The forgiving tree: a self-healing distributed data structure

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that the following process continues for up to n rounds where n is the total number of nodes initially in the network: the adversary deletesan arbitrary node from the network, then the network responds by quickly adding a small number of new edges.

We present a distributed data structure that ensures two key properties. First, the diameter of the network is never more than O(log Delta) times its original diameter, where Delta is the maximum degree of the network initially. We note that for many peer-to-peer systems, Delta is polylogarithmic, so the diameter increase would be a O(loglog n) multiplicative factor. Second, the degree of any node never increases by more than 3 over its original degree. Our data structure is fully distributed, has O(1) latency per round and requires each node to send and receive O(1) messages per round. The data structure requires an initial setup phase that has latency equal to the diameter of the original network, and requires, with high probability, each node v to send O(log n) messages along every edge incident to v. Our approach is orthogonal and complementary to traditional topology-based approaches to defending against attack.

Picking up the Pieces: Self-Healing in reconfigurable networks

We consider the problem of self-healing in networks that are reconfigurable in the sense that they can change their topology during an attack. Our goal is to maintain connectivity in these networks, even in the presence of repeated adversarial node deletion, by carefully adding edges after each attack. We present a new algorithm, DASH, that provably ensures that: 1) the network stays connected even if an adversary deletes up to all nodes in the network; and 2) no node ever increases its degree by more than 2 log n, where n is the number of nodes initially in the network. DASH is fully distributed; adds new edges only among neighbors of deleted nodes; and has average latency and bandwidth costs that are at most logarithmic in n. DASH has these properties irrespective of the topology of the initial network, and is thus orthogonal and complementary to traditional topology- based approaches to defending against attack. We also prove lower-bounds showing that DASH is asymptotically optimal in terms of minimizing maximum degree increase over multiple attacks. Finally, we present empirical results on power-law graphs that show that DASH performs well in practice, and that it significantly outperforms naive algorithms in reducing maximum degree increase.

Algorithms for Self-Healing Networks

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many social networks, such as a company's organizational chart; infrastructure networks, such as an airline's transportation network; and biological networks, such as the human brain, are also reconfigurable. Modern reconfigurable networks have a complexity unprecedented in the history of engineering, resembling more a dynamic and evolving living animal rather than a structure of steel designed from a blueprint. Unfortunately, our mathematical and algorithmic tools have not yet developed enough to handle this complexity and fully exploit the flexibility of these networks. We believe that it is no longer possible to build networks that are scalable and never have node failures. Instead, these networks should be able to admit small, and maybe, periodic failures and still recover like skin heals from a cut. This process, where the network can recover itself by maintaining key invariants in response to attack by a powerful adversary is what we call \emph{self-healing}. Here, we present several fast and provably good distributed algorithms for self-healing in reconfigurable dynamic networks. Each of these algorithms have different properties, a different set of gaurantees and limitations. We also discuss future directions and theoretical questions we would like to answer. %in the final dissertation that this document is proposed to lead to.

Self-healing systems and virtual structures

Modern networks are large, highly complex and dynamic. Add to that the mobility of the agents comprising many of these networks. It is difficult or even impossible for such systems to be managed centrally in an efficient manner. It is imperative for such systems to attain a degree of self-management. Self-healing i.e. the capability of a system in a good state to recover to another good state in face of an attack, is desirable for such systems. In this paper, we discuss the self-healing model for dynamic reconfigurable systems. In this model, an omniscient adversary inserts or deletes nodes from a network and the algorithm responds by adding a limited number of edges in order to maintain invariants of the network. We look at some of the results in this model and argue for their applicability and further extensions of the results and the model. We also look at some of the techniques we have used in our earlier work, in particular, we look at the idea of maintaining virtual graphs mapped over the existing network and assert that this may be a useful technique to use in many problem domains.

Elevated Circulation Levels of an Antiangiogenic SERPIN in Patients with Diabetic Microvascular Complications Impair Wound Healing through Suppression of Wnt Signaling

Wound healing, angiogenesis and hair follicle maintenance are often impaired in the skin of diabetic patients, but the pathogenesis has not been well understood. Here, we report that circulation levels of kallistatin, a member of the serine proteinase inhibitor (SERPIN) superfamily with anti-angiogenic activities, were elevated in Type 2 diabetic patients with diabetic vascular complications. To test the hypothesis that elevated kallistatin levels could contribute to a wound healing deficiency via inhibition of Wnt/β-catenin signaling, we generated kallistatin-transgenic (KS-TG) mice. KS-TG mice had reduced cutaneous hair follicle density, microvascular density, and panniculus adiposus layer thickness as well as altered skin microvascular hemodynamics and delayed cutaneous wound healing. Using Wnt reporter mice, our results showed that Wnt/β-catenin signaling is suppressed in dermal endothelium and hair follicles in KS-TG mice. Lithium, a known activator of β-catenin via inhibition of glycogen synthase kinase-3β, reversed the inhibition of Wnt/β-catenin signaling by kallistatin and rescued the wound healing deficiency in KS-TG mice. These observations suggest that elevated circulating anti-angiogenic serpins in diabetic patients may contribute to impaired wound healing through inhibition of Wnt/β-catenin signaling. Activation of Wnt/β-catenin signaling, at a level downstream of Wnt receptors, may ameliorate the wound healing deficiency in diabetic patients.Journal of Investigative Dermatology accepted article preview online, 24 January 2014. doi:10.1038/jid.2014.40.

