## This page contains an archive of our recent activities. Send us your thoughts on any posting through our forum!

## What's New

### SIAM Lightning Talks (Spring 2023)

### On Monday, April 24, 5:30-8:00pm in McB 455 we will be hosting student lightning talks followed by a social where you can discuss your research with interested individuals. The purpose of these lightning talks is to allow individuals to give a short, 5-10 minute introduction to their research with the hopes of fostering new collaboration.

### We plan to have about one hour of talks from 7-8 students, followed by an informal discussion/social time for the rest of the evening. We hope to see you there!

If you are interested in presenting, please fill out this form by Monday, April 17 at 11:59pm. Chosen participants will be notified by email.

### Academia to Industry (Spring 2023)

Dr. Alan Lattimer, Chief Analytics Officer for Socially Determined, will be visiting Virginia Tech to talk about his life after graduate school and the problems he’s working on now. His talk will be on February 27th from 5:30 to 6:30 PM in McBryde 455. If you’re interested, please RSVP here. There will be pizza! Contact skbender@vt.edu if you have any questions.

### 2023 SIAM Interest Meeting

Interested in applied mathematics and/or computational science? Come join the Virginia Tech SIAM Student Chapter on February 13th @5:30pm in MCB 455 for our Spring 2023 Interest Meeting. We will discuss our plans for the chapter this semester and enjoy some pizza (provided) and board games. If you’re interested in getting more involved with our organization, or just want to stop by for some free pizza, please fill out this form!

## Archive

### Joint SIAM Chapter Talk: April 15th, 2022

### Joint SIAM Chapter Talk: April 15th, 2022

Registration: Click this link

When: Friday, April 15 from 3:30 pm Eastern Time

Speaker: Dr. Lorena Guachi, BioRobotics Institute

Title: Data-driven Computer Vision: real-world automation approaches

Come join us to listen to Dr. Lorena Guachi, who is a Researcher at the BioRobotics Institute, Italy. She conducts interdisciplinary research linking Computer Vision, robotics, mechatronics, and mechanical engineering for automating clinical processes. Computer vision aims to give machines the ability to see. If we want industrial pick-and-place robots, drill robots in enabled free areas, self-driving cars, and lifelike assistants that perform natural speech patterns, we must build machines with the same visual capabilities that humans enjoy. So, how can we teach machines to see? Computer vision systems examine each and every pixel in an image to determine whether or not a specific feature is present, this is known as feature extraction. Model-based methods and data-driven methods are the two broad categories of feature extraction methods. Model-driven approaches involve hand-coding features one at a time, whereas, in data-driven approaches, the most descriptive features of each object definition are determined by the algorithms/models themselves. Whether or not a computer vision problem is best solved with model-driven or data-driven approaches depends on several factors, including the access to data, hardware or device resources, the full range of data cases, and expected variations. Therefore, the goal of this talk is to deepen data cases and the design, and adaptation of data-driven approaches for automating clinical processes.

### Joint SIAM Chapter Talk: March 11th, 2022

Compact embeddings of p-Sobolev-like cones of nuclear operators - Dr. Juan Mayorga (Yachay Tech)

Friday, March 11th, 2022 at 1:30 PM MST

Register here!

Title: Compact embeddings of p-Sobolev-like cones of nuclear operators

Come join us to listen to Dr. Juan Mayorga-Zambrano, who is a titular professor of Mathematics at Yachay Tech University. This talk will include his last works on compact embeddings. In particular, he will show that the p-Sobolev-like cone of operators is compactly embedded in the self-adjoint trace-class operators on L2. In the path, he proves regularity properties for the density function associated with self-adjoint trace-class operators on L2 as well as Gagliardo-Nirenberg type inequalities departing from Lieb-Thirring type conditions. Moreover, he applies the compactness property to minimize free energy functionals where the entropy term is generated by a Cassimir-class function related to the eigenvalue problem of the Schrödinger operator −α∆ + V, α > 0, with Dirichlet condition. You will be able to discuss and ask questions to Dr. Mayorga-Zambrano about his current work at Yachay Tech University and his career path. This talk will offer further knowledge enrichment to students in STEM.

### Joint SIAM Chapter Talk: February 16th, 2022

Dr. Sam Jacobs (Lawrence Livermore National Laboratory)

Wednesday, February 16th, 2021 at 2:00 PM EST

Register here!

Title: Learning and Learning to Learn at Scale

Abstract: Progress in deep learning is anchored on a tripod: increased computational power, more sophisticated neural network architectures, and growing datasets. Tremendous advances have been made, but we are yet to maximize what is possible. Training of neural networks for vision and language model applications are inhibited by the prohibitive cost of model exploration and model training. Scientific applications of interest to the US Department of Energy and US national laboratories face additional challenges: (1) scientific data are often hard to label and require domain expertise, (2) the measure of uncertainty required by predictive models, and (3) satisfying scientific constraints. Given these requirements and others, neural network architectures must be frequently tuned for specific scientific applications requiring extensive architecture search and hyperparameter tuning. In this talk, I will present our on-going work in large-scale training and architecture search of deep neural networks. I will discuss different parallelization techniques in an HPC-centric deep learning toolkit- Livermore Big Artificial Neural Networks (LBANN)- and its extension for fast, robust, and scalable neural architecture search. Experimental results from different application domains including small molecule antiviral drug design for CoVID-19 will be presented.

### VT-ASU Joint SIAM Chapter Talk: January 19th, 2022

The SIAM student chapters at Arizona State University and Virginia Tech hosted their first speaker of the semester! See the attached flyer for more details.

