellular automata I will discuss some questions in order to introduce the open problems session.
Lucas Gérin A connection between 2d percolation and the synchronous TASEP The aim of this talk is to describe a connection between
the geometry of the 2d percolation infinite cluster, an important object in
statistical mechanics, and the discretetime and synchronous TASEP, a 1d
interacting particle system modeling nonequilibrium phenomena (and which is
quite known in the PCA community).
Yi Jiang Angiogenesis in the Eye: the Good and the Bad
Angiogenesis, or blood vessel growth from existing ones, is an important
physiological process that occur during development, wound healing, as well as
diseases such as cancer and diabetes. I will report our recent progress in
modeling angiogenesis in the eye in two scenarios. The good refers to healthy
blood vessel growth in the retina in mouse embryos, which is a perfect
experimental model for understanding the molecular mechanism of angiogenesis.
The bad is the Kerry Landman Modelling development and disease in our “second brain” The enteric nervous system (ENS) in our gastrointestinal tract, nicknamed the ``second brain'', is responsible for normal gut function and peristaltic contraction. Embryonic development of the ENS involves the colonization of the gut wall from one end to the other by a population of proliferating neural crest cells. Failure of these cells to invade the whole gut results in the relatively common, potentially fatal condition known as Hirschsprung disease (HSCR). Probabilistic cellular automata models provide insight into the colonization process at both the individual celllevel and populationlevel. Our models generate experimentally testable predictions, which have subsequently been confirmed. These results have important implications for HSCR and highlight the significance of stochastic effects.
Chistian Maes Physical modeling and MINEP for PCA Being interested in describing and understanding physical phenomena one is
often confronted with the question what effective models to choose as
sufficiently realistic. That is true in general
Jean Mairesse Around
Probabilistic Cellular Automata
Danuta Makowiec Pacemaker rhythm by cellular automata The sinoatrial node is the primary pacemaker of the heart. Nodal dysfunction
can lead to a variety of pathological clinical syndromes. Although the basic
mechanisms underlying the selfexcitation of each Nevana Maric FlemingViot particle system driven by a random walk on naturals Random walk on naturals with negative drift and
absorption at $0$, when conditioned on survival, has uncountably many invariant
measures (quasistationary distributions, \textit{qsd}) $\nu_c$. We study
a FlemingViot (FV) particle system driven by this process. In this particle
system there are $N$ particles where each particle evolves as the random walk
described above. As soon as one particle is absorbed, it reappears,
choosing a new position Irène Marcovici The envelope PCA, a tool for sampling the invariant measure of a PCA We propose a perfect sampling algorithm for the invariant
measure of an ergodic PCA. A PCA is a finite state space Markov chain.
Therefore, coupling from the past from all possible initial configurations
provides a basic perfect sampling procedure. But it is a very inefficient one
since the number of configurations is exponential. Here, the contribution
consists in simplifying the procedure. We define a new PCA on an extended
alphabet, called the envelope PCA (EPCA). We obtain a perfect sampling procedure
for the original PCA by running the EPCA on a single initial configuration. Our
algorithm does not assume any monotonicity property of the local rule.
Carsten Mente Individual cell dynamics in cellular automaton models of interacting cell systems Latticegas cellular automaton (LGCA) models have proven
successful in the analysis of collective behavior arising from populations of
moving and interacting cells. Examples of collective cell behavior at a
macroscopic level include the formation of cell density patterns and the
dynamics of moving cell fronts. However, important microscopic observables which
emerge as a consequence of collective cell behavior, especially individual cell
trajectories, can not be simulated and analyzed with LGCA models so far since
these models cannot distinguish individual cells. Here, we introduce an
extension of the classical LGCA model, which allows labeling and tracking of
individual cells. We name these extended LGCA models "individualbased
latticegas cellular automata"(IBLGCA). Furthermore, we derive stochastic
differential equations (SDE) corresponding to specific IBLGCA models, which
permit the investigation of individual cell trajectories and the approximate
description of IBLGCA models by systems of SDEs. This
Stochastic selforganization of branched organs: on the growth of blood vessels, glands, and kidneys Morphogenesis, the formation of biological shape and
pattern during embryonic development, is a topic of intensive experimental
investigation, so the participating cell types and molecular signals continue to
be characterized in great detail. Yet this data only partly tells biologists how
molecules and cells interact dynamically to construct a biological tissue.
Probabilistic cellular automata are a great help in analyzing the mechanisms of
biological morphogenesis.
