Oluwatosin Babasola (U Georgia)
Epidemiological approach for mitigating Mpox transmission dynamics
Chenglong Bao (Tsinghua)
On the global R-linear convergence of NAG method and beyond
The Nesterov Accelerated Gradient (NAG) method is a widely-used extrapolation-based algorithm that accelerates the convergence of the gradient descent method in convex optimization problems. In this talk, we will explore the global linear convergence properties of the NAG method when applied to strongly convex functions by assuming that the extrapolation coefficient is independent of the strong convexity parameter. Moreover, we will provide a mathematical analysis that demonstrates the advantages of restart schemes in the NAG method. Finally, we will compare these results with the continuous understanding of the NAG method from the perspective of ordinary differential equations.
Margaret Beck (BU)
An overview of methods for determining the point spectrum of certain linear operators
Masato Hara (Kyoto University)
A scenario of learning dynamics by reservoir computing
Reservoir computing is a kind of machine learning, which can learn and predict time series generated by a dynamical system. We think that a reservoir can predict time series because it becomes a (semi) conjugate system with a system behind the time series. In this talk, I will sketch a scenario of learning dynamics by reservoir computing. This is a joint work with Professor Hiroshi Kokubu (Kyoto University).
Alanna Haslam-Hyde (BU)
Quantifying Patterns and Their Transitions in Spatially Extended Systems (Poster)
Sam Isaacson (BU)
Spatial Jump Process Models for Estimating Antibody-Antigen Interactions
Surface Plasmon Resonance (SPR) assays are a standard approach for quantifying kinetic parameters in antibody-antigen binding reactions. Classical SPR approaches ignore the bivalent structure of antibodies, and use simplified ODE models to estimate effective reaction rates for such interactions. In this work we develop a new SPR protocol, coupling a model that explicitly accounts for the bivalent nature of such interactions and the limited spatial distance over which such interactions can occur, to a SPR assay that provides more features in the generated data. Our approach allows the estimation of bivalent binding kinetics and the spatial extent over which antibodies and antigens can interact, while also providing substantially more robust fits to experimental data compared to classical bivalent ODE models. I will present our new modeling and parameter estimation approach, and demonstrate how it is being used to study interactions between antibodies and spike protein. I will also explain how we make the overall parameter estimation problem computationally feasible via the construction of a surrogate approximation to the (computationally-expensive) particle model. The latter enables fitting of model parameters via standard optimization approaches.
Tasso Kaper (BU)
Strong symmetry breaking in pairs of coupled, identical fast-slow oscillators
Taiga Kurokawa (Kyoto University)
Existence of transit orbits in the planar circular restricted 3-body problem via variational methods
In the past, the spacecraft trajectory had been designed using the two-body problem commonly. However, recently, the trajectory design with the three (or more)-body problem has been studied actively. In the planar restricted 3-body problem (PR3BP), the first problem in considering low-energy orbits is the existence of transit orbits. Although many numerical studies suggest the existence of transit orbits, few mathematical results show their existence. Mathematical results can be divided into two categories: those based on the perturbation theory method and those based on the variational method. The former cannot verify their existence for concrete situations, but the latter is important in that it allows us to do so. For the case of two bodies in the circular motion (PCR3BP), by minimizing Maupertuis' functional, Moeckel(2005) provided a sufficient condition for their existence. On the other hand, for the case of the elliptic motion (PER3BP), this variational structure does not work because it isn't autonomous, and no variational results had been known. We provide, for PCR3BP, the different sufficient condition from Moeckel's result by minimizing Lagrange's functional. Furthermore, by finding that this variational structure also works for non-autonomous systems, we also provide a sufficient condition for PER3BP. We also confirm numerically that these sufficient conditions are satisfied for the concrete situation when the two bodies have the same mass. In this talk, we will present these results.
Minh Le (Michigan State U)
Global existence of chemotaxis systems under nonlinear Neumann boundary conditions. (Poster)
Yuto Nakajima (Tokai University)
Transversal family of non-autonomous conformal iterated function systems
A Non-autonomous Iterated Function System (NIFS) is a sequence of collections of uniformly contracting maps. In comparison to usual iterated function systems, we allow the contractions applied at each step to vary. In this talk, we focus on a family of parameterized NIFSs. Here, we do not assume the open set condition. We show that if a parameter family of such systems satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the limit set is the minimum of the dimension of the ambient space and the Bowen dimension. Moreover, we give an example of a family of parameterized NIFSs such that the family of NIFSs satisfies the transversality condition but each NIFS does not satisfy the open set condition.
Misato Ogawa (Ochanomizu University)
The relation between the Gibbs measure for a potential which depends on the first coordinate and Double Variational Principle on XY model
The minmax problem for the sum of rate distortion dimension and the integral of a potential function is called Double Variational Principle with a potential and XY-model is a typical example for which the principle holds. On the other hand, we can construct a Gibbs measure for a continuous function on XY-model by using the Ruelle operator. Hence it is natural to ask the minmax value is attained by the Gibbs measure as an analogy of the Variational Principle for a shift with finite alphabets. In this talk we consider a potential depending only on the first coordinate on XY model and calculate the rate distortion dimension for the Gibbs measure of the potential. This is a joint work with Mao Shinoda in Ochanomizu University.
