Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

On the gradient set of Lipschitz maps

We prove that the essential range of the gradient of planar Lipschitz maps has a connected rank-one convex hull. As a corollary, in combination with the results in [Faraco, D., and Székelyhidi, Jr., L., Tartar's conjecture and localization of the quasiconvex hull in R2x2, Acta Math., to appear.] we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rank-one convexit

INSTITUTIONAL FACTORS IN HEALTH DISPARITIES

The purpose of this dissertation is to address institutional factors that may be the root cause of health disparities. Misdirected resources may help to explain why health disparities have actually increased as targeted interventions aimed at their elimination have proliferated. This dissertation examines the impacts of potential causal mechanisms on health disparities in a low-socioeconomic status population. Rather than simply reporting descriptive statistics of populations in which health disparities exist, policies can be formulated that begin to address these causal mechanisms and eliminate health disparities if closer attention is paid to the fundamental causes of health disparities. Two institutional variables are examined in the two chapters of this dissertation: transportation access to mental health services and relative health as measured by the health of proximate individuals. The theory of relative health was developed specifically for this dissertation. Data from the 2012 Consumer Assessment of Healthcare Providers and Systems and the 2012 5-year estimates from the U.S. Census American Community Survey were used

Multimodal image analysis of the human brain

Gedurende de laatste decennia heeft de snelle ontwikkeling van multi-modale en niet-invasieve hersenbeeldvorming technologieën een revolutie teweeg gebracht in de mogelijkheid om de structuur en functionaliteit van de hersens te bestuderen. Er is grote vooruitgang geboekt in het beoordelen van hersenschade door gebruik te maken van Magnetic Reconance Imaging (MRI), terwijl Elektroencefalografie (EEG) beschouwd wordt als de gouden standaard voor diagnose van neurologische afwijkingen. In deze thesis focussen we op de ontwikkeling van nieuwe technieken voor multi-modale beeldanalyse van het menselijke brein, waaronder MRI segmentatie en EEG bronlokalisatie. Hierdoor voegen we theorie en praktijk samen waarbij we focussen op twee medische applicaties: (1) automatische 3D MRI segmentatie van de volwassen hersens en (2) multi-modale EEG-MRI data analyse van de hersens van een pasgeborene met perinatale hersenschade. We besteden veel aandacht aan de verbetering en ontwikkeling van nieuwe methoden voor accurate en ruisrobuuste beeldsegmentatie, dewelke daarna succesvol gebruikt worden voor de segmentatie van hersens in MRI van zowel volwassen als pasgeborenen. Daarenboven ontwikkelden we een geïntegreerd multi-modaal methode voor de EEG bronlokalisatie in de hersenen van een pasgeborene. Deze lokalisatie wordt gebruikt voor de vergelijkende studie tussen een EEG aanval bij pasgeborenen en acute perinatale hersenletsels zichtbaar in MRI

ATTITUDES TOWARD GREEN INFRASTRUCTURE STRATEGIES FOR MORE LIVABLE AND SUSTAINABLE COMMUNITIES

Green infrastructure refers to multi-functional elements that integrate ecological and anthropogenic factors and processes to support healthy ecosystems and communities (Austin, 2014; Benedict & McMahon, 2002). While green infrastructure has been embraced by planners, there is not a great deal of research among planners regarding the public\u27s attitudes towards green land uses at the individual level. The dissertation studies explored three urban green infrastructure strategies: residential tree canopy, neighborhood green space, and community gardens; at the scale of user preferences and experiences. The first study (Chapter 3) used photo preference methodology to explore the tension between residential density and urban greening. Study results suggested several aspects of neighborhood spatial form associated with higher preference by study participants (n=212): a green canopy and neighborhood greening; a vegetative buffer between housing and street; and a provision of sense of privacy by building form and vegetation. The second study (Chapter 4) used descriptive analysis for a participatory planning and design activity to imagine an “ideal neighborhood”, as part of a larger study on urban ecology within a family science museum. Study results suggested that participants (n=172), many of whom were children, highly preferred green space as compared to other land uses when constructing imaginary neighborhoods. The project also explored engaging children in participatory planning within a museum setting and the use of this activity beyond the museum. The third study (Chapter 5) contributes to scholarship about the attitudes and experiences of community gardeners within an urban garden network. Results from the study suggest that for participants (n=112), community gardens provided a setting to engage with neighbors and build community based on a shared interest. Attachment to place and people grew from these interactions, which, for many, motivated ongoing involvement in the garden and community. The complexities of creating healthier, sustainable and adaptive urban settings makes it critical to engage urban populations in green infrastructure responses. Green spaces and elements are important to people and failure to provide the multiple benefits of access to nature in the city for all communities can have substantial costs to health as well as overall quality of life

