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The use of comparison functions has become standard in systems and control theory, particularly for the purposes of studying stability properties. The use of these functions typically allows elegant and succinct statements of stability properties such as asymptotic stability and input-to-state stability and its several variants. Furthermore, over the last 20 years several inequalities involving these comparison functions have been developed that simplify their manipulation in the service of proving more significant results. Many of these inequalities have appeared in the body of proofs or in appendices of various papers. Our goal herein is to collect these inequalities in one place.

Background: The previous epidemiological study of paediatric nephrolithiasis in Britain was conducted more than 30 years ago. Aims: To examine the presenting features, predisposing factors, and treatment strategies used in paediatric stones presenting to a British centre over the past five years. Methods: A total of 121 children presented with a urinary tract renal stone, to one adult and one paediatric centre, over a five year period (1997–2001). All children were reviewed in a dedicated stone clinic and had a full infective and metabolic stone investigative work up. Treatment was assessed by retrospective hospital note review. Results: A metabolic abnormality was found in 44% of children, 30% were classified as infective, and 26% idiopathic. Bilateral stones on presentation occurred in 26% of the metabolic group compared to 12% in the infective/idiopathic group (odds ratio 2.7, 95% CI 1.03 to 7.02). Coexisting urinary tract infection was common (49%) in the metabolic group. Surgically, minimally invasive techniques (lithotripsy, percutaneous nephrolithotomy, and endoscopy) were used in 68% of patients. Conclusions: There has been a shift in the epidemiology of paediatric renal stone disease in the UK over the past 30 years. Underlying metabolic causes are now the most common but can be masked by coexisting urinary tract infection. Treatment has progressed, especially surgically, with sophisticated minimally invasive techniques now employed. All children with renal stones should have a metabolic screen.

ABSTRACT Background: Evidence for a link between periodontal disease and several systemic diseases is growing rapidly. The infectious and inflammatory burden of chronic periodontitis is thought to have an important systemic impact. Current evidence suggests that periodontitis is associated with an increased likelihood of coronary heart disease and may influence the severity of diabetes. Scope: This paper represents a UK and Ireland cross-specialty consensus review, undertaken by a group of physicians and dentists. The consensus group reviewed published evidence (PubMed search for review and original articles), focusing on the past 5 years, on the contributory role of periodontal disease to overall health. In particular, evidence relating to a role for periodontal disease in cardiovascular disease and in diabetes was considered. Findings: Initial studies of large epidemiological data sets have sought to find links between periodontitis and systemic disease outcomes, but a causal relationship still needs to be demonstrated between periodontal disease, cardiovascular disease and diabetes through prospective studies. There is a need for prospective studies assessing the association between periodontal disease and patients at particular risk of cardiovascular events which will allow assessment of both cardiovascular disease clinical endpoints and surrogate markers of cardiovascular risk. Of note, periodontal disease is also often more severe in subjects with diabetes mellitus, a group at already increased risk for cardiovascular events. Conclusions: While further research is needed to define the population-attributable risk of periodontal disease to both cardiovascular diseases and to diabetes control and progression, health education to encourage better oral health should be considered as part of current healthy lifestyle messages designed to reduce the increasing health burden of obesity, cardiovascular disease and diabetes.

A central goal of evolutionary ecology is to understand the factors that select for particular life history strategies, such as delaying reproduction. For example, environmental variation and reproductive costs to survival and growth often select for reproductive delays in semelparous and iteroparous species. In this study, we examine how variation in reproductive cost, which we define as a reduction to growth, survival, or future reproduction after a reproductive event, may select for reproductive delay in an iteroparous Neotropical milkweed with no obvious reproductive season. We analyzed demographic data collected every 3 months for 3 years from four populations of Asclepias curassavica in Monteverde, Costa Rica. We detected costs of flowering to survival and growth that varied in magnitude between our 12 transition periods without a seasonal pattern. The populations also exhibited temporal variation in reproductive payoffs measured as seedling establishment. We incorporated these reproductive costs into demographic projection models, which predicted a delayed flowering strategy only when we included temporal variation in costs and payoffs. Temporal variation in reproductive costs and payoffs is an important selective force in the evolution of delayed flowering in iteroparous species. Further, a lack of predictable seasonal pattern to reproductive costs and payoffs may contribute to the lack of seasonal reproductive patterns observed in our study species and other Neotropical species.

Epidermal homeostasis depends on the coordinated control of keratinocyte cell cycle. Differentiation and the alteration of this balance can result in neoplastic development. Here we report on a novel DLX3-dependent network that constrains epidermal hyperplasia and squamous tumorigenesis. By integrating genetic and transcriptomic approaches, we demonstrate that DLX3 operates through a p53-regulated network. DLX3 and p53 physically interact on the p21 promoter to enhance p21 expression. Elevating DLX3 in keratinocytes produces a G1-S blockade associated with p53 signature transcriptional profiles. In contrast, DLX3 loss promotes a mitogenic phenotype associated with constitutive activation of ERK. DLX3 expression is lost in human skin cancers and is extinguished during progression of experimentally induced mouse squamous cell carcinoma (SCC). Reinstatement of DLX3 function is sufficient to attenuate the migration of SCC cells, leading to decreased wound closure. Our data establish the DLX3–p53 interplay as a major regulatory axis in epidermal differentiation and suggest that DLX3 is a modulator of skin carcinogenesis.

