Perfect refiners for permutation group backtracking algorithms

We therefore thank the VolkswagenStiftung (Grant no. 93764 ) and the Royal Society (Grant code URF\R\180015) again for their financial support of this earlier work. For financial support during the more recent advances, we thank the DFG (Grant no. WA 3089/9-1) and again the Royal Society (Grant codes RGF\EA\181005 and URF\R\180015 ).Backtrack search is a fundamental technique for computing with finite permutation groups, which has been formulated in terms of points, ordered partitions, and graphs. We provide a framework for discussing the most common forms of backtrack search in a generic way. We introduce the concept of perfect refiners to better understand and compare the pruning power available in these different settings. We also present a new formulation of backtrack search, which allows the use of graphs with additional vertices, and which is implemented in the software package VOLE. For each setting, we classify the groups and cosets for which there exist perfect refiners. Moreover, we describe perfect refiners for many naturally-occurring examples of stabilisers and transporter sets, including applications to normaliser and subgroup conjugacy problems for 2-closed groups.Publisher PDFPeer reviewe

Computing canonical images in permutation groups with Graph Backtracking

We describe a new algorithm for finding a canonical image of an object under the action of a finite permutation group. This algorithm builds on previous work using Graph Backtracking, which extends Jeffrey Leon's Partition Backtrack framework. Our methods generalise both Nauty and Steve Linton's Minimal image algorithm.Comment: This is a revised version as re-submitte

Permutation group algorithms based on directed graphs

Funding: The authors would like to thank the DFG (Grant no. WA 3089/6-1) and the VolkswagenStiftung (Grant no. 93764) for financially supporting this work and projects leading up to it. The first and third authors are supported by the Royal Society (Grant codes RGF\EA\181005 and URF\R\180015).We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures. Our techniques are inspired by and generalise 'partition backtrack', which is the current state-of-the-art algorithm introduced by Jeffrey Leon in 1991. But, instead of ordered partitions, we use labelled directed graphs to organise our backtrack search algorithms, which allows for a richer representation of many problems while often resulting in smaller search spaces. In this article we present the theory underpinning our framework, we describe our algorithms, and we show the results of some experiments. An implementation of our algorithms is available as free software in the Graph Back tracking package for GAP.Publisher PDFPeer reviewe

Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.Comment: 34 pages, 18 figures, 4 table

Thermal energy budget of electrons in the inner heliosphere: Parker Solar Probe Observations

We present an observational analysis of the electron thermal energy budget using data from Parker Solar Probe. We use the macroscopic moments, obtained from our fits to the measured electron distribution function, to evaluate the thermal energy budget based on the second moment of the Boltzmann equation. We separate contributions to the overall budget from reversible and irreversible processes. We find that a thermal-energy source must be present in the inner heliosphere over the heliocentric distance range from 0.15 to 0.47 au. The divergence of the heat flux is positive at heliocentric distances below 0.33 au, while beyond 0.33 au, there is a measurable degradation of the heat flux. Expansion effects dominate the thermal energy budget below 0.3 au. Under our steady-state assumption, the free streaming of the electrons is not sufficient to explain the thermal energy density budget. We conjecture that the most likely driver for the required heating process is turbulence. Our results are consistent with the known non-adiabatic polytropic index of the electrons, which we measure as 1.176 in the explored range of heliocentric distances.Comment: Paper accepted to The Astrophysical Journa

Athanor: High-Level Local Search Over Abstract Constraint Specifications in Essence

This paper presents Athanor, a novel local search solver that operates on abstract constraint specifications of combinatorial problems in the Essence language. It is unique in that it operates directly on the high level, nested types in Essence, such as set of partitions or multiset of sequences, without refining such types into low level representations. This approach has two main advantages. First, the structure present in the high level types allows high quality neighbourhoods for local search to be automatically derived. Second, it allows Athanor to scale much better than solvers that operate on the equivalent, but much larger, low-level representations. The paper details how Athanor operates, covering incremental evaluation, dynamic unrolling of quantified expressions and neighbourhood construction. A series of case studies show the performance of Athanor, benchmarked against several local search solvers on a range of problem classes

Radial Evolution of Thermal and Suprathermal Electron Populations in the Slow Solar Wind from 0.13 to 0.5 au: Parker Solar Probe Observations

We develop and apply a bespoke fitting routine to a large volume of solar wind electron distribution data measured by Parker Solar Probe (PSP) over its first five orbits, covering radial distances from 0.13 to 0.5 au. We characterise the radial evolution of the electron core, halo and strahl populations in the slow solar wind during these orbits. The fractional densities of these three electron populations provide evidence for the growth of the combined suprathermal halo and strahl populations from 0.13 to 0.17 au. Moreover, the growth in the halo population is not matched by a decrease of the strahl population at these distances, as has been reported for previous observations at distances greater than 0.3 au. We also find that the halo is negligible at small heliocentric distances. The fractional strahl density remains relatively constant ~1% below 0.2 au, suggesting that the rise in the relative halo density is not solely due to the transfer of strahl electrons into the halo

