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We construct families of convex domains that are biholomorphic to bounded domains, but not bounded convex domains. This is accomplished by finding an obstruction related to the Gromov hyperbolicity of the Kobayashi metric.

In this paper we establish a lower bound for the distance induced by the Kähler-Einstein metric on pseudoconvex domains with positive hyperconvexity index (e.g. positive Diederich-Fornæss index). A key step is proving an analog of the Hopf lemma for Riemannian manifolds with Ricci curvature bounded from below.

For convex domains with $C^{1,\epsilon}$ boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the automorphism group has finitely many components and the connected component of the identity is the almost direct product of a compact group and a non-compact connected simple Lie group with real rank one and finite center. In this case, we also show the limit set is homeomorphic to a sphere and prove a gap theorem: either the domain is biholomorphic to the unit ball (and the limit set is the entire boundary) or the limit set has co-dimension at least two in the boundary., Comment: 40 pages. v2: minor corrections

In this paper, we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish an analogue of the well known flat torus theorem for ${\rm CAT}(0)$ spaces., Minor revisions, to appear in the Journal of the London Mathematical Society. 20 pages. Comments welcome

Two-fifths of Africans reside in urban areas with populations of less than 250,000. Projections estimate that by 2050 an additional one billion people will live in urban areas, causing an acceleration of growth for these smaller urban areas. While research and development have focused on primary cities with large populations, less is known about the dynamics of urban growth in smaller, “secondary” urban areas (SUA’s). We document the spatial distribution and temporal patterns of SUA’s in eight countries across Southern Africa between 1975 and 2015. We further explore the relationships between SUA’s growth rates and climate, land use and geographic proximity to other urban areas. Our analysis integrates spatially explicit gridded population, land use, infrastructure and climate datasets. We use descriptive statistics and spatial lag and ordinary least squares regression models to quantify SUA growth rates across three periods and explore factors that are associated with the SUA growth patterns. Average SUA growth rates are 2.44% between 1975 and 1990. We show that the climate, distance and land use significantly relate to urbanization trajectories. In addition, we find that the proximity of SUA to the largest cities also significantly relates to urban growth. Our results highlight the importance of SUA’s within broader African urbanization trends. SUA are undergoing rapid population changes and are important components of economic development processes and livelihoods. Quantifying patterns of SUA urbanization is important for elevating these small but critically important urban areas into the broader context of sustainable urbanization in Africa.

Longitudinal clinical studies traditionally require in-person study visits which are well documented to pose barriers to participation and contribute challenges to enrolling representative samples. Remote trial models may reduce barriers to research engagement, improve retention, and reach a more representative cohort. As remote trials become more common following the COVID-19 pandemic, a critical evaluation of this approach is imperative to optimize this paradigm shift in research. The TestBoston study was launched to understand prevalence and risk factors for COVID-19 infection in the greater Boston area through a fully remote home-testing model. Participants (adults, within 45 miles of Boston, MA) were recruited remotely from patient registries at Brigham and Women’s Hospital and the general public. Participants were provided with monthly and “on-demand” at-home SARS-CoV-2 RT-PCR and antibody testing using nasal swab and dried blood spot self-collection kits and electronic surveys to assess symptoms and risk factors for COVID-19 via an online dashboard. Between October 2020 and January 2021, we enrolled 10,289 participants reflective of Massachusetts census data. Mean age was 47 years (range 18–93), 5855 (56.9%) were assigned female sex at birth, 7181(69.8%) reported being White non-Hispanic, 952 (9.3%) Hispanic/Latinx, 925 (9.0%) Black, 889 (8.6%) Asian, and 342 (3.3%) other and/or more than one race. Lower initial enrollment among Black and Hispanic/Latinx individuals required an adaptive approach to recruitment, leveraging connections to the medical system, coupled with community partnerships to ensure a representative cohort. Longitudinal retention was higher among participants who were White non-Hispanic, older, working remotely, and with lower socioeconomic vulnerability. Implementation highlighted key differences in remote trial models as participants independently navigate study milestones, requiring a dedicated participant support team and robust technology platforms, to reduce barriers to enrollment, promote retention, and ensure scientific rigor and data quality. Remote clinical trial models offer tremendous potential to engage representative cohorts, scale biomedical research, and promote accessibility by reducing barriers common in traditional trial design. Barriers and burdens within remote trials may be experienced disproportionately across demographic groups. To maximize engagement and retention, researchers should prioritize intensive participant support, investment in technologic infrastructure and an adaptive approach to maximize engagement and retention.

