13 research outputs found
Complexity of Model Testing for Dynamical Systems with Toric Steady States
In this paper we investigate the complexity of model selection and model
testing for dynamical systems with toric steady states. Such systems frequently
arise in the study of chemical reaction networks. We do this by formulating
these tasks as a constrained optimization problem in Euclidean space. This
optimization problem is known as a Euclidean distance problem; the complexity
of solving this problem is measured by an invariant called the Euclidean
distance (ED) degree. We determine closed-form expressions for the ED degree of
the steady states of several families of chemical reaction networks with toric
steady states and arbitrarily many reactions. To illustrate the utility of this
work we show how the ED degree can be used as a tool for estimating the
computational cost of solving the model testing and model selection problems
Graph-Facilitated Resonant Mode Counting in Stochastic Interaction Networks
Oscillations in a stochastic dynamical system, whose deterministic
counterpart has a stable steady state, are a widely reported phenomenon.
Traditional methods of finding parameter regimes for stochastically-driven
resonances are, however, cumbersome for any but the smallest networks. In this
letter we show by example of the Brusselator how to use real root counting
algorithms and graph theoretic tools to efficiently determine the number of
resonant modes and parameter ranges for stochastic oscillations. We argue that
stochastic resonance is a network property by showing that resonant modes only
depend on the squared Jacobian matrix , unlike deterministic oscillations
which are determined by . By using graph theoretic tools, analysis of
stochastic behaviour for larger networks is simplified and chemical reaction
networks with multiple resonant modes can be identified easily.Comment: 5 pages, 4 figure
The magnitude vector of images
The magnitude of a finite metric space has recently emerged as a novel
invariant quantity, allowing to measure the effective size of a metric space.
Despite encouraging first results demonstrating the descriptive abilities of
the magnitude, such as being able to detect the boundary of a metric space, the
potential use cases of magnitude remain under-explored. In this work, we
investigate the properties of the magnitude on images, an important data
modality in many machine learning applications. By endowing each individual
images with its own metric space, we are able to define the concept of
magnitude on images and analyse the individual contribution of each pixel with
the magnitude vector. In particular, we theoretically show that the previously
known properties of boundary detection translate to edge detection abilities in
images. Furthermore, we demonstrate practical use cases of magnitude for
machine learning applications and propose a novel magnitude model that consists
of a computationally efficient magnitude computation and a learnable metric. By
doing so, we address the computational hurdle that used to make magnitude
impractical for many applications and open the way for the adoption of
magnitude in machine learning research
Stabilization of active matter by flow-vortex lattices and defect ordering
Active systems, from bacterial suspensions to cellular monolayers, are
continuously driven out of equilibrium by local injection of energy from their
constituent elements and exhibit turbulent-like and chaotic patterns. Here we
demonstrate both theoretically and through numerical simulations, that the
crossover between wet active systems, whose behaviour is dominated by
hydrodynamics, and dry active matter where any flow is screened, can be
achieved by using friction as a control parameter. Moreover we discover
unexpected vortex ordering at this wet-dry crossover. We show that the self
organisation of vortices into lattices is accompanied by the spatial ordering
of topological defects leading to active crystal-like structures. The emergence
of vortex lattices, which leads to the positional ordering of topological
defects, suggests potential applications in the design and control of active
materials
reComBat: batch-effect removal in large-scale multi-source gene-expression data integration
With the steadily increasing abundance of omics data produced all over the world under vastly different experimental conditions residing in public databases, a crucial step in many data-driven bioinformatics applications is that of data integration. The challenge of batch-effect removal for entire databases lies in the large number of batches and biological variation, which can result in design matrix singularity. This problem can currently not be solved satisfactorily by any common batch-correction algorithm.; We present; reComBat; , a regularized version of the empirical Bayes method to overcome this limitation and benchmark it against popular approaches for the harmonization of public gene-expression data (both microarray and bulkRNAsq) of the human opportunistic pathogen; Pseudomonas aeruginosa; . Batch-effects are successfully mitigated while biologically meaningful gene-expression variation is retained.; reComBat; fills the gap in batch-correction approaches applicable to large-scale, public omics databases and opens up new avenues for data-driven analysis of complex biological processes beyond the scope of a single study.; The code is available at https://github.com/BorgwardtLab/reComBat, all data and evaluation code can be found at https://github.com/BorgwardtLab/batchCorrectionPublicData.; Supplementary data are available at; Bioinformatics Advances; online
Coloured noise from stochastic inflows in reaction-diffusion systems
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or coloured noise. Here, the main source of external noise is considered to be fluctuations in the parameter values representing the in flow of particles to the system. First, we determine which reaction systems, driven by extrinsic noise, can admit only one steady state, so that effects, such as stochastic switching, are precluded from our analysis. To analyse the steady state behaviour of reaction systems, even if the parameter values are changing, necessitates a parameter-free approach, which has been central to algebraic analysis in chemical reaction network theory. To identify suitable models we use tools from real algebraic geometry that link the network structure to its dynamical properties. We then make a connection to internal noise models and show how power spectral methods can be used to predict stochastically driven patterns in systems with coloured noise. In simple cases we show that the power spectrum of the coloured noise process and the power spectrum of the reaction-diffusion system modelled with white noise multiply to give the power spectrum of the coloured noise reaction-diffusion system
SIMBSIG: similarity search and clustering for biobank-scale data
In many modern bioinformatics applications, such as statistical genetics, or single-cell analysis, one frequently encounters datasets which are orders of magnitude too large for conventional in-memory analysis. To tackle this challenge, we introduce SIMBSIG (SIMmilarity Batched Search Integrated GPU), a highly scalable Python package which provides a scikit-learn-like interface for out-of-core, GPU-enabled similarity searches, principal component analysis and clustering. Due to the PyTorch backend, it is highly modular and particularly tailored to many data types with a particular focus on biobank data analysis.ISSN:1367-4803ISSN:1460-205
This is a Sage module which calculates phase diagrams using Sturm chains from Graph-facilitated resonant mode counting in stochastic interaction networks
Oscillations in dynamical systems are widely reported in multiple branches of physics. Critically, even a non-oscillatory deterministic system can produce cyclic trajectories when it is in a low copy number, stochastic, regime. Common methods of finding parameter ranges for stochastically driven resonances, such as direct calculation, are cumbersome for any but the smallest networks. In this paper, we provide a systematic framework to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations relying on real root counting algorithms and graph theoretic methods. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix <i>J</i><sup>2</sup>, unlike deterministic oscillations which are determined by <i>J</i>. By using graph theoretic tools, analysis of stochastic behaviour for larger interaction networks is simplified and stochastic dynamical systems with multiple resonant modes can be identified easily