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Statistical analysis of tipping pathways in agent-based models
No full textAgent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach
LARGE DEVIATIONS FOR MARKOV JUMP PROCESSES WITH UNIFORMLY DIMINISHING RATES
Get PDFWe prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise
limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss
the optimality of our assumptions on the decay of the jump rates. As a direct application of this work we relax the assumptions
needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise
naturally particularly the context of mass action kinetics
Short communication: Runout of rock avalanches limited by basal friction but controlled by fragmentation
Get PDFRock avalanches produce exceptionally long run-outs that correlate with their rock volume. Thisrelationship has been attributed to the size-dependent dynamic lowering of the effective basal friction. However,it has also been observed that run-outs of rock avalanches with similar volumes can span several orders ofmagnitude, suggesting additional controlling factors. Here, we analyse analogue models of rock avalanches,with the experiments designed to test the role of dynamic fragmentation. We show that for a fixed low basalfriction, the run-out of experimental rock avalanches varies over 2 orders of magnitude and is determined bytheir degree of fragmentation, while the basal friction acts only as an upper limit on run-out. We interpret therun-out’s dependence on fragmentation as being controlled by the competition between mobility enhancingspreading and energy-consuming fragmentation limited by basal friction. We formalize this competition into ascaling law based on energy conservation, which shows that the variation in the degree of fragmentation cancontribute to the large variation in run-out of rock avalanches seen in natur
Large-scale flow in a cubic Rayleigh-B ́enard cell: Long-term turbulence statistics and Markovianity of macrostate transitions
Get PDFWe investigate the large-scale circulation (LSC) in a turbulent Rayleigh-B ́enard convection flow
in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number
Ra = 106. The numerical studies are conducted for a single flow trajectory up to 105 convective
free-fall times to obtain a sufficient sampling of the four discrete LSC states and the two crossover
configurations which are taken in between for short periods. It is found that the statistics and
time history depends strongly on the Prandtl number Pr of the working fluid which takes values
of 0.1, 0.7, and 10. It changes from very rapid switches for the lowest Prandtl number to the
spontaneous lock in one of the four states for the whole period for the largest one. Alternatively,
we run ensembles of up to 1800 short-term simulations to study the transition probabilities between
the discrete LSC states. This second approach is also used to probe the Markov property of the
dynamics. The ensemble analysis revealed that the sample size might still be too small to conclude
firmly the Markovianity of the transition process from one LSC state to another even though it is
indicated.
PACS numbers: 47.20.Bp, 47.27-i., 02.50.G
A probabilistic algorithm for aggregating vastly undersampled large Markov chains
Get PDFModel reduction of large Markov chains is an essential step in a wide array of techniques for
understanding complex systems and for efficiently learning structures from high-dimensional data.
We present a novel aggregation algorithm for compressing such chains that exploits a specific lowrank
structure in the transition matrix which, e.g., is present in metastable systems, among others.
It enables the recovery of the aggregates from a vastly undersampled transition matrix which in
practical applications may gain a speedup of several orders of magnitude over methods that require
the full transition matrix. Moreover, we show that the new technique is robust under perturbation of
the transition matrix. The practical applicability of the new method is demonstrated by identifying a
reduced model for the large-scale traffic flow patterns from real-world taxi trip data
Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions
No full textWe investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work [Frontiers in Physics 2, 37 (2014); Eur. Phys. J. D 71, 149 (2017)]. This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory
Statistical learning of non-linear stochastic differential equations from non-stationary time-series using variational clustering
No full textParameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary non-linear drift and non-linear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based clustering approach includes a quadratic programming (QP) problem with equality and inequality constraints. We couple the QP problem to a closed-form likelihood function approach based on suitable Hermite-expansions to approximate the parameter values of the SDE model. The classification problem provides a smooth indicator function, which enables us to recover the underlying temporal parameter modulation of the one-dimensional SDE. As shown by the numerical examples, the clustering approach recovers a hidden functional relationship between the SDE model parameters and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, non-stationary, data-driven stochastic models for multiscale dynamical systems in real-world applications
PriSeT: Efficient De Novo Primer Discovery
No full textMotivation:
DNA metabarcoding is a commonly applied technique used to infer the species composition of environmental samples. These samples can comprise hundreds of organisms that can be closely or very distantly related in the taxonomic tree of life. DNA metabarcoding combines polymerase chain reaction (PCR) and next-generation sequencing (NGS), whereby a short, homologous sequence of DNA is amplified and sequenced from all members of the community. Sequences are then taxonomically identified based on their match to a reference database. Ideally, each species of interest would have a unique DNA barcode. This short, variable sequence needs to be flanked by relatively conserved regions that can be used as primer binding sites. Appropriate PCR primer pairs would match to a broad evolutionary range of taxa, such that we only need a few to achieve high taxonomic coverage. At the same time however, the DNA barcodes between primer pairs should be different to allow us to distinguish between species to improve resolution. This poses an interesting optimization problem. More specifically: Given a set of references ℛ = {R1, R2, …, Rm}, the problem is to find a primer set P balancing both: high taxonomic coverage and high resolution. This goal can be captured by filtering for frequent primers and ranking by coverage or variation, i.e. the number of unique barcodes. Here we present the software PriSeT, an offline primer discovery tool that is capable of processing large libraries and is robust against mislabeled or low quality references. It tackles the computationally expensive steps with linear runtime filters and efficient encodings.
