Resolving Prime Modules: The Structure of Pseudo-cographs and Galled-Tree Explainable Graphs

The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$ is provided by its modular decomposition tree $(T,t)$ only, if $G$ is a cograph, i.e., $G$ does not contain prime modules. In this case, $(T,t)$ explains $G$, i.e., $\{x,y\}\in E(G)$ if and only if the lowest common ancestor $\mathrm{lca}_T(x,y)$ of $x$ and $y$ has label "$1$". Pseudo-cographs, or, more general, GaTEx graphs $G$ are graphs that can be explained by labeled galled-trees, i.e., labeled networks $(N,t)$ that are obtained from the modular decomposition tree $(T,t)$ of $G$ by replacing the prime vertices in $T$ by simple labeled cycles. GaTEx graphs can be recognized and labeled galled-trees that explain these graphs can be constructed in linear time. In this contribution, we provide a novel characterization of GaTEx graphs in terms of a set $\mathfrak{F}_{\mathrm{GT}}$ of 25 forbidden induced subgraphs. This characterization, in turn, allows us to show that GaTEx graphs are closely related to many other well-known graph classes such as $P_4$-sparse and $P_4$-reducible graphs, weakly-chordal graphs, perfect graphs with perfect order, comparability and permutation graphs, murky graphs as well as interval graphs, Meyniel graphs or very strongly-perfect and brittle graphs. Moreover, we show that every GaTEx graph as twin-width at most 1.Comment: 18 pages, 3 figure

The Complement of the Djokovic-Winkler Relation

The Djokovi\'{c}-Winkler relation $\Theta$ is a binary relation defined on the edge set of a given graph that is based on the distances of certain vertices and which plays a prominent role in graph theory. In this paper, we explore the relatively uncharted ``reflexive complement'' $\overline\Theta$ of $\Theta$, where $(e,f)\in \overline\Theta$ if and only if $e=f$ or $(e,f)\notin \Theta$ for edges $e$ and $f$. We establish the relationship between $\overline\Theta$ and the set $\Delta_{ef}$, comprising the distances between the vertices of $e$ and $f$ and shed some light on the intricacies of its transitive closure $\overline\Theta^*$. Notably, we demonstrate that $\overline\Theta^*$ exhibits multiple equivalence classes only within a restricted subclass of complete multipartite graphs. In addition, we characterize non-trivial relations $R$ that coincide with $\overline\Theta$ as those where the graph representation is disconnected, with each connected component being the (join of) Cartesian product of complete graphs. The latter results imply, somewhat surprisingly, that knowledge about the distances between vertices is not required to determine $\overline\Theta^*$. Moreover, $\overline\Theta^*$ has either exactly one or three equivalence classes

Preparation And Characterization Of Composite Hollow Fiber Reverse Osmosis Membranes By Plasma Polymerization. 1. Design Of Plasma Reactor And Operational Parameters

Composite hollow fiber reverse osmosis membranes were prepared by depositing a thin layer (10-50 nm) of plasma polymers on hollow fibers with porous walls (made of polysulfone). The coating was carried out in a semicontinuous manner with six strands of substrate fibers. Operational parameters which influence reverse osmosis characteristics of composite membranes were investigated. © 1984, American Chemical Society. All rights reserved

