Applied Mathematics and Machine Learning
Department of Mathematics and Statistics
Texas Tech University
Abstract. Tumor shape significantly influences growth and metastasis. We introduce a topological feature obtained by persistent homology to characterize tumor progression in pathology and radiology images, focusing on its influence on time-to-event data. These topological features, invariant to scale-preserving transformations, capture diverse tumor shape patterns. We introduce a functional spatial Cox proportional hazards model that represents these topological features in a functional space, utilizing them as functional predictors alongside their spatial locations. This model allows for interpretable analysis of the relationship between topological shape features and survival risks.
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Abstract: The healthcare ecosystem is a complex network of patients, providers, and payers that involves a variety of nuanced decision-making processes. We give an overview of some of the challenges in the US Healthcare System and the role that AI/ML can play in helping to manage and inform clinical decisions. Specifically, we highlight two areas of research: (i) the development of computational phenotypes (or medical concepts) to improve clinical understanding and (ii) the application of AI/ML for survival analysis which can inform personalized treatment strategies. Through these efforts, AI/ML has the potential to significantly enhance both the precision and efficiency of healthcare delivery.
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Abstract PDF
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
Deep learning algorithms have recently inspired innovative strategies to address computational bottlenecks in traditional solvers for high-dimensional differential equations (DEs). Neural network (NN)-based solvers, which approximate the DE solutions using NNs, have gained significant popularity. However, achieving high accuracy with these solvers remains a challenge, and their black-box nature often limits the interpretability of their solutions.
In this talk, I will introduce the finite expression method (FEX), a symbolic approach for discovering accurate and interpretable mathematical expression solutions to DEs. FEX leverages reinforcement learning to tackle the combinatorial optimization problems inherent in solving DEs. Numerical examples of high-dimensional DEs demonstrate that FEX achieves highly accurate solutions, with relative errors approaching single-precision machine epsilon. Moreover, FEX provides interpretable insights into DE solutions, which enhances understanding of physical systems and guides the development of postprocessing techniques for refined results. By combining accuracy with interpretability, FEX offers a promising alternative to NN-based solvers for high-dimensional DEs.
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"Nanofluids: Small Name, Big Impact!" With advancements in nanotechnology and the growing need for efficient thermal management, nanofluids have emerged as innovative replacements for conventional fluids. These engineered fluids leverage the superior thermal conductivity and enhanced surface area of nanoparticles to significantly boost heat and mass transfer properties. As a result, nanofluids are revolutionizing applications in energy systems, cooling technologies, and biomedical devices, delivering unparalleled efficiency and performance in systems demanding precise thermal regulation and improved fluid dynamics.
In this talk, we will delve into nanofluids' evolution, applications, and mathematical modeling, focusing on optimizing the thermal performance of hybrid nanofluids using advanced tools like response surface methodology and artificial neural networks.
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Abstract. My presentation begins by introducing multiway count data, low-rank tensor decompositions and the notion of false zeros. I then propose a novel statistical inference paradigm for zero-inflated multiway count data that dispenses with the need to distinguish between true and false zero counts. Our approach ignores all zero entries and applies zero-truncated Poisson regression on the positive counts. Inference is accomplished via tensor completion that imposes low-rank structure on the Poisson parameter space.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
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* Meeting ID: 979 1333 6658
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Abstract. Aluminum (Al) particles are notoriously plagued with sluggish ignition and slow or incomplete combustion. Yet, the potential to harness tremendous power from these high energy density particles is on the cusp of transforming our way of life. This presentation will focus on thinking differently about using traditional diagnostic approaches in order to gain new insight and develop more accurate metal oxidation models. Experiments are purposefully designed to deconvolute energy conversion processes from metal particle combustion. Results inform our understanding of reaction energy and draw us closer to controlling energy release rates in order to harness power. Then, from comprehension of metal oxidation mechanisms, we can creatively develop strategies that will lead to their faster energy release. Harnessing more of the abundant chemical energy stored in metal particles at rates relevant to detonation time scales will have important implications for the use of metals as a power generating material in many applications.
Biography. Dr. Michelle Pantoya received her PhD from the University of California, Davis in 1999 and joined the faculty in the Mechanical Engineering Department at Texas Tech University in 2000. As the J. W. Wright Regents Endowed Chair Professor, her research focuses on studying fuel particle combustion in ways that can enhance our national safety and security. She has received many research and teaching awards including the US Presidential Early Career Award (PECASE) and the DoD Young Investigator Program Award and has over 220 archival publications on this topic. Dr. Pantoya is also the co-author of several children’s books introducing engineering to young kids (i.e., Engineering Elephants, Optimizing an Octopus & Designing Dandelions) and an advocate for elementary engineering education.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
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* Meeting ID: 979 1333 6658
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Abstract. We present an overview of sharp interface limits ($\Gamma$-limits) of bulk energies and of their gradient flows that yield classes of sharp interface energies and their gradient flows. We develop a formalism to take variational derivatives of sharp interface energies and apply this to sharp interface energies that are not trivially in the range of the bulk energy $\Gamma$-limit. This applications to faceting in brine inclusions and to membrane self-adhesion and folding without self-intersection. We show that the resulting gradient flows have a rich structure which we exploit to simplify the stability analysis. For simplicity all discussion is posed in R^2.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
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* Meeting ID: 979 1333 6658
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Abstract. This presentation introduces a novel numerical approach for quasi-static crack propagation in strain-limiting materials, employing a regularized variational model. We tackle the significant challenge of crack-tip strain singularities by formulating a logically consistent strain-energy density in terms of nonlinear constitutive relationships. The resultant problem posed as variational equality and inequality necessitates an adaptive finite element method, guided by residual-based error estimates, to resolve internal layers near the crack tip effectively. We provide a convergence analysis and validate the algorithm's effectiveness through numerical examples. This is a collaborative effort with my postdoc, Dr. Ram Manohar. Additionally, this material is based on work supported by the NSF under Grant No. 2316905.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
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Abstract. This talk is about kernels. In particular, I will bring up reproducing kernels, Bochner’s theorem, Mercer series, feature maps and random Fourier features. My idea is to bring this into machine learning and large language models. Hopefully I can tie together some of kernel method and to start thinking about better or reduced random features (via “better” kernels) which then should lead to faster and accurate machine learning models.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
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* Meeting ID: 979 1333 6658
* Passcode: Applied (Note the capital letter "A")
Abstract: We revisit the possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type. This mathematical phenomena needs to be distinguished from the usual blow-up appearing in the case of NLS with focusing nonlinearities, as it is in essence a linear phenomena based on “concurrence”. The latter is one of the conceivable explanations for oceanic and optical rogue waves. We extend the results existing in the literature in several ways. In one direction, the theory is broadened to include the Davey-Stewartson and higher order equations. In another, dispersive blow up is shown to obtain for nonlinear Schrödinger equations in spatial dimensions larger than one and for more general power-law nonlinearities.
When: 4:00 pm (GMT -5)
Where: room 011 Math (Math Basement)
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* Meeting ID: 979 1333 6658
* Passcode: Applied (note the capital letter "A")