Ida Minelli Synchronization via interacting reinforcement We consider a system of urns of Polyatype, with balls of
two colours; the reinforcement of each urn depends both on the content of the
same urn and on the average content of all urns. We show that the urns
synchronize almost surely, in the sense that the fraction of balls of a given
colour converges almost surely, as the time goes to infinity, to the same limit
for all urns. A normal approximation for a large number of urns is also
obtained. Ioana Niculescu (poster) Explaining many biological phenomena require a multiscale approach in which the cell is often the natural level of separation between the intracellular regulatory mechanisms and the emerging tissue level. For many tissue level phenomena, the internal mechanism that generates a certain cell behaviour may not be that important, as long as morphodynamically the cells behave realistic enough to serve the purpose of the model trying to explain those phenomena. Cell migration is a vital process in morphogenesis, tissue repair, disease fighting but also disease progression. We propose a phenomenological model for cell migration based on the CPM framwork, that bypasses the complex internal mechanism that drives the cell to move. We show that this simple and computational light method can be calibrated to fit many migrationshape deformation patterns (morphodynamics) including the amoeboid and keratocytelike migration. The method is suited for random as well as directional migration and is easily applied in the context of crowded multicellular and heterogeneous tissue where cells need to interact. Markus Owen Hybrid multiscale and partial differential equation models for cancer immunotherapy Cancer is a heterogeneous disease governed by interconnected processes at
multiple spatial and temporal scales. For example, variations in vascular
density and blood flow within tumours can have significant effects on nutrient
distributions. In addition, such heterogeneities can have significant
implications for the delivery and efficacy of drugs and other therapies. We have
developed multiscale mathematical models for vascular tumour growth, based upon
an extended cellular automata model for cell populations overlaid with networks
of blood vessels and the distributions of nutrients, cytokines and therapies
[1]. We have used these models to predict the efficacy of novel hypoxiatargeted
macrophagebased therapies, conventional therapies, and combination therapies.
We find that combination therapies can be highly synergistic, depending on their
relative timing, but that host tissue and tumour variability can have important
implications for therapeutic efficacy [2]. We have also begun to explore the
relationships between our hybrid cellular automaton models and more traditional
partial differential equation models.
Fernando Peruani Optimal noise maximizes collective motion in heterogeneous media We study the effect of spatial heterogeneity on the collective motion of
selfpropelled particles (SPPs). The heterogeneity is modelled as a random
distribution of either static or diffusive obstacles, which the SPPs avoid while
trying to align their movements. We find that such obstacles have a dramatic
effect on the collective dynamics of usual SPP models. In particular, we report
about the existence of an optimal (angular) noise amplitude that maximizes
collective motion. We also show that while at low obstacle densities the system
exhibits longrange order, in strongly heterogeneous media collective motion is
quasilongrange and exists only for noise values in between two critical
noise values, with
Phase transitions in PCA: erosion versus errors We consider a class of probabilistic cellular automata (PCA) of interest both in statistical physics and in computer science. They are perturbations of cellular automata (CA) that have the property of eroding blocks of impurities in an almost homogeneous configuration. A stochastic perturbation turns the CA into PCA by admitting errors in the states of the cells with some probability distribution. If the erosion is sufficient to correct the effects of errors, the PCA process can have several stationary states, providing an example of nonequilibrium phase transition. We study some properties of these stationary states when the probability of errors is small.
Damien Regnault Several aspects of probabilistic cellular automata From the point of view of a computer scientist, deterministic cellular automata are known as a parallel computation model. Different studies have introduced randomness in this model by considering probabilistic transitions. In this talk, I will present the different motivations of these studies as well as the current results and open questions.
Equilibrium and nonequilibrium statistical mechanics by means of PCA The aim of this talk is to introduce a class of PCA with some interesting
features:
Sylvain Sené Nonlinear threshold PCA in ZxZ: the central role of boundaries The general question of the influence of the environment
on dynamical systems has already been widely studied in the past decades. One of
the best known example comes from mathematical physics and is that of the
characterisation of phase transitions in the “classical” Ising Model, shown by
Dobrushin and Ruelle independently. However, this question remains of particular
interest in other contexts, closer to theoretical computer science and biology.
For instance, now that cellular automata, and more generally automata networks,
are more and more studied as dynamical systems to model and analyse the dynamics
of biological regulation networks, such as genetic networks, going further in
the understanding of the substantial influence of their environment actually is
important.
