Detecting time lag between a pair of time series using visibility graph algorithm.

Estimating the time lag between a pair of time series is of significance in many practical applications. In this article, we introduce a method to quantify such lags by adapting the visibility graph algorithm, which converts time series into a mathematical graph. Currently widely used method to detect such lags is based on cross-correlations, which has certain limitations. We present simulated examples where the new method identifies the lag correctly and unambiguously while as the cross-correlation method does not. The article includes results from an extensive simulation study conducted to better understand the scenarios where the new method performed better or worse than the existing approach. We also present a likelihood based parametric modeling framework and consider frameworks for quantifying uncertainty and hypothesis testing for the new approach. We apply the current and new methods to two case studies, one from neuroscience and the other from environmental epidemiology, to illustrate the methods further.

Estimation of Dynamic Bivariate Correlation Using a Weighted Graph Algorithm.

Dynamic correlation is the correlation between two time series across time. Two approaches that currently exist in neuroscience literature for dynamic correlation estimation are the sliding window method and dynamic conditional correlation. In this paper, we first show the limitations of these two methods especially in the presence of extreme values. We present an alternate approach for dynamic correlation estimation based on a weighted graph and show using simulations and real data analyses the advantages of the new approach over the existing ones. We also provide some theoretical justifications and present a framework for quantifying uncertainty and testing hypotheses.

The Hippocampus and Dorsolateral Striatum Integrate Distinct Types of Memories through Time and Space, Respectively.

Several decades of research have established that different kinds of memories result from the activity of discrete neural networks. Studying how these networks process information in experiments that target specific types of mnemonic representations has provided deep insights into memory architecture and its neural underpinnings. However, in natural settings reality confronts organisms with problems that are not neatly compartmentalized. Thus, a critical problem in memory research that still needs to be addressed is how distinct types of memories are ultimately integrated. Here we demonstrate how two memory networks, the hippocampus and dorsolateral striatum, may accomplish such a goal. The hippocampus supports memory for facts and events, collectively known as declarative memory and often studied as spatial memory in rodents. The dorsolateral striatum provides the basis for habits that are assessed in stimulus-response types of tasks. Expanding previous findings, the current work revealed that in male Long-Evans rats, the hippocampus and dorsolateral striatum use time and space in distinct and largely complementary ways to integrate spatial and habitual representations. Specifically, the hippocampus supported both types of memories when they were formed in temporal juxtaposition, even if the learning took place in different environments. In contrast, the lateral striatum supported both types of memories if they were formed in the same environment, even at temporally distinct points. These results reveal for the first time that by using fundamental aspects of experience in specific ways, the hippocampus and dorsolateral striatum can transcend their attributed roles in information storage.SIGNIFICANCE STATEMENT The current paradigm in memory research postulates that different types of memories reflected in separate types of behavioral strategies result from activity in distinct neural circuits. However, recent data have shown that when rats concurrently acquired in the same environment of hippocampal-dependent spatial navigation and striatal-dependent approach of a visual cue, each of the two types of memories became dependent on both the hippocampus and dorsolateral striatum. The current work reveals that the hippocampus and dorsolateral striatum use distinct and complementary principles to integrate different types of memories in time and space: the hippocampus integrates memories formed in temporal proximity, while the lateral striatum integrates memories formed in the same space.

Correction to: graph analysis of structural brain networks in Alzheimer's disease: beyond small world properties.

The original version of the article contained an error in the electronic supplementary material. The caption of the figure in the electronic supplementary material was omitted.

Place cell firing cannot support navigation without intact septal circuits.

Though it has been known for over half a century that interference with the normal activity of septohippocampal neurons can abolish hippocampal theta rhythmicity, a definitive answer to the question of its function has remained elusive. To clarify the role of septal circuits and theta in location-specific activity of place cells and spatial behavior, three drugs were delivered to the medial septum of rats: Tetracaine, a local anesthetic; muscimol, a GABA-A agonist; and gabazine, a GABA-A antagonist. All three drugs disrupted normal oscillatory activity in the hippocampus. However, tetracaine and muscimol both reduced spatial firing and interfered with the rat's ability to navigate to a hidden goal. After gabazine, location-specific firing was preserved in the absence of theta, but rats were unable to accurately locate the hidden goal. These results indicate that theta is unnecessary for location-specific firing of hippocampal cells, and that place cell activity cannot support accurate navigation when septal circuits are disrupted.

