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Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world data creates the need to rely on synthetic data for the evaluation of these methods. Existing benchmarks are limited in their scope, as they either are restricted to a "static" selection of data sets, or do not allow for a granular assessment of the methods' performance when commonly made assumptions are violated. We propose a flexible and simple to use framework for generating time series data, which is aimed at developing, evaluating, and benchmarking time series causal discovery methods. In particular, the framework can be used to fine tune novel methods on vast amounts of data, without "overfitting" them to a benchmark, but rather so they perform well in real-world use cases. Using our framework, we evaluate prominent time series causal discovery methods and demonstrate a notable degradation in performance when their assumptions are invalidated and their sensitivity to choice of hyperparameters. Finally, we propose future research directions and how our framework can support both researchers and practitioners., Comment: 17 pages, 9 figures, for associated code and data sets, see https://github.com/causalens/cdml-neurips2020

Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data., Comment: 6 pages, 4 figures

Motivation: Agent-based modeling is an indispensable tool for studying complex biological systems. However, existing simulators do not always take full advantage of modern hardware and often have a field-specific software design. Results: We present a novel simulation platform called BioDynaMo that alleviates both of these problems. BioDynaMo features a general-purpose and high-performance simulation engine. We demonstrate that BioDynaMo can be used to simulate use cases in: neuroscience, oncology, and epidemiology. For each use case we validate our findings with experimental data or an analytical solution. Our performance results show that BioDynaMo performs up to three orders of magnitude faster than the state-of-the-art baseline. This improvement makes it feasible to simulate each use case with one billion agents on a single server, showcasing the potential BioDynaMo has for computational biology research. Availability: BioDynaMo is an open-source project under the Apache 2.0 license and is available at www.biodynamo.org. Instructions to reproduce the results are available in supplementary information. Contact: lukas.breitwieser@inf.ethz.ch, a.s.hesam@tudelft.nl, omutlu@ethz.ch, r.bauer@surrey.ac.uk Supplementary information: Available at https://doi.org/10.5281/zenodo.4501515, Comment: 8 pages, 6 figures

In some cases, the function of a lesioned area can be compensated for by another area. However, it remains unpredictable if and by which other area a lesion can be compensated. We assume that similar incoming and outgoing connections are necessary to encode the same function as the damaged region. The similarity can be measured both locally using the matching index and looking at a more global scale by non-metric multidimensional scaling (NMDS). We tested how well both measures can predict the compensating area for the loss of the visual cortex in kittens. For this case study, the global comparison of connectivity turns out to be a better method for predicting functional compensation. In future studies, the extent of the similarity between the lesioned and compensating regions might be a measure of the extent to which function can be successfully recovered., Comment: Technical Report

We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. While this model has been examined for many decades, progress has been relatively recent. In particular, the derivatives of dynamic equilibria have been characterized as thin flows with resetting, which allowed for more structural results. Our two main results are based on the formulation of thin flows with resetting as linear complementarity problem and its analysis. We present a constructive proof of existence for dynamic equilibria if the inflow rate is right-monotone. The complexity of computing thin flows with resetting, which occurs as a subproblem in this method, is still open. We settle it for the class of two-terminal series-parallel networks by giving a recursive algorithm that solves the problem for all flow values simultaneously in polynomial time.

Neurostimulation using weak electric fields has generated excitement in recent years due to its potential as a medical intervention. However, study of this stimulation modality has been hampered by inconsistent results and large variability within and between studies. In order to begin addressing this variability we need to properly characterise the impact of the current on the underlying neuron populations. To develop and test a computational model capable of capturing the impact of electric field stimulation on networks of neurons. We construct a cortical tissue model with distinct layers and explicit neuron morphologies. We then apply a model of electrical stimulation and carry out multiple test case simulations. The cortical slice model is compared to experimental literature and shown to capture the main features of the electrophysiological response to stimulation. Namely, the model showed 1) a similar level of depolarisation in individual pyramidal neurons, 2) acceleration of intrinsic oscillations, and 3) retention of the spatial profile of oscillations in different layers. We then apply alternative electric fields to demonstrate how the model can capture differences in neuronal responses to the electric field. We demonstrate that the tissue response is dependent on layer depth, the angle of the apical dendrite relative to the field, and stimulation strength. We present publicly available computational modelling software that predicts the neuron network population response to electric field stimulation.

