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Normal matrices, or matrices which commute with their adjoints, are of fundamental importance in pure and applied mathematics. In this paper, we study a natural functional on the space of square complex matrices whose global minimizers are normal matrices. We show that this functional, which we refer to as the non-normal energy, has incredibly well-behaved gradient descent dynamics: despite it being nonconvex, we show that the only critical points of the non-normal energy are the normal matrices, and that its gradient descent trajectories fix matrix spectra and preserve the subset of real matrices. We also show that, even when restricted to the subset of unit Frobenius norm matrices, the gradient flow of the non-normal energy retains many of these useful properties. This is applied to prove that low-dimensional homotopy groups of spaces of unit norm normal matrices vanish; for example, we show that the space of $$d \times d$$ complex unit norm normal matrices is simply connected for all $$d \geq 2$$. Finally, we consider the related problem of balancing a weighted directed graph – that is, readjusting its edge weights so that the weighted in-degree and out-degree are the same at each node. We adapt the non-normal energy to define another natural functional whose global minima are balanced graphs and show that gradient descent of this functional always converges to a balanced graph, while preserving graph spectra and realness of the weights. Our results were inspired by concepts from symplectic geometry and Geometric Invariant Theory, but we mostly avoid invoking this machinery and our proofs are generally self-contained. 

We consider the radius of gyration of a Gaussian topological polymer G formed by subdividing a graph G' of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of G in terms of the number of subdivisions of each edge of G' and a new weighted Kirchhoff index for G'. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs. 

This dataset includes anonymized survey data collected in communities affected by the East Palestine train derailment, chemical spill, and fires. The survey was designed to capture community perceptions and experiences related to air, water, and soil sampling and testing; household and built environment impacts; and protective actions taken. Participants were eligible to participate if they were 18 years or older and lived or worked in an affected county as of February 3, 2023—the day of the derailment. The survey was open from July 20 to September 20, 2023, approximately six months after the incident. See "Notes" below for more details on the methods. The research was reviewed and approved by the Human Subjects in Research Ethics boards at the authors’ universities. This research is supported by the National Science Foundation (Award #2329409). 

Recently, there has been a surge in developing curricula and tools that integrate computing (C) into Science, Technology, Engineering, and Math (STEM) programs. These environments foster authentic problem-solving while facilitating students’ concurrent learning of STEM+C content. In our study, we analyzed students’ behaviors as they worked in pairs to create computational kinematics models of object motion. We derived a domain-specific metric from students’ collaborative dialogue that measured how they integrated science and computing concepts into their problem-solving tasks. Additionally, we computed social metrics such as equity and turn-taking based on the students’ dialogue. We identified and characterized students’ planning, enacting, monitoring, and reflecting behaviors as they worked together on their model construction tasks. This study in-vestigates the impact of students’ collaborative behaviors on their performance in STEM+C computational modeling tasks. By analyzing the relationships between group synergy, turn-taking, and equity measures with task performance, we provide insights into how these collaborative behaviors influence students’ ability to construct accurate models. Our findings underscore the importance of synergistic discourse for overall task success, particularly during the enactment, monitoring, and reflection phases. Conversely, variations in equity and turn-taking have a minimal impact on segment-level task performance. 

Accurate quantification of machined surface roughness is crucial to the characterization of part performance measures, including aerodynamics and biocompatibility. Given this cruciality, there exists a need for predictive metrology models which can predict the surface roughness before a part leaves a machine to reduce metrologyinduced bottlenecks and improve production planning efficiency under emergent production paradigms, e.g., Industry 4.0. Current predictive metrology approaches in machining generally train machine learning models on all available input features at once. However, this approach yields a high number of free parameters during all states of training, possibly leading to suboptimal prediction results because of the complexity of simultaneously optimizing all parameters at once. In addition, previous machine learning-enabled surface roughness prediction studies have used limited test dataset sizes, which reduces the reliability and robustness of the reported results. To address these limitations, this study proposes a two-stage model training approach based on domainincremental learning, wherein a second stage of training is performed using an expanded input domain. The proposed method is evaluated on a 3,000-element experimentally collected testing dataset of machined H13 tool steel surfaces, where it achieves 16.3 % roughness prediction error compared to the 29.5 % error of the conventional single-stage training approach, indicating the suitability of the two-stage training method for reducing surface roughness prediction error. 