Graph analysis of structural brain networks in Alzheimer's disease: beyond small world properties.

Changes in brain connectivity in patients with early Alzheimer's disease (AD) have been investigated using graph analysis. However, these studies were based on small data sets, explored a limited range of network parameters, and did not focus on more restricted sub-networks, where neurodegenerative processes may introduce more prominent alterations. In this study, we constructed structural brain networks out of 87 regions using data from 135 healthy elders and 100 early AD patients selected from the Open Access Series of Imaging Studies (OASIS) database. We evaluated the graph properties of these networks by investigating metrics of network efficiency, small world properties, segregation, product measures of complexity, and entropy. Because degenerative processes take place at different rates in different brain areas, analysis restricted to sub-networks may reveal changes otherwise undetected. Therefore, we first analyzed the graph properties of a network encompassing all brain areas considered together, and then repeated the analysis after dividing the brain areas into two sub-networks constructed by applying a clustering algorithm. At the level of large scale network, the analysis did not reveal differences between AD patients and controls. In contrast, the same analysis performed on the two sub-networks revealed that small worldness diminished with AD only in the sub-network containing the areas of medial temporal lobe known to be heaviest and earliest affected. The second sub-network, which did not present significant AD-induced modifications of 'classical' small world parameters, nonetheless showed a trend towards an increase in small world propensity, a novel metric that unbiasedly quantifies small world structure. Beyond small world properties, complexity and entropy measures indicated that the intricacy of connection patterns and structural diversity decreased in both sub-networks. These results show that neurodegenerative processes impact volumetric networks in a non-global fashion. Our findings provide new quantitative insights into topological principles of structural brain networks and their modifications during early stages of Alzheimer's disease.

Applications of temporal kernel canonical correlation analysis in adherence studies.

Adherence to medication is often measured as a continuous outcome but analyzed as a dichotomous outcome due to lack of appropriate tools. In this paper, we illustrate the use of the temporal kernel canonical correlation analysis (tkCCA) as a method to analyze adherence measurements and symptom levels on a continuous scale. The tkCCA is a novel method developed for studying the relationship between neural signals and hemodynamic response detected by functional MRI during spontaneous activity. Although the tkCCA is a powerful tool, it has not been utilized outside the application that it was originally developed for. In this paper, we simulate time series of symptoms and adherence levels for patients with a hypothetical brain disorder and show how the tkCCA can be used to understand the relationship between them. We also examine, via simulations, the behavior of the tkCCA under various missing value mechanisms and imputation methods. Finally, we apply the tkCCA to a real data example of psychotic symptoms and adherence levels obtained from a study based on subjects with a first episode of schizophrenia, schizophreniform or schizoaffective disorder.

Contributions of Hippocampus and Striatum to Memory-Guided Behavior Depend on Past Experience.

UNLABELLED: The hippocampal and striatal memory systems are thought to operate independently and in parallel in supporting cognitive memory and habits, respectively. Much of the evidence for this principle comes from double dissociation data, in which damage to brain structure A causes deficits in Task 1 but not Task 2, whereas damage to structure B produces the reverse pattern of effects. Typically, animals are explicitly trained in one task. Here, we investigated whether this principle continues to hold when animals concurrently learn two types of tasks. Rats were trained on a plus maze in either a spatial navigation or a cue-response task (sequential training), whereas a third set of rats acquired both (concurrent training). Subsequently, the rats underwent either sham surgery or neurotoxic lesions of the hippocampus (HPC), medial dorsal striatum (DSM), or lateral dorsal striatum (DSL), followed by retention testing. Finally, rats in the sequential training condition also acquired the novel "other" task. When rats learned one task, HPC and DSL selectively supported spatial navigation and cue response, respectively. However, when rats learned both tasks, HPC and DSL additionally supported the behavior incongruent with the processing style of the corresponding memory system. Thus, in certain conditions, the hippocampal and striatal memory systems can operate cooperatively and in synergism. DSM significantly contributed to performance regardless of task or training procedure. Experience with the cue-response task facilitated subsequent spatial learning, whereas experience with spatial navigation delayed both concurrent and subsequent response learning. These findings suggest that there are multiple operational principles that govern memory networks. SIGNIFICANCE STATEMENT: Currently, we distinguish among several types of memories, each supported by a distinct neural circuit. The memory systems are thought to operate independently and in parallel. Here, we demonstrate that the hippocampus and the dorsal striatum memory systems operate independently and in parallel when rats learn one type of task at a time, but interact cooperatively and in synergism when rats concurrently learn two types of tasks. Furthermore, new learning is modulated by past experiences. These results can be explained by a model in which independent and parallel information processing that occurs in the separate memory-related neural circuits is supplemented by information transfer between the memory systems at the level of the cortex.

