Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes

Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors $\mathcal{A}$ which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, $$u_t = u_{xx} + f(x,u,u_x)\,,$$ on the unit interval $0 < x<1$ with Neumann boundary conditions. Equilibria $v_t=0$ are assumed to be hyperbolic. Geometrically, we study the resulting Thom-Smale dynamic complex with cells defined by the fast unstable manifolds of the equilibria. The Thom-Smale complex turns out to be a regular cell complex. In the first two papers we characterized 3-ball Sturm attractors $\mathcal{A}$ as 3-cell templates $\mathcal{C}$. The characterization involves bipolar orientations and hemisphere decompositions which are closely related to the geometry of the fast unstable manifolds. An equivalent combinatorial description was given in terms of the Sturm permutation, alias the meander properties of the shooting curve for the equilibrium ODE boundary value problem. It involves the relative positioning of extreme 2-dimensionally unstable equilibria at the Neumann boundaries $x=0$ and $x=1$, respectively, and the overlapping reach of polar serpents in the shooting meander. In the present paper we apply these descriptions to explicitly enumerate all 3-ball Sturm attractors $\mathcal{A}$ with at most 13 equilibria. We also give complete lists of all possibilities to obtain solid tetrahedra, cubes, and octahedra as 3-ball Sturm attractors with 15 and 27 equilibria, respectively. For the remaining Platonic 3-balls, icosahedra and dodecahedra, we indicate a reduction to mere planar considerations as discussed in our previous trilogy on planar Sturm attractors.Comment: 73+(ii) pages, 40 figures, 14 table; see also parts 1 and 2 under arxiv:1611.02003 and arxiv:1704.0034

Service Learning Across the Curriculum: A Collaboration to Promote Smoking Cessation

This paper focuses on how pedagogy, service, and scholarship can be combined across the advertising curriculum through service learning, which invigorates collaboration among faculty members, student teams, and advertising professionals. The authors demonstrate how service learning projects integrate curricula using a community-based client, ultimately leading to scholarship and professional outcomes. Specifically, this study analyzes the launch of a service learning-based smoking cessation campaign on a Midwest college campus

Abuse Experienced by Persons with Severe Mental Illness

Background: Abuse among person with severe mental illness is a serious public health concern and over the several decades researchers have focused on violence perpetrated by person with mental illness giving little consideration to the fact that severity and chronicity of mental disorder makes a person susceptible to all kinds of abuse. The current study attempts to identify three types of abuse-physical, sexual and psychological by using socio-ecological framework which takes into consideration individual, family and socio-cultural factors which acts as a risk or protective factors against abuse. Methods/Design: The study will screen severity of mental illness&nbsp;and abuse among men and women by using standardized screening tools. The first phase of the study focuses on developing risk and protective factors checklist through in-depth interviews and focused group discussions. The second phase of the study is identifying risk and protective factors of abuse by administering the checklist on 257 persons with severe mental illness. Qualitative data will be analyzed by using thematic analysis and quantitative data will be analyzed by testing for normality and accordingly using parametric and non-parametric test.&nbsp; Logistic regression model will be used to identify risk and protective factors for the abuse. Discussion: This study would help to understand abuse from ecological perspective and develop a framework for risk management by capitalizing on what people know, what they can do, where they can go and how they can utilize indigenous resources to buffer the effect of abuse

The future of electrical power grids: a direction rooted in power electronics

Electrical power grids are changing with a focus on ensuring energy sustainability and enhanced power quality for all sectors. Over the last few decades, there has been a change from a centralized to a decentralized paradigm, which is the consequence of a large-scale incorporation of new electrical technologies and resultant equipment. Considering the foreseeable continuation of changes in electrical power grids, a direction rooted in power electronics with a focus on hybrid AC/DC grids, including the support of solid-state transformers and unified systems, is presented in this paper. Converging on hybrid AC/DC grids, DC grids (structured as unipolar and bipolar) and coupled and decoupled AC configurations are analyzed. On the other hand, in the context of solid-state transformers, feasible structures are analyzed, including the establishment of hybrid AC/DC grids, and the assessment of gains for boosting power quality is presented. Unified power electronics systems are also of fundamental importance when contextualized within the framework of future power grids, presenting higher efficiency, lower power stages, and the possibility of multiple operations to support the main AC grid. In this paper, such subjects are discussed and contextualized within the framework of future power grids, encompassing highly important and modern structures and their associated challenges. Various situations are characterized, revealing a gradual integration of the cited technologies for future power grids, which are also known as smart grids.This work was supported by FCT—Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020

