Comparison of No-Test Telehealth and In-Person Medication Abortion.

Importance: In the US, access to medication abortion using history-based (no-test) eligibility assessment, including through telehealth and mailing of mifepristone, has grown rapidly. Additional evidence on the effectiveness and safety of these models is needed. Objective: To evaluate whether medication abortion with no-test eligibility assessment and mailing of medications is as effective as in-person care with ultrasonography and safe overall. Design, Setting, and Participants: Prospective, observational study with noninferiority analysis. Sites included 4 abortion-providing organizations in Colorado, Illinois, Maryland, Minnesota, Virginia, and Washington from May 2021 to March 2023. Eligible patients were seeking medication abortion up to and including 70 days' gestation, spoke English or Spanish, and were aged 15 years or older. Exposure: Study groups reflected the model of care selected by the patient and clinicians and included: (1) no-test (telehealth) eligibility assessment and mailing of medications (no-test + mail) (n = 228); (2) no-test eligibility assessment and pickup of medications (no-test + pickup) (n = 119); or (3) in-person with ultrasonography (n = 238). Main Outcomes and Measures: Effectiveness, defined as a complete abortion without the need for repeating the mifepristone and misoprostol regimen or a follow-up procedure, and safety, defined as an abortion-related serious adverse event, including overnight hospital admission, surgery, or blood transfusion. Outcomes were derived from patient surveys and medical records. Primary analysis focused on the comparison of the no-test + mail group with the in-person with ultrasonography group. Results: The mean age of the participants (N = 585) was 27.3 years; most identified as non-Hispanic White (48.6%) or non-Hispanic Black (28.1%). Median (IQR) gestational duration was 45 days (39-53) and comparable between study groups (P = .30). Outcome data were available for 91.8% of participants. Overall effectiveness was 94.4% (95% CI, 90.7%-99.2%) in the no-test + mail group and 93.3% (95% CI, 88.3%-98.2%) in the in-person with ultrasonography group in adjusted models (adjusted risk difference, 1.2 [95% CI, -4.1 to 6.4]), meeting the prespecified 5% noninferiority margin. Serious adverse events included overnight hospitalization (n = 4), blood transfusion (n = 2), and emergency surgery (n = 1) and were reported by 1.1% (95% CI, 0.4%-2.4%) of participants, with 3 in the no-test + mail group, 3 in the in-person with ultrasonography group, and none in the no-test + pickup group. Conclusions and Relevance: This prospective, observational study found that medication abortion obtained following no-test telehealth screening and mailing of medications was associated with similar rates of complete abortion compared with in-person care with ultrasonography and met prespecified criteria for noninferiority, with a low prevalence of adverse events.

Pharmacists' knowledge, perspectives, and experiences with mifepristone dispensing for medication abortion.

BACKGROUND: The U.S. Food and Drug Administration (FDA) restricts dispensing of mifepristone for medication abortion to certified health care providers at clinical facilities, thus prohibiting pharmacist dispensing. Allowing mifepristone dispensing by pharmacists could improve access to medication abortion. OBJECTIVE: To assess the feasibility of pharmacists dispensing mifepristone to patients who have undergone evaluation for eligibility and counseling for medication abortion by a clinician. METHODS: Before providing a study training on medication abortion, we administered baseline surveys to pharmacists who participated in a multisite mifepristone-dispensing intervention. The survey assessed medication abortion knowledge-using a 15-item score-and perceptions about the benefits and challenges of the model. We administered follow-up surveys in the study's final month that also assessed the pharmacists' satisfaction and experiences with mifepristone dispensing. To investigate the association of the study intervention with the pharmacists' knowledge, perceptions, and experiences dispensing mifepristone, we conducted multivariable linear regression analyses using generalized estimating equation models, accounting for clustering by individual. RESULTS: Among the 72 pharmacists invited from 6 pharmacies, 47 (65%) completed the baseline surveys, and 56 (78%) received training. At the study's end (mean 18 months later), 43 of the 56 pharmacists who received training (77%) completed the follow-up surveys. At follow-up, 36 (83%) respondents were very or somewhat satisfied with mifepristone dispensing, and 24 (56%) reported experiencing no challenges dispensing mifepristone. Four (6%) of the 72 pharmacists invited objected to participating in mifepristone dispensing. In regression analyses, average knowledge scores, perceived ease of implementation, and level of support for the pharmacist-dispensing model were higher at follow-up (P < 0.001). CONCLUSION: Most pharmacists were willing to be trained, dispensed mifepristone with few challenges when given the opportunity, were satisfied with the model, and had higher knowledge levels at follow-up. Our findings support removal of FDA's restriction on pharmacist dispensing of mifepristone.