ImportanceRemote clinical trials may reduce barriers to research engagement resulting in more representative samples. A critical evaluation of this approach is imperative to optimize this paradigm shift in research.ObjectiveTo assess design and implementation factors required to maximize enrollment and retention in a fully remote, longitudinal COVID-19 testing study.DesignFully remote longitudinal study launched in October 2020 and ongoing; Study data reported through July 2021.SettingBrigham and Women’s Hospital, Boston MAParticipantsAdults, 18 years or older, within 45 miles of Boston, MA.InterventionMonthly and “on-demand” at-home SARS-CoV-2 RT-PCR and antibody testing using nasal swab and dried blood spot self-collection kits and electronic surveys to assess symptoms and risk factors for COVID-19.Main OutcomesEnrollment, retention, and lessons learned.ResultsBetween October 2020 and January 2021, we enrolled 10,289 participants reflective of Massachusetts census data. Mean age was 47 years (range 18-93), 5855 (56.9%) were assigned female sex at birth, 7181(69.8%) reported being White non-Hispanic, 952 (9.3%) Hispanic/Latinx, 925 (9.0%) Black, 889 (8.6%) Asian, and 342 (3.3%) other and/or more than one race. Lower initial enrollment among Black and Hispanic/Latinx individuals required an adaptive approach, leveraging connections to the medical system, coupled with community partnerships to ensure a representative cohort. Longitudinal retention was higher among participants who were White non-Hispanic, older, working remotely, and with lower socioeconomic vulnerability. Considerable infrastructure, including a dedicated participant support team and robust technology platforms was required to reduce barriers to enrollment, promote retention, ensure scientific rigor, improve data quality, and enable an adaptive study design to increase real-world accessibility.ConclusionsThe decentralization of clinical trials through remote models offers tremendous potential to engage representative cohorts, scale biomedical research, and promote accessibility by reducing barriers common in traditional trial design. Our model highlights the critical role that hospital-community partnerships play in remote recruitment, and the work still needed to ensure representative enrollment. Barriers and burdens within remote trials may be experienced disproportionately across demographic groups. To maximize engagement and retention, researchers should prioritize intensive participant support, investment in technologic infrastructure and an adaptive approach to maximize engagement and retention.Trial RegistrationN/AKey PointsQuestionLongitudinal clinical studies typically rely on in-person interactions to support recruitment, retention, and implementation. We define factors that promote demographically representative recruitment and retention through implementation of a fully remote COVID-19 study.FindingsRemote trial models can reduce barriers to research participation and engage representative cohorts. Recruitment was strengthened by leveraging the medical system. Implementation highlighted participant burdens unique to this model, underscoring the need for a significant participant support team, robust technological infrastructure, and an adaptive, iterative approach.MeaningAs remote trials become more common following the COVID-19 pandemic, methodologies to ensure accessibility, representation, and efficiency are crucial.

Since the seminal 2012 Special Issue of the Journal of Peace Research about climate change and conflict, at least 35 review papers on the topic have been published. To our knowledge, none of these reviews focused on water and conflict specifically. In order to address this research gap, the present article conducts a systematic review of scholarship examining the linkages between water and conflict, focusing on quantitative studies using secondary data sources. This review focuses on the African continent given projections about the intersection between water issues and conflict in this region, as well as the popularity of this portion of the world in studies of climate change and conflict. We discuss the findings of papers reviewed and propose six avenues for future research. As research about this topic advances, it will require attention to nuances in data processing, integration, and modeling across spatial and temporal scales, if the outcomes of this body of scholarship are to be leveraged to guide the decision making of governing bodies.

The accuracy of weather forecasts has experienced remarkable improvements over the recent decades and is now considered important tools for developing the climate resilience of smallholder farmers, particularly as climate change upends traditional farming calendars. However, the effect of observations of climate change on the use of weather forecasts has not been studied. In an analysis of smallholder farming in Zambia, Kenya, and Jamaica, we document low weather forecast use, showing that perceptions of changes in the climate relate to views on forecast accuracy. Drawing on detailed data from Zambia, we show that weather forecast use (or not) is associated with perceptions of the accuracy (or inaccuracy) of the forecast, with rates of weather forecast use far lower among those who believe climate change impacts forecast accuracy. The results suggest a novel feedback whereby climate change erodes confidence in weather forecasts. Thus, in a changing climate where improvements in weather forecasts have been made, farmers thus experience a double disadvantage whereby climate change disrupts confidence in traditional ways of knowing the weather and lowers trust in supplementary technical forecasting tools.

