Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related Field

Graphical models for marked point processes based on local independence

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some (but not necessarily all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non-causality, so that the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, called delta-separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependencies as well as computational simplifications are discussed.Comment: To appear in the Journal of the Royal Statistical Society Series

Algorithms of causal inference for the analysis of effective connectivity among brain regions

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity

An experimental study of the efficiency of optimal control for lifting machines

The article is devoted to the synthesis of optimal speed performance control, in which the Pontryagin maximum principle and the phase-plane method are used to search for switching points of the relay control function. A crane trolley model and computer control system, able to implement the automatic movement of the trolley according to the optimal laws, were developed. The conducted experimental study allowed us to establish that the operating cycle of the traveling mechanism can be reduced by 1.5-3.1 times using optimal speed performance control

Understanding object-oriented source code from the behavioural perspective

Comprehension is a key activity that underpins a variety of software maintenance and engineering tasks. The task of understanding object-oriented systems is hampered by the fact that the code segments that are related to a user-level function tend to be distributed across the system. We introduce a tool-supported code extraction technique that addresses this issue. Given a minimal amount of information about a behavioural element of the system that is of interest (such as a use-case), it extracts a trail of the methods (and method invocations) through the system that are needed in order to achieve an understanding of the implementation of the element of interest. We demonstrate the feasibility of our approach by implementing it as part of a code extraction tool, presenting a case study and evaluating the approach and tool against a set of established criteria for program comprehension tools