Registration: https://cutt.ly/GIt6ULb

When: Wednesday, January 19 from 2:00 pm Eastern Time

Speaker: Dr. Saad Qadeer

Biography: Saad is a postdoctoral research associate at PNNL working on multiscale modeling and high-order numerical methods. Prior to joining PNNL, he was a postdoc at UNC Chapel Hill. He obtained his PhD from UC Berkeley under the supervision of Jon Wilkening, and did his undergraduate work at LUMS, Pakistan.

Title: High-Order Numerical Methods on Complex Domains

Abstract: Any physical theory relies on a mathematical model, typically in the form of a Partial Differential Equation (PDE), the solutions of which yield the predictions of the theory. Barring some simple cases, the solutions are found numerically by devising efficient algorithms. However, this task becomes harder as the physical domain becomes more complicated. Conventional techniques typically yield low order accuracy and end up requiring a balance between accuracy, and computational effort. In this talk, I will discuss some of my efforts towards developing numerical methods for complex geometries. One such common yet largely unexplored domain is the three-dimensional cylinder. Employing carefully chosen basis functions, leads to powerful solvers and allows us to address challenges such as the nonlinear Faraday wave problem. Next, we shall move beyond domain-specific approaches and identify the subtle issues underlying the shortcomings of the generic low accuracy methods. After providing an overview of some of the proposed methods to overcome these issues, I shall present the Projection Extension method, a novel approach that yields highly accurate solutions on a large array of complex domains. The technique leverages simple ideas to great effect, with the result that it is straightforward to apply, implement, and generalize, and allows us to compute demonstrably accurate solutions to several challenging models, including heat flow and Newtonian and viscoelastic fluid problems.

### SIAM Virtual Career Fair: March 3rd, 2021

Join us for the upcoming SIAM Virtual Career Fair! The event is scheduled for Wednesday, March 3, 2021 from 10:00 a.m. – 2:00 p.m. and 3:00 p.m. - 5:00 p.m. EST, alongside the SIAM Conference on Computational Science and Engineering (CSE21). All you need to participate is an Internet connection. Registration is free for job seekers, who can sign up here.

Employers will be recruiting for interns, postdocs, and full-time positions.

What is the Virtual Career Fair?

The Virtual Career Fair is an event at which you can chat with employers about working in various industries. It is a great opportunity for you to meet government and industry representatives and discuss what they look for in candidates and what each employer may have to offer. The event is held primarily for graduate students and recent graduates, but job seekers at all career stages are encouraged to attend.

How Can I Participate?

To participate in the career fair, you simply need to be a SIAM member or registered for CSE21. And if you’re a student, remember you can be nominated for free membership by any non-student member of SIAM.

### Patrick O'Neil - "Mathematics in Industry" Speaker: Feb 17, 2021

This presentation was by Patrick O'Neil, who is the Chief Data Scientist at BlackSky in Herndon, Virginia.

[The recording of this presentation is not available due to the speaker's organizational restrictions]

Patrick is currently the Chief Data Scientist at BlackSky, where he started working years ago as an intern. During his internship, Patrick developed the core algorithms that form the foundation of Spectra AI, the company’s AI/ML-powered predictive geospatial analytics platform. Spectra AI automatically analyzes millions of data elements each day, including satellite imagery, IoT data and information from global sensor and signal networks, to track activity around the world. When the global pandemic hit, Patrick and his team built a system to monitor social mixing from space, integrate the observations into the latest epidemiology models, and provide critical risk assessments to the U.S. Air Force.

Patrick is an affiliate faculty member at George Mason University and works closely with the school’s Geography and Geoinformation Sciences department and the Center for Mathematics and Artificial Intelligence. He serves on the Dean’s Advisory Board and the diversity team for the College of Science. He also serves on the Virginia Dept. of Education Data Science Advisory Board, helping define mathematics curricula for the state’s high schools.

Recap of Patrick's presentation:

BlackSky is a global monitoring company, building machine learning and artificial intelligence models as a part of the new "space revolution".

Patrick worked in industry before going back to grad school, which allowed him to better understand what he wanted to focus on learning during his graduate degree. He had the opportunity to participate in many internships during graduate school, and highly recommends students to take the same approach to their careers.

BlackSky uses satellites for building a database to power the geospatial revolution, and Patrick notes that "static geospatial intelligence is obsolete in a dynamic world". BlackSky's geospatial intelligence database (GIDB) aggregates, enriches, and delivers high-velocity geospatial intelligence from global sensors. The GIDB accounts for economic indicators, stockpile volumetrics, live reporting, radio activity, asset positioning, and human mobility. Effectively, they are trying to track the global economy in real-time.

All of that is powered by "Spectra AI", BlackSky's portfolio of data feeds that Patrick is in charge of building. BlackSky has 24 global satellites taking over 100,000 daily observations, and Spectra AI takes raw data to insightful information through natural language processing, computer vision, tracking and prediction, epidemiology modeling, tipping & cueing, and time series analysis. From a functional standpoint, Spectra AI consists of three main components for event processing, detection, and movement.

Additional advice from Patrick discussed during Q&A:

For internship opportunities at BlackSky, send an e-mail to Patrick with a resume and description of research interests and skills.

Regarding privacy concerns for their data: they are not trying to track individuals but rather moving objects. There are datasets out there where privacy is a major concern, but BlackSky does not participate in this data collection.