Water insecurity may precipitate interpersonal conflict, although no studies to date have rigorously examined these relationships. We examined relationships between household demographics, water insecurity, regional conflict, and interpersonal conflict over water. Using survey data from eight sub-Saharan African countries, we found that interpersonal conflict within and outside the home is associated with multiple domains of water insecurity, particularly accessibility. Furthermore, we found that higher levels of remote violence and protests are associated with greater within household conflict, whereas riots and violent armed conflict are associated with greater conflict between neighbors. Our findings expand upon the current literature by examining factors affecting interpersonal conflict over water, which may become increasingly important as precipitation patterns and land temperatures change in this region.

We develop a theory of Anosov representation of geometrically finite Fuchsian groups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov in this sense. We establish analogues of many properties of traditional Anosov representations. In particular, we show that our Anosov representations are stable under type-preserving deformations and that their limit maps vary analytically. We also observe that our Anosov representations fit into the previous frameworks of relatively Anosov and relatively dominated representations developed by Kapovich-Leeb and Zhu., 45 pages, typos corrected, and more details added to Section 8 and Appendix B

We study the homeomorphic extension of biholomorphisms between convex domains in $\mathbb C^d$ without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between the Gromov boundary and the topological boundaries of the domains and the dynamical properties of commuting 1-Lipschitz maps in Gromov hyperbolic spaces. This approach not only allows us to prove extensions for biholomorphisms, but for more general quasi-isometries between the domains endowed with their Kobayashi distances., Comment: 27 pages; final version, to appear Math. Ann

Deviations in rainfall duration and timing are expected to have wide-ranging impacts for people in affected areas. One of these impacts is the potential for increased levels of conflict and accordingly, researchers are examining the relationship between climate variability and conflict. Thus far, there is a lack of consensus on the direction of this relationship. We contribute to the climate variability and conflict literature by incorporating Markov transitional probabilities into panel logit models to analyze how monthly deviations in rainfall affect the likelihood that a grid cell transitions to an above average level of conflict in Sub-Saharan Africa. To control for differences in seasons across the continent, we model this relationship for each of the regions of Sub-Saharan Africa separately - East, Central, West, and Southern. We find significant seasonal and regional effects between rainfall and the probability that a grid cell transitions from a state of peace to a state of conflict. In particular, above average rainfall is associated with a higher likelihood of transitioning into conflict during the dry season. Further, each region has specific months-primarily those associated with prime crop harvest periods-where variations in rainfall significantly influence conflict. We also find regional variations in the linkage between rainfall and conflict type related to the types of conflict that predominate in particular regions of Sub- Saharan Africa. These findings are important for policymakers because they suggest additional law enforcement and/or peacekeeping resources may be needed in times of above average rainfall. Policies that provide financial support for farmers or other sectors, such as mining, that are impacted by rainfall patterns may also be a useful strategy for conflict mitigation.

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts cocompactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have [Formula: see text] boundary, and have word hyperbolic dividing group. In this paper we study a notion of convexity in complex projective space and show that the only divisible complex convex sets with [Formula: see text] boundary are the projective balls.

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain must be strongly pseudoconvex. One consequence of our general result is the following: for any dimension there exists some ϵ > 0 \epsilon > 0 so that if the squeezing function on a smoothly bounded convex domain is greater than 1 − ϵ 1-\epsilon outside a compact set, then the domain is strongly pseudoconvex (and hence the squeezing function limits to one on the boundary). Another consequence is the following: for any dimension d d there exists some ϵ > 0 \epsilon > 0 so that if the holomorphic sectional curvature of the Bergman metric on a smoothly bounded convex domain is within ϵ \epsilon of − 4 / ( d + 1 ) -4/(d+1) outside a compact set, then the domain is strongly pseudoconvex (and hence the holomorphic sectional curvature limits to − 4 / ( d + 1 ) -4/(d+1) on the boundary).

Trends in urbanization and urban food insecurity in sub-Saharan Africa (SSA) have stimulated critical debates around the potential benefits of urban agriculture (UA) to urban livelihoods. Some scholars suggest that UA can contribute to the food quantity, food quality and income needs of urban households. However, much of the evidence cited comes from single case studies, with particular attention paid to large cities and high-income countries. There is a resulting gap in understanding regarding what role UA plays in the food security of households in smaller African cities and towns. These smaller urban areas are likely to house a large fraction of SSA’s urban population in future and are important sites for early intervention by policymakers. Our analysis is based on survey data collected from 2,687 low- and low-middle income households in 18 urban areas with populations of less than 200,000 across Zambia and Kenya. We perform statistical analyses to investigate the association between UA and household food security and assess which types of households are engaged in UA. We found that 33% of households in our sample are engaged in UA and there was limited statistical significance in terms of the relationship between UA and household food security. Our results reveal three key barriers to UA, namely settlement formality, property rights, and distance from food retailers. These barriers imply the need for urban planners and policymakers to revisit how decisions are made about issues such as residential development, land tenure, transport infrastructure, and the use of space in cities, as these affect the ability of households to produce, sell, and access food. Policy and planning mechanisms should further recognize the embeddedness of UA within African urban food systems, in which traditional markets, informal trading, and modern food retail also play an integral role.

