The Cheeger’s constant, also known as the isoperimetric number, is a constant that helps describe the bottleneck present in a graph, if any. Some fields, such as computer networks, have an interest in this constant due to the application of the constant in their field. We examined randomly generated connected graphs and their isoperimetric numbers by developing algorithms to calculate it.

One of the major challenges in education is accurately quantifying a student’s knowledge and skills. Since we cannot directly measure a student’s true intelligence, we rely on test performance, which serves as an imperfect representation of their abilities. This issue arises in many statistical applications where the key problem involves a population in which each individual possesses an underlying ability or trait that cannot be directly observed but can only be inferred through proxy variables. However, these proxies are often contaminated, providing only a noisy or imperfect approximation of the true latent variable.
This project focuses on techniques for recovering latent variables from noisy data. In this context, "recovery" refers to estimating the latent variable using indirect observations. Assuming a linear relationship between the latent trait and the observed proxy variables, we can estimate model parameters and subsequently recover the values of the latent variables.
Specifically, we will examine statistical approaches to latent variable recovery when the test contains items that exhibit differential item functioning (DIF). This means that certain test items do not solely measure the intended knowledge or ability but are also biased toward specific groups. The objective is to develop methods that detect the presence of DIF and adjust for it, allowing for a more accurate estimation of the underlying abilities.
To illustrate these methods, we will use the Holzinger-Swineford dataset, a well-known dataset in psychometrics used to analyze cognitive abilities across multiple domains. This dataset includes 88 observations with scores in five areas: Mechanical Comprehension, Verbal or Visual Comprehension, Algebra Operations, Analytical Operations, and Statistical Reasoning. By applying a linear contamination model, we aim to recover each student's latent ability while accounting for DIF.

Oral Reading Accuracy (ORA) is an important metric for evaluating a student's reading proficiency, measuring how accurately a reader can read words aloud. Traditional ORA evaluations performed by human assessors often require significant time and labor. This study explores the potential of integrating a speech recognition system into ORA assessments to improve efficiency. We analyzed ORA data from 507 elementary school students across ten passages of different lengths and difficulties. Both human evaluators and AI systems recorded the number of words read correctly. The misclassification rates of these scores are divided into two components: True Positive (correct words are identified as correct), and True Negative (incorrect words are identified as correct). This second study expands upon Method of Moments method to estimate these misclassification rates. We apply Generalized Method of Moments which incorporates additional variance information. To compare the two approaches' accuracy, we apply the m-out-of-n Bootstrap method to estimate their standard errors and compare their reductions in estimator variance. Additionally, we introduce a Contaminated Data Solution to address real-world scenarios where true count data is unavailable and only contaminated observed data is observed.

Several viruses can cause cells to fuse into large multinucleated cells called syncytia. Syncytia formation allows the virus to spread without entering the extracellular space, where it might be exposed to immune responses. However, there is evidence that antibodies can also hinder the fusion process. This project uses mathematical analysis to find different possible infection outcomes. A stability analysis of the coinfection model is used to find the fixed points of the model and their stability. This gives us parameter space regions that lead to different possible infection outcomes. Simulations were made to verify the mathematical analysis and see how different syncytia formation properties affect the resulting dynamics. These findings could help develop strategies for controlling viral spread.

Graphene Quantum Dots (GQDs) are nanoscale carbon based graphene sheets that exhibit unique fluorescent properties throughout a wide range of wavelengths. Given their uniquely small size, low toxicity, biocompatibility, and fluorescent capabilities, GQDs have many unique and important roles. To name a few, GQDs are used in drug delivery, fluorescent imaging, and biosensing thanks to their unique ability to fluoresce under different wavelengths of light. Furthermore, there are different types of GQDs with their own unique properties. Knowing this, five amphipathic molecules, called surfactants, were added to two different types of GQDs to test if they would impact the resulting fluorescence. Furthermore, concentrations of these added surfactants were varied to test how different concentrations of a given surfactant might affect the fluorescence for a given GQD. We observed that some of these surfactants provided a beneficial boost to GQDs fluorescence, while others slightly inhibited the fluorescence. Moreover, we saw that the increase in fluorescence varied based on the concentration of surfactant added yielding lower fluorescence for extremely low and high concentrations, while increasing the fluorescence at a more moderate concentration.