Regarding ethical concerns for their data: BlackSky has a humanitarian group that identifies where information can be helpful, and is able to provide it free of charge.

### Nitsan Ben-Gal Nguyen - "Mathematics in Industry" Speaker: Feb 3, 2021

This presentation was by Nitsan Ben-Gal Nguyen, who is a Data Science Specialist at 3M in Saint Paul, Minnesota.

[This presentation was not recorded due to the speaker's organizational restrictions]

Nitsan Ben-Gal is a Data Science Specialist in the Artificial Intelligence Group within the Corporate Research Laboratories at 3M Company. She earned her B.S. in Mathematics and Physics from the University of Michigan in 2004, and her Ph.D. in Applied Mathematics from Brown University in 2010 with a concentration in Dynamical Systems. From 2007 to 2014 Nitsan worked at international research labs at the Freie Universität Berlin, the Weizmann Institute of Science in Israel, and the Institute for Mathematics and its Applications in Minnesota, before joining 3M in 2014. She has worked in the Corporate Research Labs through her 6 years at 3M, giving her the opportunity to develop technologies and products for divisions ranging from the Chemical Analytics Lab, Construction and Home Improvement Markets, Oral Care Solutions, Personal Safety, Traffic Solutions, and more. She is currently working on AI in Manufacturing, Healthcare, and Air Quality domains.

Recap of Nitsan's presentation:

Dr. Ben-Gal's early aspirations ranged from running her own business, working in the financial sector, and then to becoming a mathematician or physicist. During college, the many opportunities that arose led her towards becoming an applied mathematician. Since 2014, she has been working as a mathematician in the industry after leaving academia.

At 3M, Dr. Ben-Gal works in the Corporate Research Systems Lab, which is just one of several branches of corporate research within the organization. For those asking what a mathematician can do with their skills in the industry, the following are some answers:

Clear the air

Improve health and appearance

Improve ease and accuracy of security procedures

Analyze chemical properties

Protect workers

Create tools to save time and improve brainstorming

Distinguish people's preferences

Develop new materials

Sell more products

These answers show that a mathematician can make an impact on many aspects of the industry. A few examples of what projects Dr. Ben-Gal has been involved with at 3M include:

Air quality: involving technologies such as sensor integration and time series analysis, and challenges posed through multimodal data fusion and data annotation.

Digital orthodontics: involving technologies such as robotic motion planning and 3D mesh processing, and challenges posed through noisy and/or limited data.

Digitally enhancing physical products, such as in the data science and merchandising lab, the Post-It Plus app, and optimizing display quality for various electronics.

Advice for mathematicians on the job market:

Always work on improving the resume through projects and skills, and workshopping your resume with others.

Network, network, network.

Prepare an "elevator speech" for all research experience.

Many employees are not hired for their expertise, but their ability to develop the required expertise.

A "mathematical mind" is great for industry, but the mindset of pursuing only those areas of math in which you have deep expertise is detrimental. One needs to be open to learning many new areas of math and science throughout an industrial career.

Do not let a job title or preferred qualifications section discourage applying. Preferred qualifications are like a Christmas list; having all the basic qualifications and 40% of the preferred qualifications makes a good candidate.

Do not wait for a job posting - network and seek out opportunities.

Additional advice from Nitsan discussed during Q&A:

Q: In the industry, how does one manage working outside of their expertise if they are faced with a time-constrained problem with which they have no experience?

A: These time-constrained situations do not typically happen for those who are not already experts in the subject matter. Otherwise, the initial action is to propose a solution or approach after a certain initial period of time to see if it may lead to further action. Admitting a lack of experience but then trying to learn and help is a valued attitude to take.

Q: Does 3M have any room for employees without PhDs or graduate degrees?

A: Yes, there are many roles for all degree levels. While some more senior entry roles are restricted to candidates with Ph.D. or a Masters plus work/internship experience, an employee who enters with a Bachelors can move into these types of positions with time and proven success at leading research efforts. It is more vital to have the relevant skills required for a position. PhDs are good indicators to the hiring company of an individual's ability to learn the necessary skills for a position and do independent research.

Q: Does 3M have internships?

A: Yes, see https://www.3m.com/3M/en_US/careers-us/. 3M has internships for undergraduate, master's, and PhD students. As of today there are a small number of remaining slots available this year. If you do not see a relevant internship posting on the Careers page, please send your resume directly to Dr. Ben-Gal for consideration if any positions remain unfilled.

Q: What is different about the academic setting?

A: Academia is very open and individuals have more control over their schedules. There is more uncertainty in academia in terms of receiving project funding or writing impactful papers, which leads to added pressure to take on more projects and have less free time. Neither academia nor industry positions are advantageous over the other, since each are suited for different lifestyles and individual needs.

### Pavel Bochev - "Mathematics in Industry" Speaker: Dec 2, 2020

This presentation was by Pavel Bochev, who is a Computational Mathematician at Sandia National Laboratories in Albuquerque, New Mexico.

Click here to watch a recording of the presentation!

Pavel is a Senior Scientist at Sandia National Laboratories in Albuquerque where he works in the Center for Computing Research. Pavel’s research interests include compatible discretization for partial differential equations, optimization and control problems, and the development of new, property preserving heterogeneous numerical methods for complex applications relevant to the mission of the US Department of Energy and the National Nuclear Security Administration.