By considering intrinsic geometric conditions, we introduce a new class of domains in complex Euclidean space. This class is invariant under biholomorphism and includes strongly pseudoconvex domains, finite type domains in dimension two, convex domains, C -convex domains, and homogeneous domains. For this class of domains, we show that compactness of the ∂ ¯ -Neumann operator on ( 0 , q ) -forms is equivalent to the boundary not containing any q-dimensional analytic varieties (assuming only that the boundary is a topological submanifold). We also prove, for this class of domains, that the Bergman metric is equivalent to the Kobayashi metric and that the pluricomplex Green function satisfies certain local estimates in terms of the Bergman metric.

In this paper we study the global geometry of the Kobayashi metric on domains in complex Euclidean space. We are particularly interested in developing necessary and sufficient conditions for the Kobayashi metric to be Gromov hyperbolic. For general domains, it has been suggested that a non-trivial complex affine disk in the boundary is an obstruction to Gromov hyperbolicity. This is known to be the case when the set in question is convex. In this paper we first extend this result to $\mathbb{C}$-convex sets with $C^1$-smooth boundary. We will then show that some boundary regularity is necessary by producing in any dimension examples of open bounded $\mathbb{C}$-convex sets where the Kobayashi metric is Gromov hyperbolic but whose boundary contains a complex affine ball of complex codimension one.

In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When the target manifold is strictly convex, our results imply that each non-trivial homotopy class contains at most one projective map. These results are motivated by the theory of holomorphic maps between compact complex manifolds., 18 pages

In this paper we study the automorphism group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a “polynomial ellipsoid” (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only if the limit set of the automorphism group intersects at least two closed complex faces of the set. The proof relies on a detailed study of the geometry of the Kobayashi metric and ideas from the theory of non-positively curved metric spaces. We also obtain a number of other results including the Greene–Krantz conjecture in the case of uniform non-tangential convergence, new results about continuous extensions (of biholomorphisms and complex geodesics), and a new Wolff–Denjoy theorem.

In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be relatively hyperbolic in terms of the geometry of the convex domain. This answers a question of Danciger-Gu\'eritaud-Kassel and is analogous to a result of Hruska-Kleiner for ${\rm CAT}(0)$ spaces., Comment: Minor revisions, final version to appear in Geometry & Topology. 96 pages, 2 figures. Comments welcome

We show that if a bounded domain in complex Euclidean space with $\mathcal{C}^{1,1}$ boundary covers a compact manifold, then the domain is biholomorphic to the unit ball., 23 pages. v2: minor changes in exposition, corrected some typos

Persisting gender inequities across political, economic, and public life have motivated global agendas to increase women’s leadership at all levels of society. Gender quotas offer one solution to encourage equitable gender representation in public decision-making by specifying a target number of women to serve on publicly-elected bodies. For natural resource governance sectors, can gender quotas promote women’s representation and participation in leadership? In 2010, Kenya enacted a new Constitution that included an article mandating that no one gender should make up greater than two-thirds of the composition of public committees. This ‘two-thirds gender rule’ also applies to community-level governance of water resources through water user resource associations, which were formally recognized in 2002. We present a study of community-based water committee compliance with Kenya’s national two-thirds gender rule based on surveys, focus groups, and interviews with water committee members. We show that Kenya’s gender quota has been moderately successful in increasing women’s representation on water committees. However, men hold more higher-level leadership positions than women, who typically serve as treasurers. Although there were no statistically significant differences between men and women’s self-reported participation frequency in various committee activities, men contributed significantly more hours per week to committee activities, facilitated meetings more frequently, and were more willing to lead meetings. Based on this leadership gap, we examine the sufficiency of a gender quota to promote equal leadership opportunities for women. We find that realizing the vision of a gender quota is conditional on how individuals are represented on community-based environmental committees as well as how individuals participate in committee activities.