Chihiro Oguri (Ochanomizu University)
Is the penalty function of the hard square shift stable?
The fundamental difference between subshift of finite type(SFT) in d=1 and that in d=2 is revealed by Gonschorowski et.al., i.e., the penalty function of every SFT in d=1 has the stablity but there exists a SFT in d=2 whose penalty function is unstable. However, the SFT in d=2 in their paper is far from 'chaotic'. Hence it is natural to ask whether the stability of the penalty function of SFT in d=2 with 'sufficiently chaotic' property. In this talk we consider the penalty function of the hard square shift.
Kayode Oshinubi (N. Ariz. U)
Dynamical modeling of infectious disease spread using data-driven models
Kohki Sakamoto (U Tokyo)
Harmonic measures in percolation clusters on hyperbolic groups
Vaibhava Srivastava (Iowa St. U)
The effect of "fear" on two species competition
Yoshiki Takeguchi (Kyoto University)
Design of low-thrust spacecraft trajectories with minimum costs by optimal control and dynamical systems approaches
In this talk, we consider the problem of computing low-thrust spacecraft trajectories with minimum costs from the Earth to the Moon or Mars. The spacecraft is modeled by the restricted three- or four-body problem. Optimal control and dynamical systems approaches are used, so that low-thrust trajectories are computed by numerical continuation of boundary value problems of Hamiltonian systems obtained via Pontryagin's maximum principle. I will also give preliminary numerical results for low-thrust trajectories from a circular orbit to another around the Earth.
Takayuki Watanabe (Chubu University)
On the stochastic bifurcations regarding random iterations of rational maps
We consider random iterations of rational maps on the Riemann sphere and investigate the stochastic bifurcation of them. For example, adding independent noise to iteration of $z \mapsto z^2 - 1$ yeilds a dynamical system that is qualitatively different from the original dynamical system, even if the noise size is relatively small. We give some quantitative estimates of bifurcation parameters and present beautiful figures of random Julia sets.
Jinxin Xue (Tsinghua)
Generic dynamics of the mean curvature flows
The mean curvature flow is to evolve a hypersurface in Euclidean space using the mean curvatures at each point as the velocity field. The flow has good smoothing property, but also develops singularities. The singularities are modeled on an object called shrinkers, which give homothetic solutions to the flows. As there are infinitely many shrinkers that seem impossible to classify, it is natural to explore the idea of generic mean curvature flows that is to introduce a generic perturbation of the initial conditions. In this talk, we shall explain our work on this topic, including perturbing away nonspherical and noncylindrical shrinkers, and generic isolatedness of cylindrical singularities.
The talk is based on a series of works jointly with Ao Sun.
Kazuyuki Yagasaki (Kyoto University)
Some Recent Results on Nonintegrability of Dynamical Systems
In this talk, we review some recent results on nonintegrability of dynamical systems.
I begin with a definition of integrability for general systems. After briefly reviewing
the classical work of Poincare and Kozlov, the differential Galois theory, and the
Morales-Ramis theory, I explain a new technique to prove the nonintegrability of
nearly integrable systems. We apply the technique to the restricted three-body
problem and time-periodic perturbations of single-degree-of-freedom Hamiltonian
systems. The former result improves the work of Poincare and the latter is related
to the subharmonic Melnikov method. I also briefly state my results for normal forms
of codimension-two bifurcations and three- or four-dimensional systems with
degenerate equilibria.
Takumi Yagi (Kyoto University)
Hyperbolicity for horocyclic perturbations of semi-parabolic Hénon maps
We consider a family of dissipative quadratic complex Hénon maps $H_{a,t}$ with $a\in\mathbb{D}_{\delta}$ and $t\in [0,1]$, where $\delta>0$ is a small number. Suppose that $H_{a,t}$ has a fixed point $\textbf{q}_{a,t}\in\mathbb{C}^2$, depending continuously on $a$ and $t$, with one eigenvalue $\lambda_t$ such that $\lambda_t\to \lambda_0={\rm exp}(2\pi i p/r),(p,r)\in\mathbb{Z}\times\mathbb{N}$ as $t\to 0$.
Let $\lambda_t/\lambda_0$ be expressed by ${\rm exp}(L_t+i\theta_t)$ and suppose $\theta_t\to 0$ as $t\to 0$. We say that $\{H_{a,t}\} is a horocyclic perturbation if $\theta_t^2=o(L_t)$.
We see that $H_{a,t}$ is hyperbolic if $\theta_t=O(L_t)$ and $L_t\neq 0$.
On the other hand, it is difficult to show the hyperbolicity for horocyclic perturbations.
We introduce some ideas to compute the hyperbolicity for horocyclic perturbations.
Caiwei Zhang (BU)
Jump Process Simulation Algorithms for Modeling Biological Systems with Memory Optimization (Poster)
Wenjun Zhao (Brown)
Quantifying Patterns and Their Transitions in Spatially Extended Systems
Our thanks to the following organizations for workshop funding:
Boston University Department of Mathematics
and Statistics
Boston University Graduate
School of Arts and Sciences