Piotr Slowinski Probabilistic cellular automata with nonunique spacetime phases
I will use
spacetime phases to describe some properties of probabilistic cellular automata
(PCA). Spacetime phases are probability distributions over state as a function
of space and time that arise from initial probabilities in the past. In
particular, I will focus on PCA with nonunique phase and show how spacetime
phases can be used to analyse emergence in such systems. To illustrate the most
interesting phenomena I will use numerical demonstration. Furthermore, I will
present examples of emergence in PCA used in ecology and economy.
Siamak Taati Statistical equilibrium in deterministic cellular automata Some deterministic cellular automata have long been observed to demonstrate
thermodynamic behavior: starting from a random configuration, they undergo a
transient dynamics until they reach a state of macroscopic equilibrium. An
example is the Ising cellular automaton which can be seen as a deterministic and
microscopically reversible variant of a Gibbs sampler (or a microcanonical
sampler). I will discuss some results and open problems regarding (approach to) Anja VossBöhme PCA for modeling interacting cell systems Understanding the mechanisms that control tissue organization during
development belongs to the most fundamental goals in developmental biology.
Quantitative approaches and mathematical models are essential to deduce the
consequences of existing morphogenetic hypotheses, thus providing the basis for
experimental testing and theoretical understanding. One approach to questions
concerning patterning in developing organisms is to consider tissues as huge
populations of cells which behave according to certain rules that depend on
their genetic programs and inner structure as well as the states and actions of
directly neighboring cells. Then, tissue organization can be understood as
emergent behavior that results from local intercellular interaction.
PRACTICAL INFORMATION● VenueEurandom, Mathematics and Computer Science Dpt, TU Eindhoven, Den Dolech 2, 5612 AZ EINDHOVEN, The Netherlands
Eurandom is located on the campus of
Eindhoven University of
Technology, in the
brand new
TU/e
Metaforum building
(4th floor) (about
the building). The university is
located at 10 minutes walking distance from Eindhoven main railway station (take
the exit north side and walk towards the tall building on the right with the
sign TU/e). The conference will be held at the Eindhoven Technical University. The TU/e is a relatively young university. It was founded some 50 years ago and is situated in the southern part of The Netherlands in the city of Eindhoven, well known as the hometown of the giant in Electronics, the Philips Company, and the famous football club, PSV Eindhoven. The TU/e intends to be a research driven, design oriented university of technology at an international level, with the primary objective of providing young people with an academic education within the ‘engineering science & technology’ domain.
● RegistrationDeadline for contribution (talk/poster) : closed Deadline for contribution (poster): closed Deadline for registration: closed ● Accommodation / FundingSome limited funds are available to contribute to local and travel costs. Participants have to arrange their own hotel booking. For hotels around the university, please see: Hotels (please note: prices listed are "best available"). More hotel options can be found on the webpages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.
Remark: Note that due to a concert at the Eindhoven Philips Stadion on June 789, it may be difficult to find accommodation before the June 9 in the city centre of Eindhoven.
● TravelFor those arriving by plane, there is a convenient direct train connection between Amsterdam Schiphol airport and Eindhoven. This trip will take about one and a half hour. For more detailed information, please consult the NS travel information pages or see Eurandom web page location. Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl The University can be reached easily by car from the highways leading to Eindhoven (for details, see our route descriptions or consult our map with highway connections.
● Conference facilities : Conference room, Metaforum Building MF11&12The meetingroom is equipped with a data projector, an overhead projector, a projection screen and a blackboard. Please note that speakers and participants making an oral presentation are kindly requested to bring their own laptop or their presentation on a memory stick.
● Conference SecretariatUpon arrival, participants should register with the workshop officer, and collect their name badges. The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the daytoday running of the conference: registration, issuing certificates and receipts, etc.
● CancellationShould you need to cancel your participation, please contact Patty Koorn, the Workshop Officer.
● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl SPONSORSThe organisers acknowledge the financial support/sponsorship of:
Other events of interest around this meeting● Mark Kac Seminar, June 14, 2013, Utrecht ● NDNS+ Applied Dynamical Systems Summer School 2013: Emergent Dynamics of Discrete & Stochastic Multiscale Systems: analysis & simulation, TU Eindhoven ● FIRST conference (1214.06),TU Eindhoven
Links to meetings on related topics
● Automata and JAC 2012 (Sept. 2012) ●
Rencontres autour des Automates Cellulaires
Probabilistes (LIAFA, Paris, Jan. 2013)
● Automata 2013 (Sept 2013)
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