Structural covariance analysis is a widely used structural MRI analysis method which characterises the co-relations of morphology between brain regions over a group of subjects. To our knowledge, little has been investigated in terms of the comparability of results between different data sets or the reliability of results over the same subjects in different rescan sessions, image resolutions, or FreeSurfer versions. In terms of comparability, our results show substantial differences in the structural covariance matrix between data sets of age- and sex-matched healthy human adults. These differences persist after site correction, they are exacerbated by low sample sizes, and they are most pronounced when using average cortical thickness as a morphological measure. Down-stream graph theoretic analyses further show statistically significant differences. In terms of reliability, substantial differences were also found when comparing repeated scan sessions of the same subjects, and image resolutions and FreeSurfer versions of the same image. We could further estimate the relative measurement error and showed that it is largest when using thickness. With simulated data, we argue that cortical thickness is least reliable because of larger relative measurement errors. Practically, we make the following recommendations (1) pooling subjects across sites into one group should be avoided, particularly if sites differ in image resolutions, demographics, or preprocessing; (2) surface area and volume should be preferred as morphological measures over cortical thickness; (3) a large number of subjects should be used to estimate structural covariance; (4) measurement error should be assessed where repeated measurements are available; (5) if combining sites is critical, univariate site-correction is insufficient, but error covariance should be explicitly measured and modelled.

Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider range of problems. References, which are often specified by the decision maker's preference in different forms, are a very effective method to improve the performance of algorithms but have not been fully explored in literature. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state of the arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.

Budget Minimization is a scheduling problem with precedence constraints, i.e., a scheduling problem on a partially ordered set of jobs $(N, \unlhd)$. A job $j \in N$ is available for scheduling, if all jobs $i \in N$ with $i \unlhd j$ are completed. Further, each job $j \in N$ is assigned real valued costs $c_{j}$, which can be negative or positive. A schedule is an ordering $j_{1}, \dots, j_{\vert N \vert}$ of all jobs in $N$. The budget of a schedule is the external investment needed to complete all jobs, i.e., it is $\max_{l \in \{0, \dots, \vert N \vert \} } \sum_{1 \le k \le l} c_{j_{k}}$. The goal is to find a schedule with minimum budget. Rafiey et al. (2015) showed that Budget Minimization is NP-hard following from a reduction from a molecular folding problem. We extend this result and prove that it is NP-hard to $\alpha(N)$-approximate the minimum budget even on bipartite partial orders. We present structural insights that lead to arguably simpler algorithms and extensions of the results by Rafiey et al. (2015). In particular, we show that there always exists an optimal solution that partitions the set of jobs and schedules each subset independently of the other jobs. We use this structural insight to derive polynomial-time algorithms that solve the problem to optimality on series-parallel and convex bipartite partial orders.

Dynamic multiobjective optimisation has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of existing dynamic multiobjective test problems have not been rigorously constructed and analysed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more importantly, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features is then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite is more challenging to the dynamic multiobjective optimisation algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites can not., Comment: 19 pages, 22 figures and 7 tables

The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part of the input. Restricting to $2$-DSPP with strictly positive lengths, it becomes solvable in polynomial time. We extend this result by allowing zero edge lengths and give a polynomial time algorithm based on dynamic programming for $2$-DSPP on undirected graphs with non-negative edge lengths., Comment: 6 pages, 4 figures

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence MRI based diagnosis is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood. In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissue. Analysing white matter structures of 32 subjects we incorporated our findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis. Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics. We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits.

We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. We focus on the probabilities of rare events (large deviations). First, we discuss a PT (parity-time) symmetry that appears in ensembles of trajectories where a current is constrained to have a large (non-typical) value. We analyse the heat flow in such ensembles, and compare it with non-equilibrium steady states. Second, we consider pathwise large deviations that are defined by considering many copies of a system. We show how the probability currents in such systems can be decomposed into orthogonal contributions, that are related to convergence to equilibrium and to dissipation. We discuss the implications of these results for modelling non-equilibrium steady states., Comment: final version, 21 pages

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory. For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within Macroscopic Fluctuation Theory, which describes hydrodynamic limits of such microscopic models.c Fluctuation Theory, which describes hydrodynamic limits of such microscopic models., Comment: 36 page, 1 figure

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are \emph{antisymmetric} under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium., Comment: 27 pages, 8 figures

Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into two types - low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Here we explore whether these two patterns arise from fundamentally different mechanisms. Here, we use a previously established computational model of neocortical tissue, and validate it as an adequate model using clinical recordings of focal seizures. We then reproduce the two onset patterns in their most defining properties and investigate the possible mechanisms underlying the different focal seizure onset patterns in the model. We show that the two patterns are associated with different mechanisms at the spatial scale of a single ECoG electrode. The LAF onset is initiated by independent patches of localised activity, which slowly invade the surrounding tissue and coalesce over time. In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event. We find that such a global transition is enabled by an increase in the excitability of the "healthy" surrounding tissue, which by itself does not generate seizures, but can support seizure activity when incited. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically reported difference in surgical outcomes. Finally, we demonstrate in the model how changes in tissue excitability could be elucidated, in principle, using active stimulation. Taken together, our modelling results suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern, as well as in the surgical outcome.