Medical and midwifery students' views on the use of conscientious objection in abortion care, following legal reform in Chile: a cross-sectional study.

BACKGROUND: In August 2017, Chile lifted its complete ban on abortion by permitting abortion in three limited circumstances: 1) to save a woman's life, 2) lethal fetal anomaly, and 3) rape. The new law allows regulated use of conscientious objection (CO) in abortion care, including allowing institutions to register as objectors. This study assesses medical and midwifery students' support for CO, following legal reform. METHODS: From October 2017 to May 2018, we surveyed medical and midwifery students from seven universities located in Santiago, Chile. Universities included 4 secular (2 public and 2 private) and 3 private religiously-affiliated universities; all offering medical degrees with a specialization in obstetrics and gynecology (ob-gyn) and five offering midwifery degrees. We used generalized estimating equations (GEE) to identify characteristics associated with student support for CO, intentions to use CO to refuse to care for someone seeking abortion, and support for CO at the institutional level. RESULTS: 333 of the 413 eligible students who opened the survey, completed the questions on conscientious objection; 26% were seeking medical degrees with an ob-gyn specialty, 25% were seeking midwifery degrees, and 49% were seeking medical degrees and had not yet decided their specialty. While nearly all endorse requirements for conscientious objecting clinicians to inform (92%) and refer (91%) abortion-seeking patients, a minority (18%) would personally use conscientious objection to avoid caring for a patient seeking abortion (12% secular and 39% religious university students). About half of religious-university students (52%) and one-fifth of secular-university (20%) students support objections at the institutional level. CONCLUSIONS: Most students support the regulated use of CO which preserves patients' access to abortion care. Religious-university student views on the use of conscientious objection in abortion care are discordant with those of their institutions which currently support institutional-level objections.

Covariant Image Representation with Applications to Classification Problems in Medical Imaging.

Images are often considered as functions defined on the image domains, and as functions, their (intensity) values are usually considered to be invariant under the image domain transforms. This functional viewpoint is both influential and prevalent, and it provides the justification for comparing images using functional Lp -norms. However, with the advent of more advanced sensing technologies and data processing methods, the definition and the variety of images has been broadened considerably, and the long-cherished functional paradigm for images is becoming inadequate and insufficient. In this paper, we introduce the formal notion of covariant images and study two types of covariant images that are important in medical image analysis, symmetric positive-definite tensor fields and Gaussian mixture fields, images whose sample values covary i.e., jointly vary with image domain transforms rather than being invariant to them. We propose a novel similarity measure between a pair of covariant images considered as embedded shapes (manifolds) in the ambient space, a Cartesian product of the image and its sample-value domains. The similarity measure is based on matching the two embedded low-dimensional shapes, and both the extrinsic geometry of the ambient space and the intrinsic geometry of the shapes are incorporated in computing the similarity measure. Using this similarity as an affinity measure in a supervised learning framework, we demonstrate its effectiveness on two challenging classification problems: classification of brain MR images based on patients' age and (Alzheimer's) disease status and seizure detection from high angular resolution diffusion magnetic resonance scans of rat brains.

Interest in and Support for Alternative Models of Medication Abortion Provision Among Patients Seeking Abortion in the United States.

