Note on islands in path-length sequences of binary trees

An earlier characterization of topologically ordered (lexicographic) path-length sequences of binary trees is reformulated in terms of an integrality condition on a scaled Kraft sum of certain subsequences (full segments, or islands). The scaled Kraft sum is seen to count the set of ancestors at a certain level of a set of topologically consecutive leaves is a binary tree.Comment: 4 page

Disjunctive analogues of submodular and supermodular pseudo-Boolean functions

AbstractWe consider classes of real-valued functions of Boolean variables defined by disjunctive analogues of the submodular and supermodular functional inequalities, obtained by replacing in these inequalities addition by disjunction (max operator). The disjunctive analogues of submodular and supermodular functions are completely characterized by the syntax of their disjunctive normal forms. Classes of functions possessing combinations of these properties are also examined. A disjunctive representation theory based on one of these combination classes exhibits syntactic and algorithmic analogies with classical DNF theory

Equational characterization of Boolean function classes

Cataloged from PDF version of article.Several noteworthy classes of Boolean functions can be characterized by algebraic identities (e.g. the class of positive functions consists of all functions f satisfying the identity f(x) V f(y) V f(x V y) = f(x V y)). We give algebraic identities for several of the most frequently analyzed classes of Boolean functions (including Horn, quadratic, supermodular, and submodular functions) and proceed then to the general question of which classes of Boolean functions can be characterized by algebraic identities. We answer this question for function classes closed under addition of inessential (irrelevant) variables. Nearly all classes of interest have this property. We show that a class with this property has a characterization by algebraic identities if and only if the class is closed under the operation of variable identification. Moreover, a single identity suffices to characterize a class if and only if the number of minimal forbidden identification minors is finite. Finally, we consider characterizations by general first-order sentences, rather than just identities. We show that a class of Boolean functions can be described by an appropriate set of such first-order sentences if and only if it is closed under permutation of variables. © 2000 Elsevier Science B.V. All rights reserved

POEMS neuropathy: optimising diagnosis and management

POEMS syndrome is a rare and disabling autoinflammatory condition characterised by a typical peripheral neuropathy and the presence of a monoclonal plasma cell disorder. The acronym 'POEMS' represents the complex and multisystem features of the disease, including polyneuropathy, organomegaly, endocrinopathy, a monoclonal plasma cell disorder and skin disease. The diagnosis of POEMS is a significant challenge because of the heterogeneity of clinical presentations and variation of POEMS features. Patients are often misdiagnosed with another cause of inflammatory neuropathy and receive one or more ineffective immunomodulatory medications, resulting in delayed diagnosis and further clinical deterioration before a diagnosis is made. University College London Hospitals sees one of the largest reported POEMS cohorts in Europe, and runs a multispecialist clinic to assist with diagnosis, treatment and ongoing support. This review draws upon our experience to present the typical features of POEMS syndrome and highlight diagnostic conundrums commonly experienced, supplemented with clinical cases. We provide an investigative guide for clinicians when considering POEMS as the diagnosis, and propose a treatment algorithm that centres on the site and degree of monoclonal cell proliferation

Does a Drop-in and Case Management Model Improve Outcomes for Young Adults Experiencing Homelessness: A Case Study of YouthLink

This study used two approaches to examine YouthLink as an example of a drop-in and case management model for working with youth experiencing homelessness. These approaches investigated the same group of 1,229 unaccompanied youth, ages 16 to 24 and overwhelmingly Black, who voluntarily visited or received services from YouthLink in 2011. Both approaches looked at the same metrics of success over the same time period, 2011 to 2016. One approach—Study Aim 1—examined the drop-in and case management model overall, asking whether YouthLink's service model resulted in better outcomes. It compared a YouthLink cohort with a group of highly similar youth who did not visit YouthLink but may have received similar services elsewhere. A second approach—Study Aim 2—investigated within the YouthLink cohort the ways in which YouthLink's drop-in and case-management approach worked toward achieving the desired outcomes

Osteoporosis in young adults: pathophysiology, diagnosis, and management

Postmenopausal osteoporosis is mainly caused by increased bone remodeling resulting from estrogen deficiency. Indications for treatment are based on low areal bone mineral density (aBMD, T-score ≤ −2.5), typical fragility fractures (spine or hip), and more recently, an elevated 10-year fracture probability (by FRAX®). In contrast, there is no clear definition of osteoporosis nor intervention thresholds in younger individuals. Low aBMD in a young adult may reflect a physiologically low peak bone mass, such as in lean but otherwise healthy persons, whereas fractures commonly occur with high-impact trauma, i.e., without bone fragility. Furthermore, low aBMD associated with vitamin D deficiency may be highly prevalent in some regions of the world. Nevertheless, true osteoporosis in the young can occur, which we define as a T-score below −2.5 at spine or hip in association with a chronic disease known to affect bone metabolism. In the absence of secondary causes, the presence of fragility fractures, such as in vertebrae, may point towards genetic or idiopathic osteoporosis. In turn, treatment of the underlying condition may improve bone mass as well. In rare cases, a bone-specific treatment may be indicated, although evidence is scarce for a true benefit on fracture risk. The International Osteoporosis Foundation (IOF) convened a working group to review pathophysiology, diagnosis, and management of osteoporosis in the young, excluding children and adolescents, and provide a screening strategy including laboratory exams for a systematic approach of this conditio