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Purpose: Low-field MRI has been assumed to be implant-friendly based on limited studies. However, RF-induced heating due to an implant is a complex resonance phenomenon, highly dependent on the implant's configurations and the applied RF frequencies. This study aims to evaluate the RF heating of DBS implants during MRI at low-field strengths compared to higher field 1.5 T MRI. Methods: A commercial deep brain stimulation (DBS) implant was used in full system as well as lead only configurations to evaluate and compare RF heating during MR imaging at 0.55 T and 1.5 T. The transfer function of the device at both configurations was measured and validated at each of the frequencies, which was then used for the in vivo prediction of RF heating for realistic DBS configurations at head, chest and abdomen imaging landmarks. Results: For the lead only case, the RF heating due to the DBS was substantially smaller during imaging at 0.55 T compared to that at 1.5 T. However, for the full DBS system (longer implant), the RF heating at 0.55 T was comparable to and for some cases even higher than that at 1.5 T, reaching a level that poses risk of tissue damage in patients. Conclusions: While RF heating generally tends to be lower at low-field MRI, the case with longer implanted leads demands extra caution, due to the higher possibility of matching resonant condition at low-field-strength frequencies. Thus, specific risk evaluation for each implant and configuration is required rather than assuming that lower field strength imaging is safer.

One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those able to go faster, an instructor must be prepared to give problems of different difficulty levels. Using Dirichlet's Theorem as a case study, we create and discuss a family of problems in number theory that highlight the relative strengths and weaknesses of different ways to approach a question and show how to invite students to extend the problems and explore research-level mathematics.

It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologies such as finite element, finite difference, and discontinuous Galerkin methods fail to give convergent methods because they cannot overcome the gap. This paper is a continuation of a 2018 paper by Feng-Schnake, where a promising enhanced finite element method was proposed to overcome the LGP in the classical Mani\`a's problem. The goal of this paper is to provide a complete $\Gamma$-convergence proof for this enhanced finite element method, hence establishing a theoretical foundation for the method. The crux of the convergence analysis is the construction of a new finite element interpolant that helps to build a recovery sequence for proving a $\Gamma$-convergence result due to its strong approximation properties in Sobolev spaces. Numerical tests are also provided to verify the theoretical results., Comment: 22 pages, 5 tables

Virtual Reality (VR) is quickly establishing itself in various industries, including training, education, medicine, and entertainment, in which users are frequently required to carry out multiple complex cognitive and physical activities. However, the relationship between cognitive activities, physical activities, and familiar feelings of cybersickness is not well understood and thus can be unpredictable for developers. Researchers have previously provided labeled datasets for predicting cybersickness while users are stationary, but there have been few labeled datasets on cybersickness while users are physically walking. Thus, from 39 participants, we collected head orientation, head position, eye tracking, images, physiological readings from external sensors, and the self-reported cybersickness severity, physical load, and mental load in VR. Throughout the data collection, participants navigated mazes via real walking and performed tasks challenging their attention and working memory. To demonstrate the dataset's utility, we conducted a case study of training classifiers in which we achieved 95% accuracy for cybersickness severity classification. The noteworthy performance of the straightforward classifiers makes this dataset ideal for future researchers to develop cybersickness detection and reduction models. To better understand the features that helped with classification, we performed SHAP(SHapley Additive exPlanations) analysis, highlighting the importance of eye tracking and physiological measures for cybersickness prediction while walking. This open dataset can allow future researchers to study the connection between cybersickness and cognitive loads and develop prediction models. This dataset will empower future VR developers to design efficient and effective Virtual Environments by improving cognitive load management and minimizing cybersickness.

This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical condition. Each admissible control is known to produce a nontrivial corresponding state by applying the Mountain Pass Theorem to fractional equations. The main theoretical contribution is the construction of a suitable set of admissible controls on which the the standard existence theory for control problems with linear and semi-linear state constraints can be adapted. Extra care is taken to explain what new difficulties arise for these types of control problems, to justify the limitations of this theory. For completeness, the corresponding local elliptic control problem is also studied., Comment: 13 pages

We introduce a quantum mechanical formalism for computing the electric polarization arising in two-dimensional (2D) antiferromagnets (AFMs) as a result of {\bf both} spin and orbital transport effect of magnons. We first show that an applied temperature gradient in a 2D collinear honeycomb AFM gives rise to accumulations of magnons having both orbital moment and spin moment at the edges of the 2D AFM as the manifestation of the magnon Nernst effects. We then use our formalism to show that such magnon Nernst effects, in the presence of the Dzyaloshinskii-Moriya Interaction (DMI), induce electric polarization that can be measured experimentally. Finally, we demonstrate the value of this formalism by using it to predict the properties of two 2D honeycomb AFMs, one each with N\'eel and zigzag order. These results integrate advances in magnonics, spinorbitronics, and orbitronics to create a unified framework that can be used to understand and control the manipulation of magnetic states in 2D AFMs through the magnon spin and orbital degrees of freedom., Comment: 11 pages, 5 figures

