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 $J^2$ , unlike deterministic oscillations which are determined by $J$. 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

reComBat: Batch effect removal in large-scale, multi-source omics data integration

With the steadily increasing abundance of omics data produced all over the world, some-times decades apart and 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 and coincide of both batches and desired, biological variation resulting in design matrix singularity. This problem currently cannot be solved by any common batch correction algorithm. In this study, we present reComBat, a regularised version of the empirical Bayes method to overcome this limitation. We demonstrate our approach for the harmonisation of public gene expression data of the human opportunistic pathogen Pseudomonas aeruginosa and study a several metrics to empirically demonstrate that 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