Stony Brook University Applied Mathematics and Statistics

Speaker: Il Memming Park, Department of Neurology and Behavior, Stony Brook University Place: B203 Time: Mon, 09/23/2019 - 19:00 Abstract How does the brain represent information and process it? By controlling and analyzing the input to and output from the brain -- the sensory stimulus and the behavior -- we have made great advances in modeling cognitive computation which is often well described by simple mathematical models such as a network of noisy leaky integrators and comparators. However, despite extensive efforts, how the brain implements those computations as a biophysical system is still largely unknown. One of the main obstacles is the subsampling problem: there are many (hundreds to hundreds of millions of) neurons across brain areas involved in transforming sensory information to producing the behavior, however, our experimental technology has been limited to observing neural signals from a small fraction of neurons in a handful of areas at the same time. This vast subsampling has limited our ability to infer the physical implementation of cognitive computation in the brain. We had to heavily rely on theoretical principles, intuition, and imagination as to how they might be implemented by a complex network of spiking neurons. Fortunately, recent advances in neural recording technology is allowing us access to several orders of magnitude more neurons at a high temporal precision. This is opening up new opportunities to directly infer the neural implementations: how external and internal information is represented in the population, and how it is transformed over time and across areas. Even for the simplest cognitive processes, such a bottom-up approach has not been successful so far in uncovering the underlying neural dynamics. In this presentation, I lay a principled approach that can tackle the subsampling problem by exploiting the low-dimensional structure of tasks and neural variability. This new approach to studying neural codes and computation is possible through advances in statistical and machine learning techniques aimed at extracting interpretable, i.e., scientifically useful, mathematical models. We have developed interpretable probabilistic models and Bayesian inference algorithms suitable for reverse engineering neural computation from large-scale population data.  

  Dr. Joseph Mitchell, the Chair of Applied Mathematics and Statistics at Stony Brook University, visited SUNY Korea to give a special speech in Fall 2019 commencement. Please visit the link below to find the special speech by Dr. Joseph Mitchell to our first AMS graduated students at SUNY Korea. http://ams.sunykorea.ac.kr/node/378  

Speaker: Tan Cao, AMS SUNY Korea  Place: B203 Academic Building Time: Mon, 11/25/2019 - 18:40 Abstract Optimal control theory is a branch of applied mathematics that deals with finding a control law for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy.  Optimal control is a mathematical optimization method for deriving optimal policies and is an extension of the calculus of variations, dating back to the formulation of Bernoull's brachistochrone problem more than 300 years ago. Optimal control can also be seen as a control strategy in control theory.  Bernoulli's Challenge In the June 1696 issue of Acta Eruditorum, Bernoulli posed the following challenge:  “Given two points A and B in the vertical plane, for a moving particle m, how to find the path AmB descending along which by its own gravity and beginning to be urged from the point A, it may in the shortest time reach B?” This problem, which sounds much better in Latin in its English translation, is the so-called brachistochrone problem, named by combining the two Greek words for the ‘’shortest” (brachistos) and “time” (chronos). In this AMS seminar talk, we will review some basic knowledge of Calculus and discuss an approach how to solve the Brachistochrone Problem.   

Speaker: Yongtang Shi, Nankai University  Place: Academic Building B203 Time: Mon, 10/28/2019 - 18:40 Abstract Ramsey theory is an old and difficult area in extremal combinatorics. In this talk, we will introduce Ramsey numbers and Gallai-Ramsey Numbers of graphs. Especially, Gallai-Ramsey Number of complete graphs with four vertices will be presented. Disjoint work with Henry Liu, Colton Magnant, Akira Saito, and Ingo Schiermeyer.  

Speaker: Hyeuk Kim, Division of Big Data and Management Engineering, Hoseo University Place: B207 Time: Tue, 10/01/2019 - 18:40 Abstract A particle matter is the important issue in control and reduction of pollutants in Korea nowadays. Many atmospheric scientists have tried to predict a particle matter for a long time. In this presentation, we introduce a data mining approach to predict PM2.5 and use a special data source such as a satellite.  

