Inference of time-varying networks through transfer entropy, the case of a Boolean network model

Reconstructing regime-dependent causal relationships from observational time series

Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Niño Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.

A Boolean Logical model for Reprogramming of Testes-derived male Germline Stem Cells into Germline pluripotent stem cells

BACKGROUND AND OBJECTIVE

Male germline stem (GS) cells are responsible for the maintenance of spermatogenesis throughout the adult life of males. Upon appropriate in vitro culture conditions, these GS cells can undergo reprogramming to become germline pluripotent stem (GPS) cells with the loss of spermatogenic potential. In recent years, voluminous data of gene transcripts in GS and GPS cells have become available. However, the mechanism of reprogramming of GS cells into GPS cells remains elusive. This study was designed to develop a Boolean logical model of gene regulatory network (GRN) that might be involved in the reprogramming of GS cells into GPS cells.

METHODS

The gene expression profile of GS and GPS cells (GSE ID: GSE11274 and GSE74151) were analyzed using R Bioconductor to identify differentially expressed genes (DEGs) and were functionally annotated with DAVID server. Potential pluripotent genes among the DEGs were then predicted using a combination of machine learning [Support Vector Machine (SVM)] and BLAST search. Protein isoforms were identified by pattern matching with UniProt database with in-house scripts written in C++. Both linear and non-linear interaction maps were generated using the STRING server. CellNet is used to study the relationship of GRNs between the GS and GPS cells. Finally, the GRNs involving all the genes from integrated methods and literature was constructed and qualitative modelling for reprogramming of GS to GPS cells were done by considering the discrete, asynchronous, multivalued logical formalism using the GINsim modeling and simulation tool.

RESULTS

Through the use of machine learning and logical modeling, the present study identified 3585 DEGs and 221 novel pluripotent genes including Tet1, Cdh1, Tfap2c, Etv4, Etv5, Prdm14, and Prdm10 in GPS cells. Pathway analysis revealed that important signaling pathways such as core pluripotency network, PI3K-Akt, WNT, GDNF and BMP4 signalling pathways were important for the reprogramming of GS cells to GPS cells. On the other hand, CellNet analysis of GRNs of GS and GPS cells revealed that GS cells were similar to gonads whereas GPS cells were similar to ESCs in gene expression profile. A logical regulatory model was developed, which showed that TGFβ negatively regulated the reprogramming of the GS to GPS cells, as confirmed by perturbations studies.

CONCLUSION

The study identified novel pluripotent genes involved in the reprogramming of GS cells into GPS cells. A multivalued logical model of cellular reprogramming is proposed, which suggests that reprogramming of GS cells to GPS cells involves signalling pathways namely LIF, GDNF, BMP4, and TGFβ along with some novel pluripotency genes.

Improving on transfer entropy-based network reconstruction using time-delays: Approach and validation

Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.

Application of symbolic recurrence to experimental data, from firearm prevalence to fish swimming

Recurrence plots and recurrence quantification analysis are powerful tools to study the behavior of dynamical systems. What we learn through these tools is typically determined by the choice of a distance threshold in the phase space, which introduces arbitrariness in the definition of recurrence. Not only does symbolic recurrence overcome this difficulty, but also it offers a richer representation that book-keeps the recurrent portions of the phase space. Using symbolic recurrences, we can construct recurrence plots, perform quantification analysis, and examine causal links between dynamical systems from their time-series. Although previous efforts have demonstrated the feasibility of such a symbolic framework on synthetic data, the study of real time-series remains elusive. Here, we seek to bridge this gap by systematically examining a wide range of experimental datasets, from firearm prevalence and media coverage in the United States to the effect of sex on the interaction of swimming fish. This work offers a compelling demonstration of the potential of symbolic recurrence in the study of real-world applications across different research fields while providing a computer code for researchers to perform their own time-series explorations.

Behavioural and life-history responses of mosquitofish to biologically inspired and interactive robotic predators

Invasive alien species threaten biodiversity worldwide and contribute to biotic homogenization, especially in freshwaters, where the ability of native animals to disperse is limited. Robotics may offer a promising tool to address this compelling problem, but whether and how invasive species can be negatively affected by robotic stimuli is an open question. Here, we explore the possibility of modulating behavioural and life-history responses of mosquitofish by varying the degree of biomimicry of a robotic predator, whose appearance and locomotion are inspired by natural mosquitofish predators. Our results support the prediction that real-time interactions at varying swimming speeds evoke a more robust antipredator response in mosquitofish than simpler movement patterns by the robot, especially in individuals with better body conditions that are less prone to take risks. Through an information-theoretic analysis of animal-robot interactions, we offer evidence in favour of a causal link between the motion of the robotic predator and a fish antipredator response. Remarkably, we observe that even a brief exposure to the robotic predator of 15 min per week is sufficient to erode energy reserves and compromise the body condition of mosquitofish, opening the door for future endeavours to control mosquitofish in the wild.

Media coverage and firearm acquisition in the aftermath of a mass shooting

With an alarming frequency, the United States is experiencing mass shooting events, which often result in heated public debates on firearm control. Whether such events play any role in recent dramatic increases in firearm prevalence remains an open question. This study adopts an information-theoretic framework to analyse the complex interplay between the occurrence of a mass shooting, media coverage on firearm control policies and firearm acquisition at both national and state levels. Through the analysis of time series from 1999 to 2017, we identify a correlation between the occurrence of a mass shooting and the rate of growth in firearm acquisition. More importantly, a transfer entropy analysis pinpoints media coverage on firearm control policies as a potential causal link in a Wiener-Granger sense that establishes this correlation. Our results demonstrate that media coverage may increase public worry about more stringent firearm control and partially drive increases in firearm prevalence.

Transfer entropy on symbolic recurrences

Recurrence quantification analysis offers a powerful framework to investigate complexity in dynamical systems. While several studies have demonstrated the possibility of multivariate recurrence quantification analysis, information-theoretic tools for the discovery of causal links remain elusive. Particularly enticing is to formulate information-theoretic tools on symbolic recurrence plots, which alleviate some of the methodological challenges of traditional recurrence plots and offer a richer representation of recurrences. Toward this aim, we establish a probability space in which we ground a theory of information that encodes information in the recurrences of the symbols. We introduce transfer entropy on symbolic recurrences as a tool to guide the inference of the strength and direction of the interaction between dynamical systems. We demonstrate statistically reliable discovery of causal links on synthetic and experimental time series, from only two time series or a larger dataset with multiple realizations. The proposed approach brings together recurrence plots, information theory, and symbolic dynamics to empower researchers and practitioners with effective means to visualize and quantify interactions in dynamical systems.

Detecting switching leadership in collective motion

Detecting causal relationships in complex systems from the time series of the individual units is a pressing area of research that has attracted the interest of a broad community. As an open area of study, this entails the development of methodologies to unravel causal relationships that evolve over time, such as switching of leader-follower roles in animal groups. Here, we augment the information theoretic measure of transfer entropy to establish a fitness function suitable for optimal partitioning of time series data to robustly detect leadership switches in collective behavior. The fitness function computes the information outflow from any agent in the group and rewards large sample sizes while normalizing with respect to available information. Our results indicate that for information-rich interactions, leadership switches within a group can be detected over relatively short time durations, with more than 90% accuracy. On a real soccer dataset, instances of leadership counted using the proposed approach are interestingly correlated with ball possession.