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- Creators: Bliss, Daniel
Description
With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series approaches that remove trends, cycles, and serial dependency have been used. These analyses permit the study of the relationship between random shocks (perturbations) in the presumed causal series and changes in the outcome series, but do not permit the study of the relationships between cycles. Liu and West (2016) proposed a multilevel approach that permitted the study of potential between subject relationships between features of the cycles in two series (e.g., amplitude). However, I show that the application of the Liu and West approach is restricted to a small set of features and types of relationships between the series. Several authors (e.g., Boker & Graham, 1998) proposed a connected mass-spring model that appears to permit modeling of more general cyclic relationships. I showed that the undamped connected mass-spring model is also limited and may be unidentified. To test the severity of the restrictions of the motion trajectories producible by the undamped connected mass-spring model I mathematically derived their connection to the force equations of the undamped connected mass-spring system. The mathematical solution describes the domain of the trajectory pairs that are producible by the undamped connected mass-spring model. The set of producible trajectory pairs is highly restricted, and this restriction sets major limitations on the application of the connected mass-spring model to psychological data. I used a simulation to demonstrate that even if a pair of psychological time-varying variables behaved exactly like two masses in an undamped connected mass-spring system, the connected mass-spring model would not yield adequate parameter estimates. My simulation probed the performance of the connected mass-spring model as a function of several aspects of data quality including number of subjects, series length, sampling rate relative to the cycle, and measurement error in the data. The findings can be extended to damped and nonlinear connected mass-spring systems.
ContributorsMartynova, Elena (M.A.) (Author) / West, Stephen G. (Thesis advisor) / Amazeen, Polemnia (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2019
Description
The power of science lies in its ability to infer and predict the
existence of objects from which no direct information can be obtained
experimentally or observationally. A well known example is to
ascertain the existence of black holes of various masses in different
parts of the universe from indirect evidence, such as X-ray emissions.
In the field of complex networks, the problem of detecting
hidden nodes can be stated, as follows. Consider a network whose
topology is completely unknown but whose nodes consist of two types:
one accessible and another inaccessible from the outside world. The
accessible nodes can be observed or monitored, and it is assumed that time
series are available from each node in this group. The inaccessible
nodes are shielded from the outside and they are essentially
``hidden.'' The question is, based solely on the
available time series from the accessible nodes, can the existence and
locations of the hidden nodes be inferred? A completely data-driven,
compressive-sensing based method is developed to address this issue by utilizing
complex weighted networks of nonlinear oscillators, evolutionary game
and geospatial networks.
Both microbes and multicellular organisms actively regulate their cell
fate determination to cope with changing environments or to ensure
proper development. Here, the synthetic biology approaches are used to
engineer bistable gene networks to demonstrate that stochastic and
permanent cell fate determination can be achieved through initializing
gene regulatory networks (GRNs) at the boundary between dynamic
attractors. This is experimentally realized by linking a synthetic GRN
to a natural output of galactose metabolism regulation in yeast.
Combining mathematical modeling and flow cytometry, the
engineered systems are shown to be bistable and that inherent gene expression
stochasticity does not induce spontaneous state transitioning at
steady state. By interfacing rationally designed synthetic
GRNs with background gene regulation mechanisms, this work
investigates intricate properties of networks that illuminate possible
regulatory mechanisms for cell differentiation and development that
can be initiated from points of instability.
existence of objects from which no direct information can be obtained
experimentally or observationally. A well known example is to
ascertain the existence of black holes of various masses in different
parts of the universe from indirect evidence, such as X-ray emissions.
In the field of complex networks, the problem of detecting
hidden nodes can be stated, as follows. Consider a network whose
topology is completely unknown but whose nodes consist of two types:
one accessible and another inaccessible from the outside world. The
accessible nodes can be observed or monitored, and it is assumed that time
series are available from each node in this group. The inaccessible
nodes are shielded from the outside and they are essentially
``hidden.'' The question is, based solely on the
available time series from the accessible nodes, can the existence and
locations of the hidden nodes be inferred? A completely data-driven,
compressive-sensing based method is developed to address this issue by utilizing
complex weighted networks of nonlinear oscillators, evolutionary game
and geospatial networks.
Both microbes and multicellular organisms actively regulate their cell
fate determination to cope with changing environments or to ensure
proper development. Here, the synthetic biology approaches are used to
engineer bistable gene networks to demonstrate that stochastic and
permanent cell fate determination can be achieved through initializing
gene regulatory networks (GRNs) at the boundary between dynamic
attractors. This is experimentally realized by linking a synthetic GRN
to a natural output of galactose metabolism regulation in yeast.
Combining mathematical modeling and flow cytometry, the
engineered systems are shown to be bistable and that inherent gene expression
stochasticity does not induce spontaneous state transitioning at
steady state. By interfacing rationally designed synthetic
GRNs with background gene regulation mechanisms, this work
investigates intricate properties of networks that illuminate possible
regulatory mechanisms for cell differentiation and development that
can be initiated from points of instability.
ContributorsSu, Ri-Qi (Author) / Lai, Ying-Cheng (Thesis advisor) / Wang, Xiao (Thesis advisor) / Bliss, Daniel (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Arizona State University (Publisher)
Created2015