### The DATA-INSPIRE REU program

The DATA-INSPIRE REU program prepares students interested in using data science in their careers and who have demonstrated interest in the topics covered by our Institute. The students work one on one with a mentor, have regular communications with their mentors, and participate in regular meetings and seminars. DATA-INSPIRE supports four or five students each summer. The activities of the program are coordinated with those of the long-established DIMACS REU program, which typically has about 40 students. Including the TRIPODS REUs in a greater group provides a much richer experience. Through interactions and presentations by the students and speakers, close to 40 other students are exposed to the topics and ideas of our TRIPODS project. The weekly REU Seminar Series features local and outside speakers to introduce students to a variety of specific research areas related to data science. The students also participate in presentations and workshops about a) careers and graduate school (including a panel of graduate directors from the CS, Math, and Statistics departments in Rutgers and former REU students now in graduate school); b) ethical behavior in the sciences; c) good technical communication skills, including writing abstracts, creating posters, and giving presentations; d) developing project websites; e) financial advising. The REU group visits partner industrial research institutes such as Nokia Bell Labs in Murray Hill, NJ and IBM Research in Yorktown Heights, NY. The program culminates with the student presentation of their TRIPODS work to the entire DIMACS REU group and with the students completing their research papers on their summer work.

The students who participated at the DATA-INSPIRE REU program are the following:

#### 2023:

Jordan Chong (NYU) – Mentor: J. Gao

Marcus Gozon (U. Michigan) – Mentor: J.J. Yu

Matt Lu (Washingthon U. – St Louis) – Mentor: J. Gao

Ethan Regal (Gannon) – Mentor: G. Guo

#### 2022:

Michael Bsales (Notre Dame) – Mentor: C. Nelson

Iris Horng (U. Pennsylvania) – Mentor: J. Gao

Liron Karpati (U. Maryland – College Park) – Mentor: J. Gao

Nithya Nalluri (TCNJ) – Mentor: C. Nelson

#### 2021:

Anna Cusenza (UCLA) – Mentor: K. Mischaikow

Jacob Gorenburg (Haverford College) – Mentor: D. Pennock

Soham Palande (Rutgers University) – Mentor: J. Gao

Yousef Sayes (NJIT) – Mentor: K. Mischaikow

Fiona Shafer (Rutgers University) – Mentor: C. Nelson

#### 2020:

Sarah Fleetwood (Winthrop University) – Mentor: K. Mischaikow

Polina Kochetova (Rutgers University) – Mentor: J.J. Yu

Chih-Yun Tseng (U. Maryland – College Park) – Mentor: K. Mischaikow

Adam Zheleznyak (U. Pennsylvania) – Mentor: K. Mischaikow

### Selected Achievements by REU Students

**2020:**

The Dynamic Signatures Generated by Regulatory Networks (DSGRN) software allows for a nearly instantaneous computational analysis of the global dynamics of (genetic) regulatory networks. DSGRN is extremely efficient because identification of global dynamics at a given set of parameter values is essentially equivalent to performing topological sort on a directed graph and it has a priori solved the problem of decomposing parameter space. In particular, given a regulatory network, there are stored lists from which the decomposition of parameter space is identified. The mathematically difficult, computationally challenging part is to determine these lists. DSGRN can work with lists that model functions determined by up to 4 monotone functions. **Adam Zhelenznyak (U Penn)** worked on extending this for non-monotone functions and succeeded for special cases. In DSGRN combinatorial models have continuous parameterizations, which makes it easy to map DSGRN parameters onto families of traditional ODE models. **Chih Yun Tseng (U Maryland)** focused on using rigorous methods based on the contraction mapping theorem to try to prove that fixed points whose existence is suggested by DSGRN are present in the ODE models. Such theorems work extremely well if given an appropriate initial guess. Chih-Yun found methods to move from DSGRN data to identifying appropriate initial guesses. **Marie Fleetwood (Winthrop U)** worked on simulating classical ODE models for ecological systems with the goal of comparing her results with output from an extension of DSGRN developed to study tropic networks. **Polina Kochetova (Rutgers U)** studied object rearrangement (see Group C above). She has shown that finding the minimum number of items that need to be moved to temporary locations, or buffers, in order to move all objects to their goals is equivalent to finding a minimum feedback vertex set for a dependency graph. She made progress on the related problem of the minimum number of active buffers required, i.e., the minimum number of items that need to be simultaneously stored in temporary locations in order to resolve the graph.

**2021:**

Research with the **2020 REU student Adam Zheleznyak (U Penn)** continued under the mentorship of co-PI Mischaikow, working on efficient software, called DSGRN, that takes as input a network represented as an annotated directed graph and outputs the global dynamics over a large high-dimensional parameter space, where the annotation indicates whether one node activates or represses another node, This is essentially equivalent to an assumption that the effect of one node on another is represented by a monotone increasing or decreasing function. A consequence of Adam’s work is that we can now consider models where this monotonicity assumption is no longer necessary. This is a significant achievement and we have begun to prepare a paper on these results.

**2021 REU student Soham Palande (Rutgers)** worked on dynamic models of network evolution when both node opinions and social ties evolve over time, under the mentorship of Jie Gao. Node opinions (e.g., views on a number of topics) are updated by social influence from neighbors; while social ties are updated by the agreement and disagreement of node opinions. Soham focused on the case of multi-dimensional opinions and investigated a variety of models for social tie formulation. His results using computer simulations have confirmed Gao’s conjectures that the system converges to potentially polarized states.

**2022:**

**2022 REU students Iris Horng (Upenn) and Liron Karpati (University of Maryland College Park)** worked on geometric and topological analysis on brain connectome data. A connectome at the macroscale (millimeter resolution) attempts to capture large brain systems that can be parcellated into anatomically distinct modules (areas, parcels or nodes), each having a distinct pattern of connectivity. In this project Horng and Karpati studied brain connectome data derived from functional MRI images, where brain data is represented by a network in which edges capture correlation of activities in different areas of the brain. Horng and Karpati applied geometric and topological tools including discrete network curvature and persistence homology to study the brain data. In particular, these tools led them to new insights about both robust topological features (persistent cycles) and curvature weighted path motifs.