Let $(\phi_t)$ be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let $\Omega$ be the starlike at infinity domain image of the Koenigs function of $(\phi_t)$. In this paper we completely characterize the type of convergence of the orbits of $(\phi_t)$ to the Denjoy-Wolff point in terms of the shape of $\Omega$. In particular we prove that the convergence is non-tangential if and only if the domain $\Omega$ is `quasi-symmetric with respect to vertical axes'. We also prove that such conditions are equivalent to the curve $[0,\infty)\ni t\mapsto \phi_t(z)$ being a quasi-geodesic in the sense of Gromov. Also, we characterize the tangential convergence in terms of the shape of $\Omega$., Comment: 25 pages, 3 figures

In this paper we establish two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with $C^2$ boundary. This appears to be the first boundary Schwarz lemma for general holomorphic self maps that requires no strong pseudoconvexity or finite type assumptions. The second is for biholomorphisms of domains who have an invariant K\"ahler metric with bounded sectional curvature. This second result applies to holomorphic homogeneous regular domains and appears to be the first boundary Schwarz lemma that makes no assumptions on the regularity of the boundary., Comment: 42 pages. Comments welcome. v2: minor edits

Functional genomics networks are widely used to identify unexpected pathway relationships in large genomic datasets. However, it is challenging to compare the signal-to-noise ratios of different networks and to identify the optimal network with which to interpret a particular genetic dataset. We present GeNets, a platform in which users can train a machine-learning model (Quack) to carry out these comparisons and execute, store, and share analyses of genetic and RNA-sequencing datasets.

A major bottleneck in network-based analyses of genomic data is quantitatively comparing biological signal in different networks and to identifying the optimal network dataset to answer a particular biological question. Towards these aims, we developed a unified web platform 9Broad Institute Web Platform for Genome Networks (GeNets)9, where users can compare biological signal of networks, and execute, store, and share network analyses. We designed a machine learningmachine-learning algorithm (Quack) which), which uses topological features to can quantify the overall and pathway-specific biological signals in networks, thus enabling users to choose the optimal network dataset for their analyses. We illustrated a typical workflow using GeNets to identify interesting autism candidate genes in the network that, when compared to four other networks, best recapitulates established neurodevelopmental pathway information. GeNets is a scalable, general and uniquely enabling computational framework for analyzing, managing and sharing analyses of genetic datasets using heterogeneous functional genomics networks, for example, from single-cell transcriptional analyses.

In this paper we prove: if a bounded domain with $C^2$ boundary covers a manifold which has finite volume with respect to either the Bergman volume, the K\"ahler-Einstein volume, or the Kobayashi-Eisenman volume, then the domain is biholomorphic to the unit ball. This answers an old question of Yau. Further, when the domain is convex we can assume that the boundary only has $C^{1,\epsilon}$ regularity., Comment: 16 pages. Comments welcome

In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for convex domains with \(C^\infty \) boundary being of finite type in the sense of D’Angelo is equivalent to the Gromov hyperbolicity of the Kobayashi metric. We also show that bounded domains which are locally convexifiable and have finite type in the sense of D’Angelo have Gromov hyperbolic Kobayashi metric. The proofs use ideas from the theory of the Hilbert metric.

For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to ${ \rm Aut}(\mathbb{B}_k)$. Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension $2k-1$. As applications we prove a new finite jet determination theorem and a Tits alternative theorem. The geometry of the Kobayashi metric plays an important role in the paper., 33 pages. v3: minor revisions. Final version to appear in Advances in Mathematics

In this paper we show that many projective Anosov representations act convex cocompactly on some properly convex domain in real projective space. In particular, if a non-elementary word hyperbolic group is not commensurable to a non-trivial free product or the fundamental group of a closed hyperbolic surface, then any projective Anosov representation of that group acts convex cocompactly on some properly convex domain in real projective space. We also show that if a projective Anosov representation preserves a properly convex domain, then it acts convex cocompactly on some (possibly different) properly convex domain. We then give three applications. First, we show that Anosov representations into general semisimple Lie groups can be defined in terms of the existence of a convex cocompact action on a properly convex domain in some real projective space (which depends on the semisimple Lie group and parabolic subgroup). Next, we prove a rigidity result involving the Hilbert entropy of a projective Anosov representation. Finally, we prove a rigidity result which shows that the image of the boundary map associated to a projective Anosov representation is rarely a $C^2$ submanifold of projective space. This final rigidity result also applies to Hitchin representations., 62 pages. Final version

In this paper we consider the following question: For bounded domains with smooth boundary, can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain? Our approach to answering this question is based on understanding the dynamical behavior of real geodesics in the Kobayashi metric and allows us to prove a number of results for domains with low regularity. For instance, we show that for convex domains with $C^{2,\epsilon}$ boundary strong pseudoconvexity can be characterized in terms of the behavior of the squeezing function near the boundary, the behavior of the holomorphic sectional curvature of the Bergman metric near the boundary, or any other reasonable measure of the complex geometry near the boundary. The first characterization gives a partial answer to a question of Forn{\ae}ss and Wold. As an application of these characterizations, we show that a convex domain with $C^{2,\epsilon}$ boundary which is biholomorphic to a strongly pseudoconvex domain is also strongly pseudoconvex., Comment: 27 pages. v2: minor revisions