Pavel earned his Magister of Mathematics degree from the University of Sofia, Bulgaria in 1987 and his PhD in Mathematics in 1994 from Virginia Tech. His thesis was awarded the SIAM Student paper prize for 1994. In 2012 Pavel was elected a Fellow of the Society for Industrial and Applied Mathematics. He is also a recipient of 2014 US Department of Energy’s E. O. Lawrence Medal in the category of “Computer, information and knowledge sciences”. This award honors U.S. scientists and engineers, at mid-career, for exceptional contributions in research and development supporting the Department of Energy and its mission to advance the national, economic and energy security of the United States. In 2017 Pavel was awarded the Thomas J.R. Hughes Medal by the U.S. Association for Computational Mechanics for his contributions to the field of numerical partial differential equations.

Pavel has authored and co-authored over 100 research papers, two books and several book chapters, and has given numerous plenary and invited lectures in the US and abroad. He served two terms as Editor-in-Chief of the SIAM Journal on Numerical Analysis and is currently member of the editorial boards of SINUM and RINAM.

Recap of Pavel's presentation:

The title of Pavel's talk was: "What does a computational scientist do at a national lab?"

Pavel was born and raised in Sofia, Bulgaria. After finishing high school, Pavel spent two years in the Bulgarian army before starting university. Pavel finished his undergraduate and masters studies in Bulgaria. Following the fall of the Berlin Wall in 1989, Pavel was able to apply to PhD programs in the US and consequently ended up at Virginia Tech. After his PhD, his first job was as a professor of mathematics at UT-Arlington for 6 years. Since 2000, Pavel has been at Sandia Labs in Albuquerque, New Mexico.

Since he has often been asked about the difference between working in a university compared to a national lab, Pavel presented a table identifying the main distinctions. Another question Pavel has often been asked is if one can do foundational theoretical work and still thrive in a national lab. To this question he answers "yes, but with the right mindset"; in the industry setting, the goals of the organization must be prioritized before one's own. He states that one of the biggest challenges in lab research is crossing the "valley of death" between "great science" and "impacting the mission" of the organization. Nevertheless, Pavel has been able to stay engaged in the mathematics research community during his time at Sandia by writing books, editing journals, and writing research papers.

The main technical discussion for this presentation was on optimization-based modeling (OBM). This included a discussion of the following topics:

heterogeneous numerical methods (HNMs), including:

achieving stability and accuracy (structural aspects)

preserving physical properties (qualitative aspects)

assembling the parts into HNMs and solving them

combining coupling, splitting, and preservation of properties into an optimization problem by using a divide and conquer approach

Basic OBM patterns for coupling/splitting and preservation of properties

Examples of OBM problems

Additional advice from Pavel discussed during Q&A:

Asked about the unifying framework of the lab in terms of numerical methods and schemes used, Pavel answered that often a new problem is solved with existing pieces coming from multiple owners. One typically has to combine legacy codes and other ideas that exist to answer current questions, rather than working from a clean slate.

Information about internships: they are announced around September or October. A good strategy would be to identify a potential lab mentor and start planning in the late summer for applying. Internships are 12 weeks long in the summer, and the work is typically agency-sponsored. Very often, the intern continues collaborating with the mentor in the lab after the internship has finished. A benefit of a lab internship for students is having the opportunity to do research in areas that might not be related to current university research.

### Jeanne Atwell - "Mathematics in Industry" Speaker: Nov 11, 2020

This presentation was by Jeanne Atwell, who is a Senior Director of Advanced Mission Solutions at Ball Aerospace in Boulder, Colorado.

Click here to watch a recording of the presentation!

Dr. Jeanne Atwell earned a B.S. degree in Mathematics from the University of North Carolina at Charlotte, a M.S. degree from Oregon State University, and a Ph.D. in Applied Mathematics at Virginia Polytechnic Institute and State University. In the earlier part of her 20+ years at Ball Aerospace, Jeanne filled roles including data scientist, systems engineer, technical manager, and functional manager. She has supported programs in all phases of the program lifecycle, from architecture studies to requirements development to post-delivery support, including serving as Chief Engineer on programs and proposals. In her previous role, she led the group chartered to develop technology, mission concepts, and a diversified customer base for Ball’s National Defense business unit. Currently, Jeanne is responsible for capture and execution of a transformational mission partner opportunity.

Recap of Jeanne's presentation:

Jeanne's presentation focused on a discussion of the overlap between mathematics and aerospace engineering.

When Jeanne was preparing for her undergraduate degree, she was interested in aerospace engineering. She was given advice by a professor in the Aerospace Engineering department at UNC Charlotte about the benefit of doing a degree in mathematics instead; a math degree would give her the foundational skills for not only aerospace engineering, but also most other fields of engineering.

Since entering the aerospace industry, Jeanne has been responsible for tasks including algorithm development, system modeling, mission architecture, data analysis, research and development, and people management.

An explanation of the overlap between math and aerospace was described by a case study. In this case study, step 1 is to identify the question. By classifying and considering events that overlap in time, the important information needs to be dissected and analyzed. Step 2 would be to write the problem in mathematical form that is understandable, such as a matrix equation that is typically solved using linear algebra techniques. Consequently, step 3 is to solve the math problem. The difficulty in step 3 is that, unlike in textbooks, sometimes the chosen problems do not necessarily have answers. Then, step 3a would be to break down the difficult problem into several simpler problems which are more recognizable, and consequently solve those simpler problems. Typically, step 3b would be to find a solution that isn't perfect (due to complexity of the problem), but gets the job done. However, the margin of error must always be kept under control due to the high stakes of the intended application. Therefore, steps 4, 5, 6, and so on are dedicated to solving layers of subproblems.

