- The applied math seminar is held on Wednesdays at 3PM in Keller 402 during the fall of 2018. If you would like to join the mailing list or present a talk, please contact Evan Gawlik.
- Speaker: Elizabeth Gross, UH Manoa Department of Mathematics
- Title: Distinguishing and inferring phylogenetic networks
- Abstract: Phylogenetic trees are graphical summaries of the evolutionary history of a set of species. In a phylogenetic tree, the interior nodes represent extinct species, while the leaves represent extant, or living, species. While trees are a natural choice for representing evolution visually, by restricting to the class of trees, it is possible to miss more complicated events such as hybridization and horizontal gene transfer. For more complete descriptions, phylogenetic networks, directed acyclic graphs, are increasingly becoming more common in evolutionary biology. In this talk, we will discuss Markov models on phylogenetic networks and explore how understanding their algebra and geometry can aid in establishing identifiability, a property necessary for meaningful statistical inference. In addition, we will describe a method for network inference that combines computational algebraic geometry and statistical learning.
- No seminar
- Speaker: Hong-Ming Yin, Washington State University Department of Mathematics and Statistics
- Title: On a corporate bond pricing model with credit rating migration risks and stochastic interest rate
- Abstract: In this paper we study a corporate bond-pricing model with credit rating migration and a stochastic interest rate. The volatility of bond price in the model strongly depends on potential credit rating migration and stochastic change of the interest rate. This new model improves the previous existing models in which the interest rate is considered to be a constant. The existence, uniqueness and regularity of the solution for the model are established. Moreover, some properties including the smoothness of the free boundary are obtained. Furthermore, some numerical computations are presented to illustrate the theoretical results.
- Speaker: Daisuke Takagi, UH Manoa Department of Mathematics
- Title: Inverse problems in predator and prey sensing
- Abstract: Fish and plankton may evade predators and capture prey by sensing disturbances in the surrounding fluid. In this talk I consider the inverse problem of using the perceived data to locate the source of the signal. The theory informs suitable strategies for sensing objects remotely.
- Speaker: Peter Sadowski, UH Manoa Department of Information and Computer Sciences
- Title: Deep Learning: the New Workhorse of Science
- Abstract: Current excitement about artificial intelligence is largely due to the surprising effectiveness of deep learning with neural networks, and these models are quickly becoming an important tool in scientific data analysis. Neural network models are particularly well-suited for modeling high-dimensional data including images, video, sequences, and graphs, and they are replacing laboriously hand-engineered data processing pipelines with learned, end-to-end models. In this talk I will discuss my work applying deep learning to problems in high-energy physics as well as new projects in climate, atmospheric, and ocean sciences.
- Speaker: Jonghyun (Harry) Lee, UH Manoa Department of Civil and Environmental Engineering
- Title: A parallel black-box Fast Multipole Method and its applications in spatial interpolation and inverse modeling
- Abstract: Recent advances in computational resources and sensor technology open up a new opportunity to characterize unknown quantities such as subsurface permeability or coastal bathymetry at small scale. However, identification of such unknowns becomes more computationally challenging than ever with big environmental data analytics and expensive high-fidelity simulations. In this talk, I will present a black-box Fast Multipole Method, PBBFMM3D, for evaluating (covariance) matrix-vector product or pair-wise particle interactions in a very efficient manner. PBBFMM3D applies to all non-oscillatory smooth kernel functions and only requires the kernel evaluations at data points. It has $O(N)$ complexity as opposed to $O(N^2)$ complexity from a direct computation. I present convergence and scalability results, as well as a few applications with widely used parameter estimation techniques, e.g., Kriging, and Kalman Filtering.
- Speaker: Lee Altenberg, UH Manoa Department of Information and Computer Sciences
- Title: Application of spectral graph theory to evolutionary dynamics
- Abstract: The dynamics of biological evolution combine two fundamental processes: natural selection and genetic variation. Mathematically, selection enters as an operator of multiplication (e.g a diagonal matrix), while variation production enters as a stochastic matrix (for mutation or dispersal, or a tensor in the case of sexual reproduction). Many questions in evolutionary dynamics boil down to size of the spectral radius of the product of diagonal and stochastic matrices. The spectral radius give the the long-term aggregate growth rate of the population or genotype. The spectral radius corresponds to the mutational robustness of a population at a mutation-selection balance.