Signed graph embedding: when everybody can sit closer to friends than enemies

Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions, recent empirical studies have proved that they fail to reflect some current practices in real social networks. In this paper we address the issue of drawing signed graphs and capturing such social interactions. We relax the previous assumptions to define a drawing as a model in which every vertex has to be placed closer to its neighbors connected via a positive edge than its neighbors connected via a negative edge in the resulting space. Based on this definition, we address the problem of deciding whether a given signed graph has a drawing in a given $\ell$-dimensional Euclidean space. We present forbidden patterns for signed graphs that admit the introduced definition of drawing in the Euclidean plane and line. We then focus on the $1$-dimensional case, where we provide a polynomial time algorithm that decides if a given complete signed graph has a drawing, and constructs it when applicable

Why Is Liberal Peace-building So Difficult? Some Lessons from Central America

The termination of war is mostly seen as a basis not just for recovery but for a fundamental transformation or change in development paths towards peace, stability and development. The Central American peace processes of the last decades were one of the first laboratories for the liberal peace-building paradigm which assumes that the threefold transformation to peace, democracy and market economy is a self-strengthening process leading to sustainable development. Although none of the three countries slipped back into war, serious deficits remain. This paper introduces an analytical framework that aims at interrelating the threefold transformation with the impact generated by four processes. These include the repercussions generated by the international system on a country’s society, its historical, cultural and social foundations, the legacies of violence and the peacebuilding initiatives the country concerned has witnessed. The comparative analysis of changes in the public security sector, the political system, conflict resolution and the use of resources show why there is so much path dependency that can explain the deficits of transformation.Peace-building, path-dependency, public security, political system, conflict resolution, resource use, Central America

Focal adhesion is associated with lithium response in bipolar disorder: evidence from a network-based multi-omics analysis

Lithium (Li) is one of the most effective drugs for treating bipolar disorder (BD), however, there is presently no way to predict response to guide treatment. The aim of this study is to identify functional genes and pathways that distinguish BD Li responders (LR) from BD Li non-responders (NR). An initial Pharmacogenomics of Bipolar Disorder study (PGBD) GWAS of lithium response did not provide any significant results. As a result, we then employed network-based integrative analysis of transcriptomic and genomic data. In transcriptomic study of iPSC-derived neurons, 41 significantly differentially expressed (DE) genes were identified in LR vs NR regardless of lithium exposure. In the PGBD, post-GWAS gene prioritization using the GWA-boosting (GWAB) approach identified 1119 candidate genes. Following DE-derived network propagation, there was a highly significant overlap of genes between the top 500- and top 2000-proximal gene networks and the GWAB gene list (Phypergeometric = 1.28E–09 and 4.10E–18, respectively). Functional enrichment analyses of the top 500 proximal network genes identified focal adhesion and the extracellular matrix (ECM) as the most significant functions. Our findings suggest that the difference between LR and NR was a much greater effect than that of lithium. The direct impact of dysregulation of focal adhesion on axon guidance and neuronal circuits could underpin mechanisms of response to lithium, as well as underlying BD. It also highlights the power of integrative multi-omics analysis of transcriptomic and genomic profiling to gain molecular insights into lithium response in BD.publishedVersio

Focal adhesion is associated with lithium response in bipolar disorder: evidence from a network-based multi-omics analysis

Lithium (Li) is one of the most effective drugs for treating bipolar disorder (BD), however, there is presently no way to predict response to guide treatment. The aim of this study is to identify functional genes and pathways that distinguish BD Li responders (LR) from BD Li non-responders (NR). An initial Pharmacogenomics of Bipolar Disorder study (PGBD) GWAS of lithium response did not provide any significant results. As a result, we then employed network-based integrative analysis of transcriptomic and genomic data. In transcriptomic study of iPSC-derived neurons, 41 significantly differentially expressed (DE) genes were identified in LR vs NR regardless of lithium exposure. In the PGBD, post-GWAS gene prioritization using the GWA-boosting (GWAB) approach identified 1119 candidate genes. Following DE-derived network propagation, there was a highly significant overlap of genes between the top 500- and top 2000-proximal gene networks and the GWAB gene list (Phypergeometric = 1.28E–09 and 4.10E–18, respectively). Functional enrichment analyses of the top 500 proximal network genes identified focal adhesion and the extracellular matrix (ECM) as the most significant functions. Our findings suggest that the difference between LR and NR was a much greater effect than that of lithium. The direct impact of dysregulation of focal adhesion on axon guidance and neuronal circuits could underpin mechanisms of response to lithium, as well as underlying BD. It also highlights the power of integrative multi-omics analysis of transcriptomic and genomic profiling to gain molecular insights into lithium response in BD