The 40th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE) will be held at NC State University, Raleigh, NC, on November 12-13, 2022. The conference promotes research and education in differential equations and their applications by bringing together leading experts and young researchers in this field. It provides a unique experience for the Southeastern-Atlantic region due to its research focus, size and location, as well as its strong commitment to building regional research networks and mentoring the next generation of mathematicians who work in differential equations. This year SEARCDE will be focused on the following themes: (i) Applications of differential equations, especially to problems in life sciences, (ii) Mathematical control and related topics, and (iii) Applied analysis of differential equations. The confirmed plenary speakers for SEARCDE 2020 are: (1) Piermarco Cannarsa (University of Rome Tor Vergata), (2) Giovanna Guidoboni (University of Missouri), (3) Irena Lasiecka (University of Memphis), and (4) Daniel (University of California Berkeley). The 40th SEARCDE will also celebrate and honor the life and contributions of H.T. Banks, a prominent researcher in differential equations and their applications and professor at NC State, who passed away this past December. SEARCDE is committed to inclusion and diversity. This year the conference will be held ``in cooperation with the Association for Women in Mathematics (AWM)".

We will develop and deploy a broad array of cutting edge experimental and modeling approaches to design and evaluate TIPs for the adaptive control of influenza viruses. We will experimentally evaluate TIP candidate libraries for their effects on the replication, transmission, evolution, and pathogenicity of influenza virus populations using single particle/single cell analysis methodologies. We will develop new conceptualizations of viral functional organization that are based on the intrinsic genotypic and phenotypic heterogeneity of influenza populations, including designed TIPs, at the within-host level. These conceptualizations will serve as the core for assessing the relevant level(s) of selection acting on influenza viruses and for the development of multi scale models of TIP-target virus. These conceptualizations and models will feed back into experimental TIP design and phenotypic evaluation. Our aim is to make fundamental discoveries about how viral population structure at the cellular, organismal, and between-host levels influences viral evolution and transmission, and to leverage these discoveries for the design of successful TIPs. Current approaches to influenza-based TIP development are based on trial-and-error evaluation of the ability of a small number of TIP candidates to limit disease in mouse models. Influenza viruses exist as genetically and phenotypically heterogeneous populations, and yet virtually nothing is known at the molecular, cellular, or organismal level about how TIPs influence the evolution and pathogenesis of target virus populations, and the idea of evolved resistance and/or tolerance of TIPs has not been seriously considered. Effective TIPs must control and/or eliminate viral populations, yet principles of population biology have scarcely been applied to the study of DIPs or TIPs. Based on current SOA, we still do not know what specific features will make a good TIP, making the rational design of improved TIPs impossible. Our proposal will innovate by characterizing the population dynamics and population genetics of TIPs and target virus in unprecedentedly high resolution and then leveraging this information to rationally design TIPs to re engineer the emergent properties of viral populations. DIPs/TIPs appear to exploit intracellular and intercellular population dynamics to reproduce at the expense of infectious genomes. These infectious genomes are highly complex, heterogeneous communities of genetically and phenotypically distinct particles or ���������������individuals������������������ that act collectively to transmit between hosts. As selection on collective behavior drives adaptive function organization, emergent behaviors at the level of the within-host viral community are expected and need to be understood. Thus, a quantitative and conceptually appropriate perspective on viral population biology and structure must be central to TIP design and evaluation. We will dissect the dynamic network of cooperative and antagonistic interactions within these highly heterogeneous viral populations using a combination of novel single particle/single cell experimental approaches including: (a) multiplexed nanoprobes; (b) microfluidic systems; (c) single particle assays; and (d) highly accurate, ultra-deep single molecule population sequencing. This information will allow us to mechanistically determine how TIP genotypes and phenotypes alter the emergent behaviors of complex viral populations, both in vitro and in an animal transmission model, and will be used to test and refine our conceptual framework and corresponding models for viral functional organization, including identification of the level(s) at which selection acts. The multi-scale models will in turn yield predictions and serve as a basis for understanding the experimental findings on TIP/target virus dynamics and co-evolution. As such, they will direct in the identification of TIP genotypic and phenotypic features critical for effective control of influenza populations. The proposed work will deliver a low-cost and evolutionarily stable therapeutic to m

This project will train undergraduate and graduate students, together with postdoctoral fellows, in creating mathematical models of biological systems and confronting them with biological data. Combining approaches from applied mathematics and statistics, trainees will learn a wide range of modeling and parameter estimation methodologies, producing cohorts of mathematical scientists that have received an interdisciplinary training and who are versed in cutting-edge modeling and statistical techniques.

