We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in graph data analysis. In particular, we focus on the capacity of these features to retain informative variability and relations in the data (e.g., between individual graphs, or in aggregate), while relating our construction to previous theoretical results that establish the stability of similar transforms to families of graph deformations. We demonstrate the application the our geometric scattering features in graph classification of social network data, and in data exploration of biochemistry data.
Anredera cordifolia, a climber and member of the Basellaceae family, has long been a traditional medicine used for the treatment of hyperglycemia in China. Two water-soluble polysaccharides, ACP1-1 and ACP2-1, were isolated from A. cordifolia seeds by hot water extraction. The two fractions, ACP1-1 and ACP2-1 with molecular weights of 46.78 kDa ± 0.03 and 586.8 kDa ± 0.05, respectively, were purified by chromatography. ACP1-1 contained mannose, glucose, galactose in a molar ratio of 1.08:4.65:1.75, whereas ACP2-1 contained arabinose, ribose, galactose, glucose, mannose in a molar ratio of 0.9:0.4:0.5:1.2:0.9. Based on methylation analysis, ultraviolet and Fourier transform-infrared spectroscopy, and periodate oxidation the main backbone chain of ACP1-1 contained (1→3,6)-galacturonopyranosyl residues interspersed with (1→4)-residues and (1→3)-mannopyranosyl residues. The main backbone chain of ACP2-1 contained (1→3)-galacturonopyranosyl residues interspersed with (1→4)-glucopyranosyl residues.
It is well known that individuals experience difficulties with depressive symptoms and functional status after traumatic brain injury. However, it is unclear what the relationship is between these 2 phenomena and whether there is a biological explanation for. In this secondary analysis, we examined whether depressive symptoms explained postinjury functional status and whether chronic stress and salivary cortisol influenced this relationship. Participants included 75 persons within 24 months of their injury dates who were evaluated or treated in specialty clinics. All participants and a family member or significant other completed survey data, and 50 of the participants provided cortisol data. Results indicated that chronic stress, measured using Cohen's Perceived Stress Scale, completely mediated the relationship between depressive symptoms, measured using the Center for Epidemiological Studies Depression Scale, and psychological functioning, measured using the Patient Competency Rating Scale. Furthermore, those who provided cortisol data displayed hypocortisolemia in their 12-hr profile. Results from this analysis suggest that interventions focused on addressing the chronic stress experience may be important in limiting depressive symptoms and improving psychological functioning. Longitudinal study of this phenomenon is required to understand the progression of chronic stress after traumatic brain injury.
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