Computational and Applied Mathematics Seminar

Location and Time

University of Wyoming, Ross Hall 247, Fridays from 4:10-5:00 (unless otherwise stated).

Seminar Chairs

Professors Craig C. Douglas and Rongsong Liu.

Support

The CAM seminar series is currently supported through volunteers and the financial contributions by the UW Mathematics Department, MGNet.org, and and an energy grant from ExxonMobil.

Schedule

For Spring 2019, the speakers are as follows:

Date Speaker From/Note
February 15 Dongwoo Sheen Seoul National University
March 1 Xiukun Hu University of Wyoming
March 8 Yun Li University of Wyoming
March 29 Chen Xu University of Wyoming
April 19 Mauricio Kritz LNCC
April 26 Mauricio Kritz LNCC

* Thursday Colloquium in AG 1030, ** Joint CAM - Analysis seminar

We are constantly looking for speakers for the current academic year! The topics can be original research, a survey of an area, or an interesting paper or papers that would interest the CAM community. If you would like to speak, please contact me by email.

The schedule, titles, and abstracts from Fall 2018 are here.

Titles and Abstracts

February 15

An Introduction to the Idea of an Algebraic Multiscale Method
Prof. Dongwoo Sheen, Department of Mathematics, Seoul National University

We introduce an algebraic multiscale method. The idea is motivated from the algebraic multigrid method (AMG), which is an iterative scheme to accurately approximate the solution to a linear system of equations. Our approach differs in investigating in how to obtain a rough approximation to the original algbraic system arising from modeling heterogeneous materials. We discuss in detail how macroscopic basis functions can be formulated and result in a reduced macroscopic linear system based on the knowledge of the microscopic linear system, with significant redution of dimensions.

March 1

Performance and Scalability Analysis of a Coupled Dual Porosity Stokes Model Implemented with FEniCS
Xiukun Hu, Department of Mathematics and Statistcs, University of Wyoming

A coupled dual porosity Stokes model has been proposed in recent years to help modeling fractured porous media with large conduits. A numerical solution of such a model that works in both 2D and 3D in parallel has been implemented using FEniCS. In this paper, we test the convergence of this implementation with sample problems in both 2D and 3D, investigate the performance and scalability of this implementation thoroughly, and compare the performance between different solvers and preconditioners.

March 8

Cracking the Neural Code: In Vivo Deep Brain Calcium Imaging in Freely Behaving Mice
Yun Li, Department of Zoology and Physiology, University of Wyoming

One of the core questions in neuroscience is to understand how neuronal activities carry information to guide behavior. A direct approach is to simultaneously record large-scale neural activities in vivo from the intact brain while animal freely performs behavioral tasks. Such measurement could potentially establish detailed mechanisms by which activities of individual neurons/neural ensembles code the animal’s behavior. We recently developed a custom miniature fluorescent microscope (miniScope) system that enables large-scale in vivo neural calcium imaging from freely behaving mice. We employed this approach to simultaneously record calcium activities from principle neurons in the medial prefrontal cortex (mPFC) when mice freely explored restrained social targets. We demonstrated that mPFC principle neurons formed two parallel neural ensembles, one positively and the other negatively correlated with a particular annotated behavior (ON and OFF ensembles, respectively). These mPFC neural ensembles are spatially intermingled and functionally interacted to carry real-time information relevant not only to behavior, but also to salience/novelty of the explored targets.

March 29

Computing the Society: Developing Understanding through Datafication
Prof. Chen Xu, Department of Geography, University of Wyoming

Social media data provide a great opportunity to investigate human behavior or event flow in cities. Despite the advantages of social media data in these investigations, the data heterogeneity and big data size pose challenges to researchers seeking to identify useful information from the raw data. This talk introduces the use of social media data in understanding the society through two case studies. In the first case study, we use a centrographic approach for studying people’s daily activity spaces. The second case study demonstrates an efficient approach based on machine learning and geovisualization to identify events and trace the development of these events in real-time. We conducted an empirical study to delineate the temporal and spatial evolution of a natural event (heavy precipitation) and a social event (Pope Francis’ visit to the US). By investigating multiple features of Twitter data (message, author, time, and geographic location information), this talk demonstrates how voluntary local knowledge from tweets can be used to depict city dynamics, discover spatiotemporal characteristics of people’s behaviors and events, and convey real-time information.

April 19

Environmental Probes
Prof. Mauricio Kritz, LNCC

Environmental and ecological interacting units are actually identified by their trophic webs. Hence, the study of changes in these systems leads naturally to ‘systems of variable structure’ because trophic webs are indeed interaction graphs that retract the interaction (structure) of the phenomenon. Since circa 2005, we have been developing a conceptual design for a probe ‘capable of detecting structural changes in trophic webs’, a task that strongly relies on ideas of organization and data-driven computation [Douglas et al, 2015]. A recent project proposal still under analysis opened the possibility of effectively constructing a prototype to refine and further develop tools for continuously monitoring of environmental systems. In this talk, I shall present the latest additions to the probe’s design and discuss the programming, mathematical, and practical challenges related to it.

CC Douglas, TM de Andrade Soares, and MV Kritz — A data driven scientific ap-proach to environmental probes. In S. Ravela and A. Sandu, editors, Dynamic Da-ta-Driven Environmental Systems Science, volume 8964 of Lec- ture Notes in Computer Science, chapter 9, pages 89–99. Springer International Publishing Switzerland, New York, nov 2015. ISBN 978-3-319-25137-0. doi: 10.1007/978-3-319-25138-7 9. URL http://link.springer.com/chapter/10.1007/978-3-319-25138-7 9.

April 26

From Systems To Organizations
Prof. Mauricio Kritz, LNCC

One drawback that slowed down the development of the system science intellectual framework, since the beginning of the 1990s, is the difficulty encountered in representing and handling two cases in the systems framework: phenomena of variable structure and phenomena where some interacting elements may be phenomena themselves, which results in a ‘system of systems’. Situations that are common in living and complex phenomena, for instance, when studying environmental changes (characterized by changes in trophic chains) or when picturing a cell as formed by organelles, represented by systems, and other elements in an integrated manner. I recently introduced a definition of organization in which an abstract model leads to a space of organizations that allow for creating mathematical tools to handle organizations and reason in terms of them [Kritz, 2017]. In the formalism that springs from this definition and its model, organization is an immediate generalization of the system concept. After a quick introduction of the necessary concepts and constructs, I shall discuss how to represent and handle variable structure and ‘systems of systems’ models in the space of organizations. Key concepts in this discussion, that do not belong to the organizations framework, will be interaction graphs, collective observables, and thing types.

MV Kritz – From Systems to Organizations. Systems, 5(1):23, Mar. 2017. doi: 10.3390/sys- tems5010023. URL http://www.mdpi.com/2079-8954/5/1/23.

This web page is maintained by Prof. Craig C. Douglas

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