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.

The mend of the bend-flexor pollicis longus tendon has an additional pulley distal to its point of angulation

The tendon of flexor pollicis longus angulates at the trapezio-metacarpal joint level. The degree of angulation varies with extent of radial/ulnar deviation (Rack and Ross [1984] J. Physiol. 351:99–110). We report a fibrous pulley at this level that helps stabilize the tendon and facilitates its action. The morphology of the pulley is described. We believe that it has an important role to play in the unique function of the tendon facilitating the movement of the thumb perpendicular to the plane of the thumbnail. Clin. Anat. 21:427–432, 2008. © 2008 Wiley-Liss, Inc

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

DEX: self-healing expanders

The role of LL-37 in periodontal wound healing

Introduction: As a result of chronic inflammation during periodontal disease the junctional epithelium becomes micro-ulcerated. The inflammatory process is mediated by both bacterial and host cell products. Host defence peptides such as defensins, secretory leucocyte protease inhibitor (SLPI) and the sole human cathelicidin, LL-37, are secreted by both periodontal cells and neutrophils into gingival crevicular fluid (GCF). They have the ability to modulate the immune response in periodontitis and are thought to have a potential role in periodontal wound healing. Objectives: The aims of this study were to determine the role of LL-37 in the production of Interleukin (IL)-8, IL-6, hepatocyte growth factor (HGF) and basic-fibroblast growth factor (bFGF) by gingival fibroblasts. The role of LL-37 in modulating total matrix metalloproteinase (MMP) activity and expression of tissue inhibitors of metalloproteinase (TIMP)-1 and -2 by gingival fibroblasts was also investigated. Methods: Primary gingival fibroblasts were co-cultured with concentrations of LL-37 (1, 5 and 10µg/ml) for 24 hours and their supernatants tested for levels of IL-8 and IL-6, HGF, bFGF, TIMP-1 and TIMP-2 by ELISA. Rates of MMP turnover in the supernatants were tested by fluorogenic assay using fluorescence resonance energy transfer (FRET) peptide substrates. Cytotoxicity was measured by MTT assay. Statistical significance was measured using the independent t-test and p<0.05 was considered significant. Results: LL-37 significantly upregulated levels of IL-8, IL-6, HGF, bFGF and TIMP-1 (p<0.05) in a dose-dependent fashion. LL-37 significantly decreased the total MMP activity (p<0.05). None of the LL-37 concentrations tested were cytotoxic to gingival fibroblasts. Conclusion: These results indicate that LL-37 is involved in periodontal wound healing. LL-37 increased levels of proinflammatory cytokines and increased levels of growth factors involved in re-epithelialisation. LL-37 has the ability to regulate remodelling of the periodontium by controlling MMP overactivity both directly and by stimulating production of inhibitors by gingival fibroblasts.

Compact Routing Messages in Self-Healing Trees

Existing compact routing schemes, e.g., Thorup and Zwick [SPAA 2001] and Chechik [PODC 2013], often have no means to tolerate failures, once the system has been setup and started. This paper presents, to our knowledge, the first self-healing compact routing scheme. Besides, our schemes are developed for low memory nodes, i.e., nodes need only O(log2 n) memory, and are thus, compact schemes.
We introduce two algorithms of independent interest: The first is CompactFT, a novel compact version (using only O(log n) local memory) of the self-healing algorithm Forgiving Tree of Hayes et al. [PODC 2008]. The second algorithm (CompactFTZ) combines CompactFT with Thorup-Zwick’s treebased compact routing scheme [SPAA 2001] to produce a fully compact self-healing routing scheme. In the self-healing model, the adversary deletes nodes one at a time with the affected nodes self-healing locally by adding few edges. CompactFT recovers from each attack in only O(1) time and ∆ messages, with only +3 degree increase and O(log∆) graph diameter increase, over any sequence of deletions (∆ is the initial maximum degree).
Additionally, CompactFTZ guarantees delivery of a packet sent from sender s as long as the receiver has not been deleted, with only an additional O(y log ∆) latency, where y is the number of nodes that have been deleted on the path between s and t. If t has been deleted, s gets informed and the packet removed from the network.

Conversations with remarkable teachers an exploration of teaching as healing

Through analysis and interpretation of transcribed taped conversations with two remarkable University teachers, Joel Shack and Harry Whittier, an articulation of perception and metaphor that exists in effective teaching, emerges as life giving or transformational. Creative insight and interpretation connect teaching to life. This work demonstrates how insightful conversations about teaching relate to poetic essence (Joel), energy (Harry), and healing (Ray), all aspects of a similar perceptual, creative and transformative process. Teachers shape education and excellent teaching inspires insofar as it is inspirited. Effective teaching is highly conscious and intentional. So much depends on how aware the teacher is, how the teacher sees what s/he is doing and how this doing/teaching is received. The effective teacher, attentive to how this energy works, can provoke positive change in consciousness both in the student, in education and in society. My study draws attention to the healing power of the teacher as he/she teaches and to the process of dialogue as teachers talk about what they do and don't do. For inherent in conversation and dialogue is the desire to affirm whole perceptions of existence. Dialogue and conversation is necessary to creating the kind of consciousness that will aid the reflective and conscientious teacher. The effective teacher attempts to effect change, to make things better. I call this transforming process, healing. And what creates this healing is the life, the attitude and approach of the teacher. The teacher's energy and consciousness, the teacher's perception of meaning, is the active but implicit ingredient in this transformative and healing process. These conversations are creative, theoretical, illuminating and even practical. It is my hope that the contents of these conversations will inspire potential teachers who can consider the vocation of teaching as a healing process that promises to generate positive growth in mind, body and spirit.

Managing Stress and Pain to Prevent Patient Discomfort, Distress and Delayed Wound Healing.

Evidence suggests stress slows the healing of wounds but pain may also play a part. Regular assessment could improve patients' quality of life and recovery time.

Tissue healing of immediate implant placement in extraction sockets with titanium versus zirconium oxide implants : an experimental study in the beagle dog

Tese de doutoramento, Medicina Dentária (Periodontologia), Universidade de Lisboa, Faculdade de Medicina Dentária, 2016

Wound healing and cancer progression in Opisthorchis viverrini associated cholangiocarcinoma

Letter to the editor