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We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of [Johansson and Linusson 2007]. In particular, we give a uniform proof of an exponential upper bound for the number of alternating sign matrices classically avoiding one of twelve particular patterns, and a super-exponential lower bound for all other single-pattern avoidance classes. We also show that for any fixed integer $k$, there is an exponential upper bound for the number of alternating sign matrices that classically avoid any single permutation pattern and contain precisely $k$ negative ones. Finally, we prove that there must be at most $3$ negative ones in an alternating sign matrix which classically avoids both $2143$ and $3412$, and we exactly enumerate the number of them with precisely $3$ negative ones.

Even as the incidence of mosquito-borne diseases like West Nile Virus (WNV) in North America has risen over the past decade, effectively modelling mosquito population density or, the abundance has proven to be a persistent challenge. It is critical to capture the fluctuations in mosquito abundance across seasons in order to forecast the varying risk of disease transmission from one year to the next. We develop a process-based mechanistic weather-driven Ordinary Differential Equation (ODE) model to study the population biology of both aqueous and terrestrial stages of mosquito population. The progression of mosquito lifecycle through these stages is influenced by different factors, including temperature, daylight hours, intra-species competition and the availability of aquatic habitats. Weather-driven parameters are utilised in our work, are a combination of laboratory research and literature data. In our model, we include precipitation data as a substitute for evaluating additional mortality in the mosquito population. We compute the \textit{Basic offspring number} of the associated model and perform sensitivity analysis. Finally, we employ our model to assess the effectiveness of various adulticides strategies to predict the reduction in mosquito population. This enhancement in modelling of mosquito abundance can be instrumental in guiding interventions aimed at reducing mosquito populations and mitigating mosquito-borne diseases such as the WNV.

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., Comment: 28 pages

We consider sorting procedures for permutations making use of pop stacks with a bypass operation, and explore the combinatorial properties of the associated algorithms., Comment: In Proceedings GASCom 2024, arXiv:2406.14588

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., Comment: 22 pages, 9 figures

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., Comment: 22 pages. To appear in Discrete Mathematics & Theoretical Computer Science, vol. 27:1, Permutation Patterns 2024

Socioeconomic factors such as income have historically driven equity-focused education grant funding. The events of 2020, from the murder of George Floyd and other Black Americans to the COVID-19 pandemic, heightened scrutiny into ongoing racial injustice and disparities in the United States. In fall 2021, Grantmakers for Education set out to determine whether and how many of its members were moving from intention to action, making grantmaking decisions with explicit attention to racial and ethnic groups that have been historically marginalized. Results show it is clear there is movement among Grantmakers for Education members to increase support for racial equity. However, to really make a difference, funders need to be ready to maintain funding for the long term. With contentious elections on the horizon that will place race and education at the center of many divisive debates, will funders stay the course? Working together can move intention to action to support racial equity and justice for learners nationwide.

During the COVID-19 pandemic, different countries, regions, and communities constructed various epidemic models to evaluate spreading behaviors and assist in making mitigation policies. Model uncertainties, introduced by complex transmission behaviors, contact-tracing networks, time-varying spreading parameters, and human factors, as well as insufficient data, have posed arduous challenges for model-based approaches. To address these challenges, we propose a novel framework for data-driven counterfactual analysis, strategy evaluation, and feedback control of epidemics, which leverages statistical information from epidemic testing data instead of constructing a specific model. Through reverse engineering the reproduction number by quantifying the impact of the intervention strategy, this framework tackles three primary problems: 1) How severe would an outbreak have been without the implemented intervention strategies? 2) What impact would varying the intervention strength have had on an outbreak? 3) How can we adjust the intervention intensity based on the current state of an outbreak? Specifically, we consider the epidemic intervention policies such as the testing-for-isolation strategy as an example, which was successfully implemented by the University of Illinois Urbana-Champaign (UIUC) and Purdue University (Purdue) during the COVID-19 pandemic. By leveraging data collected by UIUC and Purdue, we validate the effectiveness of the proposed data-driven framework.

West Nile virus (WNV) is prevalent in the United States but it shows considerable divergence in transmission patterns and spatio-temporal intensity.It is to be noted that the mechanism that drives the transmission potential of WNV is described by the abilities of host species to maintain and disseminate the pathogens pertinent with different eco-epidemiological factors that have an influence on the contact rates amongst the interacting species.There is growing evidence that several vectors exhibit strong feeding preferences towards different host communities.We construct a process based weather driven ordinary differential equation (ODE) model to understand the impact of one vector species Culex pipiens, preferred avian and non-preferred human hosts and compared it surveillance data for the Culex pipiens complex collected in Cook County, Illinois, USA.In our mechanistic model, we also demonstrate that adulticide treatments produced significant reductions in the Culex pipiens population.We take into account the feeding index that can be described as the ratio between observed frequency of mosquitoes feeding on one host compared to another host, divided by the expected frequency of mosquitoes feeding on these two hosts based on the presence of the particular hosts to develop this transmission model for WNV. Our findings demonstrate that the interplay between the feeding index and mosquito abatement strategy is rather a complex phenomenon and it induces a heterogeneous contact rates that should be included while modelling multi-host, multi-vector transmission model.

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.