DEX: Self-Healing Expanders

We present a fully-distributed self-healing algorithm DEX, that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders - whose expansion properties hold deterministically - that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only probabilistic guarantees on the network expansion which rapidly degrade in a dynamic setting, in particular, the expansion properties can degrade even more rapidly under adversarial insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only O(log n) rounds and O(log n) messages are needed with high probability (n is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table (DHT) on top of DEX, with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have guaranteed properties (constant bounded degree and expansion) despite dynamic changes.

Report on the Remedying the Past, Healing for the Future Conference

Spiritual capital and democratization in Zimbabwe:A case study of a progressive charismatic congregation

Throughout Africa, charismatic Christianity has been caricatured as an inhibitor of democratization. Its adherents are said either to withdraw from the rough and tumble of politics ('pietism') or to preach a prosperity gospel that encourages believers to pour their resources into their churches in the hope that God will 'bless' them. Both courses of action are said to encourage such people to be politically quietist, with no interest in democratization or other forms of political activity. This is said to thwart democratization. This article utilizes an ethnographic case study of a 'progressive' charismatic congregation in Harare, Zimbabwe, in 2007, to provide evidence that 'pietism' and 'prosperity' are not the only options for charismatic Christianity. Drawing on the concept of 'spiritual capital', it argues that some varieties of charismatic Christianity have the resources to contribute to democratization. For example, this congregation's self-styled 'de-institutionalization' process is opening up new avenues for people to learn democratic skills and develop a worldview that is relationship-centred, participatory, and anti-authoritarian. The article concludes that spiritual capital can be a useful tool for analysing the role of religions in democratizations. It notes, however, that analysts should take care to identify and understand what variety of spiritual capital is generated in particular situations, focusing on the worldviews it produces and the consequences of those worldviews for democratization. © 2009 Taylor & Francis.

How should teaching on whole person medicine, including spiritual issues, be delivered in the undergraduate medical curriculum in the United Kingdom?

Background

Although the General Medical Council recommends that United Kingdom medical students are taught ‘whole person medicine’, spiritual care is variably recognised within the curriculum. Data on teaching delivery and attainment of learning outcomes is lacking. This study ascertained views of Faculty and students about spiritual care and how to teach and assess competence in delivering such care.

A questionnaire comprising 28 questions exploring attitudes to whole person medicine, spirituality and illness, and training of healthcare staff in providing spiritual care was designed using a five-point Likert scale. Free text comments were studied by thematic analysis. The questionnaire was distributed to 1300 students and 106 Faculty at Queen’s University Belfast Medical School.

351 responses (54 staff, 287 students; 25 %) were obtained. >90 % agreed that whole person medicine included physical, psychological and social components; 60 % supported inclusion of a spiritual component within the definition. Most supported availability of spiritual interventions for patients, including access to chaplains (71 %), counsellors (62 %), or members of the patient’s faith community (59 %). 90 % felt that personal faith/spirituality was important to some patients and 60 % agreed that this influenced health. However 80 % felt that doctors should never/rarely share their own spiritual beliefs with patients and 67 % felt they should only do so when specifically invited. Most supported including training on provision of spiritual care within the curriculum; 40-50 % felt this should be optional and 40 % mandatory. Small group teaching was the favoured delivery method. 64 % felt that teaching should not be assessed, but among assessment methods, reflective portfolios were most favoured (30 %). Students tended to hold more polarised viewpoints but generally were more favourably disposed towards spiritual care than Faculty. Respecting patients’ values and beliefs and the need for guidance in provision of spiritual care were identified in the free-text comments.

Students and Faculty generally recognise a spiritual dimension to health and support provision of spiritual care to appropriate patients. There is lack of consensus whether this should be delivered by doctors or left to others. Spiritual issues impacting patient management should be included in the curriculum; agreement is lacking about how to deliver and assess.

DEX: self-healing expanders

Incorporation of spiritual care as a component of healthcare and medical education: comparison of viewpoints of healthcare providers from a rural community hospital in Uganda with those of medical students from United Kingdrom

This study addresses cultural differences regarding views on the place for spirituality within healthcare training and delivery. A questionnaire was devised using a 5-point ordinal scale, with additional free text comments assessed by thematic analysis, to compare the views of Ugandan healthcare staff and students with those of (1) visiting international colleagues at the same hospital; (2) medical faculty and students in United Kingdom. Ugandan healthcare personnel were more favourably disposed towards addressing spiritual issues, their incorporation within compulsory healthcare training, and were more willing to contribute themselves to delivery than their European counterparts. Those from a nursing background also attached a greater importance to spiritual health and provision of spiritual care than their medical colleagues. Although those from a medical background recognised that a patient’s religiosity and spirituality can affect their response to their diagnosis and prognosis, they were more reticent to become directly involved in provision of such care, preferring to delegate this to others with greater expertise. Thus, differences in background, culture and healthcare organisation are important, and indicate that the wide range of views expressed in the current literature, the majority of which has originated in North America, are not necessarily transferable between locations; assessment of these issues locally may be the best way to plan such training and incorporation of spiritual care into clinical practice.