In summary, three ideas are similar in both mathematics and aerospace:

Calculations and computation involve concepts such as linear algebra, differential equations, and numerical analysis

Abstraction of problems (recognizing how to solve problems framed within a different context)

Meticulously logical thinking

Additional advice from Jeanne discussed during Q&A:

The learning curve for working in the aerospace industry coming from an academic background in mathematics varies depending on the task, such as simply learning vocabulary versus understanding the techniques used to solving engineering problems that aren't based on mathematics alone.

The main difficulty of jumping from academia to industry without any prior internships involves learning workplace practices that are not relative to the academic setting.

Ball Aerospace hires summer interns in October, so her advice to those interested in the aerospace industry is to start looking very early for available jobs.

The programming languages she learned in graduate school are Maple, Mathematica and Matlab, but at work she mostly used Matlab for many years. However, Python has become the industry language of choice in recent years, and knowing both Python and Matlab is encouraged.

### Hoan K. Nguyen - "Mathematics in Industry" Speaker: Nov 4, 2020

This presentation was by Hoan K. Nguyen, who is a Principal Research Scientist at Information System Laboratories (ISL) in San Diego, California.

Click here to watch a recording of the presentation!

Dr. Hoan K. Nguyen (PhD, Applied Mathematics, Virginia Tech) is a Principal Research Scientist at ISL and she is currently the principal investigator (PI) and Co-PI on multiple NAVAIR and AFRL SBIR/STTR radar projects. Dr. Nguyen has over 15 years of experience providing direct analytic support to multiple three-star flag officers in the U.S. military. She served as a special staff to the Commander, Naval Air Forces, Commanding General, III MEF, Commander, U.S. Third Fleet, U.S. Army Rapid Equipping Force, and the Combined Joint Task Force Paladin. In her roles, Dr. Nguyen deployed with the staff to Afghanistan, Nepal, and the Philippines, for real world operations and embarked on multiple Naval platforms, such as aircraft carriers, amphibious ships, and MV-22, just to name a few. She also led a wide range of studies to include the development of new training readiness metrics, operational assessment metrics, mishaps analysis, combat power analysis, OPLAN feasibility analysis, and emerging technologies assessments. Dr. Nguyen has published over a dozen peer-reviewed papers and several dozen CNA research papers. Her current research interests include optimization methods, radar scheduling algorithms and radar signal processing.

Recap of Hoan's presentation:

Dr. Nguyen's talk was focused on her background, how mathematics is used in her projects at work, and challenges/lessons that she has learned over the years.

Hoan came to Virginia Tech as an undergraduate in 1997. She only chose to major in mathematics since she could not decide between computer science and engineering, and mathematics seemed to provide a solid foundation in either of those directions. After her undergrad, Hoan worked at the Naval Research Lab as a mathematician for several years. Although she originally planned to focus on completing her bachelor's degree, she was persuaded after a few years of industry work to come back to Virginia Tech for a graduate degree. After eventually completing her PhD in Applied Mathematics at Virginia Tech, Hoan was a Postdoc at SAMSI/CRSC in North Carolina and then Senior Research Scientist at the Center for Naval Analyses (CNA). With CNA, Hoan worked at US military bases in places such as Afghanistan and Japan.

Hoan highlighted a few projects during her career in the industry. One project required optimizing aircraft carrier schedules through the use of genetic algorithms. This project stressed that, in real-world operations, very often the method chosen to solve a problem is based on convenience rather than finding what works best. Another project during her time in Afghanistan required geometry to analyze indirect fire coming from the Taliban. This project taught her that around 80% of the time working in her industry position is spent trying to identify the correct problem, as opposed to trying to find solutions to problems that might not accurately reflect what is needed. She also worked on building logistic regression models to analyze naval aviation mishaps and optimizing and controlling radar scheduling in the presence of limited resources.

The main challenges she finds in her work are acquiring sufficient data to analyze or identify a problem, balancing deadlines with high-quality results, and finding a work-life balance. The main lessons learned have been the importance of clear and frequent communication, excellent personality and teamwork traits, and being an advocate and speaking up for oneself.

Additional advice from Hoan discussed during Q&A:

She found that, while many real-world problems have similarities with textbook problems, graduate school allowed her to ask better questions in her workplace and changed her view on the problems she worked on.

After finishing her undergraduate degree, she thought she knew everything about mathematics. However, after finishing her PhD, she correctly realized how little she truly knew about mathematics.

She found that most people have a great amount of respect for individuals with mathematics degrees.

The main difference between mathematicians and engineers in her industry are that engineers will do whatever they can do ensure a problem is solved, whereas mathematicians want to ensure the fundamental accuracy of a proposed solution.

There are student internships available at ISL.

The difference between government and private industry work is that private companies are focused on meeting deadlines and profit goals, whereas government jobs provide more time to work on research and development and publish papers.

### Alan Lattimer - "Mathematics in Industry" Speaker: Oct 21, 2020

This presentation was by Alan Lattimer, who is a Data Scientist at Socially Determined in Washington, DC.

Click here to watch a recording of the presentation!

Alan Lattimer runs the data science team and leads analytic strategy for Socially Determined, a company focused on social determinants of health and their impact on disease outcomes and healthcare utilization patterns. His background is in computational mathematics, and he is passionate about using his skills to make a positive impact on vulnerable populations. Dr. Lattimer has a BS in Computer Science and an MS and Ph.D. in Mathematics, all from Virginia Tech.