With cancer rates increasing at an alarming rate, many traditional methods for cancer treatment begin to feel outdated. This is where engineering nanomaterials, such as Graphene Quantum Dots (GQDs), offer a promising approach to making chemotherapy a more targeted treatment and therefore minimizing the side effects. This study focuses on optimizing drug delivery mechanisms using GQDs, specifically Reduced Graphene Quantum Dots (RGQDs) synthesized via a top-down approach from reduced graphene oxide, and Hyaluronic Acid Graphene Quantum Dots (HAGQDs) synthesized bottom-up from hyaluronic acid. The process is done by loading chemotherapeutics Gemcitabine, Paclitaxel, and Doxorubicin (DOX) HCl onto GQDs through sonication, this is followed by a centrifugal purification which isolates properly drug-loaded GQDs. To evaluate their controlled release, photothermal properties of GQDs are utilized. Samples are excited with an 808 nm laser at 1, 5, and 10 minutes, and they are later compared to a control group. This analysis provides insights into how laser stimulation affects drug release efficiency, paving the way for advancements in GQD based cancer treatments.

Some viruses have the ability to form syncytia. Syncytia are multi-nucleated cells formed via membrane fusion. Syncytia formation allows viruses to spread infection to other cells without entering the extracellular space where it could be exposed to antiviral drugs or immune responses such as antibodies. This project explores how syncytia formation can help viruses avoid antiviral drugs. Drug efficacy parameters are applied to a mathematical model of differential equations to explore the impact of antiviral drugs on cell infection, cell fusion, and viral production to model respiratory syncytial virus. The models show that as syncytia formation increases the drugs become less effective. This information will help physicians treat patients with syncytia forming viruses.

After the COVID-19 pandemic, over 40 million children worldwide are at risk of measles due to delayed vaccination and temporary SARS-CoV-2 viral dominance. The lasting immunosuppression caused by the disease presents a major health threat, and treatment options are urgently needed, especially for low- and middle-income countries. The manuscript by Cox et al. (2024) explores features of canine distemper virus (CDV) in ferrets, using this model as a surrogate for measles to evaluate two possible antiviral treatments, ERDRP-0519 and GHP-88309. Ferrets were infected with a lethal challenge of CDV and treated with either drug or therapeutic vaccination. We aim to characterize both the infection dynamics and efficacy of the two drug treatments using the data from the PBMC (peripheral blood mononuclear cell) associated viremia titers of CDV infected ferrets and the lymphocyte counts measured during the duration of the study. A differential mathematical model was fitted to the experimental data by minimizing the sum of squared residuals (SSR), and errors in the parameter fits were estimated using Monte Carlo Markov Chain (MCMC). We visualized the key parameter distributions for each dataset using histograms, allowing us to directly compare how each treatment influences infection dynamics. The results revealed that ERDRP-0519 reduced viral entry and enhanced clearance while GHP-88309 improved target cell growth and increased the rate of infected cell death. These findings suggest that both drugs are potentially effective measles treatment options, with ERDRP-0519 having a direct antiviral effect and GHP-88309 aiding in immune recovery. Overall, these insights provide a foundation for optimizing treatment strategies and highlight the potential for both drugs to combat measles and related morbillivirus infections, especially in areas with limited resources and vaccines.

Gliomas account for approximately 27% of all primary central nervous system tumors and exhibit highly aggressive growth patterns, making conventional treatments ineffective. Previous research has demonstrated that a replication-competent Sindbis virus (SINV) combined with cytokines (IL-7, IL-12, and GM-CSF) shows promising results in slowing down glioma progression. While prior research demonstrated that SINV combined with cytokines reduces tumor growth, a quantitative understanding of its effects remains limited. This study aims to develop and fit a mathematical model of oncolytic virus infection to data from previous research to quantify key biological processes in glioma treatment. By parameterizing the Sindbis virus-glioma interaction and estimating the effects of cytokine therapy, this model aims to evaluate the efficacy of different SINV variants, with and without cytokine combinations, in controlling tumor growth. We use an Ordinary Differential Equation (ODE) model to describe tumor growth inhibition by the oncolytic SINVs. The model includes variables for uninfected and infected tumor cells, viral load, and cytokine concentration. The data extracted from published tumor growth curves will be used to estimate key parameters, including viral replication rate, tumor growth rate, and cytokine effects. Parameter fitting will be conducted by minimizing the Sum of Squared Residuals (SSR) between model predictions and experimental data. Error in the parameters will be estimated through bootstrapping to find the best fit parameters with 95% confidence intervals. Preliminary analysis suggests that the model effectively captures tumor growth rates observed in the experimental data. Parameter estimation provides insights into the viral infection rate, cytokine-induced tumor suppression, and the timing of viral injections. These findings will help refine our understanding of how the SINVs and cytokine therapy interact in glioma treatment. This study provides a quantitative framework for evaluating the therapeutic effects of an oncolytic SINV combined with cytokines in glioma treatment. By providing parameter estimates for key biological processes, our model can help optimize treatment strategies and guide future experimental research in oncolytic virotherapy.

