Operations between sets in geometry

An investigation is launched into the fundamental characteristics of operations on and between sets, with a focus on compact convex sets and star sets (compact sets star-shaped with respect to the origin) in $n$-dimensional Euclidean space $\R^n$. For example, it is proved that if $n\ge 2$, with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, and associative if and only if it is $L_p$ addition for some $1\le p\le\infty$. It is also demonstrated that if $n\ge 2$, an operation * between compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, and has the identity property (i.e., $K*\{o\}=K=\{o\}*K$ for all compact convex sets $K$, where $o$ denotes the origin) if and only if it is Minkowski addition. Some analogous results for operations between star sets are obtained. An operation called $M$-addition is generalized and systematically studied for the first time. Geometric-analytic formulas that characterize continuous and GL(n)-covariant operations between compact convex sets in terms of $M$-addition are established. The term "polynomial volume" is introduced for the property of operations * between compact convex or star sets that the volume of $rK*sL$, $r,s\ge 0$, is a polynomial in the variables $r$ and $s$. It is proved that if $n\ge 2$, with three trivial exceptions, an operation between origin-symmetric compact convex sets is continuous in the Hausdorff metric, GL(n) covariant, associative, and has polynomial volume if and only if it is Minkowski addition

A Study of Mineral Impurities within the Georgia Kaolins

The mining industry located along the fall line region of central Georgia has been and remains as one of the largest global exporters of the clay mineral kaolinite. Among the kaolin deposits in that region, the Cretaceous Buffalo Creek formation and the Eocene Jeffersonville member contain the most commercially viable kaolin to extract and process for resale. The minerals of the sand and silt fractions of these kaolin units were separated via dense liquid separation and analyzed for comparison by X-ray diffraction, scanning electron microscopy, and elemental analysis. The dense fractions are enriched in select heavy minerals (zircon and rutile) and trace elements (rare earth). These elemental enrichments and the differences in the mineral maturity of these gangue (grit) fractions suggest differences in the provenance of the gangue minerals between these two different kaolins

Dynamic Resource Allocation in Conservation Planning

Consider the problem of protecting endangered species by selecting patches of land to be used for conservation purposes. Typically, the availability of patches changes over time, and recommendations must be made dynamically. This is a challenging prototypical example of a sequential optimization problem under uncertainty in computational sustainability. Existing techniques do not scale to problems of realistic size. In this paper, we develop an efficient algorithm for adaptively making recommendations for dynamic conservation planning, and prove that it obtains near-optimal performance. We further evaluate our approach on a detailed reserve design case study of conservation planning for three rare species in the Pacific Northwest of the United States

The access control double bind: how everyday interfaces regulate access and privacy, enable surveillance, and enforce identity.

Access controls are an inescapable and deceptively mundane requirement for accessing digital applications and platforms. These systems enable and enforce practices related to access, ownership, privacy, and surveillance. Companies use access controls to dictate and enforce terms of use for digital media, platforms, and technologies. The technical implementation of these systems is well understood. However, this paper instead uses digital game software and platforms as a case study to analyze the broader socio-technical, and often inequitable, interactions these elements regulate across software systems. Our sample includes 200 digital games and seven major digital gaming platforms. We combine close reading and content analysis to examine the processes of authentication and authorization within our samples. While the ubiquity of these systems is a given in much academic and popular discourse, our data help empirically ground this understanding and examine how these systems support user legibility and surveillance, and police identities in under-examined ways. We suggest changes to the policies and practices that shape these systems to drive more transparent and equitable design

Enabling GPU Accelerated Computing in the SUNDIALS Time Integration Library

As part of the Exascale Computing Project (ECP), a recent focus of development efforts for the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been to enable GPU-accelerated time integration in scientific applications at extreme scales. This effort has resulted in several new GPU-enabled implementations of core SUNDIALS data structures, support for programming paradigms which are aware of the heterogeneous architectures, and the introduction of utilities to provide new points of flexibility. In this paper, we discuss our considerations, both internal and external, when designing these new features and present the features themselves. We also present performance results for several of the features on the Summit supercomputer and early access hardware for the Frontier supercomputer, which demonstrate negligible performance overhead resulting from the additional infrastructure and significant speedups when using both NVIDIA and AMD GPUs

Printable microscale interfaces for long-term peripheral nerve mapping and precision control

The nascent field of bioelectronic medicine seeks to decode and modulate peripheral nervous system signals to obtain therapeutic control of targeted end organs and effectors. Current approaches rely heavily on electrode-based devices, but size scalability, material and microfabrication challenges, limited surgical accessibility, and the biomechanically dynamic implantation environment are significant impediments to developing and deploying advanced peripheral interfacing technologies. Here, we present a microscale implantable device – the nanoclip – for chronic interfacing with fine peripheral nerves in small animal models that begins to meet these constraints. We demonstrate the capability to make stable, high-resolution recordings of behaviorally-linked nerve activity over multi-week timescales. In addition, we show that multi-channel, current-steering-based stimulation can achieve a high degree of functionally-relevant modulatory specificity within the small scale of the device. These results highlight the potential of new microscale design and fabrication techniques for the realization of viable implantable devices for long-term peripheral interfacing.https://www.biorxiv.org/node/801468.fullFirst author draf

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever increasing size and complexity. Recently, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using IMEX and low-order operator splitting schemes. However, there have been few performance studies that compare different classes of multirate integrators on complex application problems. We study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits the work of Emmet et al. (2014) on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but run at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed implicit-explicit MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both

A dialogue in support of social justice

There are kinds of dialogue that support social justice and others that do the reverse. The kinds of dialogue that support social justice require that anger be bracketed and that hiding in safe spaces be eschewed. All illegitimate ad hominem/ad feminem attacks are ruled out from the get-go. No dialogical contribution can be down-graded on account of the communicator’s gender, race, or religion. As well, this communicative approach unapologetically privileges reason in full view of theories and strategies that might seek to undermine reasoning as just another illegitimate form of power. On the more positive side, it is argued in this paper that social justice dialogue will be enhanced by a kind of “communicative upgrading,” which amplifies “person perception,” foregrounds the impersonal forces within our common social spaces rather than the “baddies” within, and orients the dialogical trajectory toward the future rather than the past. Finally, it is argued in this paper that educators have a pressing responsibility to guide their students through social justice dialogue so that their speech contributes to the amelioration of injustice, rather than rendering the terrain more treacherous