In this paper, we propose Deep Data Assimilation (DDA), an integration of Data Assimilation (DA) with Machine Learning (ML). DA is the Bayesian approximation of the true state of some physical system at a given time by combining time-distributed observations with a dynamic model in an optimal way. We use a ML model in order to learn the assimilation process. In particular, a recurrent neural network, trained with the state of the dynamical system and the results of the DA process, is applied for this purpose. At each iteration, we learn a function that accumulates the misfit between the results of the forecasting model and the results of the DA. Subsequently, we compose this function with the dynamic model. This resulting composition is a dynamic model that includes the features of the DA process and that can be used for future prediction without the necessity of the DA. In fact, we prove that the DDA approach implies a reduction of the model error, which decreases at each iteration; this is achieved thanks to the use of DA in the training process. DDA is very useful in that cases when observations are not available for some time steps and DA cannot be applied to reduce the model error. The effectiveness of this method is validated by examples and a sensitivity study. In this paper, the DDA technology is applied to two different applications: the Double integral mass dot system and the Lorenz system. However, the algorithm and numerical methods that are proposed in this work can be applied to other physics problems that involve other equations and/or state variables.

No abstract

Many functional magnetic resonance imaging (fMRI) studies have indicated that Granger causality analysis (GCA) is a suitable method for revealing causal effects between brain regions. The purpose of the present study was to identify neuroimaging biomarkers with a high sensitivity to amnestic mild cognitive impairment (aMCI). The resting-state fMRI data of 30 patients with Alzheimer's disease (AD), 14 patients with aMCI, and 18 healthy controls (HC) were evaluated using GCA. This study focused on the "triple networks" concept, a recently proposed higher-order functioning-related brain network model that includes the default-mode network (DMN), salience network (SN), and executive control network (ECN). As expected, GCA techniques were able to reveal differences in connectivity in the three core networks among the three patient groups. The fMRI data were pre-processed using DPARSFA v2.3 and REST v1.8. Voxel-wise GCA was performed using the REST-GCA in the REST toolbox. The directed (excitatory and inhibitory) connectivity obtained from GCA could differentiate among the AD, aMCI and HC groups. This result suggests that analysing the directed connectivity of inter-hemisphere connections represents a sensitive method for revealing connectivity changes observed in patients with aMCI. Specifically, inhibitory within-DMN connectivity from the posterior cingulate cortex (PCC) to the hippocampal formation and from the thalamus to the PCC as well as excitatory within-SN connectivity from the dorsal anterior cingulate cortex (dACC) to the striatum, from the ECN to the DMN, and from the SN to the ECN demonstrated that changes in connectivity likely reflect compensatory effects in aMCI. These findings suggest that changes observed in the triple networks may be used as sensitive neuroimaging biomarkers for the early detection of aMCI.

Background: Alzheimer's disease (AD) is a progressive neurodegenerative disease characterized by memory impairment. Previous studies have largely focused on alterations of static brain activity occurring in patients with AD. Few studies to date have explored the characteristics of dynamic brain activity in cognitive impairment, and their predictive ability in AD patients.Methods: One hundred and eleven AD patients, 29 MCI patients, and 73 healthy controls (HC) were recruited. The dynamic amplitude of low-frequency fluctuation (dALFF) and the dynamic fraction amplitude of low-frequency fluctuation (dfALFF) were used to assess the temporal variability of local brain activity in patients with AD or mild cognitive impairment (MCI). Pearson's correlation coefficients were calculated between the metrics and subjects' behavioral scores. Results:The results of analysis of variance indicated that the AD, MCI, and HC groups showed significant variability of dALFF in the cerebellar posterior and middle temporal lobes. In AD patients, these brain regions had high dALFF variability. Significant dfALFF variability was found between the three groups in the left calcarine cortex and white matter. The AD group showed lower dfALFF than the MCI group in the left calcarine cortex.Conclusions: Compared to HC, AD patients were found to have increased dALFF variability in the cerebellar posterior and temporal lobes. This abnormal pattern may diminish the capacity of the cerebellum and temporal lobes to participate in the cerebrocerebellar circuits and default mode network (DMN), which regulate cognition and emotion in AD. The findings above indicate that the analysis of dALFF and dfALFF based on functional magnetic resonance imaging data may give a new insight into the neurophysiological mechanisms of AD.

The purpose of this study was to explore the differences in interhemispheric functional connectivity in patients with Alzheimer's disease (AD) and amnestic mild cognitive impairment (aMCI) based on a triple network model consisting of the default mode network (DMN), salience network (SN), and executive control network (ECN). The technique of voxel-mirrored homotopic connectivity (VMHC) analysis was applied to explore the aberrant connectivity of all patients. The results showed that: (1) the statistically significant connections of interhemispheric brain regions included DMN-related brain regions (i.e. precuneus, calcarine, fusiform, cuneus, lingual gyrus, temporal inferior gyrus, and hippocampus), SN-related brain regions (i.e. frontoinsular cortex), and ECN-related brain regions (i.e. frontal middle gyrus and frontal inferior); (2) the precuneus and frontal middle gyrus in the AD group exhibited lower VMHC values than those in the aMCI and healthy control (HC) groups, but no significant difference was observed between the aMCI and HC groups; and (3) significant correlations were found between peak VMHC results from the precuneus and Mini Mental State Examination (MMSE) and Montreal Cognitive Scale (MOCA) scores and their factor scores in the AD, aMCI, and AD plus aMCI groups, and between the results from the frontal middle gyrus and MOCA factor scores in the aMCI group. These findings indicated that impaired interhemispheric functional connectivity was observed in AD and could be a sensitive neuroimaging biomarker for AD. More specifically, the DMN was inhibited, while the SN and ECN were excited. VMHC results were correlated with MMSE and MOCA scores, highlighting that VMHC could be a sensitive neuroimaging biomarker for AD and the progression from aMCI to AD.