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

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

On the Stability of Compactified D=11 Supermembranes

We prove D=11 supermembrane theories wrapping around in an irreducible way over $S^{1} \times S^{1}\times M^{9}$ on the target manifold, have a hamiltonian with strict minima and without infinite dimensional valleys at the minima for the bosonic sector. The minima occur at monopole connections of an associated U(1) bundle over topologically non trivial Riemann surfaces of arbitrary genus. Explicit expressions for the minimal connections in terms of membrane maps are presented. The minimal maps and corresponding connections satisfy the BPS condition with half SUSY.Comment: 15 pages, latex. Added comments in conclusions and more reference

On compression of Bruhat-Tits buildings

We obtain an analog of the compression of angles theorem in symmetric spaces for Bruhat--Tits buildings of the type $A$. More precisely, consider a $p$-adic linear space $V$ and the set $Lat(V)$ of all lattices in $V$. The complex distance in $Lat(V)$ is a complete system of invariants of a pair of points of $Lat(V)$ under the action of the complete linear group. An element of a Nazarov semigroup is a lattice in the duplicated linear space $V\oplus V$. We investigate behavior of the complex distance under the action of the Nazarov semigroup on the set $Lat(V)$.Comment: 6 page

Mild Cognitive Impairment in Parkinson's Disease - What Is It?

PURPOSE OF REVIEW: Mild cognitive impairment is a common feature of Parkinson’s disease, even at the earliest disease stages, but there is variation in the nature and severity of cognitive involvement and in the risk of conversion to Parkinson’s disease dementia. This review aims to summarise current understanding of mild cognitive impairment in Parkinson’s disease. We consider the presentation, rate of conversion to dementia, underlying pathophysiology and potential biomarkers of mild cognitive impairment in Parkinson’s disease. Finally, we discuss challenges and controversies of mild cognitive impairment in Parkinson’s disease. RECENT FINDINGS: Large-scale longitudinal studies have shown that cognitive involvement is important and common in Parkinson’s disease and can present early in the disease course. Recent criteria for mild cognitive impairment in Parkinson’s provide the basis for further study of cognitive decline and for the progression of different cognitive phenotypes and risk of conversion to dementia. SUMMARY: Improved understanding of the underlying pathology and progression of cognitive change are likely to lead to opportunities for early intervention for this important aspect of Parkinson’s disease

A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern-Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.Comment: 15 pages, 7 figure