Injective split systems

A split system $\mathcal S$ on a finite set $X$, $|X|\ge3$, is a set of bipartitions or splits of $X$ which contains all splits of the form $\{x,X-\{x\}\}$, $x \in X$. To any such split system $\mathcal S$ we can associate the Buneman graph $\mathcal B(\mathcal S)$ which is essentially a median graph with leaf-set $X$ that displays the splits in $\mathcal S$. In this paper, we consider properties of injective split systems, that is, split systems $\mathcal S$ with the property that $\mathrm{med}_{\mathcal B(\mathcal S)}(Y) \neq \mathrm{med}_{\mathrm B(\mathcal S)}(Y')$ for any 3-subsets $Y,Y'$ in $X$, where $\mathrm {med}_{\mathcal B(\mathcal S)}(Y)$ denotes the median in $\mathcal B(\mathcal S)$ of the three elements in $Y$ considered as leaves in $\mathcal B(\mathcal S)$. In particular, we show that for any set $X$ there always exists an injective split system on $X$, and we also give a characterization for when a split system is injective. We also consider how complex the Buneman graph $\mathcal B(\mathcal S)$ needs to become in order for a split system $\mathcal S$ on $X$ to be injective. We do this by introducing a quantity for $|X|$ which we call the injective dimension for $|X|$, as well as two related quantities, called the injective 2-split and the rooted-injective dimension. We derive some upper and lower bounds for all three of these dimensions and also prove that some of these bounds are tight. An underlying motivation for studying injective split systems is that they can be used to obtain a natural generalization of symbolic tree maps. An important consequence of our results is that any three-way symbolic map on $X$ can be represented using Buneman graphs.Comment: 22 pages, 3 figure

Mozambique's Future: Modeling Population and Sustainable Development Challenges

What are the prospects for sustainable development over the next 20 years in Mozambique? Although it looks as if much of the development prospects are determined by such inherently unpredictable events as war, peace, and weather calamities, there are also many changes and patterns which have a long-term stability and which change only slowly over time. For example, socio-demographic changes, such as labor force skills, and population health have a long momentum. These are very important indicators for the economic development potential of a country. Also, although it is impossible to predict a particular year of heavy rains or droughts, there are long time series of weather from which we can calculate the country's vulnerability to single- or multiple-year weather disasters. To focus our efforts in answering this bold question, we concentrate on four issues: (1) Can poverty be erased in the next 20 years? (2) How will school enrollment lead to higher skills in the labor force by 2020? (3) What role will water play in development, in particular, water provision by rain to rural areas, and infrastructure to cities? (4) And, most importantly, what will be the impacts of the HIV/AIDS pandemic in the next decades

A better climate for disaster risk management

Climate-related disasters are by far the most frequent natural disasters, exacting a heavy toll on people and economies. Their frequency and economic losses have steadily increased over the past few decades, stretching the response capacities of governments and humanitarian organizations. One of the many ways this challenge can be addressed is by making more effective use of the increasing wealth of climate information and tailoring it to the needs of those who could use it, to better predict and prepare for such disasters before they occur. Written in partnership with a range of humanitarian organizations, A Better Climate for Disaster Risk Management is the third in the Climate and Society Publication series. This issue highlights recent advances in the use of climate information to manage risks and improve livelihoods, such as new partnerships and user-designed information platforms. It draws together and analyzes experiences from 17 case studies that capture the current state of knowledge. It also highlights research innovations in technical boxes throughout the publication. A problem-solving framework is used to demonstrate the challenges and opportunities facing disaster risk managers in using climate science with a three step approach: identifying the problem, developing tools, and taking action, reflected in the chapter titles. The case studies and experiences presented in this book draw on a wealth of practical experience from within the humanitarian community. They acknowledge the enormous effort and investment by very many national and local governments, international organizations, and an increasing range of other actors in the field of climate information for disaster risk management. This publication adds to the growing body of knowledge, focusing on the experiences of a number of mostly non-governmental actors, especially the International Federation of Red Cross and Red Crescent Societies, and how through partnerships, they have helped to integrate state of the art climate science and information into improved decision-making. Exploring the use of climate information for disaster risk management, it identifies both the achievements and the obstacles associated with this endeavour. From them are distilled the lessons learned, and a series of recommendations. Of these, effective partnership is highlighted as the single most critical ingredient for success. Climate information that can be acted upon is best created in dialogue between the users and providers, and partnerships between climate scientists and disaster risk managers should promote knowledge sharing, trust, and the development of innovative solutions. Efforts to better apply climate information in disaster risk management should first focus on immediate opportunities and potential ‘quick wins’. Practical engagements can be fostered by initially concentrating on countries and regions with relatively good seasonal forecast skills, and where humanitarian decisions can be influenced to provide large and immediate returns on investment. Disaster risk managers must, however, improve their understanding of the potential as well as the limitations of climate information, as the development of realistic expectations is vital to maintaining trust in the information and those who provide it. Cases demonstrate that when climate information can be integrated into existing decision-making support tools or systems, it becomes an important piece of the information that is considered and taken up in the routine activities of disaster risk managers. The relative contribution that seasonal, decadal, and long-term trends make to current and future climate also needs to be better understood. To achieve the goal of providing relevant climate services to support disaster risk management, climate information providers such as national meteorological services must tailor their information to the problem at hand, either by refining products through iterative interaction with partners or by simplifying the presentation. Although there have been many achievements and advances, much potential remains to be realized. Herein lies the opportunity: to build trust and improve the sharing of knowledge between the providers of climate services, and those who can use those services to enhance disaster risk management, jointly reducing human suffering and achieving more sustainable development

