Information theory has long been used to quantify interactions between two variables. With the rise of complex systems research, multivariate information measures have been increasingly used to investigate interactions between groups of three or more variables, often with an emphasis on so called synergistic and redundant interactions. While bivariate information measures are commonly agreed upon, the multivariate information measures in use today have been developed by many different groups, and differ in subtle, yet significant ways. Here, we will review these multivariate information measures with special emphasis paid to their relationship to synergy and redundancy, as well as examine the differences between these measures by applying them to several simple model systems. In addition to these systems, we will illustrate the usefulness of the information measures by analyzing neural spiking data from a dissociated culture through early stages of its development. Our aim is that this work will aid other researchers as they seek the best multivariate information measure for their specific research goals and system. Finally, we have made software available online which allows the user to calculate all of the information measures discussed within this paper.

Summary Source memory is a representation of the origin (source) of information. When source information is bound together, it makes a memory episodic, allowing us to differentiate one event from another [1, 2]. Here we asked if rats remember the source of encoded information. Rats foraged for distinctive flavors of food that replenished (or failed to replenish) at its recently encountered location according to a source-information rule. To predict replenishment, rats needed to remember where they had encountered a preferred food type (chocolate) with self-generated (walking along a runway encountering chocolate) or experimenter-generated (placement of the rat at the chocolate site by an experimenter) cues. Three lines of evidence implicate the presence of source memory. First, rats selectively adjusted revisits to the chocolate location based on source information, under conditions in which familiarity of events could not produce successful performance. Second, source memory was dissociated from location memory by different decay rates. Third, temporary inactivation of the CA3 region of the hippocampus with lidocaine selectively eliminated source memory, suggesting that source memory is dependent upon an intact hippocampus. Development of an animal model of source memory may be valuable to probe the biological underpinnings of memory disorders marked by impairments in source memory.

Understanding the mechanisms of distributed computation in cellular automata requires techniques for characterizing the emergent structures that underlie information processing in such systems. Recently, techniques from information theory have been brought to bear on this problem. Building on this work, we utilize the new technique of partial information decomposition to show that previous information-theoretic measures can confound distinct sources of information. We then propose a new set of filters and demonstrate that they more cleanly separate out the background domains, particles, and collisions that are typically associated with information storage, transfer, and modification in cellular automata.

Source memory represents the origin (source) of information. Recently, we proposed that rats (Rattus norvegicus) remember the source of information. However, an alternative to source memory is the possibility that rats selectively encoded some, but not all, information rather than retrieving an episodic memory. We directly tested this 'encoding failure' hypothesis. Here, we show that rats remember the source of information, under conditions that cannot be attributed to encoding failure. Moreover, source memory lasted at least seven days but was no longer present 14 days after studying. Our findings suggest that long-lasting source memory may be modelled in non-humans. Our model should facilitate attempts to elucidate the biological underpinnings of source memory impairments in human memory disorders such as Alzheimer's disease.