Kai Morino

Dynamical robustness in complex networks: the crucial role of low-degree nodes

Many social, biological, and technological networks consist of a small number of highly connected components (hubs) and a very large number of loosely connected components (low-degree nodes). It has been commonly recognized that such heterogeneously connected networks are extremely vulnerable to the failure of hubs in terms of structural robustness of complex networks. However, little is known about dynamical robustness, which refers to the ability of a network to maintain its dynamical activity against local perturbations. Here we demonstrate that, in contrast to the structural fragility, the nonlinear dynamics of heterogeneously connected networks can be highly vulnerable to the failure of low-degree nodes. The crucial role of low-degree nodes results from dynamical processes where normal (active) units compensate for the failure of neighboring (inactive) units at the expense of a reduction in their own activity. Our finding highlights the significant difference between structural and dynamical robustness in complex networks.

Intermittent Androgen Suppression: Estimating Parameters for Individual Patients Based on Initial PSA Data in Response to Androgen Deprivation Therapy

When a physician decides on a treatment and its schedule for a specific patient, information gained from prior patients and experience in the past is taken into account. A more objective way to make such treatment decisions based on actual data would be useful to the clinician. Although there are many mathematical models proposed for various diseases, so far there is no mathematical method that accomplishes optimization of the treatment schedule using the information gained from past patients or “rapid learning” technology. In an attempt to use this approach, we integrate the information gained from patients previously treated with intermittent androgen suppression (IAS) with that from a current patient by first fitting the time courses of clinical data observed from the previously treated patients, then constructing the prior information of the parameter values of the mathematical model, and finally, maximizing the posterior probability for the parameters of the current patient using the prior information. Although we used data from prostate cancer patients, the proposed method is general, and thus can be applied to other diseases once an appropriate mathematical model is established for that disease.

Discovery of Glaucoma Progressive Patterns Using Hierarchical MDL-Based Clustering

In this paper, we propose a method to cluster the spacial patterns of the visual field in glaucoma patients to analyze the progression patterns of glaucoma. The degree of progression in the visual field of glaucoma patients can be divided into several regions by straight line boundaries, we call this specific structure Direct Product Structure in this paper. Since we can observe the direct product structure in the visual fields, we propose a bottom-up hierarchical clustering method to embed this structure into the clustering structure. In our method, according to the minimum description length (MDL) principle, we select the best cluster division so that the total code length required for encoding the data as well as the clustering structure is minimum. We can thereby select the clusters that are robust to the noise in the position of the direct product structure for clustering. We demonstrate the effectiveness of our method using an artificial dataset and a real glaucoma dataset. Our proposed method performed better than existing methods for both datasets. For the real glaucoma dataset in particular, our method discovered the characteristic progressive patterns of glaucoma as specific features of clusters. These patterns agree with clinical knowledge. Furthermore, we show that our clusters can be applied to improve the accuracy of predicting glaucoma progression. Thus, our clusters contain rich information of glaucoma, and hence can contribute to further development in glaucoma research.

Predicting glaucoma progression using multi-task learning with heterogeneous features

We consider the prediction of glaucomatous visual field loss based on patient datasets. It is critically important to predict how rapidly the disease is progressing in an individual patient. However, the number of measurements for each patient is so small that a reliable predictor cannot be constructed from the data of a single patient alone. In this paper, we propose a novel multi-task learning approach to this issue. Patient data consist of three features: patient ID, 74-dimensional visual loss values, and inspection time. We reduce the prediction problem into one of matrix completion for these features. Specifically, by assuming heterogeneity in the three features, we introduce similarity measures that reflect the unique statistical nature of the respective features to solve a specific type of matrix decomposition problem. For example, we employ Gaussian kernels as a similarity measure for visual field loss and a linear regression-type relation for the time feature. We empirically demonstrate that our proposed method works significantly better than the existing methods.

