Events
Department of Mathematics and Statistics
Texas Tech University
Although basketball is a dynamic process sport, with 5 plus 5 players competing on both offense and defense simultaneously, learning some static information is predominant for professional players, coaches and team mangers. In order to have a deep understanding of field goal attempts among different players, we proposed two different approaches to learn the shooting habits of different players over the court and the heterogeneity among them. First approach is a mixture of finite mixtures (MFM) model to capture the heterogeneity of shot selection among different players based on Log Gaussian Cox process (LGCP). Second approach is a zero inflated Poisson model with clustered regression coefficients. Our proposed method can simultaneously estimate the number of groups and group configurations. We apply both proposed model to the National Basketball Association (NBA), for learning players’ shooting habits and heterogeneity among different players over the 2017–2018 regular season.
Dr. Yang's Job Colloquium talk is sponsored by the Statistics seminar group. Please virtually attend via this Zoom link.
We study the biharmonic equation with Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem as a system of Poisson equations. Our method differs from the usual mixed method that leads to two Poisson problems but only applies to convex domains; our decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulting system. In addition, we derive optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings. This is joint work with Hengguang Li and Zhimin Zhang.
This Job Candidate Colloquium is sponsored by the Applied Math seminar group, and you are invited to attend Wednesday the 17th at 4 PM CST (UT-6) via this Zoom link.
We will discuss a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We will discuss a recent result regarding a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we will explain that a spiral gives rise to such solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922, despite significant progress of the theory of vortex sheets and Birkhoff-Rott equations. We will also show well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane. This is joint work with P. Kokocki and T. Cieślak.
Dr. Ożański's Job Colloquium talk is sponsored by the PDGMP seminar group. Please virtually attend via this Zoom link.
We will discuss several isoperimetric problems
for geometric and functional characteristics of polygons with
$n\ge 3$ sides. I will demonstrate several methods, which can be
used to attack these problems, explain remaining difficulties,
and mention several challenging questions, which remain open for
long time.
To join the talk on Zoom please click
here.
N/A
Motivated by the Canham-Helfrich model for lipid bilayers, the minimization of the Willmore energy subject to the constraint of fixed isoperimetric ratio has been extensively studied throughout the last decade. In this talk, we consider a dynamical approach by introducing a non-local $L^2$-gradient flow for the Willmore energy which preserves the isoperimetric ratio. For topological spheres with initial energy below an explicit threshold, we show global existence and convergence to a Helfrich immersion as $t\to\infty$. Our proof relies on a blow-up procedure and a constrained version of the Lojasiewicz-Simon gradient inequality.
Watch online via this Zoom link.We investigate a pair of surjective local ring maps $S_1\leftarrow
R\to S_2$ between local commutative rings and their relation to the
canonical projection $R\to S_1\otimes_R S_2$, where $S_1,S_2$ are
Tor-independent over $R$. The main result asserts a structural
connection between the homotopy Lie algebra of $S$, denoted $\pi(S)$,
in terms of those of $R,S_1$ and $S_2$, where $S=S_1\otimes_R
S_2$. Namely, $\pi(S)$ is the pullback of (restricted) Lie algebras
along the maps $\pi(S_i)\to \pi(R)$ in a wide variety cases, including
when the maps above have residual characteristic zero. Consequences to
the main theorem include structural results on Andr\'{e}--Quillen
cohomology, stable cohomology, and Tor algebras, as well as an
equality relating the Poincar\'{e} series of the common residue field
of $R,S_1,S_2$ and $S$, and that the map $R\to S$ can never be Golod.
Join the seminar via this
Zoom link
Abstract: This talk will focus on the development and implementation of a systematic trading strategy.
It will cover the life cycle of systematic trading, the common pitfalls of backtesting,
and the out-of-sample stability of a systematic strategy.