Mathematical modeling of viral kinetics can be used to gain further insight into the viral replication cycle and virus-host interactions. However, many virus dynamics models do not incorporate the cell-to-cell heterogeneity of virus yield or the time-dependent factor of virus production. A recent study of the kinetics of the vesicular stomatitis virus (VSV) in single BHK cells determined that both the virus production rate and the yield of virus particles vary widely between individual cells of the same cell population. We used the results of this study to determine the distribution that best describes the time course of viral production within single cells. The best distribution was then used to incorporate time-varying production into a standard model of viral kinetics. The best-fit model was determined by fitting potential distributions to cumulative viral production from single cells and comparing the Akaike Information Criterion (AIC). The results show that the best fit for most cells was log-normal. Time-dependent viral production was modeled with an integro-differential equation that incorporated the log-normal probability distribution into a standard constant production model of viral kinetics. This time-dependent model was compared to one of constant production by examining the differences between the viral peak, time of the peak, upslope, downslope, and area under the curve. These findings could have further-reaching implications for helping define the time course and nature of a particular virus infection within the human body as well as improving the dose-timing and efficacy of anti-viral treatments.

Syncytia are multinucleated cells that can occur due to virus infection of cells. Mathematical models in the form of ordinary differential equations can be used to simulate the growth of syncytia. Several novel ODE models can explain syncytia growth. Before employing these models on actual data, it is essential to analyze their structural (theoretical) and practical identifiability using computer software. Structural identifiability is an inherent property of each model and its parameters, referring to our ability to determine parameter values for the model given particular experimental measurements. Practical Identifiability analysis of a model is concerned with determining our ability to accurately determine parameter values given experimental error. Combining these two techniques enables us to determine whether or not the parameters of our syncytia models can be accurately determined. Obtaining accurate parameter values allows us to make conclusions about our data that can provide insight into the nature of the spread of syncytia. From this, we can plan experiments to parameterize the syncytia growth in the contexts of our models.

Mpox virus is a type of virus similar to smallpox that can cause diseases in humans. Several experiments have been done to collect data on how mpox evolves within an infected host. This data can be analyzed within the context of mathematical models to determine important characteristics of mpox. From this analysis, we can estimate the growth rate, reproduction number, and infecting time of mpox.  We can also construct confidence intervals to estimate the error in our predictions using bootstrapping.  Bootstrapping allows us to analyze parameter correlations within mpox data to understand how parameter values within the model affect each other in our model. From these values and confidence intervals, we can learn about how mpox evolves within the body over time. This information, in turn, may allow us to make predictions on how mpox evolves within people during infection that could inform future treatment regimens.

Iron zinc oxides are multifunctional materials with applications in luminescent devices, catalysis, spintronics, and gas sensors. Specifically, iron-doped zinc oxide (FeZnO) combines magnetic and chemical stability properties, making it suitable for technological and environmental applications. This study explores how synthesis parameters, including pH and dopant concentration, influence the morphology and properties of FeZnO nanoparticles. Hydrothermal synthesis was employed to prepare FeZnO with iron doping concentrations ranging from 1–10% and ZnO. Morphological and compositional analyses were performed using scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). We also observed doped FeZnO antibacterial action for some of the synthesized samples in e-coli cultures. Future work will focus on improving dopant distribution, exploring antibacterial activity, and leveraging computational tools to refine material design for specific applications.