Terahertz (THz) radiation, spanning from 0.3 to 3x10^12 Hz, fills the crucial gap between the microwave and infrared spectral range. THz technology has found applications in various fields, from imaging and sensing to telecommunication and biosensing. However, the full potential of these applications is often hindered by the need for precise control and manipulation of the frequency and polarization state, which typically requires external THz modulators. Here, we demonstrate a hybrid THz source that overcomes this limitation. Our device consists of two THz emitters integrated into one single device, enabling pulse shaping and chirality control of the emitted radiation without additional external components. The two sources are a spintronic emitter and a semiconductor photoconductive antenna (PCA). Using a combination of dual-wavelength excitation, allowing for control of the relative time delay between the two laser excitation pulses, and tuning external parameters for each emitter (i.e., biasing voltage for the PCA and magnetic field for the spintronic THz emitter) enables precise control of the mixing of the two signals and results in frequency, polarization, and chirality control of the overall THz radiation. This on-chip hybrid emitter provides an essential platform for engineered THz radiation with wide-ranging potential applications.

The Vera C. Rubin Observatory is a unique facility for survey astronomy that will soon be commissioned and begin operations. Crucial to many of its scientific goals is the achievement of sustained high image quality, limited only by the seeing at the site. This will be maintained through an Active Optics System (AOS) that controls optical element misalignments and corrects mirror figure error to minimize aberrations caused by both thermal and gravitational distortions. However, the large number of adjustment degrees of freedom available on the Rubin Observatory introduces a range of degeneracies, including many that are \textit{noise-induced} due to imperfect measurement of the wavefront errors. We present a structured methodology for identifying these degeneracies through an analysis of image noise level. We also present a novel scaling strategy based on Truncated Singular Value Decomposition (TSVD) that mitigates the degeneracy, and optimally distributes the adjustment over the available degrees of freedom. Our approach ensures the attainment of optimal image quality, while avoiding excursions around the noise-induced subspace of degeneracies, marking a significant improvement over the previous techniques adopted for Rubin, which were based on an Optimal Integral Controller (OIC). This new approach is likely to also yield significant benefits for all telescopes that incorporate large numbers of degrees of freedom of adjustment., Comment: 19 pages, 8 figures, 4 tables. Submitted to ApJ

Diffusion models have emerged as a powerful tool for generating high-quality images from textual descriptions. Despite their successes, these models often exhibit limited diversity in the sampled images, particularly when sampling with a high classifier-free guidance weight. To address this issue, we present Kaleido, a novel approach that enhances the diversity of samples by incorporating autoregressive latent priors. Kaleido integrates an autoregressive language model that encodes the original caption and generates latent variables, serving as abstract and intermediary representations for guiding and facilitating the image generation process. In this paper, we explore a variety of discrete latent representations, including textual descriptions, detection bounding boxes, object blobs, and visual tokens. These representations diversify and enrich the input conditions to the diffusion models, enabling more diverse outputs. Our experimental results demonstrate that Kaleido effectively broadens the diversity of the generated image samples from a given textual description while maintaining high image quality. Furthermore, we show that Kaleido adheres closely to the guidance provided by the generated latent variables, demonstrating its capability to effectively control and direct the image generation process., Comment: 22 pages, 14 figures

Text-to-image generative models have become a prominent and powerful tool that excels at generating high-resolution realistic images. However, guiding the generative process of these models to consider detailed forms of conditioning reflecting style and/or structure information remains an open problem. In this paper, we present LoRAdapter, an approach that unifies both style and structure conditioning under the same formulation using a novel conditional LoRA block that enables zero-shot control. LoRAdapter is an efficient, powerful, and architecture-agnostic approach to condition text-to-image diffusion models, which enables fine-grained control conditioning during generation and outperforms recent state-of-the-art approaches., Comment: for the project page and code, view https://compvis.github.io/LoRAdapter/

Recent advancements in image generation have made significant progress, yet existing models present limitations in perceiving and generating an arbitrary number of interrelated images within a broad context. This limitation becomes increasingly critical as the demand for multi-image scenarios, such as multi-view images and visual narratives, grows with the expansion of multimedia platforms. This paper introduces a domain-general framework for many-to-many image generation, capable of producing interrelated image series from a given set of images, offering a scalable solution that obviates the need for task-specific solutions across different multi-image scenarios. To facilitate this, we present MIS, a novel large-scale multi-image dataset, containing 12M synthetic multi-image samples, each with 25 interconnected images. Utilizing Stable Diffusion with varied latent noises, our method produces a set of interconnected images from a single caption. Leveraging MIS, we learn M2M, an autoregressive model for many-to-many generation, where each image is modeled within a diffusion framework. Throughout training on the synthetic MIS, the model excels in capturing style and content from preceding images - synthetic or real - and generates novel images following the captured patterns. Furthermore, through task-specific fine-tuning, our model demonstrates its adaptability to various multi-image generation tasks, including Novel View Synthesis and Visual Procedure Generation.

