Generalized Newton's Method based on Graphical Derivatives

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and $B$-differentiable versions of Newton's method for nonsmooth Lipschitzian equations

Gender differences in a Drosophila transcriptomic model of chronic pentylenetetrazole induced behavioral deficit

A male Drosophila model of locomotor deficit induced by chronic pentylenetetrazole (PTZ), a proconvulsant used to model epileptogenesis in rodents, has recently been described. Antiepileptic drugs (AEDs) ameliorate development of this behavioral abnormality. Time-series of microarray profiling of heads of male flies treated with PTZ has shown epileptogenesis-like transcriptomic perturbation in the fly model. Gender differences are known to exist in neurological and psychiatric conditions including epileptogenesis. We describe here the effects of chronic PTZ in Drosophila females, and compare the results with the male model. As in males, chronic PTZ was found found to cause a decreased climbing speed in females. In males, overrepresentation of Wnt, MAPK, TGF-beta, JAK-STAT, Cell communication, and Dorso-Ventral axis formation pathways in downregulated genes was previously described. Of these, female genes showed enrichment only for Dorso-Ventral axis formation. Most significant, ribosomal pathway was uniquely overrepresented in genes downregulated in females. Gender differences thus exist in the Drosophila model. Gender neutral, Dorso-Ventral axis formation may be considered as the candidate causal pathway in chronic pentylenetetrazole induced behavioral deficit. Prior evidence of developmental mechanisms in epileptogenesis underscores the usefulness of fly model. Gender specific pathways may provide a lead for understanding brain dimorphism in neuropsychiatric disorders

Computational Modelling of Brain Network Dynamics in Psychotic and Affective Disorders

This dissertation explores the role of dynamic functional connectivity (dFC) as an intermediate phenotype linking neurobiological characteristics and clinical outcomes in psychotic and affective disorders. The thesis aims to reveal alterations in dFC in psychotic and affective patients, study the impact of neurobiology on static and dynamic FC patterns, and identify neurobiological processes which might contribute to static and dynamic FC changes in psychotic and affective disorder. Study I, which compared dFC patterns of patients with recent-onset psychosis (ROP), patients with recent-onset depression (ROD), individuals with a clinical high risk for psychosis (CHR), and healthy individuals, found diagnosis-specific alterations in ROP and ROD patients as well as transdiagnostic alterations exhibited by all patient groups. We also identified a dFC pattern which was significantly correlated with psychosis symptom severity across the patient groups. Study II investigated the relationship between neurobiological characteristics and static and dynamic FC using brain network modelling, identifying FC correlates of global coupling and excitatory synaptic coupling, as well as model fits. In addition, this study investigated the effect of altering regional model parameters on global FC, showing that distinct small subsets of regions produced outsized effects on static and dynamic FC and regional effects were correlated with network structure. Study III employed brain network modelling of static and dynamic FC to reveal an increase in regional recurrent excitation in CHR individuals and ROD patients compared to healthy controls and ROP patients. Integrating the findings from these three studies, this dissertation contributes to the understanding of the role of dFC in psychotic and affective disorders, providing evidence for neurobiological underpinnings and clinical consequences of alterations to dFC