Towards Urban Resilience - Proceedings - International Workshop - Barcelona 2017

The complexity of urban systems and the uncertainty of the impact of urbanization and climate change ask for new ways of thinking about planning objectives and solidarity in action. Cities are complex, adaptive systems of networked services and infrastructures. Growing urban populations, the concentration of resources and capital, unclear contingency planning, the often inadequate and environmentally unsound water supply and sewage management, the menacing continual destruction of ecosystems, and out-dated infrastructures and buildings, all present massive challenges to city planning. With the goal of strengthening resilience, there has been a lasting change of perspective in planning. The scope has been broadened from a specialized viewpoint to an interdisciplinary understanding of interactions and processes within the cityscape. Resilience is an anticipatory principle that transcends risk reduction and attempts to mitigate the effects of system failures while increasing capacities. The overall aim is to combine resilience strategies and sustainability by: i) enhancing sustainable urbanization ii) improving ecosystems and nature-based solutions iii) developing climate change adaptation and mitigation iv) strengthening community-based approaches and social resilience Developing a network is an important step to promote resource-sensitive urban design and enable educational and professional shift towards resilience and sustainability. Thus, the International Workshop at UIC Barcelona in cooperation with UN-Habitat’s City Resilience Profiling Programme (CRPP) and TU Darmstadt will offer the possibility to bring innovative ideas on resilience to discussion. The joint research hub, Urban Resilience Institute (URI), in cooperation with UN-Habitat CRRP aims to analyse practices and processes in the design of resilient and sustainable cities. The hub will gather young researchers from the European Joint Doctorate Programme within the Mundus Urbano Consortium, and from the Fellowship Programme on “Urban Infrastructures in Transition: The Case of African Cities,” as well as the research group on Critical Infrastructures at TU Darmstadt. Currently working from academic institutions based in Europe, researchers from Germany, India, Italy, Kenya, Lebanon, Uganda, and Spain, will present their research projects in four sessions covering the topics of: critical infrastructures, resource-sensitive urban design, housing and land management, and post-crisis emergency reconstruction; opening for discussion on conceptional approaches “towards urban resilience” with international researchers, Master- and PhD-students. Sessions: A_Critical Infrastructures: As the dependency on technology increases, there is a growing need to reflect on the role of infrastructures to sustain human activities. Infrastructures are critical for the functioning of society, not only as the physical components in cities, or ‘hardware,’ but also as structures embedded with the intangible essence of human groups and our understanding of them in specific contexts and throughout time. B_Resource-sensitive Urban Design: In face of rapid urbanization and the negative impacts of climate change on natural and built environments, this session calls analysis of practices and processes of resource-sensitive urban design. Urban design can contribute towards an educational and professional shift towards resilience and sustainability by focusing on integrative approaches, such as district-based networks, low-impact approaches, and climate-adaptive planning and building. C_Resilience and Multi-level Governance: This session seeks cross-scalar and multi-level frameworks which help in understanding cities as complex and adaptive systems. Contributions should problematize urbanization processes and include tools and strategies which explain scalar arrangements of nature and power. The role of international and global frameworks will deem necessary in laying the base for transition and transformation of cities, and to contribute to the development of urban resilience. D_Post-Crisis Emergency Reconstruction and Upgrading: This session aims at understanding refugee camps as a form of urbanization and sets the basis for rethinking camp design and their temporality. Contributions should bridge social structures and their physical transformations, as a means for their integral regeneration. This session looks at examples where resilience in the social fabric of informal settlements and low housing estates can create a sense of belonging and act as a force for their physical upgrading

Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

Social outcomes of community-based rangeland management in post-socialist Mongolia: Influential factors and favorable institutional designs

Includes bibliographical references.2015 Summer.Community-based rangeland management (CBRM) has been proposed as a promising option to reduce rural poverty and resource degradation in post-socialist Mongolia. To date, research on CBRM in Mongolia has been limited to small samples and case studies within one or two ecological zones. Results have been mixed, with some studies showing favorable outcomes and others no effect or negative impacts of CBRM. Few studies have directly compared the outcomes of formally organized CBRM with management by traditional herder neighborhood groupings, or attempted to identify the causal mechanisms that explain variations in CBRM outcomes. Using data from 142 pastoral groups and 706 member households across 36 counties (soum) in four ecological zones, I assessed social outcomes of CBRM organizations in comparison with non-CBRM groups, explored causal mechanisms underlying these social outcomes, and examined the effects of external facilitation on institutional design of formal CBRM organizations. I found that formal groups had more information sources, stronger leadership, greater knowledge exchange, cooperation and more rules. Members of formal groups were more proactive in addressing resource management issues and used more rangeland practices than traditional neighborhoods. However, the two types of groups did not differ on most livelihood measures and had a weak difference in social capital. Four factors, access to diverse information sources, leadership, knowledge exchange and resource management rules, significantly facilitated the effect of formal organization on pastoralists’ traditional and innovative rangeland practices, proactive behavior and social networks. Importantly, information diversity had a triggering effect on other three mediating variables creating a sequential chain of information diversity leadership knowledge exchange rules. This ordered chain of four mediators explains the mechanisms through which formal organization leads to comparatively greater social outcomes. I also found that these mediated effects on members’ proactive behavior and social networking varied among ecological zones. Donor facilitation approach significantly influenced CBRM group attributes and external environments, but did not affect institutional arrangements. Small group size, homogeneous interests, and heterogeneity of well-being predicted higher levels of intermediate outcomes including information diversity, leadership, and income diversity. Institutional arrangements such as the presence of sanctions, group-devised rules, frequent meetings, and recording documents increased cooperation, rules and information diversity. Similarly, access to training and local government support provided a favorable external environment for achieving intermediate outcomes. Regarding ultimate social outcomes, group characteristics such as dependence on livestock, homogeneity of interests and leader legitimacy were critical for increasing social capital, livelihoods, rangeland practices, and proactive behavior. Frequent meetings of group leaders had the greatest influence on ultimate social outcomes. Local government support and ongoing donor support were associated with increased trust and norms of reciprocity, rangeland management practices, proactiveness, and per capita livestock holdings. Overall, group attributes and external environment had a greater influence on social outcomes of pastoral CBRMs in Mongolia than institutional arrangements. I found strong evidence that formal CBRM is leading to increased social outcomes across Mongolia. Many CBRM facilitation strategies were shown to be adequate for fostering social outcomes of the pastoral groups. Early achievements of individual household level variables such as rangeland practices and behavior appeared to be “fast” variables that respond quickly to new institutions. In contrast, building social capital and reaching livelihood improvement may be “slow” variables that require time and larger scale changes. Globally, the promising case of CBRM in Mongolia may encourage mobile pastoral communities elsewhere to cooperate on the sustainable management of their resources. However, as this study showed, careful facilitation is needed to achieve intermediate outcomes, and consideration of the distinct dynamics of local resource systems is a necessary prerequisite for achieving increased social outcomes