arXiv subjects

Rebecca Smith

Publications and source records attributed to Rebecca Smith.

At least 19 recordsLinked to original sources

arXiv2025

Forecasting West Nile virus with deep graph encoders

West Nile virus is a significant, and growing, public health issue in the United States. With no human vaccine, mosquito control programs rely on accurate forecasting to determine when and where WNV will emerge. Recently, spatial Graph neural networks (GNNs) were shown to be a powerful tool for WNV forecasting, significantly improving over traditional methods. Building on this work, we introduce a new GNN variant that linearly connects graph attention layers, allowing us to train much larger models than previously used for WNV forecasting. This architecture specializes general densely connected GNNs so that the model focuses more heavily on local information to prevent over smoothing. To support training large GNNs we compiled a massive new dataset of weather data, land use information, and mosquito trap results across Illinois. Experiments show that our approach significantly outperforms both GNN and classical baselines in both out-of-sample and out-of-graph WNV prediction skill across a variety of scenarios and over all prediction horizons.

stat.AP↗

arXiv2025

AI-Educational Development Loop (AI-EDL): A Conceptual Framework to Bridge AI Capabilities with Classical Educational Theories

This study introduces the AI-Educational Development Loop (AI-EDL), a theory-driven framework that integrates classical learning theories with human-in-the-loop artificial intelligence (AI) to support reflective, iterative learning. Implemented in EduAlly, an AI-assisted platform for writing-intensive and feedback-sensitive tasks, the framework emphasizes transparency, self-regulated learning, and pedagogical oversight. A mixed-methods study was piloted at a comprehensive public university to evaluate alignment between AI-generated feedback, instructor evaluations, and student self-assessments; the impact of iterative revision on performance; and student perceptions of AI feedback. Quantitative results demonstrated statistically significant improvement between first and second attempts, with agreement between student self-evaluations and final instructor grades. Qualitative findings indicated students valued immediacy, specificity, and opportunities for growth that AI feedback provided. These findings validate the potential to enhance student learning outcomes through developmentally grounded, ethically aligned, and scalable AI feedback systems. The study concludes with implications for future interdisciplinary applications and refinement of AI-supported educational technologies.

cs.CY↗

arXiv2025

Sorting permutations using a pop stack with a bypass

We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never been investigated previously. In the present paper, we give a characterization of sortable permutations in terms of forbidden patterns and reinterpret the resulting enumerating sequence using a class of restricted Motzkin paths. Moreover, we describe an algorithm to compute the set of all preimages of a given permutation, thanks to which we characterize permutations having a small number of preimages. Finally, we provide a full description of the preimages of principal classes of permutations, and we discuss the device consisting of two pop stacks in parallel, again with a bypass operation.

cs.DM↗

arXiv2024

Key-avoidance for alternating sign matrices

We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given set of permutation patterns in several instances. We show that ASMs whose key avoids $231$ are permutations, thus any known enumeration for a set of permutation patterns including $231$ extends to ASMs. We furthermore enumerate by the Catalan numbers ASMs whose key avoids both $312$ and $321$. We also show ASMs whose key avoids $312$ are in bijection with the gapless monotone triangles of [Ayyer, Cori, Gouyou-Beauchamps 2011]. Thus key-avoidance generalizes the notion of $312$-avoidance studied there. Finally, we enumerate ASMs with a given key avoiding $312$ and $321$ using a connection to Schubert polynomials, thereby deriving an interesting Catalan identity.

math.CO↗

arXiv2024

Pop Stacks with a Bypass

We consider sorting procedures for permutations making use of pop stacks with a bypass operation, and explore the combinatorial properties of the associated algorithms.

cs.DM↗

arXiv2024

Where to place a mosquito trap for West Nile Virus surveillance?

The rapid spread of West Nile Virus (WNV) is a growing concern. With no vaccines or specific medications available, prevention through mosquito control is the only solution to curb the spread. Mosquito traps, used to detect viral presence in mosquito populations, are essential tools for WNV surveillance. But how do we decide where to place a mosquito trap? And what makes a good trap location, anyway? We present a robust statistical approach to determine a mosquito trap's ability to predict human WNV cases in the Chicago metropolitan area and its suburbs. We then use this value to detect the landscape, demographic, and socioeconomic factors associated with a mosquito trap's predictive ability. This approach enables resource-limited mosquito control programs to identify better trap locations while reducing trap numbers to increase trap-based surveillance efficiency. The approach can also be applied to a wide range of different environmental surveillance programs.

stat.AP↗

arXiv2024

Sorting inversion sequences

We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and generalizations, some of which we apply here. We give the classification of several classes of sortable inversion sequences in terms of pattern avoidance. We are able to provide an exact enumeration of some of the sortable classes in question using both classical approaches and a more recent strategy utilizing generating trees.