Relative contributions of CA3 and medial entorhinal cortex to memory in rats.

The hippocampal CA1 field processes spatial information, but the relative importance of intra- vs. extra-hippocampal sources of input into CA1 for spatial behavior is unclear. To characterize the relative roles of these two sources of input, originating in the hippocampal field CA3 and in the medial entorhinal cortex (MEC), we studied effects of discrete neurotoxic lesions of CA3 or MEC on concurrent spatial and nonspatial navigation tasks, and on synaptic transmission in afferents to CA1. Lesions in CA3 or MEC regions that abolished CA3-CA1, or reduced MEC-CA1 synaptic transmission, respectively, impaired spatial navigation and unexpectedly interfered with cue response, suggesting that in certain conditions of training regimen, hippocampal activity may influence behavior otherwise supported by nonhippocampal neural networks. MEC lesions had milder and temporary behavioral effects, but also markedly amplified transmission in the CA3-CA1 pathway. Extensive behavioral training had a similar, but more modest effect on CA3-CA1 transmission. Thus, cortical input to the hippocampus modulates CA1 activity both directly and indirectly, through heterosynaptic interaction, to control information flow in the hippocampal loop. Following damage to hippocampal cortical input, the functional coupling of separate intra- and extra-hippocampal inputs to CA1 involved in normal learning may initiate processes that support recovery of behavioral function. Such a process may explain how CA3 lesions, which do not significantly modify the basic features of CA1 neural activity, nonetheless impair spatial recall, whereas lesions of EC input to CA1, which reduce the spatial selectivity of CA1 firing in foraging rats, have only mild effects on spatial navigation.

Memory modulates journey-dependent coding in the rat hippocampus.

Neurons in the rat hippocampus signal current location by firing in restricted areas called place fields. During goal-directed tasks in mazes, place fields can also encode past and future positions through journey-dependent activity, which could guide hippocampus-dependent behavior and underlie other temporally extended memories, such as autobiographical recollections. The relevance of journey-dependent activity for hippocampal-dependent memory, however, is not well understood. To further investigate the relationship between hippocampal journey-dependent activity and memory, we compared neural firing in rats performing two mnemonically distinct but behaviorally identical tasks in the plus maze: a hippocampus-dependent spatial navigation task and a hippocampus-independent cue response task. While place, prospective, and retrospective coding reflected temporally extended behavioral episodes in both tasks, memory strategy altered coding differently before and after the choice point. Before the choice point, when discriminative selection of memory strategy was critical, a switch between the tasks elicited a change in a field's coding category, so that a field that signaled current location in one task coded pending journeys in the other task. After the choice point, however, when memory strategy became irrelevant, the fields preserved coding categories across tasks, so that the same field consistently signaled either current location or the recent journeys. Additionally, on the start arm, firing rates were affected at comparable levels by task and journey; on the goal arm, firing rates predominantly encoded journey. The data demonstrate a direct link between journey-dependent coding and memory and suggest that episodes are encoded by both population and firing rate coding.

Representing episodes in the mammalian brain.