Oncolytic Herpes Simplex Viruses (oHSVs) target a wide range of different cells and specific mutations, allowing them to proliferate in tumor cells. Recent work has modified the virus to preferentially enter cells bearing epidermal growth factor receptors (EGFRs). This study focuses on characterizing the efficacy of different strains of EGFR-targeting oHSV by fitting a mathematical model that includes an interferon response to experimental data from U251 tumor-bearing mice. Using a combination of parameter fitting, optimization techniques, and ordinary differential equations (ODEs), we modeled tumor growth, viral dynamics, and immune response. Our findings suggest that an interferon-inclusive model best explains the growth and oHSV treatment of EGFR-bearing tumors. These results highlight the importance of immune interactions in oncolytic viral therapy and contribute to optimizing oHSV-based treatments for better clinical outcomes.

Among the most life-threatening diseases, cancer poses a major issue and affects over fifty million people worldwide. To overcome the challenges associated with conventional chemotherapy, affecting both cancerous and normal cells, here we develop folic acid-functionalized Graphene Quantum Dots (GQDs) targeted to folate receptors overexpressed in a variety of cancer cell lines. GQDs due to their high biocompatibility and intrinsic fluorescence-based imaging capabilities have recently emerged as promising theragnostic agents. In this project, we synthesized GQDs utilizing the bottom up synthesis method and functionalized them with folic acid. The efficacy of the Folic acid functionalized GQDs (FAGQDs) is evaluated through their internalization study in cancerous (HeLa) and normal (HEK-293) cells by utilizing the intrinsic fluorescence of FAGQDs.

The use of fluorescent compounds as biological markers or probes is widely used in assays for probing various properties, including but not limited to pH, temperature, or the presence of various proteins. This has allowed fluorescence to enter the fields of microscopy, diagnostics, and spectroscopy. Among the many dyes used for such applications are those that exhibit phosphorescence. Unlike fluorescence, which has a lifetime of several nanoseconds, phosphorescence lifetimes can be several seconds, allowing for the use of techniques such as gated detection, which can eliminate distracting background noise or Raman scattering. Since phosphorescence uses the triplet state rather than the singlet state, it requires less energy, which correlates with longer wavelengths. The phosphorescence emission of some dyes can extend from 425nm (blue) to 675nm (red), which encompasses almost the entire visible spectrum. This is especially useful when considering that longer wavelengths may be used when utilizing direct triplet state excitation, which allows for excitation wavelengths well into the visible range. The ability to utilize longer excitation wavelengths has numerous possibilities, among which include being safe to use with live cells, which opens the door for using phosphorescence as a technique for biological imaging. Not only does phosphorescence allow imaging to occur at longer wavelengths, which mitigates damage to cells and minimizes exposure to harmful ultraviolet radiation, but it also allows for much more affordable equipment and procedures, possibly making diagnostic care more accessible.

Multipartite viruses are a unique class of viruses that divide their genome into multiple segments, each packaged into a separate viral particle. Unlike traditional viruses, which encapsulate their entire genome within a single particle, multipartite viruses require all genome segments to infect the same host cell for successful replication. This study investigates the infection dynamics of multipartite viruses through mathematical modeling, with a focus on bipartite and tripartite viruses. By comparing their behavior to single-particle viruses, we analyze the factors influencing viral persistence and spread. Our results indicate that the higher number of particles in a virus, the harder it is to maintain an infection. While multipartite infections exhibit shorter durations of infections compared to single-particle infections, their ability to persist suggests a potential benefit. These findings can help develop an understanding into the adaptive mechanisms of multipartite viruses and contribute to a broader understanding of viral evolution and host-virus interactions.

Surface plasmon–coupled emission (SPCE) is a powerful phenomenon that utilizes the near-field interaction between excited fluorophores and thin metallic films, together with a glass substrate, to significantly improve fluorescence detection sensitivity. By coupling the fluorophore’s oscillating dipole to surface plasmons, SPCE channels a substantial fraction of the emitted photons into a defined angle, generating a highly directional and polarized emission that can achieve up to 50% light collection efficiency. This intrinsically wavelength-resolved emission not only simplifies optical system design but also elevates the signal-to-noise ratio by reducing background interference. Compared to conventional isotropic free-space fluorescence, SPCE’s strong directional control and enhanced collection enable the detection of analytes at extremely low limits. Hence, this paper elucidates how SPCE’s unique advantages can be leveraged to achieve highly sensitive detection of critical biomarkers, paving the way for more rapid and efficient diagnostic applications.

