MIDAS Spacekime Analytics R&D Pitch (Fall 2020)

Transcript:

Hello, my name is Ivo Dinov, I'm a MIDAS faculty working on mathematical modeling, statistical computing, and data science methods, as well as health analytics applications. In this brief, MIDAS R&D pitch, I would like to, number one, summarize a new analytical method called space-kime analytics. Then I will show one example using neuroimaging functional magnetic resonance imaging data (fMRI). And number three, call for partnerships with students, researchers, and faculty that may be interested in data science and open computation problems. So let's start off with the space-kime analytics. The basic idea is that we are going to complexify the notion of time, kime=complex-time. So in this diagram, the three-dimensional space is compressed into a one-dimensional line that goes right over here. And then, what we typically referred to as time represents this radial direction that's perpendicular and independent of the spatial location that goes radially outward in the three-dimensional scene. Now, every point on these concentric circles at a given spatial location is associated with two coordinates. The radius, which is commonly referred to ordinal event characterization, and the second one is the phase that basically tells you how far in either direction each event extends to. Events are essentially points on these concentric circles that are anchored at specific spatial location. So, we try to generalize time-series to what we call kime-surfaces. Imagine the situation where you have a set of time-series. All these time series are here modeled as these black curves. So here is one time-series, here's another time-series that goes across the kime-surface. And here's a third time-series The heights of these surfaces represent the intensity T the given radial location, 1, 2, 3, etcetera as the time increases. And as you can see in different colors, we have the different phases from yellow to green, blue, and down to read. So, in other words, we are trying to model naturally occurring ordinal temporal signals (time-series) as more complex manifolds, which we call kime-surfaces. So let's look at one specific example here. This is a series of what's called fMRI, functional magnetic resonance imaging data. So you can see you have about a 160 time points and everyone time point. You can actually read out the intensities. At time 107 and the intensity is 72. And you have a smoother version of that same curve. So, imagine you have a lot of these time series and they're all subject to various stimuli (conditions). Starting with a stimulus (ON) back to to baseline (OFF), repeated stimulus-rest conditions. So this process continues on and on several times. And the reason why we do these experiments repeatedly under exactly the same conditions is to be able to get essentially a better representation of these phase angles, which, we don't necessarily observe directly . In other words, we repeat these experiments multiple times. And then, we try to make inference about a process -- what brain region controls, or responds, to certain physical, visual, audio, tactile, or other stimulus. In essence, what we are going to do sample from a symmetric distribution the phases from -Pi to +Pi to reconstruct these kime-surfaces. Here is a surfaces constructed of the fMRI signal at the ON-state, as you can see here. This is during the period of when the stimulus is being applied. These ON-state surfaces correspond to OFF-state surface reconstructions, right up here, as you can see. So these OFF-states are also reconstructed as different OFF kime-surfaces. Obviously what statisticians are interested in is the surface-difference, that correspond to brain regions As you can see here, we can actually detect which time and which phase each of these intensities corresponds to. And of course, they do look a little bit different, right? So what we naturally do is we subtract them away. And now we have a very interesting kime-surface that can be analyzed using Gaussian random field theory of the excursion sets beyond certain critical values. Now. We also have a way of transforming signals from temporal dimension into the complex time or "kime" or using continuous operators. The Laplace transform provides one such strategy that allows us to go from, from time-series curves to kime-surface manifolds. We can go from individual lines to 2-manifolds Here is the corresponding Laplace transform of a function. And then we can actually see which signal corresponds to this specific function. And this is a time series that corresponds to this specific Laplace transform kime-surface. The methods that we develop rely on mathematical algorithms, and apply data science methods to essentially propose strategies for kime-surface reconstructions from data, which is observed natively as time-series. Number two, we also explore certain statistical properties of these reconstructions. And here's a formulation of the spacekime analytics as a Bayesian framework. And then we develop complex artificial intelligence (AI) or machine learning (ML) methods. If you, or your students, or your colleagues are interested in this research, or any of the open problems or challenges, you can either look at the www.Spacekime.org website or send me an email. I'll be happy to meet and discuss with you. Thank you.

SHORT (3-min) Clip of the video