For the past five years prof. Dinov
has been working on designing, implementing, testing and
documenting mathematical and statistical models for studying and
analyzing biomedical data, multi-modal images, genomics sequences,
and other natural phenomena. Details about these projects are
available in technical reports
and research papers. Dr. Dinov's
Funding Sources are summarized here.
Examples of ongoing projects include:

__Other research projects include__:

**Project 1**: 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.**Project 2**: (Big) Data Science (Research, Development, Training):- Compressive Big Data Analytics framework
- SOCR Big Data Services (e.g., Dashboard)
- Michigan Institute for Data Science (MIDAS) Graduate Data Science Certificate Program

**Project 3**: Open-Science Projects: 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 8 Million users (2014) of these open-science resources.**Resource Type****Description****Examples****Data Web-services**

Annual Users:15,000Research-derived, simulated, translational and clinical data archives. Dashboard for mashing multi-source socioeconomic and medical datasets, big data analytics, graphical data exploration and discovery UMich SOCR Data

UCLA SOCR Data Archive

SOCR Dashboard**Data Web-services**

Annual Users:15,000Research-derived, simulated, translational and clinical data archives. Dashboard for mashing multi-source socioeconomic and medical datasets, big data analytics, graphical data exploration and discovery UMich SOCR Data

UCLA SOCR Data Archive

SOCR Dashboard**Computational Infrastructure**

Annual Users:400,000Comprehensive collection of web-tools for demonstrating probability, statistics, mathematics and engineering concepts. These include probability calculators, statistics analysis tools, data modeling and visualization, virtual games, simulations and experiments UMich SOCR Services

Probability Distributome Resource

SOCR Tables and high-precision calculators

SOCR GitHub Source Code

SOCR JIRA/Atlassian PM System

SOCR GoogleCode SVN**Analysis Tools**

Annual Users:8,000Modern HTML5 resources for exploratory analytics, data discovery, simulation, and visualization SOCR HTML5 Webapps

SOCR XTK BrainViewer**Learning Resources**

Annual Users:1,800,000Community-built, open-access and multilingual resources blending information technology, scientific techniques and modern pedagogical concepts SOCR Probability and Statistics EBook (UMich)

SOCR Probability and Statistics EBook (UCLA)

Scientific Methods for Health Sciences (EBook)

Scientific Methods for Health Sciences (Courses)

SOCR Wiki Service (UMich)

SOCR Wiki Service (UCLA)**Project 4**: The Genomics and Informatics Project is focused on the design, execution, validation and open dissemination of graphical pipeline protocols for sequence processing, mapping, analysis, and visualization.**Project 5**: The Interactive Visualization of Multimodal Imaging Data 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.**Project 6**: The Statistical Computing Project develops new open-source, efficient and portable computational libraries for diverse types of statistical data analyses.

**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. Thecasting 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.