Recap of Alan's presentation:

Alan's talk was focused on examples of how mathematics and data science are used in the healthcare industry, and he offered insight into leveraging a mathematics background in the workplace.

Alan spent 8 years in the US Navy, after which he went back to school and obtained a bachelor's degree in computer science from Virginia Tech. Then, for 10 years he developed software in the healthcare industry, after which he returned to Virginia Tech for a Master's and PhD in Mathematics.

Since finishing his PhD, Alan has worked exclusively in industry positions. His first role was in an engineering firm working on topics related to computational fluid dynamics, robotics, and machine learning. Since then, he has worked for Socially Determined as the person in charge of the risk analytics and data science group. His role at Socially Determined involves overseeing mathematical and statistical models, and guiding strategy of the group.

As an example of what Alan does, an important part of strategy in their company is understanding social determinants of health (SDOH). SDOH are environmental factors in which people live, learn, work, or stay active that affect health risks and outcomes. The models and problems they work on are geared towards understanding when and how to intervene in these communities to maintain a healthy population. Being that there is an estimated amount of 3.6 trillion dollars in yearly US health care expenditures, Socially Determined provides each stakeholder with visibility into 50% of the factors that influence utilization patterns, costs and outcomes of healthcare that are otherwise unknown.

Currently, there are two main models in SDOH factors. The first are targeted research studies (similar to academic work) which tend to be very specific and try to draw correlations between SDOH and an individual's health. Although these studies give great insight into specific cases, they cannot be used to make conclusions about the general population. Hence, creating broadly applicable intervention strategies from targeted research studies is challenging. The second are broad generalizations of risk, which are too general to apply to a specific community, do not provide insight for local intervention strategies, and do not show any financial benefit of taking action.

The proposed middle ground between these two main models is to build community-specific SDOH risk measures, create methods to continuously track an individual SDOH, and fuse individual and community risks within that specified region. Some of the risk domains and drivers of these communities are food landscape, housing environment, transportation network, economic climate, and health literacy. By assigning quantitative risk scores for each factor, community SDOH risk profiles can be created at town, county and state levels across the US.

Alan discussed several case studies in his talk. One case study was about methods used for predicting health outcome within communities. The techniques used for these methods involved correlations, risk clustering, and principal component analysis on millions of health insurance claims. These methods provide 9 discrete health categories in which individuals are classified, and in which the factors pushing an individual up or down between categories could be analyzed.

As a final thought to those attending the presentation inclined towards pursuing a career in industry, Alan gave the following advice:

Be ready to learn on your own

Remember to finish the test before starting extra credit work

Use your problem-solving skills to set your self apart and show your worth

Seek domain knowledge

What makes mathematics the most powerful degree in Alan's opinion, but also provides an initial drawback: Mathematics is "domain agnostic" (i.e. a generally relative skill). As George Box famously said: "All models are wrongs, but some are useful". Domain expertise is critical to understanding what is measurable within the domain, and superior knowledge of the domain can set individuals apart in their work.

Additional advice from Alan discussed during Q&A:

Ethics plays a very important role in data science within the healthcare industry.

There is always new information coming out from the Centers for Disease Control and Prevention (CDC) or research studies about factors leading to certain diseases, but rigorous standards are in place before validation of this new information is considered. Since most studies are directed, and the metrics Socially Determined uses are not directed, many times the new information is not relevant to the factors being analyzed (such as trying to prove a mathematical statement by assuming the conclusion is true).

Healthcare experts and data science experts work together for a holistic understanding on organizational goals.

Reach out to Alan if you are interested in learning about available internships and full-time positions at Socially Determined.

### Mouhacine Benosman - "Mathematics in Industry" Speaker: Oct 9, 2020

This presentation was by Mouhacine Benosman, who is a Senior Principal Research Scientist at MERL in Boston, Massachusetts.

Click here to watch a recording of the presentation!

Before coming to MERL in 2010, Mouhacine worked at universities in Reims University, France and Strathclyde University, Scotland before spending 5 years as a Research Scientist with the Temasek Laboratories at the National University of Singapore. His research interests include modeling and control of flexible systems, nonlinear robust and fault tolerant control, multi-agent control with applications to smart-grid and robotics, estimation and control of partial differential equations with applications to thermo-fluid models, learning-based adaptive control for nonlinear systems, and control-theory based optimization algorithms with application to machine learning. Mouhacine has published more than 50 peer-reviewed journal articles and conference papers, and has more than 20 patents in the field of mechatronics systems control. He is a senior member of the IEEE, Associate Editor of the Control System Society Conference Editorial Board, Associate Editor of the Journal of Optimization Theory and Applications, Associate Editor of the Journal of Advanced Control for Applications, Associate Editor of the IEEE Control Systems Letters, and Senior Editor of the International Journal of Adaptive Control and Signal Processing.

Recap of Mouhacine's presentation:

One of the main motivators for Mouhacine's shift from academia to an industry position was driven by his desire to make more of an impact on everyday life. Mitsubishi Electric Research Laboratories (MERL) located near the MIT campus in Boston is considered to be the most fundamental lab for Mitsubishi Electric. Working at MERL, the researchers are given more freedom to find solutions that are critical in the long-term, rather than focusing only on immediate problems. Every one of the 60 researchers at MERL has a PhD, and they contribute to around 80 new patents and 150 research papers every year. In addition, every year there are about 80 students that participate in their internship program, coming from some of the strongest universities in the world (including Virginia Tech), providing them with key partnerships with many academic institutions. The available internships can be found on their website.