In this paper we introduce a new class of domains in complex Euclidean space, called Goldilocks domains, and study their complex geometry. These domains are defined in terms of a lower bound on how fast the Kobayashi metric grows and an upper bound on how fast the Kobayashi distance grows as one approaches the boundary. Strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this Goldilocks condition, but we also present families of Goldilocks domains that have low boundary regularity or have boundary points of infinite type. We will show that the Kobayashi metric on these domains behaves, in some sense, like a negatively curved Riemannian metric. In particular, it satisfies a visibility condition in the sense of Eberlein and O'Neill. This behavior allows us to prove a variety of results concerning boundary extension of maps and to establish Wolff-Denjoy theorems for a wide collection of domains., 36 pages. v2: minor changes, final version to appear in Advances in Mathematics

Objective: Angiosarcoma (AS) is a rare soft tissue sarcoma, with an incidence of 300 cases/yr and a 5-year DSS of 30%. The low incidence has impeded large-scale research efforts. To address this, we launched a patient-partnered genomics study which seeks to empower patients to accelerate research by remotely sharing their samples and clinical information. Methods: We developed a website (ASCproject.org) to allow remote acquisition of medical records (MR), saliva, blood, and archival tissue from patients in the US and Canada. Whole-exome sequencing (WES) of ~20,000 genes is performed on tumor and matched germline DNA. Transcriptome analysis is performed on tumor RNA. Ultra-low pass whole-genome sequencing (ULP-WGS) and in some cases WES is performed on cell free DNA (cfDNA) obtained from blood samples. Clinical data including information about demographics, diagnosis, treatments, and responses are obtained via patient-reported data (PRD) and through MR abstraction. The resulting clinically annotated genomic database is shared widely to identify genomic drivers and mechanisms of response and resistance to therapies. Results: Since launch on March 13 2017, 321 patients with AS have registered. The average age of patients is 56 yrs (range 22-89). Primary locations of AS were primary breast (24%), breast with prior radiation (20%), head/face/neck/scalp (HFNS) (21%), bone/limb (9%), abdominal (3%), heart (3%), lung (1%), liver (1%), lymph (0.5%), multiple locations (11%), and other locations (5%). 142 (48%) reported being disease free at the time of enrollment. To date, 153 saliva kits, 167 MRs, 43 blood samples, and 97 tissue samples have been obtained. WES analysis is complete for 14 samples.ULP-WGS is complete for 10 cfDNA samples, and WES on 4 cfDNA samples. Transcriptome sequencing is complete for 9 tumor samples. We identified several previously described genes known to be altered in AS, including recurrent alterations in KDR and TP53. Tumor mutational burden (TMB) and mutational signature activities were quantified for each tumor sample. All three of the AS from the HFNS in the initial cohort exhibited a high TMB (>150 mutations) and dominant UV light signature (COSMIC Signature 7). Based on this, we hypothesized that HFNS AS might respond well to immune checkpoint inhibitors. We identified through PRD 56 patients with HFNS AS who reported what medications they received. Of these, 2 reported receiving immune checkpoint inhibitors for the treatment of metastatic disease. Both patients had refractory metastatic HFNS AS and reported receiving off-label anti-PD1 therapy. Both had complete or near-complete responses following immunotherapy, and currently report having no evidence of disease. Clinical responses were confirmed through review of MRs. Sequencing is currently being performed on tumor samples from both patients. Conclusion: A patient-partnered approach enabled rapid identification and enrollment of over 300 patients with AS, an exceedingly rare cancer, in 15 months. We were able to obtain tumor, blood, saliva samples to perform genomic analyses, which were then merged with detailed clinical information. PRD, clinical, and genomic data generated from the first 12 patients and 14 samples have been released on cbioportal.org. Additional data will be released in six-month intervals. Initial results show high TMB and a UV signature in 3 out of 3 patients with HFNS AS. In addition, we identified 2 patients with HFNS AS who had extraordinary responses to immunotherapy. These findings suggest a common genomic basis for HFNS AS and could provide rationale for clinical interventions using checkpoint inhibitors for these AS. Analyses of additional samples are under way to further characterize mutational signatures in HFNS AS and implications for patient care. This study serves as proof of principle that patient-partnered genomics efforts can democratize cancer research for exceedingly rare cancers. Citation Format: Corrie Painter, Esha Jain, Michael Dunphy, Elana Anastasio, Mary McGillicuddy, Rachel Stoddard, Beena Thomas, Sara Balch, Kristin Anderka, Katie Larkin, Niall Lennon, Yen-Lin Chen, Andrew Zimmer, Esme O. Baker, Simone Maiwald, Jen Lapan, Jason L. Hornick, Chandrajit Raut, George Demetri, Eric S. Lander, Todd Golub. High mutation burden and response to immune checkpoint inhibitors in angiosarcomas of the scalp and face [abstract]. In: Proceedings of the Fourth CRI-CIMT-EATI-AACR International Cancer Immunotherapy Conference: Translating Science into Survival; Sept 30-Oct 3, 2018; New York, NY. Philadelphia (PA): AACR; Cancer Immunol Res 2019;7(2 Suppl):Abstract nr B085.