In analysis and design of nonlinear dynamical systems, (nonlinear) scaling of Lyapunov functions has been a central idea. This paper proposes a set of tools to make use of such scalings and illustrates their benefits in constructing Lyapunov functions for interconnected nonlinear systems. First, the essence of some scaling techniques used extensively in the literature is reformulated in view of preservation of dissipation inequalities of integral input-to-state stability (iISS) and input-to-state stability (ISS). The iISS small-gain theorem is revisited from this viewpoint. Preservation of ISS dissipation inequalities is shown to not always be necessary, while preserving iISS which is weaker than ISS is convenient. By establishing relationships between the Legendre–Fenchel transform and the reformulated scaling techniques, this paper proposes a way to construct less complicated Lyapunov functions for interconnected systems.

Key Points Provides overview of possible aetiology of gingival overgrowth. Discusses history and key clinical features which aid in diagnosis. Discussion of systemic disease which may contribute to gingival overgrowth Most commonly, gingival overgrowth is a plaque-induced inflammatory process, which can be modified by systemic disease or medications. However, rare genetic conditions can result in gingival overgrowth with non-plaque-induced aetiology. It is also important to appreciate the potential differential diagnoses of other presentations of enlarged gingival tissues; some may be secondary to localised trauma or non-plaque-induced inflammation and, albeit rarely, others may be manifestations of more sinister diseases or lesions. A definitive diagnosis will then enable an appropriate management strategy. This paper aims to discuss clinical features and diagnoses for conditions presenting with gingival overgrowth and other enlargements of gingival tissues.

The management of spinal cord ependymomas in Neurofibromatosis Type 2 (NF2) has traditionally been conservative, in contrast to the management of sporadic cases; the assumption being that, in the context of NF2, they did not cause morbidity. With modern management and improved outcome of other NF2 tumours, this assumption, and therefore the lack of role for surgery, has been questioned. To compare the outcome of conservative treatment of spinal ependymomas in NF2 with surgical intervention in selected patients. Retrospective review at two NF2 centers, Manchester, UK and Paris/Lille, France. In Manchester patients were managed conservatively. In France surgery was a treatment option. Inclusion in the study was based on tumor length of greater than 1.5 cm. The primary parameter assessed was acquired neurological deficit measured by the Modified McCormick Outcome Score. 24 patients from Manchester and 46 patients from France were analyzed. From Manchester, 27% of these patients deteriorated during the course of follow-up. This effectively represents the natural history of ependymomas in NF2. Of the surgical cases, 23% deteriorated postoperatively, but only 2/18 (11%) of those operated on in the NF2 specialist centers. Comparison of the two specialist centers Manchester/France showed a significantly improved outcome (P = 0.012, χ2 test) in the actively surgical center. Spinal ependymomas produce morbidity. Surgery can prevent or improve this in selected cases but can itself can produce morbidity. Surgery should be considered in growing/symptomatic ependymomas, particularly in the absence of overwhelming tumor load where bevacizumab is the preferred option.

Key Points Suggests that gingival overgrowth management requires a structured approach including preventative, non-surgical cause-related therapy and in some cases surgical interventions. Highlights that failure of cause-related treatment to eliminate aesthetic, functional and speech related complications of gingival overgrowth is likely to indicate surgical intervention. Demonstrates that surgical techniques may include a gingivectomy or apically repositioned flap. Suggests that a variety of techniques may be used to perform a gingivectomy including scalpel, electrosurgery and laser methods. The effective and predictable management of gingival overgrowth requires correct diagnosis and consideration of aetiological factors, as discussed in Part 1 ( BDJ 2017; 222: 85–91 ). Initial management should involve cause-related therapy, which may resolve or reduce the lesion. If functional, aesthetic and maintenance complications persist following this phase; further treatment may be required in the form of surgery. This paper discusses management strategies, including management of aetiological factors and surgical techniques.

Conservation management for environmental sustainability is now ubiquitous. The ecological effects of these actions are well-intentioned and well-known. Although conservation biologists and managers increasingly incorporate evolutionary considerations into management plans, the evolutionary consequences of management strategies have remained relatively unexplored and unconsidered. But what are the evolutionary consequences? Here, we advocate a new research agenda focused on identifying, predicting, and countering the evolutionary consequences of conservation management. We showcase the examples of park creation and invasive species management, and speculate further on five other major methods of management. Park creation may cause selection for altered dispersal and behavior that utilizes human foods and structures. Management of invasive species may favor the evolution of resistance to or tolerance of control methods. In these and other cases, evolution may cause deviations from the predicted consequences of management strategies optimized without considering evolution, particularly when management results in or coincides with major environmental change, if population size change strongly, or if life histories are short enough to allow more rapid evolution. We call for research focused on: (1) experimental predictions and tests of evolution under particular management strategies, (2) widespread monitoring of managed populations and communities, and (3) meta-analysis and theoretical study aimed at simplifying the process of evolutionary prediction, particularly at systematizing a means of identifying traits likely to evolve due to likely existing genetic variance or high mutation rates. Ultimately, conservation biologists should incorporate evolutionary prediction into management planning to prevent the evolutionary domestication of the species that they are trying to protect.