Dynamical Robustness of Complex Biological Networks

Dynamical behavior of biological systems is maintained by interactions between biological units such as neurons, cells, proteins, and molecules. It is a challenging issue to understand robustness of biological interaction networks from a viewpoint of dynamical systems. In this chapter, we introduce the concept of dynamical robustness in complex networks and demonstrate its application to biological networks. First, we introduce the framework for studying the dynamical robustness through analyses of coupled Stuart-Landau oscillators with various types of network structures. Second, based on the framework, we examine the dynamical robustness of neuronal firing activity in networks of synaptically coupled Morris-Lecar neuron models. Our analyses suggest that a consideration of both network structure and dynamics is crucial in elucidating biological robustness.

Robustness of oscillatory behavior in correlated networks.

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

Multi-view Learning over Retinal Thickness and Visual Sensitivity on Glaucomatous Eyes

Dense measurements of visual-field, which is necessary to detect glaucoma, is known as very costly and labor intensive. Recently, measurement of retinal-thickness can be less costly than measurement of visual-field. Thus, it is sincerely desired that the retinal-thickness could be transformed into visual-sensitivity data somehow. In this paper, we propose two novel methods to estimate the sensitivity of the visual-field with SITA-Standard mode 10-2 resolution using retinal-thickness data measured with optical coherence tomography (OCT). The first method called Affine-Structured Non-negative Matrix Factorization (ASNMF) which is able to cope with both the estimation of visual-field and the discovery of deep glaucoma knowledge. While, the second is based on Convolutional Neural Networks (CNNs) which demonstrates very high estimation performance. These methods are kinds of multi-view learning methods because they utilize visual-field and retinal thickness data simultaneously. We experimentally tested the performance of our methods from several perspectives. We found that ASNMF worked better for relatively small data size while CNNs did for relatively large data size. In addition, some clinical knowledge are discovered via ASNMF. To the best of our knowledge, this is the first paper to address the dense estimation of the visual-field based on the retinal-thickness data.

Time Correlation Calculation Method Based on Delayed Coordinates

An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M →∞ is extrapolated from this approximation for the first few values of M . This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the

Personalizing Androgen Suppression for Prostate Cancer Using Mathematical Modeling

Using a dataset of 150 patients treated with intermittent androgen suppression (IAS) through a fixed treatment schedule, we retrospectively designed a personalized treatment schedule mathematically for each patient. We estimated 100 sets of parameter values for each patient by randomly resampling each patient’s time points to take into account the uncertainty for observations of prostate specific antigen (PSA). Then, we identified 3 types and classified patients accordingly: in type (i), the relapse, namely the divergence of PSA, can be prevented by IAS; in type (ii), the relapse can be delayed by IAS later than by continuous androgen suppression (CAS); in type (iii) IAS was not beneficial and therefore CAS would have been more appropriate in the long run. Moreover, we obtained a treatment schedule of hormone therapy by minimizing the PSA of 3 years later in the worst case scenario among the 100 parameter sets by searching exhaustively all over the possible treatment schedules. If the most frequent type among 100 sets was type (i), the maximal PSA tended to be kept less than 100 ng/ml longer in IAS than in CAS, while there was no statistical difference for the other cases. Thus, mathematically personalized IAS should be studied prospectively.

Temporal Network Change Detection Using Network Centralities

In this paper, we propose a novel change detection method for temporal networks. In usual change detection algorithms, change scores are generated from an observed time series. When this change score reaches a threshold, an alert is raised to declare the change. Our method aggregates these change scores and alerts based on network centralities. Many types of changes in a network can be discovered from changes to the network structure. Thus, nodes and links should be monitored in order to recognize changes. However, it is difficult to focus on the appropriate nodes and links when there is little information regarding the dataset. Network centrality such as PageRank measures the importance of nodes in a network based on certain criteria. Therefore, it is natural to apply network centralities in order to improve the accuracy of change detection methods. Our analysis reveals how and when network centrality works well in terms of change detection. Based on this understanding, we propose an aggregating algorithm that emphasizes the appropriate network centralities. Our evaluation of the proposed aggregation algorithm showed highly accurate predictions for an artificial dataset and two real datasets. Our method contributes to extending the field of change detection in temporal networks by utilizing network centralities.