Findings of the East Africa Humanitarian Climate Risk Management Workshop

The East African humanitarian community is looking for ways to better respond to the challenges presented by climate risks, including climate change, but is struggling to access appropriate and targeted scientific data that can inform their operations. Recent advances in science and technology have produced a variety of new tools for humanitarian organizations working on climate risk management. Humanitarian actors have an enormous opportunity to utilize these tools to inform risk reduction, preparedness and contingency planning, as well as program implementation. Despite such advances, many challenges remain to the practical application of these tools in the humanitarian context. Often times, climate information is too technical or lacks the context necessary for use in humanitarian planning and operations. Thus, climate information must be tailored to specific needs and presented in formats that are readily accessible to these users. In response, the United Nations Office for the Coordination of Humanitarian Affairs (UNOCHA), in close collaboration with the International Federation of Red Cross/Red Crescent Societies (IFRC), initiated the development of a 2-day Humanitarian Climate Risk Management Workshop on 23- 24 February 2010. Initiatives that enable interaction can help to bridge the divide between humanitarian practitioners and climate experts; feedback provided by end-users can guide research and development of new prediction technologies and tools, as well as more appropriate packaging of current information. At the same time, humanitarian actors need to evaluate how such information can usefully inform their decision-making at various timescales. The challenge of decision-making under uncertainty must be addressed if climate information is to be used effectively within humanitarian planning, preparedness, and response. This workshop aimed to address such barriers to the use of climate information

Effects of Developmental Exposure to 2,2′,4,4′,5-Pentabromodiphenyl Ether (PBDE-99) on Sex Steroids, Sexual Development, and Sexually Dimorphic Behavior in Rats

Increasing concentrations of polybrominated flame retardants, including polybrominated diphenyl ethers (PBDEs), in breast milk cause concern about possible developmental effects in nursed babies. Because previous studies in rats have indicated effects on sex steroids and sexually dimorphic behavior after maternal exposure to polychlorinated biphenyls (PCBs), our goal in the present study was to determine if developmental exposure to 2,2′,4,4′,5-pentabromodiphenyl ether (PBDE-99) induces similar endocrine-mediated effects. Pregnant rats were exposed to vehicle or PBDE-99 (1 or 10 mg/kg body weight, daily during gestational days 10–18). For comparison, we also included a group exposed to the technical PCB mixture Aroclor 1254 (30 mg/kg body weight, daily). PBDE exposure resulted in pronounced decreases in circulating sex steroids in male offspring at weaning and in adulthood. Female offspring were less affected. Anogenital distance was reduced in male offspring. Puberty onset was delayed in female offspring at the higher dose level, whereas a slight acceleration was detected in low-dose males. The number of primordial/primary ovarian follicles was reduced in females at the lower dose, whereas decline of secondary follicles was more pronounced at the higher dose. Sweet preference was dose-dependently increased in PBDE-exposed adult males, indicating a feminization of this sexually dimorphic behavior. Aroclor 1254 did not alter sweet preference and numbers of primordial/primary and secondary follicles but it did affect steroid concentrations in males and sexual development in both sexes. PBDE concentrations in tissues of dams and offspring were highest on gestational day 19. These results support the hypothesis that PBDEs are endocrine-active compounds and interfere with sexual development and sexually dimorphic behavior