Title: Forecasting patient-specific treatment response to neoadjuvant chemotherapy in triple-negative breast cancer via MRI-based digital twins

Abstract: Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant chemotherapy (NAT) to downstage the tumor and improve the outcome of subsequent breast conservation surgery. In this study, we integrated quantitative magnetic resonance imaging (MRI) data with biology-based mathematical modeling to address the currently unmet need for accurate prediction of TNBC response to NAT on an individual patient basis. Specifically, dynamic contrast-enhanced MRI and diffusion-weighted MRI was acquired in 56 patients before, after two, and after four cycles of Adriamycin/Cytoxan (A/C), and again after Taxol as part of the ARTEMIS (NCT02276443) trial. A biology-based mathematical model was established based on the reaction-diffusion equation to characterize the mobility of tumor cells, tumor proliferation, and treatment-induced cell death. Pre- and mid-treatment images were used for model calibration on a patient-specific basis. Two evaluation Frameworks were built: 1. using images acquired before and after two cycles of A/C for calibration and predicting tumor status after A/C, and 2. using images acquired before, after two cycles, and after four cycles of A/C for calibration and predicting response after NAT. For Framework 1, the Pearson correlation coefficients between the predicted and measured patient-specific, post-A/C changes in tumor cellularity and volume were 0.95 and 0.94, respectively. For Framework 2, the biologically-based model achieved an area under the receiver operator characteristic curve of 0.89 (sensitivity/specificity = 0.72/0.95) for differentiating pathological complete response (pCR) from non-pCR, which is statistically superior (P < 0.05) to the value of 0.78 (sensitivity/specificity = 0.72/0.79) achieved by the tumor volume measured after four cycles of A/C. Overall, our biology-based mathematical model successfully captured the patient-specific, spatiotemporal dynamics of TNBC response to NAT, providing highly accurate predictions of NAT response.  

Title: Is a Classification Procedure Good Enough?—A Goodness-of-Fit Assessment Tool for Classification Learning

Abstract: In recent years, many nontraditional classification methods, such as random forest, boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the classification error rate and the like are important, they do not address a fundamental question: Is the classification method underfitted? To our best knowledge, there is no existing method that can assess the goodness of fit of a general classification procedure. Indeed, the lack of a parametric assumption makes it challenging to construct proper tests. To overcome this difficulty, we propose a methodology called BAGofT that splits the data into a training set and a validation set. First, the classification procedure to assess is applied to the training set, which is also used to adaptively find a data grouping that reveals the most severe regions of underfitting. Then, based on this grouping, we calculate a test statistic by comparing the estimated success probabilities and the actual observed responses from the validation set. The data splitting guarantees that the size of the test is controlled under the null hypothesis, and the power of the test goes to one as the sample size increases under the alternative hypothesis. For testing parametric classification models, the BAGofT has a broader scope than the existing methods since it is not restricted to specific parametric models (e.g., logistic regression). Extensive simulation studies show the utility of the BAGofT when assessing general classification procedures and its strengths over some existing methods when testing parametric classification models.

Computational modeling using a novel continuum approach coupled with Pathway-informed neural networks to optimize Dynein-mediated centrosome positioning in Polarized cells

Microtubules (MTs) are cytoskeletal polymers that interact with motor proteins such as dynein to position the centrosomes and nucleus within a cell. Centrosome positioning specifies the cell’s division plane by determining the location and orientation of the mitotic spindle. In polarized cells, centrosome alignment along the polarity axis causes the cell to divide asymmetrically, producing unequal daughter cells. Proper centrosome positioning is critical during development where it is required for important processes such as cell fate specification. Improper centrosome positioning is implicated in disease processes: cancer cells often exhibit abnormal centrosome positioning prior to division. While many studies have focused on centrosome movement during mitosis, centrosomes are often positioned prior to mitosis. This movement prior to mitosis when the centrosomes are associated with the intact pronuclear envelope is not well understood. Many aspects of dynein-mediated centrosome movement are highly nonlinear and rely on biochemical, mechanical and geometric features in the cell that are difficult to investigate experimentally. Mathematical modeling can easily deal with this complexity, bridging the varying time and space scales, and provide a fundamental understanding of the mechanisms of positioning centrosomes. This model provides the key features required to integrate modeling and experiments on early embryos of the C. elegans to elucidate the interplay between biochemical, mechanical and geometric signals that act to position centrosomes in polarized cells through the following aims. The same non-linear framework for confined geometries is extended to create a comprehensive data driven digital twin of an individual’s mental health profile and analyze spatiotemporal behavior. Although dynamic study and modeling of depression-related behavior exist in literature, we employ a novel digital twin model that combines Sensitive, Exposed, Induced and Excluded models with Disease-informed neural networks to identify progression and intensity of depression related behavior. 

Title: The Model Behind ChatGPT

Abstract: This will be a general talk to introduce a deep learning model called Generative Pre-training Transformer (GPT). First, I will discuss in concept the machine learning approach for the task of question-answering. Then I will describe language modeling and some models such as recurrent neural network (RNN) models for that task. Finally, I will present the Transformer as well as the GPT models that have led to ChatGPT.