INTRODUCTION: Medication abortion is safe and effective, but restrictions still limit patients from accessing this method. Alternative models of medication abortion provision, namely advance provision, over-the-counter (OTC), and online, could help improve access to care for some, although there is limited evidence about abortion patients' interest in these models. METHODS: Between 2017 and 2019, we administered a cross-sectional survey to abortion patients at 45 clinics across 15 U.S. states to explore their interest in and support for advance provision, OTC, and online abortion access. We assessed relationships between sociodemographic characteristics and interest in and support for each model using bivariate logistic regressions and present perceived advantages and disadvantages of each model, as described by a subset of participants. RESULTS: Among 1,965 people enrolled, 1,759 (90%) initiated the survey. Interest in and support for advance provision was highest (72% and 82%, respectively), followed by OTC (63% and 72%) and online access (57% and 70%). In bivariate analyses, non-Hispanic Black and Asian/Pacific Islander respondents expressed lower interest and support for the online model and Alaska Native/Native American respondents expressed higher interest in an OTC model, as compared with white respondents. Among 439 participants naming advantages and disadvantages of each model, the most common advantages included convenience and having the abortion earlier. The most common disadvantages were not seeing a provider first and possibly taking pills incorrectly. CONCLUSIONS: Although most abortion patients expressed interest in and support for alternative models of medication abortion provision, variation in support across race/ethnicity highlights a need to ensure that abortion care service models meet the needs and preferences of all patients, particularly people from historically underserved populations.

Failure of the Law to Grant Access to Legal Abortion in Chile.

Introduction: In 2017, Chile decriminalized abortion on three grounds: (i) if the pregnant person's life is at risk, (ii) fetal nonviability, and (iii) rape or incest. This multicase study explores the experiences of pregnant people legally entitled to but denied access to legal abortion in Chile. Methods: Through a snowball sampling approach, we recruited adult Chilean residents who sought, were eligible for, and were denied a legal abortion after September 2017. We conducted semistructured interviews with participants to explore their experiences in seeking and being denied legal abortions. We recorded and transcribed the interviews, then coded and analyzed the transcriptions to identify common themes. Results: We identified four women who met the eligibility criteria. The interviews revealed five common themes in their experiences: (i) disparate levels of social support in accessing abortion, (ii) abundant access barriers, (iii) forced pregnancy, (iv) abortion stigma, and (v) a failure of the law to provide access to abortion. Discussion and Health Equity Implications: Although the 2017 law expanded legal access to abortion in Chile, significant barriers remain. Compounded with social stigma, and the socioeconomic disparities in abortion access, pregnant people continue to face insurmountable obstacles in obtaining legal abortions, even when their lives are at risk and the pregnancy is not viable. The state must prioritize equity of access to legal abortions. Future studies should continue to explore the challenges people face accessing legal abortion care to inform strategies to ensure people are able to obtain the quality care that they are legally entitled to.

An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices.

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N symmetric positive-definite matrices. For this manifold, we choose the Log-Euclidean metric as its Riemannian metric since it is easy to compute and has been widely used in a variety of applications. By using the Log-Euclidean distance in the loss function, we derive a shrinkage estimator in an analytic form and show that it is asymptotically optimal within a large class of estimators that includes the MLE, which is the sample Fréchet mean of the data. We demonstrate the performance of the proposed shrinkage estimator via several simulated data experiments. Additionally, we apply the shrinkage estimator to perform statistical inference in both diffusion and functional magnetic resonance imaging problems.

Feasibility of exergaming for upper extremity rehabilitation in people with multiple sclerosis: prospective clinical trial.