The Vaginal Microbiome: Disease, Genetics and the Environment

The vagina is an interactive interface between the host and the environment. Its surface is covered by a protective epithelium colonized by bacteria and other microorganisms. The ectocervix is nonsterile, whereas the endocervix and the upper genital tract are assumed to be sterile in healthy women. Therefore, the cervix serves a pivotal role as a gatekeeper to protect the upper genital tract from microbial invasion and subsequent reproductive pathology. Microorganisms that cross this barrier can cause preterm labor, pelvic inflammatory disease, and other gynecologic and reproductive disorders. Homeostasis of the microbiome in the vagina and ectocervix plays a paramount role in reproductive health. Depending on its composition, the microbiome may protect the vagina from infectious or non-infectious diseases, or it may enhance its susceptibility to them. Because of the nature of this organ, and the fact that it is continuously colonized by bacteria from birth to death, it is virtually certain that this rich environment evolved in concert with its microbial flora. Specific interactions dictated by the genetics of both the host and microbes are likely responsible for maintaining both the environment and the microbiome. However, the genetic basis of these interactions in both the host and the bacterial colonizers is currently unknown. _Lactobacillus_ species are associated with vaginal health, but the role of these species in the maintenance of health is not yet well defined. Similarly, other species, including those representing minor components of the overall flora, undoubtedly influence the ability of potential pathogens to thrive and cause disease. Gross alterations in the vaginal microbiome are frequently observed in women with bacterial vaginosis, but the exact etiology of this disorder is still unknown. There are also implications for vaginal flora in non-infectious conditions such as pregnancy, pre-term labor and birth, and possibly fertility and other aspects of women’s health. Conversely, the role of environmental factors in the maintenance of a healthy vaginal microbiome is largely unknown. To explore these issues, we have proposed to address the following questions:

*1.	Do the genes of the host contribute to the composition of the vaginal microbiome?* We hypothesize that genes of both host and bacteria have important impacts on the vaginal microbiome. We are addressing this question by examining the vaginal microbiomes of mono- and dizygotic twin pairs selected from the over 170,000 twin pairs in the Mid-Atlantic Twin Registry (MATR). Subsequent studies, beyond the scope of the current project, may investigate which host genes impact the microbial flora and how they do so.
*2.	What changes in the microbiome are associated with common non-infectious pathological states of the host?* We hypothesize that altered physiological (e.g., pregnancy) and pathologic (e.g., immune suppression) conditions, or environmental exposures (e.g., antibiotics) predictably alter the vaginal microbiome. Conversely, certain vaginal microbiome characteristics are thought to contribute to a woman’s risk for outcomes such as preterm delivery. We are addressing this question by recruiting study participants from the ~40,000 annual clinical visits to women’s clinics of the VCU Health System.
*3.	What changes in the vaginal microbiome are associated with relevant infectious diseases and conditions?* We hypothesize that susceptibility to infectious disease (e.g. HPV, _Chlamydia_ infection, vaginitis, vaginosis, etc.) is impacted by the vaginal microbiome. In turn, these infectious conditions clearly can affect the ability of other bacteria to colonize and cause pathology. Again, we are exploring these issues by recruiting participants from visitors to women’s clinics in the VCU Health System.

Three kinds of sequence data are generated in this project: i) rDNA sequences from vaginal microbes; ii) whole metagenome shotgun sequences from vaginal samples; and iii) whole genome shotgun sequences of bacterial clones selected from vaginal samples. The study includes samples from three vaginal sites: mid-vaginal, cervical, and introital. The data sets also include buccal and perianal samples from all twin participants. Samples from these additional sites are used to test the hypothesis of a per continuum spread of bacteria in relation to vaginal health. An extended set of clinical metadata associated with these sequences are deposited with dbGAP. We have currently collected over 4,400 samples from ~100 twins and over 450 clinical participants. We have analyzed and deposited data for 480 rDNA samples, eight whole metagenome shotgun samples, and over 50 complete bacterial genomes. These data are available to accredited investigators according to NIH and Human Microbiome Project (HMP) guidelines. The bacterial clones are deposited in the Biodefense and Emerging Infections Research Resources Repository ("http://www.beiresources.org/":http://www.beiresources.org/). 

In addition to the extensive sequence data obtained in this study, we are collecting metadata associated with each of the study participants. Thus, participants are asked to complete an extensive health history questionnaire at the time samples are collected. Selected clinical data associated with the visit are also obtained, and relevant information is collected from the medical records when available. This data is maintained securely in a HIPAA-compliant data system as required by VCU’s Institutional Review Board (IRB). The preponderance of these data (i.e., that judged appropriate by NIH staff and VCU’s IRB are deposited at dbGAP ("http://www.ncbi.nlm.nih.gov/gap":http://www.ncbi.nlm.nih.gov/gap). Selected fields of this data have been identified by NIH staff as ‘too sensitive’ and are not available in dbGAP. Individuals requiring access to these data fields are asked to contact the PI of this project or NIH Program Staff. 
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