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SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy.Subjects Scientific

Abstract-Binder is an open source web service that lets users create sharable, interactive, reproducible environments in the cloud. It is powered by other core projects in the open source ecosystem, including JupyterHub and Kubernetes for managing cloud resources. Binder works with pre-existing workflows in the analytics community, aiming to create interactive versions of repositories that exist on sites like GitHub with minimal extra effort needed. This paper details several of the design decisions and goals that went into the development of the current generation of Binder.Index Terms-cloud computing, reproducibility, binder, mybinder.org, shared computing, accessibility, kubernetes, dev ops, jupyter, jupyterhub, jupyter notebooks, github, publishing, interactivityBinder is a free, open source, and massively publicly available tool for easily creating sharable, interactive, reproducible environments in the cloud.The scientific community is increasingly unified around reproducibility. A survey in 2016 of 1,576 researchers reported that 90% of respondents believed there exists a reproducibility crisis in the scientific community. A majority of respondents also reported difficulty reproducing the work of colleagues [Bak16]. Similar results have been reported in the cell biology community [The] and the machine learning community [Pin17]. Making research reproducible requires pursuing two sub-goals, both of which are difficult to achieve: as well as the "data heavy" approach many fields are adopting, these problems become more complex yet more tractable than ever before.Fortunately, as the problem has grown more complex, the open source community has risen to meet the challenge. Tools for packaging analytics environments into "containers" allow others to re-create the computational environments needed to run analyses and evaluate results. Online communities make it easier to share and discover scientific results. A myriad of open source tools are freely available for doing analytics in open and transparent ways. New paradigms for writing code and displaying results in rich, engaging formats allow results to live next to the prose that explains their purpose.However, manual implementation of this processes is complex, and reproducing the full stack of another person's work is too labor intensive and error-prone for day-to-day use. A recent study of scientific repositories found that citation of "both visualization tools as well as common software packages (such as MATLAB) was a widespread failure" [SSM18]. As a result, the technical barriers limit practical reproducibility. To lower the technical barriers of sharing computational work, we introduce Binder 2.0, a tool that we believe makes reproducibility more practically possible.

BackgroundHere we present an in-depth characterization of the mechanism of sequencer-induced sample contamination due to the phenomenon of index swapping that impacts Illumina sequencers employing patterned flow cells with Exclusion Amplification (ExAmp) chemistry (HiSeqX, HiSeq4000, and NovaSeq). We also present a remediation method that minimizes the impact of such swaps.ResultsLeveraging data collected over a two-year period, we demonstrate the widespread prevalence of index swapping in patterned flow cell data. We calculate mean swap rates across multiple sample preparation methods and sequencer models, demonstrating that different library methods can have vastly different swapping rates and that even non-ExAmp chemistry instruments display trace levels of index swapping. We provide methods for eliminating sample data cross contamination by utilizing non-redundant dual indexing for complete filtering of index swapped reads, and share the sequences for 96 non-combinatorial dual indexes we have validated across various library preparation methods and sequencer models. Finally, using computational methods we provide a greater insight into the mechanism of index swapping.ConclusionsIndex swapping in pooled libraries is a prevalent phenomenon that we observe at a rate of 0.2 to 6% in all sequencing runs on HiSeqX, HiSeq 4000/3000, and NovaSeq. Utilizing non-redundant dual indexing allows for the removal (flagging/filtering) of these swapped reads and eliminates swapping induced sample contamination, which is critical for sensitive applications such as RNA-seq, single cell, blood biopsy using circulating tumor DNA, or clinical sequencing.Electronic supplementary materialThe online version of this article (10.1186/s12864-018-4703-0) contains supplementary material, which is available to authorized users.

Bose gases confined in highly-elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1d model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1d Bose gas become independent of the actual value of the 3d scattering length a 3d . In this unitary regime, the energy of the system is well described by a hard rod equation of state. We investigate the stability of quasi-1d Bose gases with positive and negative a 3d .PACS numbers: 03.75.FiIn recent years the study of quasi-1d quantum Bose gases has attracted a great deal of interest. Intriguing properties of quasi-1d gases, such as the exact mapping between interacting bosons and non-interacting fermions, have been predicted [1,2,3]. A bosonic gas that behaves as if it consisted of spinless fermions, a so-called TonksGirardeau (TG) gas, cannot be described within meanfield theory since it exhibits strong correlations; instead, a many-body framework is called for. While experimental evidence of quasi-1d behavior has been reported for bosonic atomic gases under highly-elongated harmonic confinement [4], TG gases have not been observed yet. It has been suggested, however, that TG gases can be realized experimentally for either low atomic densities or strong atom-atom interaction strengths. The 3d s-wave scattering length a 3d , and hence the strength of atomatom interactions, can be tuned to essentially any value, including zero and ±∞, by utilizing a magnetic atomatom Feshbach resonance [5,6].Utilizing a two-body Feshbach resonance, 3d degenerate gases with large scattering length a 3d have been studied experimentally and theoretically. For a 3d → ±∞, it is predicted that the behavior of the strongly-correlated gas is independent of a 3d [7]. For homogeneous 3d Bose gases, this unitary regime can most likely not be reached experimentally since three-body recombination is expected to set in when a 3d becomes comparable to the average interparticle distance. Three-body recombination leads to cluster formation, and hence "destroys" the gas-like state. The situation is different for Fermi gases, for which the unitary regime has already been achieved experimentally [6]. In this case, the Fermi pressure stabilizes the system even for large |a 3d |. It has been predicted that three-body recombination processes are suppressed for strongly interacting 1d Bose gases [8]. These studies raise the question whether a highly-elongated inhomogeneous Bose gas, that is, an inhomogeneous quasi-1d Bose gas, is stable as a 3d → ±∞.This Letter investigates the properties of a quasi-1d Bose gas at zero temperature over a wide range of interaction strengths within a microscopic, highly accurate many-body framework. We find that the system i) is well described by a 1d model Hamiltonian with contact interactions and renormalized coupling constant [2] for any ...