Signed networks (networks with positive and negative edges) commonly arise in various domains from molecular biology to social media. The edge signs -- i.e., the graph signage -- represent the interaction pattern between the vertices and can provide insights into the underlying system formation process. Generative models considering signage formation are essential for testing hypotheses about the emergence of interactions and for creating synthetic datasets for algorithm benchmarking (especially in areas where obtaining real-world datasets is difficult). In this work, we pose a novel Maximum-Likelihood-based optimization problem for modeling signages given their topology and showcase it in the context of gene regulation. Regulatory interactions of genes play a key role in the process of organism development, and when broken can lead to serious organism abnormalities and diseases. Our contributions are threefold: First, we design a new class of signage models for a given topology, and, based on the parameter setting, we discuss its biological interpretations for gene regulatory networks (GRNs). Second, we design algorithms computing the Maximum Likelihood -- depending on the parameter setting, our algorithms range from closed-form expressions to MCMC sampling. Third, we evaluated the results of our algorithms on synthetic datasets and real-world large GRNs. Our work can lead to the prediction of unknown gene regulations, novel biological hypotheses, and realistic benchmark datasets in the realm of gene regulation.

Knot mosaics are a model of a quantum knot system. A knot mosaic is a m-by-n grid where each location on the grid may contain any of 11 possible tiles such that the final layout has closed loops. Oh et al. proved a recurrence relation of state matrices to count the number of m-by-n knot mosaics. Our contribution is to use ALLSAT solvers to count knot mosaics and to experimentally try different ways to encode the AT MOST ONE constraint in SAT. We plan to use our SAT method as a tool to list knot mosaics of interest for specific classes of knots.

Introductory assignments in CS Theory ask students to construct instances of various computational models (such as finite automata, regular expressions, context-free grammars, or push-down automata) for a given language. Verifying the correctness of their model instance is challenging for beginner CS Theory students since the concepts are abstract and there are infinitely many possible inputs. The popular JFLAP software allows students to visualize the running of their instance on a specific input. We recently developed a server extension to JFLAP which checks whether a student's instance is equivalent to the instructor's solution and, if not, it returns a "witness string,'' an input string on which the student's construction and the correct solution differ.

Knot mosaics are combinatorial representations of mathematical knots. Boolean satisfiability (SAT) is an important NP-complete problem, and SAT solvers are practical software implementations to solve SAT problems. SAT solvers are rarely used in undergraduate classes, and the learning curve for SAT is steep. For our contribution, we developed a lecture and a homework assignment for undergraduate students to work with SAT formulas, to draw knot mosaics, and to run SAT solvers for counting knot mosaics. The assignment has been developed over three semesters. The assignment includes a skeleton Python encoding with over 750 lines of Python code and function documentation. We surveyed the students about their experiences with and perceptions of the assignment as well as their comments for improving the assignment. On the survey, students overwhelmingly agreed that they learned about SAT and knots, and the students earned high grades on the assignment, showing that their perception of learning was true. Our future work includes clarifying one of the assignment problems where students struggled.

Mathematical knots are interesting topological objects. Using simple arcs, lines, and crossings drawn on eleven possible tiles, knot mosaics are a representation of knots on a mosaic board. Our contribution is using SAT solvers as a tool for enumerating nontrivial knot mosaics. By encoding constraints for local knot mosaic properties, we computationally reduce the search space by factors of up to 6600. Our future research directions include encoding constraints for global properties and using parallel SAT techniques to attack larger boards.

We provide an experience report about a remote framework for early undergraduate research experiences, which was thematically focused on sensing humans computationally. The framework included three complementary components. First, students experienced a team-based research cycle online, spanning formulating research questions, conducting literature review, performing fully remote human subject data collection experiments and data processing, analyzing and making inference over acquired data with computational experimentation, and disseminating findings. Second, the virtual program offered a set of professional development activities targeted to developing skills and knowledge for graduate school and research career trajectories. Third, it offered interactional and cohort-networking programming for community-building. We discuss not only the unique challenges of the virtual format and the steps put in place to address them but also the opportunities that being online afforded to innovate undergraduate research training remotely. We evaluate the remote training intervention through the organizing team's post-program reflection and the students' perceptions conveyed in exit interviews and a mid-program focus group. In addition to outlining lessons learned about more or less successful framework elements, we offer recommendations for applying the framework at other institutions as well as how to transfer activities to in-person formats.

Computing theory is often perceived as challenging by students, and verifying the correctness of a student's automaton or grammar is time-consuming for instructors. Aiming to provide benefits to both students and instructors, we designed an automated feedback tool for assignments where students construct automata or grammars. Our tool, built as an extension to the widely popular JFLAP software, determines if a submission is correct, and for incorrect submissions it provides a "witness" string demonstrating the incorrectness.

Assignments based on meaningful real-world contexts have been shown to be valuable in introductory computing education. However, it can be difficult to distinguish the value of a broad context from the value of a particular instantiation of that context. In this work in progress, we report on our initial findings gathered from deployments of different pencil-puzzle-based assignments. Specifically, we have investigated the use of pencil puzzles as a contextual domain, working with instructors at eight institutions to deliver assignments appropriate to their situation and aligning with their existing materials. We then evaluate the assignments using student grades and survey responses regarding student perceptions of the assignments including self-assessed learning, given a wide array of demographic variables. Our initial results show that while there was some dependency of student responses on their prior programming experience, and female students' feedback were more positive about one aspect, overall these types of assignments do not appear to put particular groups of students at a strong (dis)advantage.

Equivalence of deterministic finite automata (DFAs) has been researched for several decades, but equivalence of nondeterministic finite automata (NFAs) is not as studied. Equivalence of two NFAs is a PSPACE-complete problem. NFA equivalence is a challenging theoretical problem with practical applications such as lexical analysis. Quantified boolean formulas (QBFs) naturally encode PSPACE-complete problems, and we share our preliminary work towards determining NFA equivalence via QBFs.

Computing theory analyzes abstract computational models to rigorously study the computational difficulty of various problems. Introductory computing theory can be challenging for undergraduate students, and the overarching goal of our research is to help students learn these computational models. The most common pedagogical tool for interacting with these models is the Java Formal Languages and Automata Package (JFLAP). We developed a JFLAP server extension, which accepts homework submissions from students, evaluates the submission as correct or incorrect, and provides a witness string when the submission is incorrect. Our extension currently provides witness feedback for deterministic finite automata, nondeterministic finite automata, regular expressions, context-free grammars, and pushdown automata.

Computing theory is an important part of computer science education, introducing students to computational models of increasing power to study possibilities and limitations of computation. The subject is, however, very abstract and mathematical, and students often struggle with it. Students must master various computational models, but there is often a lengthy delay from the time a model is introduced until a student gets feedback on their related assignment. During this time, the course has typically moved far ahead, and students become progressively more lost. To alleviate this problem, we developed a prototype of an automated feedback tool for CS theory, which extends the widely used JFLAP software. Our tool currently handles student submissions of deterministic and non-deterministic finite automata, regular expressions, context-free grammars, and push-down automata homework, where an instructor specifies the target language and the students receive immediate feedback on their submissions. Currently, for incorrect submissions, the feedback is in the form of a "witness'' string, specifying a string on which the submission fails. Beyond regular languages, our tool attempts to solve undecidable problems; fortunately, the undecidability does not occur on typical homework assignments. We are collecting preliminary evaluation data from students using the prototype tool in their course. In our future work, we will analyze the data, and we aim to produce automated partial credit (along with the witness feedback) using SAT and QBF solvers.