Title: The nonlinearity of regulation in biological networks

Abstract: The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed `regulatory nonlinearity', we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation, we used Taylor decomposition to approximate the models with various levels of nonlinearity. A comparison of the resulting series of approximations of the biological models with appropriate random ensembles revealed that biological regulation tends to be less nonlinear than expected. A further categorical analysis of the biological models revealed that the nonlinearity of cancer and disease networks could not only be sometimes higher than expected but are also relatively more variable. We show that this variation is caused by differences in the apportioning of information among the various orders of nonlinearity. Taken together, our results suggest, but do not imply, that biological regulation may have evolved to be more linear on average, and certain systems such as cancer may have, on the other hand, evolved to be more nonlinear.

Title: Self-Correcting Discriminator Optimization for Image and Speech Enhancement GANs

Abstract: Generative adversarial network (GAN) has become one of the most important neural network models for classical unsupervised machine learning. Various discriminator loss functions have been developed to train GAN's discriminators, most of which have a common structure: a sum of real and fake losses that depend only on the actual and generated data, respectively. One challenge associated with an equally weighted sum of two losses is that the training may benefit one loss but harm the other. We present self-correcting optimization for training a GAN discriminator, which helps avoid "harmful" training directions for parts of the discriminator loss function. Experiments validated the effectiveness of our loss functions on conditional and unconditional image generation tasks as well as speech enhancement tasks.

Title: Robust Estimation of Smooth Graph Signals from Randomized Space-time Samples

Abstract: Heat diffusion processes have found wide applications in modeling dynamical system over graphs. In this talk, I will talk about the recovery of a k-bandlimited graph signal that is an initial signal of a heat diffusion process from its space-time samples. In this work, we have proposed three random space-time sampling regimes, termed dynamical sampling techniques, that consist in selecting a small subset of space-time nodes at random according to some probability distribution. We show that the number of space-time samples required to ensure stable recovery for each regime depends on a parameter called the spectral graph weighted coherence, that depends on the interplay between the dynamics over the graphs and sampling probability distributions. Then, we propose a computationally efficient method to reconstruct k-bandlimited signals from their space-time samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we test dynamical sampling techniques on a wide variety of graphs. The numerical results on support our theoretical findings and demonstrate the efficiency.

Title: A generic framework to coarse-grain stochastic reaction networks by Abstract Interpretation

Abstract: In the last decades, logical or discrete models have emerged as a successful paradigm for capturing and predicting the behaviors of systems of molecular interactions. Intuitively, they consist in sampling the abundance of each kind of biochemical entity within finite sets of intervals and deriving transitions accordingly. On one hand, formally-proven sound derivation from more precise descriptions (such as from reaction networks) may include many fictitious behaviors. On the other hand, direct modeling usually favors dominant interactions with no guarantee on the behaviors that are neglected.

In this paper, we formalize a sound coarse-graining approach for stochastic reaction networks. Its originality relies on two main ingredients. Firstly, we abstract values by intervals that overlap in order to introduce a minimal effort for the system to go back to the previous interval, hence limiting fictitious oscillations in the coarse-grained models. Secondly, we compute for pairs of transitions (in the coarse-grained model) bounds on the probabilities on which one will occur first. 

We illustrate our ideas on two case studies and demonstrate how techniques from Abstract Interpretation can be used to design more precise discretization methods, while providing a framework to further investigate the underlying structure of logical and discrete models. 

Title:  Optimal Decision-Making in Social Networks

Abstract:
To make decisions we are guided by the evidence we collect and the opinions of friends and neighbors. How do we combine our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so, it is useful to compare them to observers that optimally integrate all evidence. Here we derive network models of rational (Bayes optimal) agents who accumulate private measurements and observe the decisions of their neighbors to make an irreversible choice between two options. The resulting information exchange dynamics has interesting properties: When decision thresholds are asymmetric, the absence of a decision can be increasingly informative over time. In a recurrent network of two agents, the absence of a decision can lead to a sequence of belief updates akin to those in the literature on common knowledge. We then consider large networks under the same framework. Using a combination of asymptotic methods and first passage time calculations, we find that when the network is sufficiently large, most agents decide correctly irrespective of whether the first agent’s decision is right or wrong. Interestingly, individuals in networks with both hasty and deliberate agents can make the right choice more quickly and more often than in networks of identical agents: Observing the choices of a small group of hasty agents can allow the more deliberate agents to make accurate decisions. Our model is tractable and readily generalizable, paving the way for the future study of different social network topologies. We conclude that diverse groups make quicker, more accurate decisions than homogenous groups.

Title: Extrapolation for eigenvalue problems: Upcycling data for faster convergence

Abstract: We will discuss accelerating convergence to numerical solutions of eigenvalue problems using a simple post-processing step applied to standard eigensolver techniques. First we will consider accelerating the standard power iteration, one of the most basic and powerful but sometimes very slow iterative methods. We will review some recent results on how we can make the power iteration faster by recombining previous iterates to form our next approximation to a solution; and, we will discuss why this works. We can also apply a similar technique to a restarted Arnoldi method to boost its performance with little additional computational cost. Numerical examples will illustrate the theory.