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Given a finite group G with an irreducible character \chi \in Irr(G), the codegree of \chi is defined by cod(\chi) = |G :\ker \chi|/\chi(1). The set of non-linear irreducible character codegrees of G is denoted by cod(G|G'). In this note, we classify all finite groups G with |cod(G|G')|> 1 and for each pair of distinct elements m, n \in cod(G|G'), m and n are coprime.

This study investigates the impact of emotionally enriched AI feedback on student engagement and emotional responses in higher education. Leveraging the Control-Value Theory of Achievement Emotions, we conducted a randomized controlled experiment involving 425 participants where the experimental group received AI feedback enhanced with motivational elements, while the control group received neutral feedback. Our findings reveal that emotionally enriched feedback is perceived as more beneficial and helps reduce negative emotions, particularly anger, towards receiving feedback. However, it had no significant impact on the level of engagement with feedback or the quality of student work. These results suggest that incorporating emotional elements into AI-driven feedback can positively influence student perceptions and emotional well-being, without compromising work quality. Our study contributes to the growing body of research on AI in education by highlighting the importance of emotional considerations in educational technology design.

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the robust model and practical usefulness of the resulting solution. We consider problems with a discrete uncertainty set affecting only the objective function. Our aim is reduce the size of the uncertainty set, while staying as true as possible to the original robust problem, measured by an approximation guarantee. Previous reduction approaches ignored the structure of the set of feasible solutions in this process. We show how to achieve better uncertainty sets by taking into account what solutions are possible, providing a theoretical framework and models to this end. In computational experiments, we note that our new framework achieves better uncertainty sets than previous methods or a simple K-means approach.

We say that a Banach algebra A has $k$-orthogonally additive property ($k$-OA property, for short) if every orthogonally additive k-homogeneous polynomial $P:\mathcal{A}\to \mathbb{C}$ can be expressed in the standard form $P(x)=\langle \gamma,x^k\rangle$, $(x\in \mathcal{A})$, for some $\gamma\in \mathcal{A}^*$. In this paper we first investigate the extensions of a $k$-homogeneous polynomial from $\mathcal{A}$ to the bidual $\mathcal{A}^{**}$; equipped with the first Arens product. We then study the relationship between $k$-OA properties of $\mathcal{A}$ and $\mathcal{A}^{**}$: This relation is specially investigated for a dual Banach algebra. Finally we examine our results for the dual Banach algebra $\ell^{1}$, with pointwise product, and we show that the Banach algebra $(\ell^{1})^{**}$ enjoys k-OA property.

We perform an observational study of modified gravity considering a potential inflationary interpretation of pulsar timing arrays (PTA). We use a motivated model known as no slip in which the gravitational wave propagation is modified. Specifically, by using two different parametrizations for the model, we find the approximate transfer functions for tensor perturbations. In this way, we obtain the spectral energy density of gravitational waves and use NANOGrav and IPTA second data release to constrain parameters of the model. We find that there is degeneracy between the model parameters $\xi$ and $c_M$. For $c_M$, we only get an upper bound on the parameter. Thus, it is difficult to constrain them with percent level accuracy with the current PTA data., Comment: 18 pages, 5 figures, 2 tables

Agricultural production requires careful management of inputs such as fungicides, insecticides, and herbicides to ensure a successful crop that is high-yielding, profitable, and of superior seed quality. Current state-of-the-art field crop management relies on coarse-scale crop management strategies, where entire fields are sprayed with pest and disease-controlling chemicals, leading to increased cost and sub-optimal soil and crop management. To overcome these challenges and optimize crop production, we utilize machine learning tools within a virtual field environment to generate localized management plans for farmers to manage biotic threats while maximizing profits. Specifically, we present AgGym, a modular, crop and stress agnostic simulation framework to model the spread of biotic stresses in a field and estimate yield losses with and without chemical treatments. Our validation with real data shows that AgGym can be customized with limited data to simulate yield outcomes under various biotic stress conditions. We further demonstrate that deep reinforcement learning (RL) policies can be trained using AgGym for designing ultra-precise biotic stress mitigation strategies with potential to increase yield recovery with less chemicals and lower cost. Our proposed framework enables personalized decision support that can transform biotic stress management from being schedule based and reactive to opportunistic and prescriptive. We also release the AgGym software implementation as a community resource and invite experts to contribute to this open-sourced publicly available modular environment framework. The source code can be accessed at: https://github.com/SCSLabISU/AgGym.

