Scientific Research

Computational and Data Science, Predictive Analytics

There are a number of challenges, opportunities, and strategies for designing, collecting, managing, processing, interrogating, analyzing and interpreting complex datasets. We develop, validate and share methods, software tools, and protocols that can be applied to a broad spectrum of Big Data problems. This includes building mathematical foundations, computational statistics algorithms, and modern scientific inference techniques to model, visualize and interpret heterogeneous biomedical data. DSPA »

Neuroscience and Brain Mapping

We are involved in challenging neuroscience projects examining brain development, maturation and aging in health and disease. Specific projects include studying normal and pathological pediatric development (e.g., Autism, ADHD, Schizophrenia), memory decline and dementia (e.g., Alzheimer's disease), and various other brain related disorders (e.g., ALS, Parkinson's disease).

Artificial Intelligence and Machine Learning

We develop meta-algorithms for data harmonization, aggregation, model-based and model-free inference (e.g., SOCR AI Bot, see AI Bot video 1 and AI Bot video 2, CBDA, DataSifter).

STEM education

We develop interactive learning modules, dynamic instructional resources, and technology-enhanced educational resources (e.g., MIDAS Graduate Data Science Certificate Program, Graduate Health Analytics Curriculum). Prob & Stats EBook » SMHS EBook »

Computational Medicine and Bioinformatics

Integration of cognitive, genetics, phenotypic, imaging, and biospecimen data requires novel strategies to represent high-dimensional and incongruent data as computable data objects. This research project aims to develop effective informatics techniques that address this difficult challenge using a scalable, reproducible, and reliable computational workflow environment (e.g., Pipeline workflows).

Spacekime Analytics

We are developing a novel theoretical foundation to extend the notion of time to the complex plane. This approach lifts the concept of time from a positive real number representing event ordering to a 2D complex-time (kime) comprising a pair of coordinates - time (t) and phase (φ). Spacekime analytics enables powerful data-driven strategies to interrogate large longitudinal data. This fundamentals research project explores time-complexity and inferential uncertainty in modeling, analyzing, and interpreting large, heterogeneous, multi-source, multi-scale, incomplete, incongruent, and longitudinal data.

Multidisciplinary Design Projects (MDP)

SOCR MDP R&D projects and other specific ongoing student, fellow, and scholar science and discovery projects are openly shared and disseminated.

Shape Modeling

Modeling of Biological Shape Form and Size. This project introduces and evaluates effective, robust and efficient techniques for representation of N-D signals in non-Euclidian spaces (e.g., cortical surfaces, nuclear envelopes, nucleoli shapes, etc.

Open-Science

Develop, validate, support, and share an open access sustainable framework for data management, computational infrastructure, analytical tools, learning resources, and web-services. There have been a total of over 16 Million users (2020) of these open-science resources.

Interactive Visualization

Dynamic iteractive visualization of multimodal imaging data is difficult. This project aims to develop new techniques and software tools for managing, processing and visualizaiton of multimodal imaging and meta-data (e.g., See the Web-based WebGL Brain Viewer.

Other Projects

• Project 1: We have developed the first fully stochastic Functional & Anatomic Sub-Volume Probabilistic Atlas (F&A SVPA) for the elderly and Alzheimer's Disease (AD) patients. This atlas allows us early diagnosis, prognosis and planning of treatment for AD subjects, based on data of their blood perfusion and brain anatomy. (F&A SVPA)
  
• Project 2:, deals with quantifying (numerically) the neurological and topological differences and similarities between pairs of (MRI, fMRI, PET, CT) brain scans. We were able to design metrics on the space of Fractal/Wavelet Transforms of signals, that help us make quantitative distinctions between equivalent medical images, using their transforms. The theoretical function estimation schemes we introduced have been used to develop an algorithm and a computer implementation for an automatic fast and robust approach to quantifying warp performance. This software package is called "Wavelet Analysis of Image Registration" (WAIR)
  
• In Project 3, we develop a new technique for determining the statistically significant metabolic variations in single/multi-subject human brain functional studies. The new method, called Sub-Volume Thresholding (SVT), models the difference images as "locally" stationary Gaussian random fields. Thus adding more flexibility to the commonly used "globally" stationary random approaches. Our model naturally encounters a class of continuous functions we showed induces a family of permissible covariance matrices (valid covariograms). Using the SVT technique we are trying to identify local perfusions and differences in groups of; left vs right hand motor studies; amnesia vs memory-retrieval deficit AD (Alzheimer's disease) patients; and groups of hallucinations vs delusion patients. If we wish to compare two images and identify corresponding anatomical features (or regions of activation, for functional data) we need to use a "warping" technique to deform one of the images to an image similar to the second one. This brings up the question of "What kind of deformation should we use?".
  
• In Project 4, we constructed a mathematical model (based on Fractal and Wavelet Analyses) that helps classifying warps and warping techniques.
  
• Segmentation of medical images is the topic of Project 5. Using the discrete dynamical system induced by our fractal transform we designed a segmentation algorithm. The two major goals in brain image segmentation are: Determining the regions of high concentration of White Matter, Gray Matter and CSF (Cerebral Spinal Fluid); and Reducing the data complexity and dimensionality.
  
• Our models, and our metrics, turn out also to be useful for image magnification.In Project 6, we compared the current state-of-the-art (bilinear) Interpolation techniques for image zoom in, to the novel Fractal magnification algorithms. We were able to show that our model outperforms the interpolation method in some aspects. Blowing up images using their fractal transforms reveals more details (at lower resolution) and avoids the smearing and blurring effects of the interpolation.
  
• Fractal-like transformations could be used for automatic pattern recognition and feature extraction. Project 7 deals with a simple application of such techniques. We are able to show that a decent pattern recognition algorithm could be used for image registration and alignment - a very useful tool for image comparison.
  
• My work in various Optimization projects includes developing, implementing and testing algorithms for solving min/max, linear/non-linear problems/systems/inequalities. Using Subdivision Traversing and other topological algorithms we introduce a class of simple, fast and robust algorithms for function optimization. The casting problem serves as a motivation in this project. When casting an airplane wing, for example, there are a number of input variables (like: Temperature, Pressure, Flow velocity, alloy proportions, etc.) and a list of output characteristics (like: Strength, Number of voids, etc.). The problem is to increase the strength of the wing, decrease the number of bubbles (voids) etc., without actually knowing the function connecting the two types of variables. Currently, this problem is approached by some sort of uniform (or random) selection of test points (input variables), conducting an experiment and observing the output. We have designed an algorithm, that solves an optimization problem to optimize the search for the "right" input based on the previously obtained functional values at prior test points.