BACKGROUND: Exergaming has been suggested as a rehabilitation method since it is more motivational for people with multiple sclerosis (MS, pwMS). However, the major disadvantage of this method is the lack of specific scenarios designed for pwMS. OBJECTIVES: This study aims to assess the feasibility of exergaming, which was developed for pwMS. METHODS: This unblinded prospective clinical trial was performed in the outpatient MS Clinic of Dokuz Eylül University Hospital. Exergaming scenarios were developed in collaboration with medical personnel consisting of physiotherapists and doctors, and computer engineers. A total of 30 participants who had definite MS diagnoses were included. The exergaming scenarios were implemented using the Microsoft Kinect. A physiotherapist applied custom-made exergames for one session. All the participants were assessed immediately after the session. The User Satisfaction Evaluation Questionnaire was used to assess the user's satisfaction with the system and exergaming. RESULTS: The mean age was 41.5, the mean Expanded Disability Status Scale was 4.5 (range between 0 and 7), and the mean disease duration was 10.0 years. Twenty patients were relapsing-remitting, and 10 were secondary-progressive. The mean scores of the User Satisfaction Evaluation Questionnaire were 4.33 (SD = 0.84) for helpfulness for rehabilitation, 1.63 (SD = 1.1) for not disturbing, 4.50 (SD = 1.07) for understandability, 4.0 (SD = 0.91) for easiness to control, and 4.33 (SD = 0.84) for enjoyability. CONCLUSION: These results showed that our custom-made exergaming scenario could be feasible in upper extremity rehabilitation in MS. More research is needed to investigate its effectiveness in the rehabilitation of upper limbs.

Cognition as a parameter in monitoring the effect of multiple sclerosis relapse treatment: A prospective controlled study.

BACKGROUND: Cognitive evaluation was considered to be very important in the relapse period, on the basis of the presence of isolated cognitive attacks and the necessity of monitoring the patient both physically and cognitively. MATERIALS AND METHODS: People with MS (pwMS) who were hospitalized during relapse were included in the study. All MS patients were evaluated by the neurologist with Expanded Disability Status Scale (EDSS), The 9 Hole Peg Test (9HPT) and the Timed 25-Foot Walk Test (T25-FWT). Additionally, all participants were examined cognitively with the Turkish version of the Brief International Cognitive Assessment for MS (BICAMS) battery. Also, schedules were indicated as during relapse before the treatment (pre-treatment) and the first month after relapse (1-month follow-up). RESULTS: A total of 140 MS patients (mean age; 34.98±10.09, mean disease duration; 6.05±5.29 years) and 86 healthy controls (mean age; 36.94±10.83) were included to the present study. The mean EDSS scores in pre-treatment in MS patients was 2.74±1.14 and decreased significantly in the 1-month follow-up (1.74±1.24; p<0.001). The mean SDMT score was lower by 8.76 points in MS patients than in HCs) in pre-treatment and 7.66 points in 1-month follow-up (p<0.001). The mean SDMT scores of all participants increased with measurement time gradually (p<0.001). CONCLUSION: In this study, it was detected which cognitive domains were affected after relapse treatment and cognitive changes in pwMS during relapse and remission periods compared to the healthy controls. All three BICAMS test scores significantly increased in one-month follow-up than the pre-treatment period. The results showed that CVLT-II and BVMT-R scores improved more in pwMS than in HCs, and also SDMT scores of pwMS showed a trend of increase, but was not a significant improvement.

A robust variational approach for simultaneous smoothing and estimation of DTI.

Estimating diffusion tensors is an essential step in many applications - such as diffusion tensor image (DTI) registration, segmentation and fiber tractography. Most of the methods proposed in the literature for this task are not simultaneously statistically robust and feature preserving techniques. In this paper, we propose a novel and robust variational framework for simultaneous smoothing and estimation of diffusion tensors from diffusion MRI. Our variational principle makes use of a recently introduced total Kullback-Leibler (tKL) divergence for DTI regularization. tKL is a statistically robust dissimilarity measure for diffusion tensors, and regularization by using tKL ensures the symmetric positive definiteness of tensors automatically. Further, the regularization is weighted by a non-local factor adapted from the conventional non-local means filters. Finally, for the data fidelity, we use the nonlinear least-squares term derived from the Stejskal-Tanner model. We present experimental results depicting the positive performance of our method in comparison to competing methods on synthetic and real data examples.

Perspectives on Alternative Models of Medication Abortion Provision Among Abortion Patients in the United States.

