Deploying Jupyter Notebooks at scale on XSEDE resources for Science Gateways and workshops

Jupyter Notebooks have become a mainstream tool for interactive computing in every field of science. Jupyter Notebooks are suitable as companion applications for Science Gateways, providing more flexibility and post-processing capability to the users. Moreover they are often used in training events and workshops to provide immediate access to a pre-configured interactive computing environment. The Jupyter team released the JupyterHub web application to provide a platform where multiple users can login and access a Jupyter Notebook environment. When the number of users and memory requirements are low, it is easy to setup JupyterHub on a single server. However, setup becomes more complicated when we need to serve Jupyter Notebooks at scale to tens or hundreds of users. In this paper we will present three strategies for deploying JupyterHub at scale on XSEDE resources. All options share the deployment of JupyterHub on a Virtual Machine on XSEDE Jetstream. In the first scenario, JupyterHub connects to a supercomputer and launches a single node job on behalf of each user and proxies back the Notebook from the computing node back to the user's browser. In the second scenario, implemented in the context of a XSEDE consultation for the IRIS consortium for Seismology, we deploy Docker in Swarm mode to coordinate many XSEDE Jetstream virtual machines to provide Notebooks with persistent storage and quota. In the last scenario we install the Kubernetes containers orchestration framework on Jetstream to provide a fault-tolerant JupyterHub deployment with a distributed filesystem and capability to scale to thousands of users. In the conclusion section we provide a link to step-by-step tutorials complete with all the necessary commands and configuration files to replicate these deployments.Comment: 7 pages, 3 figures, PEARC '18: Practice and Experience in Advanced Research Computing, July 22--26, 2018, Pittsburgh, PA, US

A-infinity algebra of an elliptic curve and Eisenstein series

We compute explicitly the A-infinity structure on the Ext-algebra of the collection $({\mathcal O}_C, L)$, where $L$ is a line bundle of degree 1 on an elliptic curve $C$. The answer involves higher derivatives of Eisenstein series.Comment: 13 pages, 3 figures; v3: added remark on the limit at the cus

Canonical decomposition of linear differential operators with selected differential Galois groups

We revisit an order-six linear differential operator having a solution which is a diagonal of a rational function of three variables. Its exterior square has a rational solution, indicating that it has a selected differential Galois group, and is actually homomorphic to its adjoint. We obtain the two corresponding intertwiners giving this homomorphism to the adjoint. We show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition, already underlined in a previous paper, in terms of order-two self-adjoint operators. From these results, we deduce a new form of decomposition of operators for this selected order-six linear differential operator in terms of three order-two self-adjoint operators. We then generalize the previous decomposition to decompositions in terms of an arbitrary number of self-adjoint operators of the same parity order. This yields an infinite family of linear differential operators homomorphic to their adjoint, and, thus, with a selected differential Galois group. We show that the equivalence of such operators is compatible with these canonical decompositions. The rational solutions of the symmetric, or exterior, squares of these selected operators are, noticeably, seen to depend only on the rightmost self-adjoint operator in the decomposition. These results, and tools, are applied on operators of large orders. For instance, it is seen that a large set of (quite massive) operators, associated with reflexive 4-polytopes defining Calabi-Yau 3-folds, obtained recently by P. Lairez, correspond to a particular form of the decomposition detailed in this paper.Comment: 40 page

Lateral-directional control of the x-15 airplane

Lateral directional control and stability characteristics of X-15 aircraf

From Bare Metal to Virtual: Lessons Learned when a Supercomputing Institute Deploys its First Cloud

As primary provider for research computing services at the University of Minnesota, the Minnesota Supercomputing Institute (MSI) has long been responsible for serving the needs of a user-base numbering in the thousands. In recent years, MSI---like many other HPC centers---has observed a growing need for self-service, on-demand, data-intensive research, as well as the emergence of many new controlled-access datasets for research purposes. In light of this, MSI constructed a new on-premise cloud service, named Stratus, which is architected from the ground up to easily satisfy data-use agreements and fill four gaps left by traditional HPC. The resulting OpenStack cloud, constructed from HPC-specific compute nodes and backed by Ceph storage, is designed to fully comply with controls set forth by the NIH Genomic Data Sharing Policy. Herein, we present twelve lessons learned during the ambitious sprint to take Stratus from inception and into production in less than 18 months. Important, and often overlooked, components of this timeline included the development of new leadership roles, staff and user training, and user support documentation. Along the way, the lessons learned extended well beyond the technical challenges often associated with acquiring, configuring, and maintaining large-scale systems.Comment: 8 pages, 5 figures, PEARC '18: Practice and Experience in Advanced Research Computing, July 22--26, 2018, Pittsburgh, PA, US

Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.Comment: 55 page

Electroencephalography (EEG) in Head Injuries

Clinical electroencephalography has gained remarkably in popularity during the past twenty years. Correspondingly we find it with more frequency in medico-legal problems, particularly the ones pertaining to head injuries