The real (complex) minimum semidefinite rank of a graph is the minimum rank among all real symmetric (complex Hermitian) positive semidefinite matrices that are naturally associated via their zero-nonzero pattern to the given graph. In this paper we give an upper bound on the minimum semidefinite rank of a graph when the graph is modified from the superposition of two graphs by cancelling some number of edges. We also provide a lower bound for the minimum semidefinite rank of a graph determined by a given cutset. When the complement of the cutset is a star forest these lower and upper bounds coincide and we can compute the minimum semidefinite rank in terms of smaller graphs. This result encompasses the previously known case in which the cut set has order two or smaller. Next we provide results for when the cut set has order three. Using these results we provide an example where the positive semidefinite zero forcing number is strictly greater than the maximum positive semidefinite nullity.

In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifolds. For any finite volume quotient we show that (up to scaling) there is a unique Patterson–Sullivan measure and this measure coincides with the harmonic measure. As an application of these results we prove that the geodesic flow on a non-flat finite volume harmonic manifold without conjugate points is topologically transitive.

The real positive semidefinite minimum rank of a graph is the minimum rank among all real positive semidefinite matrices that are naturally associated via their zero-nonzero pattern to the given graph. In this paper, we use orthogonal vertex removal and sign patterns to improve the lower bound for the real positive semidefinite minimum rank determined by the OS-number and the positive semidefinite zero forcing number.

In this paper we prove the following rigidity theorem: a generic analytic polyhedron with non-compact automorphism group is biholomorphic to the product of a complex manifold with compact automorphism group and a polydisk. Moreover, this complex manifold and the dimension of this polydisk can be explicitly described in terms of the limit set of the automorphism group., 25 pages

In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary., 27 pages

A complete Riemannian manifold without conjugate points is said to be asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank-one locally symmetric spaces of noncompact type. In this paper we show that this list exhausts the compact asymptotically harmonic manifolds under a variety of assumptions including nonpositive curvature or Gromov-hyperbolic fundamental group. We then present a new characterization of symmetric spaces amongst the set of all visibility manifolds.

Angiosarcoma (AS) is an exceedingly rare soft tissue sarcoma, with an incidence of 300 cases/yr and a 5-year disease-specific survival of 30%. The low incidence has impeded large-scale research efforts that may lead to improved clinical outcomes. To address this, we launched a nationwide clinical-genomics study in order to empower patients to accelerate research by sharing their normal and tumor samples and clinical information remotely. Patients can access the study through an online portal (ASCproject.org). Enrolled patients are mailed saliva and blood draw kits. The study team obtains medical records and stored FFPE tumor samples. All received FFPE samples are examined by an expert pathologist to confirm a diagnosis of angiosarcoma. In order to validate that our processes would enable the generation of a robust dataset from tissues acquired from multiple institutions, we sought to characterize previously described genes known to be altered in angiosarcoma (e.g., TP53, NF1, KDR, BRCA2, MET, ARID1A, POT1, BRCA1, ASXL1, KDM6A, BRAF, SETD2, PTPRB, NRAS). A total of 251 patients have enrolled since the project launched in March of 2017. Primary locations of AS are primary breast 59 (25%), breast with prior radiation 45 (19%), head/face/neck/scalp 52 (22%), bone/limb 26 (11%), abdomen 5 (2%), heart 5 (2%), lung 2 (1%), liver 1 (1%), lymph 1 (0.4%), multiple locations 25 (11%), and other locations 12 (5%); 107 (52%) reported being disease free at the time of enrollment. To date, we have received 129 saliva kits, 106 medical records, 19 blood samples, and 36 tissue samples. Whole-exome sequencing (WES) was performed on 21 FFPE/saliva matched pairs with a goal mean target coverage of 150x for tumors. Ultra-low pass whole-genome sequencing (0.1x) was performed on cell free DNA (cfDNA) from plasma in order to determine tumor fraction. Of 10 cfDNA samples sequenced, 4 samples met criteria to perform WES. Additionally, transcriptome sequencing was performed on 9 FFPE samples. Sequence data processing and analysis has been completed on the first 10 samples and is in progress for the subsequent samples. Alterations were detected in genes previously described to be affected in angiosarcoma. Recurrent mutations in TP53 were detected in 50% (5/10) of analyzed samples, comprising 3 missense mutations, 1 frameshift deletion, and 1 frameshift insertion. Alterations were seen in at least one sample in all other genes selected for this initial analysis. This initiative demonstrates the feasibility of studying tissues from geographically dispersed patients and serves as proof of concept that patient-driven genomics efforts can democratize research for exceedingly rare cancers. Enrollment is still in progress, and additional samples will be sequenced and analyzed at scale. The data generated from these studies will be deposited into the public domain in six-month intervals. Citation Format: Michael Dunphy, Esha Jain, Elana Anastasio, Mary McGillicuddy, Rachel Stoddard, Beena Thomas, Sara Balch, Kristin Anderka, Katie Larkin, Niall Lennon, Yen-Lin Chen, Andrew Zimmer, Esme O. Baker, Simone Maiwald, Jen Hendrey Lapan, Jason Hornick, Chandrajit Raut, George Demetri, Eric Lander, Todd Golub, Nikhil Wagle, Corrie Painter. The Angiosarcoma Project: Generating the genomic landscape of an exceedingly rare cancer through a nationwide patient-driven initiative [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 5384.