OBJECTIVE: Restrictions on the availability of medication abortion are a barrier to accessing early abortion. People seeking medication abortion may be interested in obtaining the medications through alternative models. The purpose of this study was to explore patient perspectives on obtaining abortion medications in advance of pregnancy or over the counter (OTC). STUDY DESIGN: Between October 2017 and August 2018, we conducted 30 in-depth interviews with abortion patients who indicated support for alternative models. We recruited patients from 10 abortion clinics in states with a range of policy environments. We analyzed interviews using inductive and deductive iterative techniques. RESULTS: Participants identified logistical benefits of these alternative models, including eliminating travel to a clinic and multiple appointments, and increased privacy around decision-making. Participants were interested in advance provision for its convenience and the sense of preparedness that would come with having the pills available at home, yet some had concerns about the pills being found or stolen. Privacy was the key factor considered for OTC access, including both the privacy benefits of avoiding a clinic and the concern of having one's privacy compromised within the community if purchasing the medications in public. CONCLUSIONS: People who have previously had a medication abortion are interested in alternative methods of provision for reasons concerning convenience, privacy, and avoiding burdens related to hostile policy environments, such as long travel distances to clinics and multiple appointments. Concerns around these models were primarily safety concerns for young people. Further research is needed to evaluate the safety, effectiveness, acceptability, and feasibility of these alternative models of providing medication abortion.

Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space.

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a non-convex optimization problem. In this paper, we propose a novel large margin classifier based on horospherical decision boundaries that leads to a geodesically convex optimization problem that can be optimized using any Riemannian gradient descent technique guaranteeing a globally optimal solution. We present several experiments depicting the competitive performance of our classifier in comparison to SOTA.

Geometric Deep Learning for Unsupervised Registration of Diffusion Magnetic Resonance Images.

Deep learning based models for registration predict a transformation directly from moving and fixed image appearances. These models have revolutionized the field of medical image registration, achieving accuracy on-par with classical registration methods at a fraction of the computation time. Unfortunately, most deep learning based registration methods have focused on scalar imaging modalities such as T1/T2 MRI and CT, with less attention given to more complex modalities such as diffusion MRI. In this paper, to the best of our knowledge, we present the first end-to-end geometric deep learning based model for the non-rigid registration of fiber orientation distribution fields (fODF) derived from diffusion MRI (dMRI). Our method can be trained in a fully-unsupervised fashion using only input fODF image pairs, i.e. without ground truth deformation fields. Our model introduces several novel differentiable layers for local Jacobian estimation and reorientation that can be seamlessly integrated into the recently introduced manifold-valued convolutional network in literature. The results of this work are accurate deformable registration algorithms for dMRI data that can execute in the order of seconds, as opposed to dozens of minutes to hours consumed by their classical counterparts.

Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures.

Brain atlas construction has attracted significant attention lately in the neuroimaging community due to its application to the characterization of neuroanatomical shape abnormalities associated with various neurodegenerative diseases or neuropsychiatric disorders. Existing shape atlas construction techniques usually focus on the analysis of a single anatomical structure in which the important inter-structural information is lost. This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas based on an information geometry framework. A shape complex is a collection of neighboring shapes - for example, the thalamus, amygdala and the hippocampus circuit - which may exhibit changes in shape across multiple structures during the progression of a disease. In this paper, we represent the boundaries of the entire shape complex using the zero level set of a distance transform function S(x). We then re-derive the relationship between the stationary state wave function ψ(x) of the Schrödinger equation [formula in text] and the eikonal equation [formula in text] satisfied by any distance function. This leads to a one-to-one map (up to scale) between ψ(x) and S(x) via an explicit relationship. We further exploit this relationship by mapping ψ(x) to a unit hypersphere whose Riemannian structure is fully known, thus effectively turn ψ(x) into the square-root of a probability density function. This allows us to make comparisons - using elegant, closed-form analytic expressions - between shape complexes represented as square-root densities. A shape complex atlas is constructed by computing the Karcher mean ψ¯(x) in the space of square-root densities and then inversely mapping it back to the space of distance transforms in order to realize the atlas shape. We demonstrate the shape complex atlas computation technique via a set of experiments on a population of brain MRI scans including controls and epilepsy patients with either right anterior medial temporal or left anterior medial temporal lobectomies.