Micro- and nanoscale metal oxides are used in a variety of applications. ZnO and Ga2O3 semiconductors are two metal oxides that have a wide bandgap and find themselves used in today’s electronics, gas sensors, and photodetectors. These two materials are also used in a wide range of temperatures, which means that the chemical bond lengths, vibrational states, defect states, and band-gaps all should be variable. In our experiments, we investigate the T-dependencies of positions, intensities, and widths of Raman peaks/bands for micro- and nanoscale ZnO and Ga2O3. In our studies, in addition to the temperature-dependent Raman spectroscopy we employ scanning electron microscopy (morphology of particles), energy dispersive X-ray spectroscopy (stochiometry) and temperature-dependent photoluminescence spectroscopy (electronic structure).

Human Immunodeficiency Virus (HIV) can exist as syncytia-forming or non-syncytia-forming strains, each utilizing different mechanisms of infection. Understanding the competition between these strains is crucial, as syncytia formation has been linked to increased disease progression and immune system decline. This study develops a mathematical model to analyze their competition, incorporating parameters such as fusion rate, syncytia lifespan, and viral production. Stability analysis and simulations will determine conditions under which one strain dominates or both coexist. By varying key parameters, we aim to understand how syncytia formation influences viral dynamics and infection persistence, providing insights into HIV pathogenesis and potential treatment strategies.

Graphene quantum dots (GQDs) have gained attention in the bioimaging community due to their biocompatibility and enhanced imaging depth in the near infra-red (NIR). Developing and optimizing a facile synthesis method of biocompatible NIR fluorescent GQDs from a variety of precursors remains, therefore, a critical task. Herein, we synthesized various GQD structures capable of fluorescing in the NIR via facile bottom-up pyrolysis of precursor materials (ascorbic acid, chitosan, citric acid, dextran, glucose, glucosamine hydrochloride, hyaluronic acid, l-glutamic acid, polyethylene glycol (PEG), sodium cholate, or sodium citrate). All synthesized GQD structures exhibit remarkable biocompatibility at concentrations of up to 1 mg/mL evaluated by an MTT assay which makes them suitable for a variety of therapeutic applications. All 11 GQD structures are successfully tracked by their NIR fluorescence in vitro bioimaging while exhibiting effective cellular internalization maximized at 12 hours in HEK293 cell line. This work provides a unique comprehensive study exploring a scalable and cost-effective process to synthesize NIR-emissive highly biocompatible GQDs from 11 precursor materials, while theoretically describing their optical properties. Due to their exceptional biocompatibility and photostable NIR emission, GQD structures developed here are expected to become prominent candidates for future clinical fluorescence imaging applications.

Modulating the Interferon Response to Enhance Oncolytic Virotherapy in Cancer Treatment
Anushka Velala, Hana Dobrovolny Ph.D
TCU Department of Physics, Fort Worth, TX
Background: Oncolytic viruses (OVs) are a promising immunotherapeutic strategy that can selectively target and lyse cancer cells while stimulating an anti-tumor immune response. However, their efficiency is often limited by the interferon (IFN) response, which acts as a key antiviral defense mechanism in host cells. Understanding the interplay between oncolytic viruses and IFN signaling is crucial for optimizing viral-based cancer therapies that have potential of success.
Hypothesis/Objective: This study aims to investigate how oncolytic viruses interact with the IFN response in a simulated tumor microenvironment. We hypothesize that higher values of variation in the IFN modulation can significantly negatively affect viral replication and therapeutic oncolytic efficacy.
Study Design and Research Methods: An analysis was conducted using a mathematical model with systems of differential equations. This model encompasses factors such as tumor growth, oncolytic infection dynamics, viral production and clearance, and the IFN-mediated immune response. Furthermore, sensitivity analysis was conducted to assess the influence of key parameters, including viral production rate, infection rate, and IFN clearance, on the treatment outcomes.
Results: Various simulations indicate that higher IFN levels correlate with reduced viral spread, leading to diminished oncolytic activity. However, parameter variations suggest that therapeutic efficacy can be optimized by adjusting certain parameters to mitigate excessive IFN responses. For instance, higher values of IFN efficacy are correlated with stronger IFN-mediated suppression of viral production, leading to lower sustained viral loads, while lower IFN efficacy levels allow for prolonged high viral replication. Similarly, IFN clearance rate affects how long IFN-induced killing of infected cells and uninfected cells persists, which can modulate the viral load over time. The most effective interferon response is a low-level response with low IFN clearance and high values of IFN efficacy, coupled with higher values of IFN-induced killing of uninfected cancer cells.
Conclusions: These findings underscore the role of the IFN response in modulating OV therapy and suggest that targeted suppression of IFN signaling could enhance OV efficacy in resistant tumors. This research provides insights for optimizing oncolytic virotherapy and improving clinical outcomes in cancer treatment, given the rising prominence of immunotherapy.

