Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation

Polynomial functors and combinatorial Dyson-Schwinger equations

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial Dyson-Schwinger equations are revealed to follow from general categorical constructions and universal properties. Rather than beginning with an equation inside a given Hopf algebra and referring to given Hochschild $1$-cocycles, our starting point is an abstract fixpoint equation in groupoids, shown canonically to generate all the algebraic structure. Precisely, for any finitary polynomial endofunctor $P$ defined over groupoids, the system of combinatorial Dyson-Schwinger equations $X=1+P(X)$ has a universal solution, namely the groupoid of $P$-trees. The isoclasses of $P$-trees generate naturally a Connes-Kreimer-like bialgebra, in which the abstract Dyson-Schwinger equation can be internalised in terms of canonical $B_+$-operators. The solution to this equation is a series (the Green function) which always enjoys a Fa\`a di Bruno formula, and hence generates a sub-bialgebra isomorphic to the Fa\`a di Bruno bialgebra. Varying $P$ yields different bialgebras, and cartesian natural transformations between various $P$ yield bialgebra homomorphisms and sub-bialgebras, corresponding for example to truncation of Dyson-Schwinger equations. Finally, all constructions can be pushed inside the classical Connes-Kreimer Hopf algebra of trees by the operation of taking core of $P$-trees. A byproduct of the theory is an interpretation of combinatorial Green functions as inductive data types in the sense of Martin-L\"of Type Theory (expounded elsewhere).Comment: v4: minor adjustments, 49pp, final version to appear in J. Math. Phy

Fostering Creativity via Technoself Enhanced Learning with Emerging Technologies

Creative and collaborative learning has profound implications for all parts of the system we have built up in our societies — not only the education systems but also the social, economic and cultural systems. Technology Enhanced Learning (TEL) research has increasingly focused on emerging technologies, Extended Reality (XR) to improve learner’s engagement in enriched multimodal learning environments. This paper recommends technoself pedagogy and investigates XR for creative learning as a frontier in TEL. In partnership with cultural sectors, we introduce the agile working process in the collaboration with the Alexandra Park and Palace Charitable Trust (AP) and report the project development of two pilot apps based on the proposed methodology. As a result, students as co-creators were engaged in pilot collaborative projects to work on the digital solutions that promote unforgettable stories. The prototypes exploited the latest development of Virtual Reality (VR), Augmented Reality (AR), and game and mobile technology. The pilot pedagogical practice focuses on providing a vibrant collaborative learning environment which fosters innovation and creativity, informed by practice, inspired by TEL research across disciplines. The collaborative learning practices also support cultural sectors to inspire their visitors and to help curators think beyond their current boundaries, providing a new, mixed media and technological approach to raise cultural awareness to wider audiences

Methylation regulation of Antiviral host factors, Interferon Stimulated Genes (ISGs) and T-cell responses associated with natural HIV control

GWAS, immune analyses and biomarker screenings have identified host factors associated within vivoHIV-1 control. However, there is a gap in the knowledge about the mechanisms that regulate the expression of such host factors. Here, we aimed to assess DNA methylation impact on host genome in natural HIV-1 control. To this end, whole DNA methylome in 70 untreated HIV-1 infected individuals with either high (>50,000 HIV-1-RNA copies/ml, n = 29) or low (<10,000 HIV-1-RNA copies/ml, n = 41) plasma viral load (pVL) levels were compared and identified 2,649 differentially methylated positions (DMPs). Of these, a classification random forest model selected 55 DMPs that correlated with virologic (pVL and proviral levels) and HIV-1 specific adaptive immunity parameters (IFNg-T cell responses and neutralizing antibodies capacity). Then, cluster and functional analyses identified two DMP clusters: cluster 1 contained hypo-methylated genes involved in antiviral and interferon response (e.g.PARP9,MX1, andUSP18) in individuals with high viral loads while in cluster 2, genes related to T follicular helper cell (Tfh) commitment (e.g.CXCR5andTCF7) were hyper-methylated in the same group of individuals with uncontrolled infection. For selected genes, mRNA levels negatively correlated with DNA methylation, confirming an epigenetic regulation of gene expression. Further, these gene expression signatures were also confirmed in early and chronic stages of infection, including untreated, cART treated and elite controllers HIV-1 infected individuals (n = 37). These data provide the first evidence that host genes critically involved in immune control of the virus are under methylation regulation in HIV-1 infection. These insights may offer new opportunities to identify novel mechanisms ofin vivovirus control and may prove crucial for the development of future therapeutic interventions aimed at HIV-1 cure. Author summary The infection with the human immunodeficiency virus (HIV), as for other viral infections, induce global DNA Methylation changes in the host genome. Herein, we identified for first time the methylation impact on host genome in untreated HIV-1 infection with different degrees ofin vivovirus control. Specifically, we observed that individuals with a better HIV-1 control showed a hypermethylation of genes associated with antiviral and interferon pathways and the hypomethylation of genes associated with the differentiation process of T follicular helper cells. Interestingly, these epigenetic imprints in host genome were strongly correlated with virus content and HIV-specific T cell responses. Therefore, we propose DNA Methylation as the regulation mechanism of host genes involved in immune HIV-1 control that could interfere in the efficacy of cure strategies. We also highlight the importance of DNA Methylation to regulate immune responses not only in HIV-1 but also in chronic infections or other pathologic situations associated with a sustained activation of the immune system