Results:
We first evaluated PriSeT on references (mostly 18S rRNA genes) from 19 clades covering eukaryotic organisms that are typical for freshwater plankton samples. PriSeT recovered several published primer sets as well as additional, more chemically suitable primer sets. For these new sets, we compared frequency, taxon coverage, and amplicon variation with published primer sets. For 11 clades we found de novo primer pairs that cover more taxa than the published ones, and for six clades de novo primers resulted in greater sequence (i.e., DNA barcode) variation. We also applied PriSeT to 19 SARS-CoV-2 genomes and computed 114 new primer pairs with the additional constraint that the sequences have no co-occurrences in other taxa. These primer sets would be suitable for empirical testing.
Availability: https://github.com/mariehoffmann/PriSe
Occurrence and transition probabilities of omega and high-over-low blocking in the Euro-Atlantic region
Get PDFStationary, long-lasting blocked weather patterns
can lead to extreme conditions such as anomalously high
temperatures or heavy rainfall. The exact locations of such
extremes depend on the location of the vortices that form the
block. There are two main types of blocking: (i) a high-overlow
block with a high located poleward of an isolated low
and (ii) an omega block with two lows that lie southeast and
southwest of the blocking high in the Northern Hemisphere.
In this work, we refine a novel method based on the kinematic
vorticity number and the point vortex theory that allows us to
distinguish between these two blocking types. Based on the
National Centers for Environmental Prediction–Department
of Energy (NCEP–DOE) Reanalysis 2 data, we study the
trends of the occurrence probability and the onset (formation),
decay (offset) and transition probabilities of high-overlow
and omega blocking in the 30-year period from 1990
to 2019 in the Northern Hemisphere (90�W–90� E) and in
the Euro-Atlantic sector (40�W–30� E). First, we use logistic
regression to investigate long-term changes in blocking
probabilities for full years, seasons and months. While trends
are small for annual values, changes in occurrence probability
are more visible and also more diverse when broken down
to seasonal and monthly resolution, showing a prominent increase
in February and March and a decrease in December.
A three-state multinomial regression describing the occurrence
of omega and high-over-low blocking reveals different
trends for both types. Particularly the February and December
changes are dominated by the omega blocking type.
Additionally, we use Markov models to describe transition
probabilities for a two-state (unblocked, blocked) and a threestate
(unblocked, omega block, high-over-low block) Markov
model. We find the largest changes in transition probabilities
in the summer season, where the transition probabilities
towards omega blocks significantly increase, while the unblocked
state becomes less probable. Prominent in winter are
decreasing probabilities for transitions from omega to highover-
low and persistence of the latter. Moreover, we show
that omega blocking is more likely to occur and to be more
persistent than the high-over-low blocking pattern
Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis
No full textAbstract
We demonstrate the application of the transition manifold framework to the late-stage fibrillation process of the NFGAILS peptide, a amyloidogenic fragment of the human islet amyloid polypeptide (hIAPP). This framework formulates machine learning methods for the analysis of multi-scale stochastic systems from short, massively parallel molecular dynamical simulations. We identify key intermediate states and dominant pathways of the process. Furthermore, we identify the optimally timescale-preserving reaction coordinate for the dock-lock process to a fixed pre-formed fibril and show that it exhibits strong correlation with the mean native hydrogen-bond distance. These results pave the way for a comprehensive model reduction and multi-scale analysis of amyloid fibrillation processes