The overriding goal of the Research Scholars Program in Mathematics at North Carolina State University (NCSU) is to attract, retain, and graduate academically talented, financially needy students, with degree in mathematics, who may not make it to graduation and into the technological workforce without additional financial resources and other support structures. The Research Scholars Program uses a multi-faced approach to provide a comprehensive educational environment for students in mathematics, especially traditionally underrepresented groups. The program integrates long established in-place campus support programs and academic initiatives at NCSU with new and innovative approaches which provide a comprehensive, challenging, yet supportive academic environment for students in mathematics These include faculty mentoring, academic advising, and enrollment in special seminars focused on career and graduate school information. The special seminars are designed to help scholarship students better understand the range of career options, prepare academically for the options, and to develop relationships with industrial people. In addition, the program includes an enhanced curriculum that includes new and innovative courses and research/internships experiences with dedicated faculty mentors/industrial partners to ensure excellent training of a new generation of mathematicians. The Research Scholars Program provides 6 scholarships at $5000 to undergraduate students to support for tuition, fees, and textbook charges per academic year. At the graduate level, the program offers 8 $10,000 need-based awards per academic year to supplement TA/RA offers made to outstanding students. Eligibility is determined according to S-STEM guidelines by a committee of mathematics faculty, a representative from the financial aid office.

The REU program at North Carolina State University (NCSU) is now ten years old and has become one of the largest REU programs in mathematics in the country. Our program is distinctive as it focuses on applications of mathematics and on building a diverse community of mathematicians. The first ten years funding of our program came from NSA, NSF and small contributions from Calabazas Creek Research, Inc. (CCR), our industrial collaborator. We now seek to renew NSF's crucial contribution so that our larger, more complex REU program will continue to provide a unique research experiences and excellent training of a new generation of mathematicians. Targeted student participants include rising senior and exceptional rising junior mathematics majors who have demonstrated academic excellence. Particular consideration will be indeed given to students from underrepresented groups as well as students from colleges and universities with limited opportunities for research. Since the program inception in 2005, we have had great success attracting women to our REU program (more than 50% of all participants) and about 25% of our REU participants are from underrepresented groups. In addition, about two-thirds of our REU students came from institutions with limited research opportunities in STEM. This success is in large part due to relationships that we have built over the years with historically black colleges and universities (HBCUs), leading Women's Colleges, and four-year colleges. If this proposal is funded, it would allow us to continue to support a large number of REU students each summer (40-47 in total of which 32 would be funded by this NSF REU proposal).

An alliance comprised of NSF Mathematical Sciences Institutes and seven major research universities with a good record of mentoring minority graduate students will offer post-doctoral fellowships to new Ph.D.s for a period of up to three years. The program specifically targets minority candidates. A typical 3 year postdoctoral fellow will spend 1 year at a national institute and 2 years at the host institution (university) which will provide mentoring and other support. Broader Impact. Despite slowly increasing numbers of undergraduate and graduate students in math coming from underrepresented groups, there remain very few minority faculty members in the mathematical sciences, especially at group I and II universities. An explicit goal of this proposal is to increase this number. Underrepresented mathematicians are choosing to pursue career paths outside of academia at higher rates than other groups. Without role models these new Ph.D.s may not envision themselves in careers at a research university. A mechanism to encourage minority candidates to pursue academic careers is required. The career track of most faculty at group I and II universities includes a strong postdoctoral experience in which they build their research portfolio and broaden their understanding of mathematics and its community. This postdoctoral fellowship program would allow strong Ph.D.s, especially those from underrepresented groups, to reach their full potential. Additionally, increasing the number of minority faculty will provide role models for undergraduates and graduate students, thereby encouraging underrepresented groups at all levels to continue in STEM fields in general and mathematics in particular. Intellectual Merit. Postdoctoral fellows will be selected for their excellent research potential. Their research will be stimulated by scholars at their host universities, and by time spent at a National Institute. Their careers will be further enhanced by the supportive, diverse communities of these particular mathematics departments and the guidance they get from mentors especially attuned to issues of diversity in mathematics. This will result in high productivity of the postdoctoral fellows during the time of their fellowship, and more importantly, an active research career to follow. Alliance Members. The Alliance universities are (listed alphabetically): Arizona State University, Howard University, Iowa Alliance (University of Iowa and Iowa State University), North Carolina State University, University of Arizona, and University of Nebraska. The Alliance NSF Mathematical Sciences Institutes are (listed alphabetically): American Institute of Mathematics (AIM), Institute for Mathematics and its Applications (IMA), Institute For Pure and Applied Mathematics (IPAM), Mathematical Biosciences Institute (MBI), Mathematical Sciences Research Institute (MSRI), Park City Mathematics Institute (PCMI/IAS), and Statistical and Applied Mathe����matical Sciences Institute (SAMSI).

