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:Eigenvalue solution via the use of a single random vector
Abtract: In this talk, we show the design of reliable and efficient eigensolvers based on the use of a single random vector in eigenvalue detection strategies. Given a region of interest, some randomized estimators applied to a spectral projector are used to detect the existence of eigenvalues. The reliability of the estimators with a single random vector are studied so as to obtain robust thresholds for eigenvalue detection. This is then combined with repeated domain partitioning to find eigenvalues to a desired accuracy. Preconditioned Krylov subspace methods are used to solve multiple shifted linear systems in the eigenvalue detection scheme and Krylov subspaces are reused for multiple shifts. We also show how another randomized strategy can be used to obtain eigenvectors reliably with little extra costs.
Title:Uncovering potential interventions for pancreatic cancer patients via mathematical modeling
Abstract: While any cancer diagnosis is life-altering, pancreatic cancer is among the most discouraging to receive because of its extreme difficulty to overcome. Recent literature suggests that the surrounding environment of pancreatic cancer cells could play a key role in their therapeutic response. Thus, there is a growing need for the discovery of intervention strategies that can attack these cancer cells and the microenvironment that protects them. To address this problem, we have built a mathematical model to computationally predict patient outcomes and test discovered control targets. Using amenable control approaches, we were able discover novel control targets as well as validate previously known results. Further, we were able to predict a hierarchy of disease aggression based on which mutations were present, in the sense that some combinations may be more difficult to treat or that the patient might see a faster decline. This is a step forward in aiding the development of personalized medicine, as treatment protocols progress in becoming more patient-specific.
Abstract: In modern data analysis, the datasets are often represented by large-scale matrices or tensors (the generalization of matrices to higher dimensions). To have a better understanding of the data, an important step is to construct a low-dimensional/compressed representation of the data that may be better to analyze and interpret in light of a corpus of field-specific information. To implement the goal, a primary tool is the matrix/tensor decomposition. In this talk, I will talk about novel matrix/tensor decompositions, CUR decompositions, which are memory efficient and computationally cheap. Besides, I will also discuss how CUR decompositions are applied to develop efficient algorithms or models to robust decomposition and completions and show the efficiency of the algorithms on some real and synthetic datasets.
Abstract: We will consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for example a sequential recommendation problem. We will introduce a CNN architecture that generates and preserves the symmetry structure in the network's convolutional layers. We will present parameterizations for the convolutional kernels that produce update rules to maintain symmetry throughout the training. Lastly, we will show that the symmetric structured networks produce improved results using fewer numbers of machine parameters.
Title: Video Denoising via Directional Fractional Order Total Variation
Abstract: Video denoising is one of the fundamental tasks in computer vision and medical imaging. In this talk, we propose a novel denoising method for spatiotemporal video data based on the Directional Fractional Order Total Variation (DFTV) regularization and Huber loss. We will begin with the basics of image denoising, introduce our DFTV regularized video denoising model, and derive an efficient numerical algorithm. Various numerical results will be presented to show the robustness and performance of our method.
Title: Identification of control targets in Boolean networks via computational algebra.
Abstract: Many problems in systems biology have the goal of finding strategies to change an undesirable state of a biological system into another state through an intervention. The identification of such strategies is typically based on a mathematical model such as Boolean networks. In this talk we will see how to find node and edge interventions using computational algebra.
Title: Geometry and Statistics: New Developments in Statistics on Manifolds
Abstract:With the increasing prevalence of modern complex data in non-Euclidean (e.g., manifold) forms, there is a growing need for developing models and theory forinference ofnon-Euclidean data. This talk first presents some recent advances in nonparametric inference on manifolds and other non-Euclidean spaces.The initial focus is on nonparametric inference based on Fréchet means.In particular, we present omnibus central limit theorems for Fréchet means for inference, which can be applied to general metric spaces includingstratified spaces, greatly expanding the current scope of inference.A robust framework based on the classical idea of median-of-means is then proposed which yieldsestimates with provable robustness and improved concentration. In addition to inferring i.i.d data, we also consider nonparametric regression problems where predictors or responses lie on manifolds. Various simulated or real data examples are considered
Title: A Feedback Control Architecture for Bioelectronic Devices with Applications to Wound Healing
Abstract: Bioelectronic devices can provide an interface for feedback control of biological processes in real-time based on sensor information tracking biological response. The main control challenges are guaranteeing system convergence in the presence of saturating inputs into the bioelectronic device and complexities from indirect control of biological systems. In this talk, we first derive a saturated-based robust sliding mode control design for a partially unknown nonlinear system with disturbance. Next, we develop a data informed model of a bioelectronic device for in silico simulations. Our controller is then applied to the model to demonstrate controlled pH of a target area. A modular control architecture is chosen to interface the bioelectronic device and controller with a bistable phenomenological model of wound healing to demonstrate closed-loop biological treatment. External pH is regulated by the bioelectronic device to accelerate wound healing, while avoiding chronic inflammation.