Memory lets the past inform the present so that we can attain future goals. In many species, these abilities require the hippocampus. Recent experiments, in which memory demand was varied while overt behavior and the environment were kept constant, have revealed firing patterns of hippocampal neurons that corresponded with memory demands and predicted performance. Although the active population appeared to be 'place cells' that signalled location, it actually included cells the activity patterns of which distinguished the recent or pending history of behavior during identical actions that occurred in the same place. Different populations of hippocampal cells fired as a rat walked along the same spatial path on the way to different goals, and coded past, present and pending events. Other experiments provide converging data that neuronal activity is modulated by goal-directed behavioral episodes. Together, these firing patterns suggest a testable mechanism of episodic memory coding: that hippocampal dynamics encode a temporally extended, hierarchically organized representation of goal-directed behavior.

Episodic memory--from brain to mind.

Neuronal mechanisms of episodic memory, the conscious recollection of autobiographical events, are largely unknown because electrophysiological studies in humans are conducted only in exceptional circumstances. Unit recording studies in animals are thus crucial for understanding the neurophysiological substrate that enables people to remember their individual past. Two features of episodic memory--autonoetic consciousness, the self-aware ability to "travel through time", and one-trial learning, the acquisition of information in one occurrence of the event--raise important questions about the validity of animal models and the ability of unit recording studies to capture essential aspects of memory for episodes. We argue that autonoetic experience is a feature of human consciousness rather than an obligatory aspect of memory for episodes, and that episodic memory is reconstructive and thus its key features can be modeled in animal behavioral tasks that do not involve either autonoetic consciousness or one-trial learning. We propose that the most powerful strategy for investigating neurophysiological mechanisms of episodic memory entails recording unit activity in brain areas homologous to those required for episodic memory in humans (e.g., hippocampus and prefrontal cortex) as animals perform tasks with explicitly defined episodic-like aspects. Within this framework, empirical data suggest that the basic structure of episodic memory is a temporally extended representation that distinguishes the beginning from the end of an event. Future research is needed to fully understand how neural encodings of context, sequences of items/events, and goals are integrated within mnemonic representations of autobiographical events.

Relative spike timing in pairs of hippocampal neurons distinguishes the beginning and end of journeys.

Episodic memory organizes experience in time, so that we can review past events and anticipate the future. In a hippocampus-dependent memory task, spike timing in pairs of simultaneously active CA1 neurons with overlapping place fields distinguished the start and end of trials. At the common starting point of different journeys, the relative spike timing of the neurons was highly correlated. As the rat approached a common goal from different starting points, however, temporal firing patterns were strongly modulated across journeys even if the cells fired in the same spatial locations within fields, implying that different processes influenced when and where cells fire. Spike timing within hippocampal ensembles may thereby help parse the beginning from the end of episodes in memory.

Prospective and retrospective memory coding in the hippocampus.

The effect of memory on hippocampal neuronal activity was assessed as rats performed a spatial task that was impaired by fornix lesions. The influences of current location, recently entered places, and places about to be entered were compared. Three new findings emerged. (1) Current, retrospective, and prospective coding were common and recorded simultaneously in neural ensembles. (2) The origin of journeys influenced firing even when rats made detours, showing that recent memory could modulate neuronal activity more than spatial trajectory. (3) Diminished retrospective coding and, more markedly, reduced prospective coding in error trials suggested that the neuronal signal was important for task performance. The population of hippocampal neurons thus encoded information about the recent past, the present, and the imminent future, consistent with a neuronal mechanism for episodic memory.

Both dorsal and ventral hippocampus contribute to spatial learning in Long-Evans rats.

The hippocampus (HPC) may be functionally heterogeneous in supporting spatial learning in rats. Thus, dorsal but not ventral HPC lesions have been reported to impair acquisition in the Morris water task which consists of finding a submerged platform in a pool filled with opaque water. To further investigate the functional differences between dorsal and ventral HPC regions, we used a one-trial matching to position water task in which the submerged platform occupied a different position during each session. This task is very sensitive to HPC damage. The results show that either dorsal or ventral HPC NMDA lesions disrupt the rapid acquisition of new place information. The acquisition deficit diminishes with training in both lesion groups. The data thus suggest that the entire HPC axis is involved in acquisition of spatial information.