We have studied the cosmic microwave background (CMB) map looking for features beyond cosmological isotropy. We began by tiling the CMB variance map (which are produced by different smoothing scales) with stripes of different sizes along the most prominent dipole direction. We were able to confirm previous findings regarding the significance of the dipole. Furthermore, we discovered that some of the higher multipoles exhibit significance comparable to the dipole which naturally depends on the smoothing scales. At the end, we discussed this result having an eye on look-elsewhere-effect. We believe our results may indicate an anomalous patch in the CMB sky that warrants further investigation., Comment: 9 pages, 8 figures, Accepted for publication in ApJ

Kirigami metamaterial sheets and tubes, owing to their capacity to undergo large elastic deformations while developing three-dimensional surface textures, have enormous potential as skins for soft robots. Here, we propose to use kirigami skins with folding hinges in this same context. These recently-introduced kirigami feature counter-rotating panels connected by pop-up folding hinges. So far, researchers have only explored auxetic and highly-symmetric versions of such patterns. Yet, some of these attributes have to be relaxed in order to explore their full potential as robotic skins. Thus, we parameterize these patterns and relax symmetry constraints, with the goal of using this same platform to obtain a wide range of shape-morphing behaviors. We use a combination of: matrix analysis tools and analytical kinematic formulas to thoroughly explore the vast design space that ensues; experiments for validation purposes; and numerical simulations to explore the mechanics of selected planar and tubular patterns. We demonstrate that it is possible to tailor parameters to obtain skins that globally expand or contract due to axial elongation, and that present asymmetric pop-ups that can yield anisotropic friction -- the most desired attribute for one-way locomotion of soft robots.

Machine learning models have the potential to identify cardiovascular diseases (CVDs) early and accurately in primary healthcare settings, which is crucial for delivering timely treatment and management. Although population-based CVD risk models have been used traditionally, these models often do not consider variations in lifestyles, socioeconomic conditions, or genetic predispositions. Therefore, we aimed to develop machine learning models for CVD detection using primary healthcare data, compare the performance of different models, and identify the best models. We used data from the UK Biobank study, which included over 500,000 middle-aged participants from different primary healthcare centers in the UK. Data collected at baseline (2006--2010) and during imaging visits after 2014 were used in this study. Baseline characteristics, including sex, age, and the Townsend Deprivation Index, were included. Participants were classified as having CVD if they reported at least one of the following conditions: heart attack, angina, stroke, or high blood pressure. Cardiac imaging data such as electrocardiogram and echocardiography data, including left ventricular size and function, cardiac output, and stroke volume, were also used. We used 9 machine learning models (LSVM, RBFSVM, GP, DT, RF, NN, AdaBoost, NB, and QDA), which are explainable and easily interpretable. We reported the accuracy, precision, recall, and F-1 scores; confusion matrices; and area under the curve (AUC) curves., Comment: 19 pages, 3 figures

Lip-based biometric authentication (LBBA) has attracted many researchers during the last decade. The lip is specifically interesting for biometric researchers because it is a twin biometric with the potential to function both as a physiological and a behavioral trait. Although much valuable research was conducted on LBBA, none of them considered the different emotions of the client during the video acquisition step of LBBA, which can potentially affect the client's facial expressions and speech tempo. We proposed a novel network structure called WhisperNetV2, which extends our previously proposed network called WhisperNet. Our proposed network leverages a deep Siamese structure with triplet loss having three identical SlowFast networks as embedding networks. The SlowFast network is an excellent candidate for our task since the fast pathway extracts motion-related features (behavioral lip movements) with a high frame rate and low channel capacity. The slow pathway extracts visual features (physiological lip appearance) with a low frame rate and high channel capacity. Using an open-set protocol, we trained our network using the CREMA-D dataset and acquired an Equal Error Rate (EER) of 0.005 on the test set. Considering that the acquired EER is less than most similar LBBA methods, our method can be considered as a state-of-the-art LBBA method.

Generative AI such as those with large language models have created opportunities for innovative assessment design practices. Due to recent technological developments, there is a need to know the limits and capabilities of generative AI in terms of simulating cognitive skills. Assessing student critical thinking skills has been a feature of assessment for time immemorial, but the demands of digital assessment create unique challenges for equity, academic integrity and assessment authorship. Educators need a framework for determining their assessments vulnerability to generative AI to inform assessment design practices. This paper presents a framework that explores the capabilities of the LLM ChatGPT4 application, which is the current industry benchmark. This paper presents the Mapping of questions, AI vulnerability testing, Grading, Evaluation (MAGE) framework to methodically critique their assessments within their own disciplinary contexts. This critique will provide specific and targeted indications of their questions vulnerabilities in terms of the critical thinking skills. This can go on to form the basis of assessment design for their tasks.