Computer simulations have become a very powerful tool for scientific research. In order to facilitate research in computational biology, the BioDynaMo project aims at a general platform for biological computer simulations, which should be executable on hybrid cloud computing systems. This paper describes challenges and lessons learnt during the early stages of the software development process, in the context of implementation issues and the international nature of the collaboration., Comment: 4th Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE4), 2016

Computer simulations have become a very powerful tool for scientific research. Given the vast complexity that comes with many open scientific questions, a purely analytical or experimental approach is often not viable. For example, biological systems (such as the human brain) comprise an extremely complex organization and heterogeneous interactions across different spatial and temporal scales. In order to facilitate research on such problems, the BioDynaMo project (\url{https://biodynamo.web.cern.ch/}) aims at a general platform for computer simulations for biological research. Since the scientific investigations require extensive computer resources, this platform should be executable on hybrid cloud computing systems, allowing for the efficient use of state-of-the-art computing technology. This paper describes challenges during the early stages of the software development process. In particular, we describe issues regarding the implementation and the highly interdisciplinary as well as international nature of the collaboration. Moreover, we explain the methodologies, the approach, and the lessons learnt by the team during these first stages.

Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan. Previous mathematical models explaining glioma incidence are framed in a rather abstract way, and do not directly relate to empirical findings. To decrease this gap between theory and experimental observations, we incorporate recent data on cellular and molecular factors underlying gliomagenesis. Since evidence implicates the adult neural stem cell as the likely cell-of-origin of glioma, we have incorporated empirically-determined estimates of neural stem cell number, cell division rate, mutation rate and oncogenic potential into our model. We demonstrate that our model yields results which match actual demographic data in the human population. In particular, this model accounts for the observed peak incidence of glioma at approximately 80 years of age, without the need to assert differential susceptibility throughout the population. Overall, our model supports the hypothesis that glioma is caused by randomly-occurring oncogenic mutations within the neural stem cell population. Based on this model, we assess the influence of the (experimentally indicated) decrease in the number of neural stem cells and increase of cell division rate during aging. Our model provides multiple testable predictions, and suggests that different temporal sequences of oncogenic mutations can lead to tumorigenesis. Finally, we conclude that four or five oncogenic mutations are sufficient for the formation of glioma.

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation especially concerning short-distance connectivity during early development, either starting at the same time for all neurons (parallel, i.e. maximally-overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e. no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency, and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network., Comment: Biol Cybern. 2015 Jan 30. [Epub ahead of print]

The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values but otherwise maximally random. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of C. elegans and human connectomes are both higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in C. elegans connectome or each region of interest (ROI) in human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared to the alternative arrangements. This implies that fewer rules are needed to encode for the organisation of neural systems.

Local field potentials (LFPs) sampled with extracellular electrodes are frequently used as a measure of population neuronal activity. However, relating such measurements to underlying neuronal behaviour and connectivity is non-trivial. To help study this link, we developed the Virtual Electrode Recording Tool for EXtracellular potentials (VERTEX). We first identified a reduced neuron model that retained the spatial and frequency filtering characteristics of extracellular potentials from neocortical neurons. We then developed VERTEX as an easy-to-use Matlab tool for simulating LFPs from large populations (>100 000 neurons). A VERTEX-based simulation successfully reproduced features of the LFPs from an in vitro multi-electrode array recording of macaque neocortical tissue. Our model, with virtual electrodes placed anywhere in 3D, allows direct comparisons with the in vitro recording setup. We envisage that VERTEX will stimulate experimentalists, clinicians, and computational neuroscientists to use models to understand the mechanisms underlying measured brain dynamics in health and disease., Comment: appears in Brain Struct Funct 2014

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs, or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings, lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatiotemporal pattern formation and propose a novel perspective for analyzing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.

Predicting brain maturity using noninvasive magnetic resonance images (MRI) can distinguish different age groups and help to assess neurodevelopmental disorders. However, group-wise differences are often less informative for assessing features of individuals. Here, we propose a simple method to predict the age of an individual subject solely based on structural connectivity data from diffusion tensor imaging (DTI). Our simple predictor computed a weighted sum of the strength of all connections of an individual. The weight consists of the fiber strength, given by the number of streamlines following tract tracing, multiplied by the importance of that connection for an observed feature--age in this case. We tested this approach using DTI data from 121 healthy subjects aged 4 to 85 years. After determining importance in a training dataset, our predicted ages in the test dataset showed a strong correlation (rho = 0.77) with real age deviating by, on average, only 10 years., Comment: Dynamic Connectome Lab, Technical Report No. 1

Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on synchrony, oscillation, and activity propagation. Understanding the link between the hierarchical organisation and processing (e.g. does consciousness structurally correlate with the top level of the hierarchy and where is the 'top' in a network?) remains one of the main challenges of the field. In addition, although neuron nodes are often treated as uniform entities, they can differ in terms of function (e.g. inhibitory vs. excitatory), morphology, or gene expression pattern., Comment: Dynamic Connectome Lab, Technical Report No. 4