The areas of research at MERL can be viewed in terms of an architectural structure: applied mathematics is the base, upon which the three pillars of signal processing, control theory, and optimization hold up artificial intelligence at the peak. Consequently, no research at MERL can be done without mathematical analysis, which is their focus alongside algorithm design in the four key areas mentioned above.

The research at MERL is divided into several areas, each using different mathematical tools. The Multimedia group uses information theory, machine learning, linear algebra, linear optimization and graph theory to study topics related to video and audio processing, information security, and compressive sensing. The Electronics and Communications group uses harmonic analysis, statistics, optimization and partial differential equations to study topics related to wireless and optical communications, power and radio frequency. The Data Analytics group (where Mouhacine works) uses optimization theory, machine learning, nonlinear dynamical systems, ergodic theory and nonlinear control theory to study topics related to predictive modeling and decision optimization. The group studying Computer Vision uses deep learning and geometry, the Mechatronics group applies control algorithms to study automobiles, trains, HVAC, satellites and factory automation, and the Algorithms group works on real-time large-scale computing and optimization in several application areas.

Mouhacine provided two examples of research at MERL in nonlinear control. The first problem discussed was elevator rope sway control for tall buildings, which mitigate the oscillations of the ropes that sway laterally and cause structural damage to the building. The steps taken are determining a model of the system, identifying the equations that describe the physics in question, searching for the most efficient solution possible, and simulating results. A second problem concerns controlling airflow in buildings through HVAC systems, and it was discussed what steps are taken to understand and estimate the dynamics involved. Other examples given were machine learning for power amplifiers, differential geometry for artificial intelligence and the design of deep neural networks.

Additional advice from Mouhacine discussed during Q&A:

In terms of how steep the learning curve is to conduct state-of-the-art research from an academic background in mathematics: it takes around a year to familiarize to the tools and problems and become familiar with existing literature.

The industry MERL is in desires results that are guaranteed to work, allowing each project to take several years and be treated almost like a PhD project.

The internships available at MERL are primarily for PhD students and Postdocs.

The research requires a great deal of analysis. Data-driven and test-based arguments are hardly ever accepted (only computer vision research is data-driven, given the nature of their field).

The proposed models and research at MERL are evaluated at testing facilities for many years to have sufficient data guaranteeing effectiveness.

Advice for undergrads and grads in hindsight: even if it isn't clear at the moment, everything being learned in classes really does matter!

One of the best student interns at MERL was a pure mathematician, since they were trained to do analytical research at a very deep level.

With a shifting focus in the industry on designing safe and rigorous solutions, a strong education in mathematics is the way of the future.

### Steve Pugh - "Mathematics in Industry" Speaker: Oct 2, 2020

This presentation was by Steve Pugh, who is a Senior Manager of Software Engineering at Capital One in Richmond, Virginia. Steve is also known for his development of Versus Sports Simulator.

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Steve Pugh is an entrepreneur, mathematician, and software engineer known for his development of Versus Sports Simulator. Steve earned Bachelor of Science and Master of Science degrees in Mathematics from Virginia Tech in 1993 and 1995 respectively. He is employed at Capital One Financial as a Senior Manager of Software Engineering and has vast experience in developing innovative products, building teams, and coaching people for high performance.

Recap of Steve's presentation:

The main focus of the talk was advice and insight for mathematics students regarding what it's like to work in the corporate world. This is a topic most math students rarely learn about through their academic studies. Shortly after finishing his Master's degree in Mathematics at Virginia Tech, Steve spent about 6 years writing code as a software engineer. From that point, a change in company strategy led to his current role at Capital One as a manager and leader of a team of software engineers. Looking back, Steve advises that students should be open to opportunities as they present themselves - technical skills are a foundation upon which many future opportunities may arise.

Steve stated that the benefit of pursuing a degree in mathematics is due to its inherent difficulty. Although it may sound unappealing at first, the disciplined study of mathematics builds an individual's skills and aptitude for solving problems that naturally arise in any situation in life. By searching job postings that contain mathematics as a keyword, it can be seen that most technical positions cannot be done easily without a strong base in mathematics.

"Life is full of problems, and math teaches you how to solve them!"

Steve used several mathematical idioms to explain "the factors that count" for working in the corporate world.

"Differentiation" can be summed up as an individual's understanding of influence, ownership, communication, teamwork, leadership, empathy, integrity, and autonomy. For those that have the same hard (technical) skills as others acquired through their degree, soft (people) skills are what can differentiate an individual's effectiveness in the organizational setting. Even if soft skills are not part of an individual's training, it is important to view these skills as an opportunity for self-development. Technical skills, perseverance, and problem-solving ability are the traits that allow an individual to be considered as a worthy candidate for a job; however, soft skills put the lid on the jar in terms of being able to produce an impact in this company role.

"Integration" can be seen as the ability to successfully integrate or immerse oneself into a workplace role. This comes through recognizing one's own strengths, and understanding how to implement these strengths in a way that would benefit their peers. Moreover, an individual's strengths are often complementary. Different traits that help an individual stand out can be combined, allowing the individual to form themselves into a unique resource to others. Finally, a passion for working within the traits that define an individual is an easy way to develop a positive working environment.

"Inflection points" are the times of change in an individual's path. How one reacts and prepares for these inflection points can significantly alter the direction of their path. In any context within an individual's life, change should be expected and anticipated. The best way to get through change is to adapt, and recognize the opportunities that it brings. If others are not able to manage this change just as well, there needs to be an individual to take charge and lead them through it - being this leader is an opportunity in itself.