The Metastatic Breast Cancer Project (MBCproject) is a research study that directly engages patients (pts) through social media and advocacy groups, and empowers them to share samples, clinical data, and experiences. The goal is to create a publicly available database of genomic, molecular, clinical, and patient-reported data to enable research. Working with pts and advocates, a website (MBCproject.org) was developed that allows pts with metastatic breast cancer (MBC) to register. Registered pts are sent an online consent form that asks for permission to obtain and analyze their medical records and samples. Once enrolled, pts are sent a saliva kit and asked to mail back a saliva sample, which is used to extract germline DNA. We contact participants' medical providers and obtain medical records and a portion of their stored tumor biopsies. Pts may be asked to mail in a blood sample, which is used to extract cell free DNA (cfDNA). Whole-exome sequencing (WES) is performed on tumor DNA, germline DNA, and cfNDA; transcriptome sequencing is performed on tumor RNA. Clinically annotated genomic data are used to study specific pt cohorts (including outliers) and to identify mechanisms of response and resistance to therapies. All de-identified data are shared via public databases. Study updates are shared with participants regularly. From 10/2015-11/2017, 4237 MBC pts registered, representing over 1,000 institutions. 95% answered the 16-question survey about their cancer, treatments, and demographic information. 2471 (58%) completed the consent form. 2,136 saliva kits were mailed to pts and 1,523 saliva samples were sent in (71%). 408 blood kits were mailed to pts and 175 blood samples have been received for cfDNA analysis. To date, we have obtained medical records from 311 pts and 190 tumors from 127 pts. In 10/2017, all data generated so far were publicly released on cbioportal.org, including WES for 103 tumors from 78 pts linked to clinical data including pathology (22 elements), medical record abstraction including all treatments and timelines/durations (67 elements), and patient-reported data (11 elements). 81% of biopsies included in this release were from the breast and 19% from metastatic sites. 75% were obtained prior to any therapy, 24% following therapy. New data will be released 4/2018 and every six months thereafter, as they are generated. Additional patient-reported data, including treatments, side effects, quality of life, family history, pregnancies, and sites of metastasis, will also be collected and shared. In summary, a patient-driven approach enabled rapid identification of thousands of MBC pts willing to share samples and clinical data. Remote acquisition of medical records, saliva, blood, and tumor tissue for pts across the U.S. is feasible. This shared clinico-genomic database should enable research in MBC and may serve as a model for patient-driven research in other cancers. Citation Format: Nikhil Wagle, Corrie Painter, Elana Anastasio, Michael Dunphy, Mary McGillicuddy, Rachel Stoddard, Esha Jain, Dewey Kim, Simona Di Lascio, Brett N. Tompson, Sara Balch, Beena Thomas, Priti Kumari, Shawn Johnson, Jamie Holloway, Ofir Cohen, Erik H. Knelson, Katie Larkin, Sam Pollock, Alicia Wong, Samira Bahl, Simone Maiwald, Andrew Zimmer, Esme O. Baker, Jen Hendry Lapan, Scott Sutherland, Scott Sassone, Viktor Adalsteinsson, Eric S. Lander, Todd R. Golub. The Metastatic Breast Cancer Project: Partnering with patients to accelerate progress in cancer research [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 5371.