math.CO↗

arXiv2022

Forecasting West Nile Virus with Graph Neural Networks: Harnessing Spatial Dependence in Irregularly Sampled Geospatial Data

Machine learning methods have seen increased application to geospatial environmental problems, such as precipitation nowcasting, haze forecasting, and crop yield prediction. However, many of the machine learning methods applied to mosquito population and disease forecasting do not inherently take into account the underlying spatial structure of the given data. In our work, we apply a spatially aware graph neural network model consisting of GraphSAGE layers to forecast the presence of West Nile virus in Illinois, to aid mosquito surveillance and abatement efforts within the state. More generally, we show that graph neural networks applied to irregularly sampled geospatial data can exceed the performance of a range of baseline methods including logistic regression, XGBoost, and fully-connected neural networks.

q-bio.PE↗

arXiv2020

Almost avoiding permutations

We investigate the notion of almost avoiding a permutation: $π$ almost avoids $β$ if one can remove a single entry from $π$ to obtain a $β$-avoiding permutation.

math.CO↗

arXiv2019

Pattern avoidance in permutations and their squares

We study permutations $p$ such that both $p$ and $p^2$ avoid a given pattern $q$. We obtain a generating function for the case of $q=312$ (equivalently, $q=231$), we prove that if $q$ is monotone increasing, then above a certain length, there are no such permutations, and we prove an upper bound for $q=321$. We also present some intriguing questions in the case of $q=132$.

math.CO↗

arXiv2019

An Involution on Involutions and a Generalization of Layered Permutations

Taking transposes of Standard Young Tableaux defines a natural involution on the set $I(n)$ of involutions of length $n$ via the the Robinson-Schensted correspondence. In some cases, this involution can be defined without resorting to the Robinson-Schensted correspondence. As a byproduct, we get an interesting generalization of layered permutations.

math.CO↗

arXiv2019

Two-stack-sorting with pop stacks

We consider the set of permutations that are sorted after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we show these permutations to be in bijection with a special family of polyominoes. As a consequence, the permutations sortable by this machine are shown to have the same enumeration as three classical permutation classes.

math.CO↗

arXiv2018

Passing through a stack $k$ times with reversals

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass sortable permutations and give computational results for some classes with larger maximal rev-tier. We also show all classes of $(t+1)$-reverse pass sortable permutations are finitely based. Additionally, a new Entringer family consisting of maximal rev-tier permutations of length $n$ was discovered along with a bijection between this family and the collection of alternating permutations of length $n-1$. We calculate generating functions for the number permutations of length $n$ and exact rev-tier $t$.

math.CO↗

arXiv2018

Passing through a stack $k$ times

We consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We define a permutation $π$ to be $k$-pass sortable if $π$ is sortable using $k$ passes through the stack. Permutations that are $1$-pass sortable are simply the stack sortable permutations as defined by Knuth. We define the permutation class of $2$-pass sortable permutations in terms of their basis. We also show all $k$-pass sortable classes have finite bases by giving bounds on the length of a basis element of the permutation class for any positive integer $k$. Finally, we define the notion of tier of a permutation $π$ to be the minimum number of passes after the first pass required to sort $π$. We then give a bijection between the class of permutations of tier $t$ and a collection of integer sequences studied by Parker. This gives an exact enumeration of tier $t$ permutations of a given length and thus an exact enumeration for the class of $(t+1)$-pass sortable permutations. Finally, we give a new derivation for the generating function in Parker's thesis and an explicit formula for the coefficients.

math.CO↗

arXiv2017

A Bijection on Classes Enumerated by the Schröder Numbers

We consider a sorting machine consisting of two stacks in series where the first stack has the added restriction that entries in the stack must be in decreasing order from top to bottom. The class of permutations sortable by this machine are known to be enumerated by the Schröder numbers. In this paper, we give a bijection between these sortable permutations of length $n$ and Schröder paths -- the lattice paths from $(0,0)$ to $(n-1,n-1)$ composed of East steps $(1,0)$, North steps $(0,1)$, and Diagonal steps $(1,1)$ that travel weakly below the line $y=x$.

math.CO↗

arXiv2013

A stack and a pop stack in series

We study sorting machines consisting of a stack and a pop stack in series, with or without a queue between them. While there are, a priori, four such machines, only two are essentially different: a pop stack followed directly by a stack, and a pop stack followed by a queue and then by a stack. In the former case, we obtain complete answers for the basis and enumeration of the sortable permutations. In the latter case, we present several conjectures.

math.CO↗

arXiv2013

A Decreasing Stack and an Increasing Stack in Series

We study a sorting machine consisting of two stacks in series where the first stack has the added restriction such that entries in the stack must be in decreasing order from top to bottom. We give the basis of the class of permutations that are sortable by this machine which shows that it is enumerated by the Schröder numbers.

math.CO↗

arXiv2009

Growth rates for subclasses of Av(321)

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates.

math.CO↗