Joint research with McDonnell Douglas Corporation

Issued as Reports [nos. 1-3], Project no. G-37-61

Analysis of EM scattering from curved surfaces

Issued as Progress report, Report, and Final report, Project no. G-37-641Library lacks diskett

Locally one dimensional numerical methods for multidimensional free surface problems

Issued as Progress reports no. [1-4], and Final report, Project no. G-37-61

Mathematical sciences : the method of lines for multi-dimensional free boundary problems

Issued as Progress report, and Final report, Project no. G-37-60

The Evaluation Of Barrier Option Prices Under Stochastic Volatility

This paperc onsiders the problem o fnumerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to effciently handle bothc ontinuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.barrier option; stochastic volatility; continuously monitored; discretely monitored; free boundary problem; method of lines; Monte Carlo simulation

The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer (1998) for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen & Toivanen (2007). The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation which is taken as the benchmark. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines

SK channel-mediated metabolic escape to glycolysis inhibits ferroptosis and supports stress resistance in C. elegans

Metabolic flexibility is an essential characteristic of eukaryotic cells in order to adapt to physiological and environmental changes. Especially in mammalian cells, the metabolic switch from mitochondrial respiration to aerobic glycolysis provides flexibility to sustain cellular energy in pathophysiological conditions. For example, attenuation of mitochondrial respiration and/or metabolic shifts to glycolysis result in a metabolic rewiring that provide beneficial effects in neurodegenerative processes. Ferroptosis, a non-apoptotic form of cell death triggered by an impaired redox balance is gaining attention in the field of neurodegeneration. We showed recently that activation of small-conductance calcium-activated K+ (SK) channels modulated mitochondrial respiration and protected neuronal cells from oxidative death. Here, we investigated whether SK channel activation with CyPPA induces a glycolytic shift thereby increasing resilience of neuronal cells against ferroptosis, induced by erastin in vitro and in the nematode C. elegans exposed to mitochondrial poisons in vivo. High-resolution respirometry and extracellular flux analysis revealed that CyPPA, a positive modulator of SK channels, slightly reduced mitochondrial complex I activity, while increasing glycolysis and lactate production. Concomitantly, CyPPA rescued the neuronal cells from ferroptosis, while scavenging mitochondrial ROS and inhibiting glycolysis reduced its protection. Furthermore, SK channel activation increased survival of C. elegans challenged with mitochondrial toxins. Our findings shed light on metabolic mechanisms promoted through SK channel activation through mitohormesis, which enhances neuronal resilience against ferroptosis in vitro and promotes longevity in vivo

A Tapestry Of Educational Technology Women Leaders In Higher Education: A Qualitative Study

A qualitative study was used to understand the experiences of 12 women, leaders in Education Technology in higher education. Through interviews, women leaders described their environment as well as personal and behavioral aspects of their work. Findings revealed four threads of descriptive concepts including relationships, leadership, persistence, and advice. Relationships were from workplaces and professional networks. Leadership was defined by vision and teamwork. Persistence was addressed as either values-based or relationship-based. The fourth thread in the findings, advice, was divided into three sub-threads: education, family (both personal and work), and managing emotions. A qualitative approach was used to highlight interview responses to demonstrate the experiences of women leaders in Education Technology in Higher Education

A stable and replicable neural signature of lifespan adversity in the adult brain

Environmental adversities constitute potent risk factors for psychiatric disorders. Evidence suggests the brain adapts to adversity, possibly in an adversity-type and region-specific manner. However, the long-term effects of adversity on brain structure and the association of individual neurobiological heterogeneity with behavior have yet to be elucidated. Here we estimated normative models of structural brain development based on a lifespan adversity profile in a longitudinal at-risk cohort aged 25 years (n = 169). This revealed widespread morphometric changes in the brain, with partially adversity-specific features. This pattern was replicated at the age of 33 years (n = 114) and in an independent sample at 22 years (n = 115). At the individual level, greater volume contractions relative to the model were predictive of future anxiety. We show a stable neurobiological signature of adversity that persists into adulthood and emphasize the importance of considering individual-level rather than group-level predictions to explain emerging psychopathology

A stable and replicable neural signature of lifespan adversity in the adult brain

Environmental adversities constitute potent risk factors for psychiatric disorders. Evidence suggests the brain adapts to adversity, possibly in an adversity-type and region-specific manner. However, the long-term effects of adversity on brain structure and the association of individual neurobiological heterogeneity with behavior have yet to be elucidated. Here we estimated normative models of structural brain development based on a lifespan adversity profile in a longitudinal at-risk cohort aged 25 years (n = 169). This revealed widespread morphometric changes in the brain, with partially adversity-specific features. This pattern was replicated at the age of 33 years (n = 114) and in an independent sample at 22 years (n = 115). At the individual level, greater volume contractions relative to the model were predictive of future anxiety. We show a stable neurobiological signature of adversity that persists into adulthood and emphasize the importance of considering individual-level rather than group-level predictions to explain emerging psychopathology