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Complex systems across various domains can be naturally modeled as signed networks with positive and negative edges. In this work, we design a new class of signage models and show how to select the model parameters that best fit real-world datasets using maximum likelihood. 

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. 

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. 

We study counting problems for several types of orientations of chordal graphs: source-sink-free orientations, sink-free orientations, acyclic orientations, and bipolar orientations, and, for the latter two, we also present linear-time uniform samplers. Counting sink-free, acyclic, or bipolar orientations are known to be #P-complete for general graphs, motivating our study on a restricted, yet well-studied, graph class. Our main focus is source-sink-free orientations, a natural restricted version of sink-free orientations related to strong orientations, which we introduce in this work. These orientations are intriguing, since despite their similarity, currently known FPRAS and sampling techniques (such as Markov chains or sink-popping) that apply to sink-free orientations do not seem to apply to source-sink-free orientations. We present fast polynomialtime algorithms counting these orientations on chordal graphs. Our approach combines dynamic programming with inclusion-exclusion (going two levels deep for source-sink-free orientations and one level for sinkfree orientations) throughout the computation. Dynamic programming counting algorithms can be typically used to produce a uniformly random sample. However, due to the negative terms of the inclusion-exclusion, the typical approach to obtain a polynomial-time sampling algorithm does not apply in our case. Obtaining such an almost uniform sampling algorithm for source-sink-free orientations in chordal graphs remains an open problem. Little is known about counting or sampling of acyclic or bipolar orientations, even on restricted graph classes. We design efficient (linear-time) exact uniform sampling algorithms for these orientations on chordal graphs. These algorithms are a byproduct of our counting algorithms, but unlike in other works that provide dynamic-programming-based samplers, we produce a random orientation without computing the corresponding count, which leads to a faster running time than the counting algorithm (since it avoids manipulation of large integers).