"Empirical observations" are the lessons learned by studying the actions of others. If someone seems to be very successful in what they do, being able to model oneself in this manner can prove to be useful. This is done by closely observing what these successful people do, identifying the specific traits that stand out, and using all possible resources to implement these methods for themselves.

"Boundary conditions" are the understanding of one's limits. These limits allow an individual to recognize an opportunity for self-development, and should be faced head-on without fear of failure. As Dr. John Burns once told Steve:

"Even if you can conclude nothing from your observations, you've still learned something."

"Groups, Rings and Fields", although a stretch of a mathematical idiom, highlights the importance of teamwork and cooperation in any endeavor. Steve stated that great teamwork involves sharing knowledge, but great innovation requires it. Consider the example of Frank Beamer, the legendary college football coach who led the Virginia Tech Hokies for 29 seasons. Beamer was keen to share his famed strategy to competitors, which may have puzzled many outside onlookers at first. However, his objective was not to raise only the quality of his team, but the entire sport, since better competitors require higher expectations from oneself as well. These continually rising standards are what lead individuals, organizations, and industries to uncharted territories.

Additional advice from Steve discussed during Q&A:

Many of the skills that Steve learned in the corporate world allowed him to succeed as an entrepreneur as well. Different experiences can prove useful in a variety of settings.

There is much more to being successful in an organization than relying solely on what math skills provide.

Machine learning is a recommended skill someone with a math background can focus on learning that may open many doors in the current industry climate.

Capital One has internships and full-time positions available, and Steve would be glad to talk to anyone interested in these opportunities. Browse https://campus.capitalone.com/full-time-programs to see what is available.

### Will Frey - "Mathematics in Industry" Speaker: Sep 25, 2020

This presentation was by Will Frey, who works as a Machine Learning Engineer at Two Six Labs in Arlington, Virginia.

Click here to watch a recording of the presentation!

Recap of Will's presentation:

A main topic of Will's discussion was how his training as a mathematician rather than an engineer led to his success in an industry position.

After finishing his undergraduate degree at Virginia Tech, there was uncertainty in what career path he wanted to pursue. So, while Will stayed in Blacksburg to complete his Master's degree, he started making connections outside of the department. These connections launched his eventual career by means of a job offer, albeit for a somewhat daunting position as a software engineer. However, Will followed the advice of Richard Branson:

“If somebody offers you an amazing opportunity but you are not sure you can do it, say yes – then learn how to do it later!”

This job offer also allowed him to realize that a strong foundation in linear algebra comes in handy in the corporate world.

At the beginning of this new venture with new expectations, it wasn't easy to feel comfortable at first. Will didn't know if he'd be capable of making the transition from mathematician to software engineer. His new role required him to develop a certain level of fearlessness. Eventually, through continued effort, the transition turned out successful. However, success didn't come linearly over time. This first big leap was only the beginning of numerous years of ups and downs working for various companies.

In his current role, Will is working on a fascinating project building a cybersecurity platform, one which gained significant media coverage. For some perspective, for those who've watched the movie "Terminator: Dark Fate", Will might be building the equivalent of Legion. Nevertheless, the graph neural networks that he works on now are essentially still mathematical concepts - beside the bountiful prevalence of linear algebra, there is also a need for understanding graph theory (a math class he wishes he took while at VT).

Mathematicians think differently than software engineers, and there are some skills Will wishes that he developed earlier on. Building modular software and software testing are very important for his position, and these are engineering tools usually not covered in a theoretical math class. Although learning how to write in a programming language such as Python will eventually sound like a good idea, restricting learning to within a Jupyter notebook can cause future headaches.

There are many open-source projects online that allow for an expanded horizon of learning. Stepping outside of this Jupyter notebook box will build confidence and comfort that can lead to publishing personal open-source projects. Furthermore, there is no harm in shamelessly asking the author questions about a public project of theirs - in fact, they usually appreciate the interest in their work. There is nothing to lose if they do not respond, and there is much to gain from potentially establishing new connections. Not only will this research into what others are doing strengthen pre-existing skills, it will help provide understanding to which skills may be important and can be learned.

For example, one should ask themselves what they know about topics such as the UNIX command line, Git, regular expressions, or if they would be able to read and understand code written in languages such as C, C++, or CUDA. These are specific skills that can appear frequently in conjunction with overarching skills.

Additional advice from Will discussed during Q&A:

1) Don't take for granted the fundamental courses such as Calculus, Linear Algebra, and Differential Equations. Backpropagation (an important machine learning concept) is just a really clever form of chain rule.

2) What a mathematician does is highly dependent on what they want to do.

3) A broad foundation of education and flexible outlook is important. An engineer is prepared to work according to his training, but a mathematician can become an engineer too.

4) Seek out mentors, through any means, that will catch mistakes early on. Learning on one's own may allow mistakes to accumulate over time.

5) Take any project being worked on seriously - a project is an gateway to a higher level of learning. Internships and projects are win/win situations. If it doesn't work out, be glad it's only temporary and avoid it in the future. If it does work out, there is always potential to build on what was learned.

6) Invest time in learning what is out there:

("Hacker news") https://news.ycombinator.com

(Open-source Python library) https://spacy.io

(For learning more Python) https://pybit.es

(Git repository search) https://grep.app

7) "Get your hands dirty [with projects]… but make sure you can still clean up the mess!"