Rodica Curtu, Ph.D. - US grants

The PIs shall develop a physics-based hydrologic model capable of simulating flood events. Their system dynamics are described by a large set of non-linear differential equations that are coupled by the selfsimilar network of stream and rivers draining the landscape. To enable the study of floods at scales compatible with significant societal impacts and climate scale effects (i.e. ~50,000 km2 basins such as the Iowa River basin that experienced severe flooding in 2008), the numerical solver requires an efficient and scalable algorithm. The exploration of complex scale interactions between atmospheric inputs and landscape properties including soil, vegetation, and topology of the river network requires tools of nonlinear dynamical systems. The confirmation of the model analysis findings requires analysis of a large dataset of empirical data. This project addresses all these issues in a way that will further the investigation and explanation of the complex behavior of floods. Comprehension of how power laws arise in flood events has implications for flood frequency prediction under changing environmental conditions. This would have profound effects on the water infrastructure design in much of the world.

Based on statistical analysis of streamflow observations from numerous stream gauges across the nation, it has been documented in the literature that the upper tail quantiles of annual streamflow peaks (thus, often floods) display power laws with respect to drainage area. However, dependence of the power law exponents has not been linked to physical characteristics of the regions and their climates. Therefore, as these characteristics might change due to human intervention (e.g. urbanization) or climatic changes, our ability to predict future flood frequency is largely speculative or ad-hoc at best. There is increasing evidence that individual flood events also display power laws with respect to drainage area. Establishment of links between the physical processes
essential to flood genesis and the exponents of the power laws of flood quantiles would enhance prediction of flood frequency. This proposal focuses on expanding the mathematical tools essential to establishing those links and improving our understanding of flood behavior across scales.

The goal of this project is to understand how the brain realizes the impressive flexibility that is a hallmark of human cognition. For example, adults can flexibly shift from conversing about current events, to feeding the cats, to cooking dinner, all without getting mixed up and cooking cat food as the main course. This ability is thought to rely on the actions and interactions of multiple brain areas. A central challenge in understanding cognitive flexibility is to understand how these brain networks change with learning and how they organize and re-organize "on-the-fly" depending on the situation. More generally, how does the brain keep track of events as they unfold but at the same time retain flexibility?

In this project, a multidisciplinary team of investigators will test a new theory of cognitive flexibility using computer modeling and functional neuroimaging data. The theory is implemented using dynamic neural fields -a specific type of neural network that can be simulated on a computer and that specifies how different areas of the cortex interact during complex tasks. Some cortical areas actively maintain neural patterns related to the lower-level details of what is happening, for instance, maintaining information about critical visual features of the pan, the items you are cooking for dinner, and so on. Other cortical areas modulate what these systems are up to. Critically, "higher-level" systems do not need to understand all the details of what is going on. They just need to help decide which general patterns of information are important in the context. It is the dialog between these different neural patterns that makes cognition flexible.

The success of this project would have far-reaching effects. The ability to modulate behavior in context-specific ways is a central achievement that impacts language skills, mathematical abilities, school and work performance, and IQ. Moreover, deficits in cognitive flexibility and so-called executive functions underlie different forms of psychopathology, such as schizophrenia, as well as many of the challenges faced by aging adults. The investigators have also established a collaboration with the Iowa Children's Museum where they will work with museum staff to design an interactive display around the theme of "Brain Play," in which children construct simple solar-powered robots that embody how the brain and body realize flexibility.

The conference "Nonlinear Dynamics and Stochastic Methods: From Neuroscience to Other Biological Applications" will be held at the University of Pittsburgh on March 10-12, 2014. Recent years have witnessed an explosion of biological data that require novel quantitative approaches for their interpretation and analysis. In parallel, concentrated efforts were made by both the government and the national universities to educate a new generation of researchers with interdisciplinary expertise in mathematics, statistics and biology. However, the demand for such specialized skills is still to be met as few mathematical and biological scientists are trained in both topics. The meeting will bring together a mix of senior and junior scientists to report on theoretical methods that proved successful in mathematical neuroscience, and to encourage their dissemination and application to modeling in computational medicine and other biological fields.

In the past two decades, among all biological fields, neuroscience is arguably the most influenced by quantitative methods. Computational models were used to propose anatomical- and functional-related hypotheses and, conversely, novel experimental findings have led to the development of new mathematical theories. While most of these theoretical advancements were driven by the investigation of the nervous system, they are general enough to be successfully translated to modeling problems in other areas of biology and medicine. The meeting will integrate education and research by introducing young investigators to a useful and effective mathematical toolbox for quantitative biology, while presenting at the same time the most recent advancements in the field.

Sounds in natural environments are complex mixtures from many different sources. This project seeks to understand how humans organize mixtures of sounds into meaningful objects. Perceptions of auditory objects arise not from any particular part of the brain, but rather from coordinated activity across many brain regions; further, binding of sounds to auditory objects may switch very rapidly. Therefore, the study of how auditory objects are formed and how rapid switching occurs requires analyzing recordings of brain activity in humans across many brain areas and at very high speed. This project aims to develop new theoretical methods for integrating and analyzing complex dynamic data sets of brain recordings from large-scale electrode arrays. The modeling approach will provide insight in the understanding of human auditory perception in both normal and clinically impaired minds.

Significant advances have been made in the past three decades characterizing neural correlates of auditory perceptions localized to the auditory cortex. Nevertheless, these neural correlates are likely not restricted to the auditory cortex, or to any particular part of the brain. To understand the neural mechanisms of auditory perceptual representation and perceptual switching, the current project combines advances in both experimental design and theory. Large-scale electrocorticography (ECoG) recordings will be collected from human subjects as they self-report their perceptions during a bistable auditory task involving rapid perceptual switching. Next, spatial-temporal patterns of cortical activation during the task will be extracted from these large time-series datasets using a data-driven method novel to neuroscience known as dynamic mode decomposition (DMD). Features extracted by DMD will then be used to build data-driven, low-dimensional dynamic models that capture the temporal evolution of multiple cortical areas, encoding both the auditory stimulus and the perceptual state.