Group testing, a method that screens subjects in pooled samples rather than individually, has been employed as a cost-effective strategy for chlamydia screening among Iowa residents. In efforts to deepen our understanding of chlamydia epidemiology in Iowa, several group testing regression models have been proposed. Different than previous approaches, we expand upon the varying coefficient model to capture potential age-varying associations with chlamydia infection risk. In general, our model operates within a Bayesian framework, allowing regression associations to vary with a covariate of key interest. We employ a stochastic search variable selection process for regularization in estimation. Additionally, our model can integrate random effects to consider potential geographical factors and estimate unknown assay accuracy probabilities. The performance of our model is assessed through comprehensive simulation studies. Upon application to the Iowa group testing dataset, we reveal a significant age-varying racial disparity in chlamydia infections. We believe this discovery has the potential to inform the enhancement of interventions and prevention strategies, leading to more effective chlamydia control and management, thereby promoting health equity across all populations.

In medical imaging, access to data is commonly limited due to patient privacy restrictions and the issue that it can be difficult to acquire enough data in the case of rare diseases.[1] The purpose of this investigation was to develop a reusable open-source synthetic image generation pipeline, the GAN Image Synthesis Tool (GIST), that is easy to use as well as easy to deploy. The pipeline helps to improve and standardize AI algorithms in the digital health space by generating high quality synthetic image data that is not linked to specific patients. Its image generation capabilities include the ability to generate imaging of pathologies or injuries with low incidence rates. This improvement of digital health AI algorithms could improve diagnostic accuracy, aid in patient care, decrease medicolegal claims, and ultimately decrease the overall cost of healthcare. The pipeline builds on existing Generative Adversarial Networks (GANs) algorithms, and preprocessing and evaluation steps were included for completeness. For this work, we focused on ensuring the pipeline supports radiography, with a focus on synthetic knee and elbow x-ray images. In designing the pipeline, we evaluated the performance of current GAN architectures, studying the performance on available x-ray data. We show that the pipeline is capable of generating high quality and clinically relevant images based on a lay person's evaluation and the Fr\'echet Inception Distance (FID) metric.

Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and technology is the fractional Schr\"odinger equation, which describes sub-and super-dispersive behavior of quantum wavefunctions induced by multiscale media. We derive a computationally efficient sixth-order split-step numerical method to converge the eigenfunctions of the FSE to arbitrary numerical precision for arbitrary fractional order derivative. We demonstrate applications of this code to machine precision for classic quantum problems such as the finite well and harmonic oscillator, which take surprising twists due to the non-local nature of the fractional derivative. For example, the evanescent wave tails in the finite well take a Mittag-Leffer-like form which decay much slower than the well-known exponential from integer-order derivative wave theories, enhancing penetration into the barrier and therefore quantum tunneling rates. We call this effect \emph{fractionally enhanced quantum tunneling}. This work includes an open source code for communities from quantum experimentalists to applied mathematicians to easily and efficiently explore the solutions of the fractional Schr\"odinger equation in a wide variety of practical potentials for potential realization in quantum tunneling enhancement and other quantum applications.

Semiconducting transition metal dichalcogenides (TMDs) are promising for high-specific-power photovoltaics due to desirable band gaps, high absorption coefficients, and ideally dangling-bond-free surfaces. Despite their potential, the majority of TMD solar cells are fabricated in a non-scalable fashion using exfoliated materials due to the absence of high-quality, large-area, multilayer TMDs. Here, we present the scalable, thickness-tunable synthesis of multilayer tungsten diselenide (WSe$_{2}$) films by selenizing pre-patterned tungsten with either solid source selenium or H$_{2}$Se precursors, which leads to smooth, wafer-scale WSe$_{2}$ films with a layered van der Waals structure. The films have charge carrier lifetimes up to 144 ns, over 14x higher than large-area TMD films previously demonstrated. Such high carrier lifetimes correspond to power conversion efficiency of ~22% and specific power of ~64 W g$^{-1}$ in a packaged solar cell, or ~3 W g$^{-1}$ in a fully-packaged solar module. This paves the way for the mass-production of high-efficiency multilayer WSe$_{2}$ solar cells at low cost.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains., Comment: Technical report