Natural transmission of Leishmania infantum through experimentally infected Phlebotomus perniciosus highlights the virulence of Leishmania parasites circulating in the human visceral leishmaniasis outbreak in Madrid, Spain

International audienceAbstractA human leishmaniasis outbreak is occurring in the Madrid region, Spain, with the parasite and vector involved being Leishmania infantum and Phlebotomus perniciosus respectively. The aim of this study was to investigate the virulence of L. infantum isolates from the focus using a natural transmission model. Hamsters were infected by intraperitoneal inoculation (IP) or by bites of sand flies experimentally infected with L. infantum isolates obtained from P. perniciosus collected in the outbreak area (IPER/ES/2012/BOS1FL1 and IPER/ES/2012/POL2FL6) and a well characterized L. infantum strain JPCM5 (MCAN/ES/98/LLM-877). Hamster infections were monitored by clinical examination, serology, culture, parasite burden, Giemsa-stained imprints, PCR, histopathology and xenodiagnostic studies. Establishment of infection of L. infantum was achieved with the JPCM5 strain and outbreak isolates by both P. perniciosus infective bites or IP route. However, high virulence of BOS1FL1 and POL2FL6 isolates was highlighted by the clinical outcome of disease, high parasite detection in spleen and liver, high parasitic loads and positivity of Leishmania serology. Transmission by bite of POL2FL6 infected flies generated a slower progression of clinical disease than IP infection, but both groups were infective to P. perniciosus by xenodiagnosis at 2 months post-infection. Conversely, hamsters inoculated with JPCM5 were not infective to sand flies. Histopathology studies confirmed the wide spread of POL2FL6 parasites to several organs. A visceral leishmaniasis model that mimics the natural transmission in nature allowed us to highlight the high virulence of isolates that are circulating in the focus. These findings contribute to a better understanding of the outbreak epidemiology

Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness

This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in ∞-groupoids. A decomposition space is a simplicial ∞-groupoid satisfying an exactness condition weaker than the Segal condition. Just as the Segal condition expresses composition, the new condition expresses decomposition. In this paper, we introduce various technical conditions on decomposition spaces. The first is a completeness condition (weaker than Rezk completeness), needed to control simplicial nondegeneracy. For complete decomposition spaces we establish a general Möbius inversion principle, expressed as an explicit equivalence of ∞-groupoids. Next we analyse two finiteness conditions on decomposition spaces. The first, that of locally finite length, guarantees the existence of the important length filtration for the associated incidence coalgebra. We show that a decomposition space of locally finite length is actually the left Kan extension of a semi-simplicial space. The second finiteness condition, local finiteness, ensures we can take homotopy cardinality to pass from the level of ∞-groupoids to the level of Q-vector spaces. These three conditions — completeness, locally finite length, and local finiteness — together define our notion of Möbius decomposition space, which extends Leroux's notion of Möbius category (in turn a common generalisation of the locally finite posets of Rota et al. and of the finite decomposition monoids of Cartier–Foata), but which also covers many coalgebra constructions which do not arise from Möbius categories, such as the Faà di Bruno and Connes–Kreimer bialgebras. Note: The notion of decomposition space was arrived at independently by Dyckerhoff and Kapranov [6] who call them unital 2-Segal spaces

Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory

This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences of ∞-groupoids. A decomposition space is a simplicial ∞-groupoid satisfying an exactness condition, weaker than the Segal condition, expressed in terms of active and inert maps in [Figure presented]. Just as the Segal condition expresses composition, the new exactness condition expresses decomposition, and there is an abundance of examples in combinatorics. After establishing some basic properties of decomposition spaces, the main result of this first paper shows that to any decomposition space there is an associated incidence coalgebra, spanned by the space of 1-simplices, and with coefficients in ∞-groupoids. We take a functorial viewpoint throughout, emphasising conservative ULF functors; these induce coalgebra homomorphisms. Reduction procedures in the classical theory of incidence coalgebras are examples of this notion, and many are examples of decalage of decomposition spaces. An interesting class of examples of decomposition spaces beyond Segal spaces is provided by Hall algebras: the Waldhausen S•-construction of an abelian (or stable infinity) category is shown to be a decomposition space. In the second paper in this series we impose further conditions on decomposition spaces, to obtain a general Möbius inversion principle, and to ensure that the various constructions and results admit a homotopy cardinality. In the third paper we show that the Lawvere–Menni Hopf algebra of Möbius intervals is the homotopy cardinality of a certain universal decomposition space. Two further sequel papers deal with numerous examples from combinatorics. Note: The notion of decomposition space was arrived at independently by Dyckerhoff and Kapranov [17] who call them unital 2-Segal spaces. Our theory is quite orthogonal to theirs: the definitions are different in spirit and appearance, and the theories differ in terms of motivation, examples, and directions

Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees

We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids

Development and enhancement of inclusion services at higher education level

Everyone is unique in their own way and it is necessary to embrace this diversity and make positive use of it. At all levels of education, differences between students can provide a good learning opportunity since every student will have different skills and ways of approaching the same problem. Therefore, universities need to offer education services that are conducive to learning, suitable and inclusive for each student. This will not only improve the education process of students with special needs but also lead to an improved service to all the involved stakeholders, such as professors and administrative personnel. Moreover, this can create a learning environment that favours the development of values such as respect and tolerance of diversity. Grounded in this philosophy of inclusive education, the government Board of the Universitat Politècnica de Catalunya (UPC) approved in 2016 its first Inclusion Plan for the period 2017-2020. More recently, the Government Board of the UPC prompted the creation of an ad-hoc Task Group (TG) to analyse and improve the existing inclusion services and/or design new ones using service design methodology. The TG was made up of volunteers from the UPC community, consisting of 10 students, 10 academic staff, and 10 administrative staff. They were assisted and guided by professional experts in service design. This paper reports the activities and results of the TG. The main focus of the TG was the planning, design, and development of inclusion services in higher education. These services aim at supporting the inclusion of students with physical disabilities, learning disabilities as well as any other special education needs (D/SN). The TG conducted a systematic process, based on service design methodology, which consisted of four broad phases. In the first phase, the TG carried out research into the experience, values, and practices of all the groups involved. This research was qualitative and based on several unstructured interviews of students, professors, faculty directors, students’ advisors, and administrative staff. A total of 14 students with special needs, 17 academic staff, and 13 administrative staff were interviewed. In the second phase, the interviews were analysed through four different models: user journey, stakeholders map, gaps map, and service plan. Such models are useful in order to identify and classify the possible opportunities for improvement. Furthermore, these models were presented and validated in a public meeting that was open to the whole UPC community, with a total of around 60 attendees. In the third phase, the most interesting and significant opportunities for improvement were chosen and prototypes for them were developed. The five projects that were selected for prototyping belong to the following areas: 1) information about inclusion services given to students when they enrol; 2) adaptation of examination procedures; 3) training of lecturers to assist students with disabilities or special needs; 4) information system with individualised data for students with disabilities or special needs; and 5) general academic regulations about inclusion. The last phase is iterative and involves modifying the prototypes until the service is optimum. The outcomes of this process are expected to be implemented at UPC during the 2019-20 academic year.Peer Reviewe