Human genetic variation is associated with Plasmodium falciparum drug resistance.

One approach to investigate if human genetic variation influences the selection of Plasmodium falciparum drug resistance is to compare the frequency of resistant infections among human populations differing in their genetic background and living in the same epidemiological context. A further complementary approach consists in comparing drug resistance among subjects differing for genes involved in drug metabolism. Here we report, from malariological surveys performed in Burkina Faso, that the prevalence of P. falciparum chloroquine-resistant infections (pfcrt 76T and/or pfmdr1 86Y alleles) differs among sympatric ethnic groups, being higher in the Mossi and Rimaibé groups than in the Fulani group (odds ratio [OR], 2.24; 95% confidence interval [CI], 1.27-3.92; P = .007). The association analysis revealed that the human CYP2C8*2 variant, known to determine a poor drug metabolizer phenotype, was associated with P. falciparum chloroquine-resistant infections (OR, 1.66; 95% CI, 1.13-2.43; P = .008). This variant is more frequent in the Mossi-Rimaibé group (23.7% ± 1.4%) than in the Fulani group (9.9% ± 2.5%; P = .0003). This study provides an example of how host genetic variation may influence the selection dynamics of a pathogen's drug resistance.

Nested Grassmannians for Dimensionality Reduction with Applications.

In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the principal nested spheres. In this paper, we propose a novel framework for constructing a nested sequence of homogeneous Riemannian manifolds. Common examples of homogeneous Riemannian manifolds include the n-sphere, the Stiefel manifold, the Grassmann manifold and many others. In particular, we focus on applying the proposed framework to the Grassmann manifold, giving rise to the nested Grassmannians (NG). An important application in which Grassmann manifolds are encountered is planar shape analysis. Specifically, each planar (2D) shape can be represented as a point in the complex projective space which is a complex Grassmann manifold. Some salient features of our framework are: (i) it explicitly exploits the geometry of the homogeneous Riemannian manifolds and (ii) the nested lower-dimensional submanifolds need not be geodesic. With the proposed NG structure, we develop algorithms for the supervised and unsupervised dimensionality reduction problems respectively. The proposed algorithms are compared with PGA via simulation studies and real data experiments and are shown to achieve a higher ratio of expressed variance compared to PGA.

Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Design.

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space namely, the Hyperbolic space. Hyperbolic space is a homogeneous Riemannian manifold of the Lorentz group which is a semi-Riemannian manifold, i.e. a manifold equipped with an indefinite metric. Most existing methods (with some exceptions) use local linearization to define a variety of operations paralleling those used in traditional deep neural networks in Euclidean spaces. In this paper, we present a novel fully hyperbolic neural network which uses the concept of projections (embeddings) followed by an intrinsic aggregation and a nonlinearity all within the hyperbolic space. The novelty here lies in the projection which is designed to project data on to a lower-dimensional embedded hyperbolic space and hence leads to a nested hyperbolic space representation independently useful for dimensionality reduction. The main theoretical contribution is that the proposed embedding is proved to be isometric and equivariant under the Lorentz transformations, which are the natural isometric transformations in hyperbolic spaces. This projection is computationally efficient since it can be expressed by simple linear operations, and, due to the aforementioned equivariance property, it allows for weight sharing. The nested hyperbolic space representation is the core component of our network and therefore, we first compare this representation - independent of the network - with other dimensionality reduction methods such as tangent PCA, principal geodesic analysis (PGA) and HoroPCA. Based on this equivariant embedding, we develop a novel fully hyperbolic graph convolutional neural network architecture to learn the parameters of the projection. Finally, we present experiments demonstrating comparative performance of our network on several publicly available data sets.

VolterraNet: A Higher Order Convolutional Network With Group Equivariance for Homogeneous Manifolds.

Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces. Analagous to the result for traditional convolutions, we prove that the Volterra functional convolutions are equivariant to the action of the isometry group admitted by the Riemannian homogeneous spaces, and under some restrictions, any non-linear equivariant function can be expressed as our homogeneous space Volterra convolution, generalizing the non-linear shift equivariant characterization of Volterra expansions in euclidean space. We also prove that second order functional convolution operations can be represented as cascaded convolutions which leads to an efficient implementation. Beyond this, we also propose a dilated VolterraNet model. These advances lead to large parameter reductions relative to baseline non-euclidean CNNs. To demonstrate the efficacy of the VolterraNet performance, we present several real data experiments involving classification tasks on spherical-MNIST, atomic energy, Shrec17 data sets, and group testing on diffusion MRI data. Performance comparisons to the state-of-the-art are also presented.

ManifoldNet: A Deep Neural Network for Manifold-Valued Data With Applications.

Geometric deep learning is a relatively nascent field that has attracted significant attention in the past few years. This is partly due to the availability of data acquired from non-euclidean domains or features extracted from euclidean-space data that reside on smooth manifolds. For instance, pose data commonly encountered in computer vision reside in Lie groups, while covariance matrices that are ubiquitous in many fields and diffusion tensors encountered in medical imaging domain reside on the manifold of symmetric positive definite matrices. Much of this data is naturally represented as a grid of manifold-valued data. In this paper we present a novel theoretical framework for developing deep neural networks to cope with these grids of manifold-valued data inputs. We also present a novel architecture to realize this theory and call it the ManifoldNet. Analogous to vector spaces where convolutions are equivalent to computing weighted sums, manifold-valued data 'convolutions' can be defined using the weighted Fréchet Mean ([Formula: see text]). (This requires endowing the manifold with a Riemannian structure if it did not already come with one.) The hidden layers of ManifoldNet compute [Formula: see text]s of their inputs, where the weights are to be learnt. This means the data remain manifold-valued as they propagate through the hidden layers. To reduce computational complexity, we present a provably convergent recursive algorithm for computing the [Formula: see text]. Further, we prove that on non-constant sectional curvature manifolds, each [Formula: see text] layer is a contraction mapping and provide constructive evidence for its non-collapsibility when stacked in layers. This captures the two fundamental properties of deep network layers. Analogous to the equivariance of convolution in euclidean space to translations, we prove that the [Formula: see text] is equivariant to the action of the group of isometries admitted by the Riemannian manifold on which the data reside. To showcase the performance of ManifoldNet, we present several experiments using both computer vision and medical imaging data sets.

"No Big Deal": A Qualitative Study of Pharmacists' Perspectives on Dispensing Mifepristone for Medication Abortion.

INTRODUCTION: Until December 2021, the United States Food and Drug Administration impeded abortion access by restricting pharmacists from dispensing mifepristone, one of two drugs used in medication abortion. This study aimed to explore pharmacists' perspectives on dispensing mifepristone. METHODS: We conducted semistructured interviews with pharmacists before and after participating in a pilot project where mifepristone was dispensed from their pharmacies. We thematically coded all interview transcripts, then summarized emergent themes related to pharmacists' support, comfort, experiences, and concerns around dispensing mifepristone. RESULTS: Between May 2018 and July 2020, we interviewed 29 pharmacists (22 at baseline and 15 at follow-up, with 8 completing both interviews) from 5 pharmacies. At both baseline and follow-up, interviewees strongly supported pharmacists dispensing mifepristone, feeling it would improve quality of care by providing more convenient medication abortion access and streamlined service delivery and take advantage of pharmacists' expertise and availability. All pharmacists interviewed at follow-up reported dispensing mifepristone except two who were willing but did not have the opportunity. Pharmacists experienced few challenges dispensing mifepristone. Their main concern was perceived discomfort that other pharmacists and pharmacy staff may experience, particularly in conservative areas or small pharmacies where pharmacists' refusal to dispense mifepristone could impede abortion access. CONCLUSIONS: Most pharmacists supported dispensing mifepristone and were comfortable doing so after education on mifepristone and medication abortion. They dispensed mifepristone without difficulty, in a similar process as dispensing other medications. With the recent removal of U.S. Food and Drug Administration restrictions prohibiting it, our findings support the feasibility of pharmacists dispensing mifepristone.