Abstract Although the “eye-mind link” hypothesis posits that eye movements provide a direct window into cognitive processing, linking eye movements to specific cognitions in real-world settings remains challenging. This challenge may arise because gaze metrics such as fixation duration, pupil size, and saccade amplitude are often aggregated across timelines that include heterogeneous events. To address this, we tested whether aggregating gaze parameters across participant-defined events could support the hypothesis that increased focal processing, indicated by greater gaze duration and pupil diameter, and decreased scene exploration, indicated by smaller saccade amplitude, would predict effective task performance. Using head-mounted eye trackers, nursing students engaged in simulation learning and later segmented their simulation footage into meaningful events, categorizing their behaviors, task outcomes, and cognitive states at the event level. Increased fixation duration and pupil diameter predicted higher student-rated teamwork quality, while increased pupil diameter predicted judgments of effective communication. Additionally, increased saccade amplitude positively predicted students’ perceived self-efficacy. These relationships did not vary across event types, and gaze parameters did not differ significantly between the beginning, middle, and end of events. However, there was a significant increase in fixation duration during the first five seconds of an event compared to the last five seconds of the previous event, suggesting an initial encoding phase at an event boundary. In conclusion, event-level gaze parameters serve as valid indicators of focal processing and scene exploration in natural learning environments, generalizing across event types. 

Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. TheParseval framesare particularly useful and important, since they provide a simple reconstruction scheme and are maximally robust against certain types of noise. In this paper we describe a theory of frames on arbitrary vector bundles—this is the natural setting for signals which are realized as parameterized families of vectors rather than as single vectors—and discuss the existence of Parseval frames in this setting. Our approach is phrased in the language of $G$-bundles, which allows us to use many tools from classical algebraic topology. In particular, we show that orientable vector bundles always admit Parseval frames of sufficiently large size and provide an upper bound on the necessary size. We also give sufficient conditions for the existence of Parseval frames of smaller size for tangent bundles of several families of manifolds, and provide some numerical evidence that Parseval frames on vector bundles share the desirable reconstruction properties of classical Parseval frames. 

Many parasitic insects, including lice, form close relationships with endosymbiotic bacteria that are crucial for their survival. In this study, we used genomic sequencing to investigate the distribution and evolutionary history of the bacterial genusSodalisacross a broad range of feather louse species spanning 140 genera. Phylogenomic analysis revealed significant diversity amongSodalislineages in feather lice and robust evidence for their independent and repeated acquisition by different louse clades throughout their radiation. Among the 1020 louse genomes analysed, at least 22% containedSodalis, distributed across 57 louse genera. Cophylogenetic analyses between theSodalisand feather louse phylogenies indicated considerable mismatch. This phylogenetic incongruence between lice andSodalis, along with the presence of distantly relatedSodalislineages in otherwise closely related louse species, strongly indicates repeated independent acquisition of this endosymbiont. Additionally, evidence of cospeciation among a few closely related louse species, coupled with frequent acquisition of these endosymbionts from free-living bacteria, further highlights the diverse evolutionary processes shapingSodalisendosymbiosis in feather lice. 

A<sc>bstract</sc> We study (multi) fermion - monopole bound states, many of which are the states that dyons adiabatically transition into as fermions become light. The properties of these bound states depend critically on the UV symmetries preserved by the fermion mass terms, their relative size, and the value ofθ. Depending on the relative size of the mass terms and the value ofθ, the bound states can undergo phase transitions as well as transition from being stable to unstable. In some simple situations, the bound state solution can be related to the Witten effect of another theory with fewer fermions and larger gauge coupling. These bound states are a result of mass terms and symmetry breaking boundary conditions at the monopole core and, consequently, these bound states do not necessarily have definite quantum numbers under accidental IR symmetries. Additionally, they have binding energies that are$$ \mathcal{O}(1) $$ $O\left(1\right)$times the fermion mass and bound state radii of order their inverse mass. As the massless limit is approached, the bound state radii approach infinity, and they become new asymptotic states with odd quantum numbers giving a dynamical understanding to the origin of semitons.