Computing Persistent Homology within Coq/SSReflect

Persistent homology is one of the most active branches of Computational Algebraic Topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this paper, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories

Formalized linear algebra over Elementary Divisor Rings in Coq

This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support essential operations of linear algebra, the classification theorem of finitely presented modules over such rings and the uniqueness of the Smith normal form up to multiplication by units. We present formally verified algorithms computing this normal form on a variety of coefficient structures including Euclidean domains and constructive principal ideal domains. We also study different ways to extend B\'ezout domains in order to be able to compute the Smith normal form of matrices. The extensions we consider are: adequacy (i.e. the existence of a gdco operation), Krull dimension $\leq 1$ and well-founded strict divisibility

Distributed Generation: Opportunities for Distribution Network Operators, Wider Society and Generators

This study explores and quantifies the benefits of connecting more distributed generation (with and without the use of smart connections) across different parties (Distribution Network Operators, wider society and generators). Different connection scenarios are proposed (with partial and full interruptible capacity quota, a mix of generation and different technology-specific curtailment levels) for integrating DG units in the constrained area of the March grid (East of England). This constitutes the trial area of the Flexible Plug and Play project, which is being implemented by UK Power Networks. The smart connection option is by far the preferred option across all the scenarios (higher NPV/MW). However, for some generators the results are very sensitive to the discount rate used (i.e. solar PV). The analysis of the distribution of benefits suggests that generators capture most of the benefits while DNOs and wider society capture much less benefit. A smart connection incentive, which recreates the benefits to DNOs from an earlier losses incentive, is proposed. In contrast with other societally desirable metrics which are usually incentivised or penalised, there is currently no direct connection between more DG MWs connected and DNO incentive payments. Our proposed smart connection incentive, by charging DG for smarter connection may help to distribute more efficiently the benefits for connecting more DG

The Embodiment of Relationships of Adult Facebookers

Part 2: CommunicationsInternational audienceIn the last decade we have seen a rise of social media. Within this landscape of online services Facebook plays an immense role in facilitating and creating bonds between people. In this paper we enter a qualitative study conducted with a small group of adult Facebookers over 58. We do so in an effort to understand what kind of relationships one can have through this digital media. The theoretical lens used is Phenomenology, which we find fruitful for more carefully looking into relationships between humans and technology

Platelet microparticles and hemostatic disturbances in renal insufficiency and cardiovascular disease

Background: Chronic kidney disease (CKD) affect up to 10-15% of the population worldwide and is a growing global health problem. Diabetes, hypertension and renal diseases, such as glomerulonephritis, are the major cause of CKD in high- and middle-income countries. CKD is a strong independent risk factor for cardiovascular disease (CVD) and CKD patients do worse after a cardiovascular event. This is only partially explained by traditional risk factors. Several non-traditional risk factors for CVD in CKD are becoming recognised, such as inflammation, oxidative stress, calcium-phosphate metabolism, endothelial dysfunction, malnutrition, anemia, and most recently gut microbiota, all in interplay with accumulating uremic toxins as renal function decline. Hemostatic disturbances including platelet dysfunction are well known in CKD, which is considered a prothrombotic state. However, the paradoxical simultaneous increased risk of bleeding is less understood. Microparticles (MPs) are small sized vesicles (100-1000 nm), which are shed into the circulation from various cells including platelets and endothelial cells due to different stimuli or apoptosis. MPs carry the same surface proteins as their parent cell, and MPs are both markers of disease and can induce inter-cellular cross talk. Platelet MPs (PMPs) are the most abundant MPs in the circulation, and the major significance is their procoagulant activity. MP concentrations are known to correlate with both CKD and CVD. Vitamin D deficiency and endothelial dysfunction is evident early in CKD and are associated with increased risk of CVD. Normal endothelial function is essential for maintained hemostasis. Vitamin D is involved in calcium-phosphate balance and upregulates production of nitric oxide, essential in endothelial function. Endothelial microparticles (EMPs) may have a role in assessing endothelial dysfunction. The overall objective of this PhD project was to elucidate some of the complex mechanism causing CKD patients to suffer such high risk for CVD, with focus on hemostatic disturbances, and platelet and endothelial microparticles. Methods and results: In study I, hemostasis was studied using a global assay in patients with severe CKD, patients on hemodialysis, and healthy controls The results demonstrated a prothrombotic state and an impaired fibrinolysis in severe CKD, as well as a tighter fibrin network assessed with scanning electron microscopy, despite normal concentrations of endogenous fibrinolysis in hibitors. In study II, platelet and endothelial microparticles were investigated in acute coronary syndrome (ACS) patients with and without CKD, using flow cytometry. PMPs and EMPs concentrations were elevated in severe CKD. Study III, a substudy of the SOLID randomized placebo-controlled trial, where paricalcitol treatment in CKD patients demonstrated beneficial effects on endothelial function and reduced proinflammatory cytokines. In our study, paricalcitol treatment reduced concentrations of intercellular adhesion molecule-1 (ICAM-1) positive MPs. Concentrations of cell-activation induced EMPs and PMPs were maintained in the paricalcitol group. Study IV investigated if biomarkers related to hemostasis, endothelial function and vascular regulation correlated with renal function in a large cohort of ACS patients, and determined their association with outcome in the subgroups with preserved and with reduced renal function. Biomarkers were quantified by proteomic methods. The biomarkers in ACS patients with reduced renal function indicated a prothrombotic state, with altered endothelial function and vascular regulation, and several of these were associated with outcome in this group. Conclusions: We confirm that CKD is associated with a prothrombotic state, and at the same time an impaired fibrinolysis potentially due to a tighter fibrin network. We show that in ACS patients with CKD, the MP profile indicate higher platelet activation and endothelial dysfunction compared with non-CKD patients, despite concurrent dual antiplatelet and statin treatment. We show that in CKD patients, paricalcitol treatment reduce concentrations of ICAM positive MPs, indicating a less proatherosclerotic endothelium. We found that in a large cohort of ACS patients with reduced renal function, the biomarker profile indicates a prothrombotic state. The biomarkers associated with outcome differ between patients with CKD and non-CKD. This indicate that in the field of biomarkers, it might not be sufficient to adjust for renal function. Rather, when renal failure is established, it could be regarded as a separate disease state with its own distinct pathophysiology