Speaker: Myoungshic Jhun, AMS SUNY Korea Place: B203 Time: Mon, 09/02/2019 - 18:40 Abstract Starting with the asymptotic properties for lattice case, the bootstrap method is used for the construction of simultaneous confidence regions for proportions of single and several multinomial populations. Furthermore, the bootstrap method is also applied to the test for independence in two-way ordinal contingency tables. Proposed bootstrap method is compared with the other methods in terms of average coverage probability by Monte Carlo simulation. Advantages of the proposed method are discussed.      

  SUNY Korea AMS students had well arrived at Stony Brook University for Fall 2019 semester. They had a great opportunity to meet with Dr. Hongshik Ahn, the AMS professor and Graduate Program Director at SBU, and Dr. Estie Arkin, the AMS professor and Undergraduate Program Director at SBU.   

Speaker: Ky Tran, SUNY Korea Place: B203 Academic Building Time: Mon, 06/03/2019 - 18:40 Abstract In this talk, we analyze the optimal harvesting problem for an ecosystem of species that experience environmental stochasticity. We take into account non-linear interactions between species, state-dependent prices, noise impacts, and species seeding. The key generalization is making it possible to not only harvest but also ‘seed’ individuals into the ecosystem. The harvesting problem becomes finding the optimal harvesting-seeding strategy that maximizes the expected total profit. We employ the viscosity solution method, Lyapunov functional approach, and the Markov chain approximation method.  

  The AMS Department and Professor Hongshik Ahn from Stony Brook University held an Info Session on May 29, 2019. Professor Ahn discussed the AMS Graduate Program as well as the Accelerated B.S./M.S. Program. Students asked questions regarding SBU courses, requirements, and suggestions.

  The AMS Department will be hosting the Mathematics Olympiad in SUNY Korea this week. The Math Olympiad will take place in Academic Building C 103 on Saturday, May 11th from 11:00 AM to 1:00 PM. 

Speaker: Ja-Yong Koo, Korea University Place: B103 Time: Thu, 05/02/2019 - 17:30 Abstract Regression analysis is one of the most commonly used methods in statistics that explores functional relationships between variables of interest. Specifically, it examines the influence of one or more predictors on a response variable. We will review the basics of linear regression analysis in which the relationships between a response variable and predictors are assumed to be linear. The focus will be on a careful and intuitive understanding of fundamental concepts of regression analysis. We will also discuss the case where the relationships between variables are highly nonlinear. Flexible regression models based on splines will be briefly introduced.  

Speaker: Donghwan Kim, KAIST Place: B203 Time: Fri, 04/05/2019 - 16:00 Abstract Many modern applications, such as machine learning and statistics, require solving large-dimensional optimization problems. First-order methods, such as a gradient method and a proximal point method, are widely used to solve such large-scale problems, since their computational cost per iteration mildly depends on the problem dimension. However, they suffer from slow convergence rates, compared to second-order methods such as Newton's method. Therefore, accelerating first-order methods has received a great interest, and this led to the development of a conjugate gradient method, a heavy-ball method, and Nesterov's fast gradient method, which we will review in this talk. This talk will then present recently proposed accelerated first-order methods, named optimized gradient method (OGM) and OGM-G.  

Speaker: Jinwon Choi, Sookmyung Women's University Place: B203 Academic Building Time: Mon, 03/11/2019 - 18:40 Abstract Enumerative geometry is an area of algebraic geometry concerned with counting number of geometric structures satisfying a given collection of geometric conditions. I will discuss basic concepts, history, and recent development.   

  Ky Q. Tran joined SUNY Korea in Spring 2019 as a professor in the Department Applied Mathematics & Statistics.  Currently, Professor Tran is teaching two math courses in SUNY Korea: MAP 103 (Proficiency Algebra) and AMS 311 (Probability Theory). 

  Qing Zhang accepted a tenure-track Assistant Professor offer from Department of Mathematics, Shantou University in China. She will start on February 25th. Qing was a Ph.D. student who was with us in SUNY Korea as an ICTCCP student for two years from spring 2016 to fall 2017. She also contributed to the AMS undergraduate education by serving as a TA for AMS 161, 261 and 301.