The overriding goal of the Integrated Undergraduate Training in Mathematics and Life Sciences at North Carolina State University (NCSU) is to attract and train undergraduates in mathematics and life sciences for academic and nonacademic careers at the interface between mathematics, computational science, and life sciences. Galileo was perhaps the first to clearly state that the laws of nature are mathematical. Indeed and nearly 40 decades later, cutting edge research at the forefront of life sciences has become more dependent on mathematical, computational, and statistical methodologies. The proposed UBM program uses a multi-faceted approach to prepare next generation of mathematicians and scientists that will meet the holistic, multi-disciplinary research problems of the 21st century. More specifically, our proposed UBM has four primary objectives. It (1) provides a focused environment to involve undergraduate students in mathematics and life sciences in cutting edge cross-disciplinary research involving a broad spectrum of applications in life sciences. For many undergraduates, this will be their first research experience and one that will encourage them to pursue interdisciplinary graduate studies in mathematics and life sciences. It (2) develops and integrates a number of research training and professional development to ensure successful training of a new generation of mathematicians and scientists. These include the development of two new courses: an applied differential equations course in which the theory and analysis of ordinary differential equations are introduced in the context of relevant biological applications and a novel course in model verification and validation. The context-rich material curriculum will be supplemented with UBM research seminars and Professional Development Modules (PDM) that will be held weekly. Students will also be encouraged and assisted by faculty mentors to make professional contacts, participate in tours of mentor's laboratories, attend conferences, and become members in student chapters of professional/academic societies. It (3) provides a team environment for interdisciplinary and collaborative research. The proposed UBM program will train a cohort of 8 undergraduates per year, divided into two groups, with joint mentoring of each 4-student group (two mathematics majors and two life sciences majors) by a pair of faculty from mathematics and life science disciplines at NCSU as well as with our collaborators who are external to NCSU . The long-term objective is to institutionalize a paradigm for training mathematics and life science students for academic and nonacademic careers that involve collaborative, interdisciplinary, team research. It (4) enhances cooperation among faculty in mathematics and life science disciplines. Intellectual Merit and Education. There has been an outburst in the last ten to twenty years in quantitative analysis of biological systems that requires new approaches at how we educate undergraduates. The NCSU UBM team is truly interdisciplinary, with members in mathematics, biomathematics, statistics, biology, chemistry, veterinary medicine and medicine. This powerful combination of areas of expertise offers a truly unique cross-disciplinary educational experience for undergraduates in life sciences and mathematics. Indeed, the project will produce future scientists with both biological skills and mathematical insight and facility. In addition, both mathematics and life science disciplines can expect to gain by this collaborative effort. To faculty in mathematics, the stimulation of biological applications will enrich the discipline of mathematics as it provokes refinements and further mathematical developments. Life science faculty will benefit from the power of mathematical tools as they provide insight available in no other way. Broader Impact. The results of the proposed UBM program will provide a vehicle for systemic institutional change in introductory mathematics and science education. Since project leadership includes key members of existing

