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Chronic medical conditions show substantial heterogeneity in their clinical features and progression. We develop the novel data-driven, network-based Trajectory Profile Clustering (TPC) algorithm for 1) identification of disease subtypes and 2) early prediction of subtype/ disease progression patterns. TPC is an easily generalizable method that identifies subtypes by clustering patients with similar disease trajectory profiles, based not only on Parkinson's Disease (PD) variable severity, but also on their complex patterns of evolution. TPC is derived from bipartite networks that connect patients to disease variables. Applying our TPC algorithm to a PD clinical dataset, we identify 3 distinct subtypes/patient clusters, each with a characteristic progression profile. We show that TPC predicts the patient's disease subtype 4 years in advance with 72% accuracy for a longitudinal test cohort. Furthermore, we demonstrate that other types of data such as genetic data can be integrated seamlessly in the TPC algorithm. In summary, using PD as an example, we present an effective method for subtype identification in multidimensional longitudinal datasets, and early prediction of subtypes in individual patients.

The dominant view in neuroscience is that changes in synaptic weights underlie learning. It is unclear, however, how the brain is able to determine which synapses should change, and by how much. This uncertainty stands in sharp contrast to deep learning, where changes in weights are explicitly engineered to optimize performance. However, the main tool for doing that, backpropagation, is not biologically plausible, and networks trained with this rule tend to forget old tasks when learning new ones. Here we introduce the Dendritic Gated Network (DGN), a variant of the Gated Linear Network, which offers a biologically plausible alternative to backpropagation. DGNs combine dendritic "gating" (whereby interneurons target dendrites to shape neuronal response) with local learning rules to yield provably efficient performance. They are significantly more data efficient than conventional artificial networks and are highly resistant to forgetting, and we show that they perform well on a variety of tasks, in some cases better than backpropagation. The DGN bears similarities to the cerebellum, where there is evidence for shaping of Purkinje cell responses by interneurons. It also makes several experimental predictions, one of which we validate with in vivo cerebellar imaging of mice performing a motor task.

One contribution of 15 to a theme issue 'Horizons of cybernetical physics' . We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks. Subject Areas: complexity KeywordsThis article is part of the themed issue 'Horizons of cybernetical physics'.

While the study of graphs has been very popular, simplicial complexes are relatively new in the network science community. Despite being are a source of rich information, graphs are limited to pairwise interactions. However, several real world networks such as social networks, neuronal networks etc. involve simultaneous interactions between more than two nodes. Simplicial complexes provide a powerful mathematical way to model such interactions. Now, the spectrum of the graph Laplacian is known to be indicative of community structure, with nonzero eigenvectors encoding the identity of communities. Here, we propose that the spectrum of the Hodge Laplacian, a higherorder Laplacian applied to simplicial complexes, encodes simplicial communities. We formulate an algorithm to extract simplicial communities (of arbitrary dimension). We apply this algorithm on simplicial complex benchmarks and on real data including social networks and language-networks, where higher-order relationships are intrinsic. Additionally, datasets for simplicial complexes are scarce. Hence, we introduce a method of optimally generating a simplicial complex from its network backbone through estimating the true higher-order relationships when its community structure is known. We do so by using the adjusted mutual information to identify the configuration that best matches the expected data partition. Lastly, we demonstrate an example of persistent simplicial communities inspired by the field of persistence homology.

We investigate the ways in which a machine learning architecture known as Reservoir Computing learns concepts such as “similar” and “different” and other relationships between image pairs and generalizes these concepts to previously unseen classes of data. We present two Reservoir Computing architectures, which loosely resemble neural dynamics, and show that a Reservoir Computer (RC) trained to identify relationships between image pairs drawn from a subset of training classes generalizes the learned relationships to substantially different classes unseen during training. We demonstrate our results on the simple MNIST handwritten digit database as well as a database of depth maps of visual scenes in videos taken from a moving camera. We consider image pair relationships such as images from the same class; images from the same class with one image superposed with noise, rotated 90°, blurred, or scaled; images from different classes. We observe that the reservoir acts as a nonlinear filter projecting the input into a higher dimensional space in which the relationships are separable; i.e., the reservoir system state trajectories display different dynamical patterns that reflect the corresponding input pair relationships. Thus, as opposed to training in the entire high-dimensional reservoir space, the RC only needs to learns characteristic features of these dynamical patterns, allowing it to perform well with very few training examples compared with conventional machine learning feed-forward techniques such as deep learning. In generalization tasks, we observe that RCs perform significantly better than state-of-the-art, feed-forward, pair-based architectures such as convolutional and deep Siamese Neural Networks (SNNs). We also show that RCs can not only generalize relationships, but also generalize combinations of relationships, providing robust and effective image pair classification. Our work helps bridge the gap between explainable machine learning with small datasets and biologically inspired analogy-based learning, pointing to new directions in the investigation of learning processes.

Many diseases display heterogeneity in clinical features and their progression, indicative of the existence of disease subtypes. Extracting patterns of disease variable progression for subtypes has tremendous application in medicine, for example, in early prognosis and personalized medical therapy. This work presents a novel, data-driven, network-based Trajectory Clustering (TC) algorithm for identifying Parkinson’s subtypes based on disease trajectory. Modeling patient-variable interactions as a bipartite network, TC first extracts communities of co-expressing disease variables at different stages of progression. Then, it identifies Parkinson’s subtypes by clustering similar patient trajectories that are characterized by severity of disease variables through a multi-layer network. Determination of trajectory similarity accounts for direct overlaps between trajectories as well as second-order similarities, i.e., common overlap with a third set of trajectories. This work clusters trajectories across two types of layers: (a) temporal, and (b) ranges of independent outcome variable (representative of disease severity), both of which yield four distinct subtypes. The former subtypes exhibit differences in progression of disease domains (Cognitive, Mental Health etc.), whereas the latter subtypes exhibit different degrees of progression, i.e., some remain mild, whereas others show significant deterioration after 5 years. The TC approach is validated through statistical analyses and consistency of the identified subtypes with medical literature. This generalizable and robust method can easily be extended to other progressive multi-variate disease datasets, and can effectively assist in targeted subtype-specific treatment in the field of personalized medicine.

We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only training data consisting of finite time samples of the component signals. We test our method on signals that are formed as linear combinations of signals from two Lorenz systems with different parameters. Comparing our nonlinear method with the optimal linear solution to the separation problem, the Wiener filter, we find that our method significantly outperforms the Wiener filter in all the scenarios we study. Furthermore, this difference is particularly striking when the component signals have similar frequency spectra. Indeed, our method works well when the component frequency spectra are indistinguishable -a case where a Wiener filter performs essentially no separation.