Hydrogen embrittlement (HE) poses a significant challenge in the mechanical integrity of iron and its alloys. This study explores the influence of hydrogen atoms on two distinct grain boundaries (GBs), $\Sigma37$ and $\Sigma3$, in body-centered-cubic (BCC) iron. Using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo approach, we examine diffusion barriers and mechanisms associated with these GBs. Our findings reveal distinct behaviors of hydrogen in different GB environments, emphasizing the elastic deformation that arises around the GB in the presence of H that leads to either the predominance of new pathways and diffusion routes or a pinning effect of H atoms. We find that, for these systems, while GB is energetically favorable for H, this element diffuses more slowly at the GBs than in the bulk. Moreover, with detailed information about the evolution landscape around GB, we find that the saturation of a GB with hydrogen both stabilizes the GB by shifting barriers associated with Fe diffusion to higher energies and smooths the energy landscape, reducing the number of diffusion events. This comprehensive analysis enhances our understanding of hydrogen's role in GB behavior, contributing valuable insights for the design and optimization of materials in hydrogen-related applications., Comment: 12 pages, 10 Figures

A subset $C$ of the vertex set of a graph $\Gamma$ is said to be $(\alpha,\beta)$-regular if $C$ induces an $\alpha$-regular subgraph and every vertex outside $C$ is adjacent to exactly $\beta$ vertices in $C$. In particular, if $C$ is an $(\alpha,\beta)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(\alpha,\beta)$-regular set of $G$ and a $(0,1)$-regular set is called a perfect code of $G$. By Sq$(G)$ and NSq$(G)$ we mean the set of all square elements and non-square elements of $G$. As one of the main results in this note, we show that a subgroup $H$ of a finite abelian group $G$ is an $(\alpha,\beta)$-regular set of $G$, for each $0\leq \alpha \leq |$NSq$(G)\cap H|$ and $0\leq \beta \leq \mathcal{L}(H)$, where $\mathcal{L}(H)=|H|$, if Sq$(G) \subseteq H$ and $\mathcal{L}(H)=|$NSq$(G)\cap H|$, otherwise. As a consequence of our result we give a very brief proof for the main results in \cite{mama, ma}. Also, we consider the dihedral group $G=D_{2n} $ and for each subgroup $H $ of $G$, by giving an appropriate connection set $S$, we determine each possibility for $(\alpha, \beta)$, where $H$ is an $(\alpha,\beta)$-regular set of $G$.

The ongoing debate regarding the most accurate accretion model for supermassive black holes at the center of quasars has remained a contentious issue in astrophysics. One significant challenge is the variation in calculated accretion efficiency, with values exceeding the standard range of $0.038 < \epsilon < 0.42$. This discrepancy is especially pronounced in high redshift supermassive black holes, necessitating the development of a comprehensive model that can address the accretion efficiency for supermassive black holes in both the low and high redshift ranges. The selection effect was removed from model construction by creating a flux- and volume-limited sample, as the range of values for estimating the accretion efficiency factor varied through different redshifts. In this study, we have focused on low redshift ($z < 0.5$) Palomar-Green quasars (79 quasars) and high redshift ($z \geq 3$) quasars with standard disks from the flux- and volume-limited QUOTAS+QuasarNET dataset (75 quasars) to establish a model for accretion efficiency. By considering the QUOTAS+QuasarNET+DL11 dataset, a peak can be seen around $z \sim 2.708$, and it seems to be related to the peak of the star formation rate ($1 < z_{SFR} < 3$). Consequently, the observed maximum and minimum values of accretion efficiency in standard disks, through the considered bond (3$\sigma$), display a significantly wider range than previously noted and differentiate over time. In redshifts higher than 2.708, the accretion efficiency shows patterns of increase as redshift decreases, while in redshifts lower than 2.708, accretion efficiency is seen to decrease with reducing redshift. This result can potentially lead to a more accurate correlation between the star formation rate in quasars and their relationship with the mass of the central supermassive black holes with a more comprehensive disk model in future studies., Comment: 26 pages, 5 figures, discussion extended

Quantum electrodynamics (QED) deals with the relativistic interaction of bosonic gauge fields and fermionic charged particles. In QED, global conservation laws of angular momentum for light-matter interactions are well-known. However, local conservation laws, i.e. the conservation law of angular momentum at every point in space, remain unexplored. Here, we use the QED Lagrangian and Noether's theorem to derive a new local conservation law of angular momentum for Dirac-Maxwell fields in the form of the continuity relation for linear momentum. We separate this local conservation law into four coupled motion equations for spin and orbital angular momentum (OAM) densities. We introduce a helicity current tensor, OAM current tensor, and spin-orbit torque in the motion equations to shed light on on the local dynamics of spin-OAM interaction and angular momentum exchange between Maxwell-Dirac fields. We elucidate how our results translate to classical electrodynamics using the example of plane wave interference as well as a dual-mode optical fiber. Our results shine light on phenomena related to the spin of gauge bosons.

