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ABSTRACT Schizophrenia (SZ) patients exhibit abnormal static and dynamic functional connectivity across various brain domains. We present a novel approach based on static and dynamic inter‐network connectivity entropy (ICE), which represents the entropy of a given network's connectivity to all the other brain networks. This novel approach enables the investigation of how connectivity strength is heterogeneously distributed across available targets in both SZ patients and healthy controls. We analyzed fMRI data from 151 SZ patients and 160 demographically matched healthy controls (HC). Our assessment encompassed both static and dynamic ICE, revealing significant differences in the heterogeneity of connectivity levels across available functional brain networks between SZ patients and HC. These networks are associated with subcortical (SC), auditory (AUD), sensorimotor (SM), visual (VIS), cognitive control (CC), default mode network (DMN), and cerebellar (CB) functional brain domains. Elevated ICE observed in individuals with SZ suggests that patients exhibit significantly higher randomness in the distribution of time‐varying connectivity strength across functional regions from each source network, compared to HC. C‐means fuzzy clustering analysis of functional ICE correlation matrices revealed that SZ patients exhibit significantly higher occupancy weights in clusters with weak, low‐scale functional entropy correlation, while the control group shows greater occupancy weights in clusters with strong, large‐scale functional entropy correlation. K‐means clustering analysis on time‐indexed ICE vectors revealed that cluster with highest ICE have higher occupancy rates in SZ patients whereas clusters characterized by lowest ICE have larger occupancy rates for control group. Furthermore, our dynamic ICE approach revealed that in HC, the brain primarily communicates through complex, less structured connectivity patterns, with occasional transitions into more focused patterns. Individuals with SZ are significantly less likely to attain these more focused and structured transient connectivity patterns. The proposed ICE measure presents a novel framework for gaining deeper insight into mechanisms of healthy and diseased brain states and represents a useful step forward in developing advanced methods to help diagnose mental health conditions.
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Occupancy times for time-dependent stage-structured models
Abstract During their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in a recent paper by Roth and Caswell for cases where the environmental conditions are constant. However, it is truly important to consider the case where environments are changing randomly or in directional way through time, so the transition probabilities between different states change over time, motivating the use of time-dependent stage-structured models. Using absorbing inhomogenous Markov chains and the discrete-time McKendrick–von Foerster equation, we derive explicit formulas for the occupancy time, its expectation, and its higher-order moments for stage-structured models with time-dependent transition rates. The results provide insights into the dynamics of long lived plant or animal populations where individuals transition in both directions between reproductive and non reproductive stages. We apply our approach to study a specific time-dependent model of the Southern Fulmar, and obtain insights into how the number of breeding attempts depends on external conditions that vary through time.
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- Award ID(s):
- 1817124
- PAR ID:
- 10363068
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Journal of Mathematical Biology
- Volume:
- 84
- Issue:
- 3
- ISSN:
- 0303-6812
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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