- A fundamental question is how the values of the diagonal fitness matrix interact with the stochastic mutation matrix to determine the spectral radius. Here, I show that the eigenvalues and eigenvectors of the mutation matrix provide upper and lower bounds to the spectral radius of the product. The spectral gap of the mutation matrix provides an upper bound. A lower bound comes from the correlations between the fitness values and the elements of the eigenvectors of the mutation matrix: high correlations between fitnesses and the eigenvectors with largest eigenvalues lead to a higher bound, while correlations with the eigenvectors having smallest eigenvalues lead to smaller lower bounds. These results are a mild generalization of the work of Collatz and Sinogowitz (1957) that initiated spectral graph theory.
- The mutational relaxation time for perturbations of genotype frequencies are therefore shown to have a deep relationship to mutational robustness. By taking a general approach, the behavior of different kinds of mutation point mutation, copy number change, epigenetic mutation, as well as non-genetic information transmission such as dispersal can be compared all within a unified framework, and their levels of robustness characterized.
- Speaker: Zhuoyuan Song, UH Manoa Department of Mechanical Engineering
- Title: New perspectives on the localization and coordination of underwater vehicles in strong geophysical circulations
- Abstract: Small autonomous robots as environmental perception instruments are often severely constrained in actuation capability, navigation system accuracy, and on-board processing capacity. The presence of ubiquitous geophysical flows tends to exacerbate challenges associated with the control and state estimation of these mobile platforms. Conventionally, background flows are considered as adversarial factors to the mobility and navigation accuracy of mobile robots. I advocate a new perspective on the role of background flows as ubiquitous navigation references and transportation .highways. for independent and networked autonomous robots. The first part of the talk introduces a novel flow-aided navigation method for long-term, mid-depth autonomous underwater vehicles (AUVs). This method leverages the dynamics of spatiotemporally varying background flows as navigation references in mitigating the accumulative error of inertial navigation. The second part of this talk proposes a distributed, multi-robot flocking and flock guidance method by modeling robot swarms as continuous fluids. An implementation for nearly fuel-optimal guidance of large AUV groups in both artificial and real-world flow fields will be presented. Finally, I will discuss how these results have motivated future research directions including 1) the design of system middleware for consistent and secure collaboration between human supervisors and autonomous robot swarms; 2) long-term autonomy with concurrent flow-aided navigation and background flow dynamics learning.
- No seminar
- Speaker: Jakob Kotas, UH Manoa Department of Mathematics
- Title: Optimal airline de-ice scheduling
- Abstract: We present a decision support framework for optimal flight re-scheduling on an airline's day of operations when de-icing suddenly becomes necessary due to snow and ice events. Winter weather, especially in areas where such weather is not commonplace, can cause cascading delays and cancellations throughout the system due to the unforeseen need to add de-ice time to each aircraft's turnaround time. Our model optimally re-schedules remaining flights of the day to minimize system delays and cancellations. The model is formulated as a mixed integer linear program (MILP). Structural properties of the model allow it to be decomposed into a finite set of linear programs (LP) and a computationally tractable algorithm for its solution is described. Finally, numerical simulations are presented for a case study of Horizon Air, a regional airline based in the Pacific Northwest of the United States.
- Speaker: Don Krasky, UH Manoa Department of Mathematics
- Title: Diffusion of swimmers jumping stochastically between multiple velocities
- Abstract: We introduce a model for dispersion of independent swimmers jumping randomly between multiple translational velocities in arbitrary dimensions. Sample trajectories of the individual swimmers are simulated using the governing stochastic differential equations. The associated Fokker-Planck equations are derived and an analytical prediction is obtained for the effective diffusion constant, which is shown to be consistent with simulations. We show adaptability of the model by fitting to three previous models of swimmers having two or three preferred velocities. We explore how stochastic vs. deterministic velocity changes and restricting certain velocity jumps result in different rates of dispersion.
- Speaker: Evan Gawlik, UH Manoa Department of Mathematics
- Title: Finite element exterior calculus for PDEs on evolving surfaces: Part II
- Abstract: (Continuation of previous week's talk.)
- Speaker: Evan Gawlik, UH Manoa Department of Mathematics
- Title: Finite element exterior calculus for PDEs on evolving surfaces: Part I
- Abstract: Finite element exterior calculus provides a unified framework for analyzing the stability and convergence of mixed finite element discretizations of partial differential equations (PDEs). The framework was originally developed for elliptic PDEs on open domains in Euclidean space, but recent efforts have extended it to time-dependent PDEs and PDEs on static surfaces. We extend the framework to another setting: parabolic PDEs posed on surfaces that evolve with time in a prescribed fashion. We prove a priori error estimates for numerical discretizations of such problems, taking into account variational crimes (discrepancies between the geometry of the exact and approximate surfaces) in the analysis.