Reducing Carbon dioxide (CO2) emission is vital at both global and national levels, given their significant role in exacerbating climate change. CO2 emission, stemming from a variety of industrial and economic activities, are major contributors to the greenhouse effect and global warming, posing substantial obstacles in addressing climate issues. It's imperative to forecast CO2 emission trends and classify countries based on their emission patterns to effectively mitigate worldwide carbon emission. This paper presents an in-depth comparative study on the determinants of CO2 emission in twenty countries with high Human Development Index (HDI), exploring factors related to economy, environment, energy use, and renewable resources over a span of 25 years. The study unfolds in two distinct phases: initially, statistical techniques such as Ordinary Least Squares (OLS), fixed effects, and random effects models are applied to pinpoint significant determinants of CO2 emission. Following this, the study leverages supervised and unsupervised machine learning (ML) methods to further scrutinize and understand the factors influencing CO2 emission. Seasonal AutoRegressive Integrated Moving Average with eXogenous variables (SARIMAX), a supervised ML model, is first used to predict emission trends from historical data, offering practical insights for policy formulation. Subsequently, Dynamic Time Warping (DTW), an unsupervised learning approach, is used to group countries by similar emission patterns. The dual-phase approach utilized in this study significantly improves the accuracy of CO2 emission predictions while also providing a deeper insight into global emission trends. By adopting this thorough analytical framework, nations can develop more focused and effective carbon reduction policies, playing a vital role in the global initiative to combat climate change.

Transforming two-dimensional (2D) images into three-dimensional (3D) volumes is a well-known yet challenging problem for the computer vision community. In the medical domain, a few previous studies attempted to convert two or more input radiographs into computed tomography (CT) volumes. Following their effort, we introduce a diffusion model-based technology that can rotate the anatomical content of any input radiograph in 3D space, potentially enabling the visualization of the entire anatomical content of the radiograph from any viewpoint in 3D. Similar to previous studies, we used CT volumes to create Digitally Reconstructed Radiographs (DRRs) as the training data for our model. However, we addressed two significant limitations encountered in previous studies: 1. We utilized conditional diffusion models with classifier-free guidance instead of Generative Adversarial Networks (GANs) to achieve higher mode coverage and improved output image quality, with the only trade-off being slower inference time, which is often less critical in medical applications; and 2. We demonstrated that the unreliable output of style transfer deep learning (DL) models, such as Cycle-GAN, to transfer the style of actual radiographs to DRRs could be replaced with a simple yet effective training transformation that randomly changes the pixel intensity histograms of the input and ground-truth imaging data during training. This transformation makes the diffusion model agnostic to any distribution variations of the input data pixel intensity, enabling the reliable training of a DL model on input DRRs and applying the exact same model to conventional radiographs (or DRRs) during inference., Comment: Website: https://pouriarouzrokh.github.io/RadRotator Online demo: https://huggingface.co/spaces/Pouriarouzrokh/RadRotator Article information: 16 pages, 11 figures

Incorporating Generative AI (GenAI) and Large Language Models (LLMs) in education can enhance teaching efficiency and enrich student learning. Current LLM usage involves conversational user interfaces (CUIs) for tasks like generating materials or providing feedback. However, this presents challenges including the need for educator expertise in AI and CUIs, ethical concerns with high-stakes decisions, and privacy risks. CUIs also struggle with complex tasks. To address these, we propose transitioning from CUIs to user-friendly applications leveraging LLMs via API calls. We present a framework for ethically incorporating GenAI into educational tools and demonstrate its application in our tool, Feedback Copilot, which provides personalized feedback on student assignments. Our evaluation shows the effectiveness of this approach, with implications for GenAI researchers, educators, and technologists. This work charts a course for the future of GenAI in education., Comment: submission to C&E AI

With the growth of textual data across online platforms, sentiment analysis has become crucial for extracting insights from user-generated content. While traditional approaches and deep learning models have shown promise, they cannot often capture complex relationships between entities. In this paper, we propose leveraging Relational Graph Convolutional Networks (RGCNs) for sentiment analysis, which offer interpretability and flexibility by capturing dependencies between data points represented as nodes in a graph. We demonstrate the effectiveness of our approach by using pre-trained language models such as BERT and RoBERTa with RGCN architecture on product reviews from Amazon and Digikala datasets and evaluating the results. Our experiments highlight the effectiveness of RGCNs in capturing relational information for sentiment analysis tasks.