The Category of Iterative Sets in Homotopy Type Theory and Univalent Foundations

When working in Homotopy Type Theory and Univalent Foundations, the traditional role of the category of sets, Set, is replaced by the category hSet of homotopy sets (h-sets); types with h-propositional identity types. Many of the properties of Set hold for hSet ((co)completeness, exactness, local cartesian closure, etc.). Notably, however, the univalence axiom implies that Ob(hSet) is not itself an h-set, but an h-groupoid. This is expected in univalent foundations, but it is sometimes useful to also have a stricter universe of sets, for example when constructing internal models of type theory. In this work, we equip the type of iterative sets V0, due to Gylterud (2018) as a refinement of the pioneering work of Aczel (1978) on universes of sets in type theory, with the structure of a Tarski universe and show that it satisfies many of the good properties of h-sets. In particular, we organize V0 into a (non-univalent strict) category and prove that it is locally cartesian closed. This enables us to organize it into a category with families with the structure necessary to model extensional type theory internally in HoTT/UF. We do this in a rather minimal univalent type theory with W-types, in particular we do not rely on any HITs, or other complex extensions of type theory. Furthermore, the construction of V0 and the model is fully constructive and predicative, while still being very convenient to work with as the decoding from V0 into h-sets commutes definitionally for all type constructors. Almost all of the paper has been formalized in Agda using the agda-unimath library of univalent mathematics

Inhibited and impulsive subgroups of socially anxious young adults: Their depressive symptoms and life satisfaction

Socially anxious people are typically thought of as being behaviorally inhibited; however, an atypical subgroup, which is impulsive rather than inhibited, has recently been identified [1]. Theoretically, inhibition and impulsivity could be viewed as different strategies for coping with anxiety that have the same goal—escape from negative emotions—but they seem to have different implications. Previous studies have found that the socially anxious-impulsive subgroup was higher on risk-prone behavior, as for example drug use, compared with a socially anxious inhibited subgroup. In this study, we aimed to identify these subgroups in a general population, and asked whether they also experience various levels of depressive symptoms and life satisfaction, as well as moderating effects of gender. Methods: Cluster analysis was used to identify subgroups of young adults (20 - 24 years old; N = 772) characterized by different profiles of social anxiety and impulsivity. These subgroups were compared on levels of internal adjustment, and the moderating effects of gender were also tested. Results: We identified five clusters, including an Anxious-Inhibited and an Anxious-Impulsive cluster. In the interaction between gender and cluster membership, gender showed evidence of moderation regarding both depressive symptoms and life satisfaction, with the young women in the Anxious-Inhibited and the Anxious-Impulsive clusters faring worst. Conclusions: We replicated previous findings demonstrating the existence of a socially anxious-impulsive subgroup, thus solidifying current knowledge that may be important when it comes to diagnostics and treatment. This may prove particularly important for young women regarding internalizing symptoms

Enhancing engagement and participation of seniors in society with the use of social media - The case of a reflective participatory design method story

An ageing population is an emerging phenomenon in Europe and the rest of the world. Seniors face issues of social isolation and loneliness. Recently the research focus in ICT design has also turned to social media that can sustain seniors’ engagement and participation in social activities even when it is physically a challenge for them to leave home. Design and re-design of social media may support seniors’ engagement and participation in social activities, contributing to mitigate the feeling of loneliness and social isolation. In this paper, the focus is on understanding seniors’ social activities and their relationship to social media which may support their relationship. With Participatory Design – a reflective design approach, we have involved seniors in reflecting on possible future social media that can support and enrich social relationships. The participative methods used are cartographic mapping and future workshop, both appropriate for seniors to get involved in reflecting,thinking and making design alternatives together with other participants. We discuss how is to involve seniors in PD and what we need to know to design better future social media that can support seniors.publishedVersio