Frustrative nonreward (FNR), an adverse reaction brought on by unexpected reward reductions or omissions, can be induced by a downshift in the quantity or quality of the reward. The consummatory successive negative contrast (cSNC) task is a well-known paradigm for studying FNR. cSNC involves monitoring the behavioral reaction to a lower reward (downshift) after exposure to a larger or better incentive. It supports the idea that an acceptable but less preferred reward will be rejected in a situation that is associated with a better and more desirable reward. The intensity of FNR depends, among other things, on the strength of the expectation of the large reward. We assumed that overtraining would enhance reward expectancy such that a reward downshift would lead to a stronger cSNC effect than that observed under regular training conditions. This would support the hypothesis that behavior (licking for sucrose) was guided by reward expectancies—an action. But overtraining often leads to habitual behavior that depends on eliciting stimuli, rather than reward expectancies. A failure to show the cSNC effect after overtraining would be consistent with the hypothesis that behavior had become automatic—a habit. Our experiment was designed to test whether overtraining in the cSNC task would result in behavior becoming either an action or a habit. In the experiment, 47 rats were exposed to different concentrations of sucrose, 32%, 16%, or 4%, and 2 training periods, overtraining for 30 sessions and regular training for 10 sessions. Animals exposed to 32% and 16% sucrose were randomly assigned to two groups depending on the amount of training they received before the downshift, either 30 (overtraining) or 10 sessions (regular training). These animals were given access to 4% sucrose after their designated training period. An unshifted control group received only access to 4% sucrose throughout training. The data obtained after 10 vs. 30 sessions of training were compared to the unshifted controls. The results showed that overtraining enhanced the cSNC effect relative to regular training, suggesting that licking was an action guided by the expectation of the current reward, rather than a habit. These results suggest that FNR induced by reward downshifts overcomes the development of a habit even after prolonged training.

Recent discussions surrounding law enforcement have highlighted varying opinions on the ability of police officers to respond effectively to mental health-related incidents. Given that 20% of police calls involve mental health or substance abuse issues, it is crucial that the general population is confident about the role of police as mental health interventionalists. The current study assessed DFW residents’ (N = 64) perceptions of the police’s ability to intervene in mental health crises utilizing in-person and online 7-point Likert scale surveys (where 1 = disagree strongly and 7 = agree strongly). Survey results showed that confidence in police’s ability to handle mental health crises increases with age, p = .04. Older participants expressed greater trust, while younger respondents were more skeptical. No significant differences were found in gender, race, ethnicity, or socioeconomic status, highlighting a generational divide in public trust. These results suggest that there is potential for improving younger individuals’ attitudes towards police intervention.

Rats use many cues when navigating to food, shelter, or a mate. The use of visual cues (e.g., landmarks) has been reported in many species. In rats, these cues include those around their start position, the experimenter, as well as landmarks located in (intramaze) or around (extramaze) the search space. In the current experiment, rats were placed into a start box with a transparent door and released onto an open field. We examined whether rats were able to discriminate between two different intramaze landmarks (wooden figurines; A and B) from the start box. Landmark A trials were reinforced with a Froot Loop© hidden in a cup behind the landmark (A+), but no Froot Loop was present on Landmark B (B-) trials or on C- trials with no landmark. Latency to the goal cup was measured and revealed no differences between the three trial types. The procedure was modified to include two response locations (to the left and right of the landmark). A+ and B+ trial types were reinforced at different cups. There was no difference in accuracy for searching the correct cup first. The use of non-visual cues, the discriminability of the landmarks, and the response cost of search will be discussed.