The REU program at North Carolina State University (NCSU) is now ten years old and has become one of the largest REU programs in mathematics in the country. Our program is distinctive as it focuses on applications of mathematics and on building a diverse community of mathematicians. Our overarching aim is to get more undergraduates interested in pursuing academic and nonacademic careers in mathematics. We achieve this by recruiting and engaging students from underrepresented groups as well as students from colleges and universities with limited opportunities for research. Since the program inception in 2005, we have had great success attracting women to our REU program (more than 50% of all participants) and about 25% of our REU participants are from the underrepresented groups (see Section g). In addition, during recent years about 65% of our REU students came from institutions with limited research opportunities in STEM (see Section d). We are particularly interested in engaging students from underrepresented groups who may not usually consider an REU program. While we have always had reasonable success with this, we realized that many capable students did not have the background to begin an REU program of an applied nature. Thus, for the last eight years, we have collaborated with several historically black colleges and universities (HBCUs) to offer enhanced research experiences to minority students. This successful and truly unique program, called REU+, offers an extra week of training for the minority students before the regular REU program starts to help boost their confidence and fill in gaps in their background as needed. This additional one week program is run jointly with faculty from their own institutions. After this initial week the students are fully integrated in the full REU program, with REU+ students distributed among the different research groups. The reaction of REU and REU+ students during the trial summer in 2007 as well as during the summers from 2008 to 2014 with this innovative program has been overwhelmingly positive and is beyond our expectations. All students interact as one cohesive unit and fully participate in all program scientific and social activities. Indeed, we now seek to continue the REU+ program (see Section a.2) with this grant application. In addition, a new feature that we add to the REU+ program is to involve the home school faculty even more by having them come back to NC State for another week during the REU summer program (currently they come at the beginning for 1 week). The one-week return visit will enable them to see the progress of the students, and better enable the faculty to work with the students on some other aspects of the project when they return to the home campus. The goal of this REU component, which is called Reinvigoration in Research (RnR) and will be described in Section a.3, is to foster research at many more HBCUs. This helps build a model where local faculty at HBCUs can direct their own students in research of various kinds during the academic year. It has become quite widely accepted that students do best when they understand that they are a valued part of a community doing important work. We accomplish this by giving REU participants the opportunity to work on applied research problems in a supportive, collaborative environment that is part of a vibrant research department with strong ties to industry and government laboratories, outstanding teaching and mentoring, and welcoming environment for underrepresented groups. Indeed, in recognition of the department's particular combination of a strong commitment to outreach, well thought-out programs for students, and its significant efforts to encourage students from underrepresented groups to continue in the study of mathematics, the American Mathematical Society (AMS) awarded the department with two national awards, the 2010 AMS Award for an Exemplary Program or Achievement in a Mathematics Department and the 2011 AMS Award for Mathematics Programs that Make a Difference. We are the only program to receive both AMS awards back-to-back. If funded this proposal would allow us to continue to support a relatively large number of students each summer (35-45 in total of which 9 would be funded by the NSA). In the mix of 9 students are 3 underrepresented, highly capable but possibly under-prepared, REU+ students. The size of the program helps the students develop their own community of a new generation of mathematicians.

The main role of the cardiovascular system is to maintain a set level of oxygen and nutrients in tissues as well as to ensure continuous removal of carbon dioxide and other metabolites. This is accomplished through tightly regulated control mechanisms. One of the main control systems promoting this regulation is the baroreflex system, which is part of the autonomic nervous system. Quantities being controlled by baroreflex regulation include blood flow and blood pressure. These quantities are kept close to their reference levels by a complex feedback control system regulating heart rate and vascular tone. Failure of this system has clinically significant consequences including dizziness, falls and reflex mediated syncope, in particular for the elderly and for patients with hypertension and diabetes. The underlying pathophysiology leads to regulatory failure, which can be difficult to analyze since the detailed physiology involved with blood flow and pressure control is not well understood, and it is difficult to study the complex regulatory responses experimentally. These facts suggest that there is a need for development of more advanced methodologies to predict blood flow and pressure regulation. In this study we propose to (i) develop a hierarchy of models ranging from reference models describing the biophysics of the baroreceptor neurons to multiscale models representing both local and systemic features of the human cardiovascular system; (ii) develop control theoretic methods for investigating autonomic mechanisms and their pathophysiology; and (iii) develop methodological and computational framework for application of complex, multiscale models of the circulatory regulation system.

North Carolina State University will support IFT in research, developing and evaluating the proposed algorithms. In particular, North Carolina State University will help IFT develop and implement frameworks for evaluating RFI from undesired RTS and 3G/4G PCS to DoD satellites. The tasks that NCSU will do are as follows. • Task 1: Subcontractor will participate in three meetings (or teleconference): kick-off, interim and final. Deliverables: Slides, attendance at the project meeting Date due: Meeting date will be scheduled at collaboration with all involved parties. • Task 2: Subcontractor will help IFT develop and generate a framework to evaluate the effects of RFI from undesired RTS and a framework to evaluate the RFI from 3G/4G PCS to DoD satellites. Deliverables: Report Date due: one month after the effective date of this subcontract. • Task 3: Subcontractor will help IFT implement the tool to evaluate RFI from undesired RTS with Matlab. Deliverables: Report and code Date due: three months after the effective date of subcontract • Task 4: Subcontractor will help IFT implement the tool to evaluate RFI from 3G/4G PCS to DoD satellites with Matlab. Deliverables: Report and code Date due: four months after the effective date of this subcontract. • Task 5: Subcontractor will assist IFT on demonstration system development and performance study. Deliverables: Report and additional code to associate Tasks 2, 3, and 4 Date due: seven months after the effective date of this subcontract.