Finitary reducibility on equivalence relations

We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular, whereas no equivalence relation can be $\Pi_{n+2}$-complete under computable reducibility, we show that, for every $n$, there does exist a natural equivalence relation which is $\Pi_{n+2}$-complete under finitary reducibility. We also show that our hierarchy of finitary reducibilities does not collapse, and illustrate how it sharpens certain known results. Along the way, we present several new results which use computable reducibility to establish the complexity of various naturally defined equivalence relations in the arithmetical hierarchy

Complexity of equivalence relations and preorders from computability theory

We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by R\le S \iff \ex f \, \forall x, y \, [xRy \lra f(x) Sf(y)]. Here $f$ is taken from a suitable class of effective functions. For us the relations will be on natural numbers, and $f$ must be computable. We show that there is a $\Pi_1$-complete equivalence relation, but no $\Pi k$-complete for $k \ge 2$. We show that $\Sigma k$ preorders arising naturally in the above-mentioned areas are $\Sigma k$-complete. This includes polynomial time $m$-reducibility on exponential time sets, which is $\Sigma 2$, almost inclusion on r.e.\ sets, which is $\Sigma 3$, and Turing reducibility on r.e.\ sets, which is $\Sigma 4$.Comment: To appear in J. Symb. Logi

A practice-based guide for creating STEM service learning courses

This practice-based article describes two undergraduate service learning (SL) courses in STEM disciplines: economics and neuroscience. We share our experiences to encourage other instructors to develop their STEM SL courses. The top five majors by degree completion in order of popularity are computer science, economics, public policy, biology and engineering at our institution, Duke University, Durham, NC (Spicer 2023); four of these are STEM, yet they represent less than 20 percent of our SL courses (Whiteman 2023). This under-representation has resulted in fewer resources that are STEM SL- specific. The resources for SL in the social sciences are well established, but do not necessarily translate well to STEM SL courses. There are many reasons to adopt SL for STEM courses. It offers students the opportunity to give back to the community and to learn in meaningful ways outside of the classroom. As described by the American Association of Colleges & Universities (AAC&U 2022a), ‘working with community partners is good preparation for citizenship, work, and life.’ We describe two basic models, the direct and indirect SL model, and how these were used in our courses. Based on our practice-based experiences, we developed four stages for our colleagues to follow when creating their STEM SL course: (1) identify course objectives; (2) build mutually beneficial partnerships; (3) design assignments; and (4) integrate reflections. Our goal was to share the course structures we developed using these stages so that others could adopt them in their STEM disciplines

Signaling Modification by GPCR Heteromer and Its Implication on X-Linked Nephrogenic Diabetes Insipidus

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VEGF(164)-mediated inflammation is required for pathological, but not physiological, ischemia-induced retinal neovascularization

Hypoxia-induced VEGF governs both physiological retinal vascular development and pathological retinal neovascularization. In the current paper, the mechanisms of physiological and pathological neovascularization are compared and contrasted. During pathological neovascularization, both the absolute and relative expression levels for VEGF(164) increased to a greater degree than during physiological neovascularization. Furthermore, extensive leukocyte adhesion was observed at the leading edge of pathological, but not physiological, neovascularization. When a VEGF(164)-specific neutralizing aptamer was administered, it potently suppressed the leukocyte adhesion and pathological neovascularization, whereas it had little or no effect on physiological neovascularization. In parallel experiments, genetically altered VEGF(164)-deficient (VEGF(120/188)) mice exhibited no difference in physiological neovascularization when compared with wild-type (VEGF(+/+)) controls. In contrast, administration of a VEGFk-1/Fc fusion protein, which blocks all VEGF isoforms, led to significant suppression of both pathological and physiological neovascularization. In addition, the targeted inactivation of monocyte lineage cells with clodronate-liposomes led to the suppression of pathological neovascularization. Conversely, the blockade of T lymphocyte-mediated immune responses with an anti-CD2 antibody exacerbated pathological neovascularization. These data highlight important molecular and cellular differences between physiological and pathological retinal neovascularization. During pathological neovascularization, VEGF(164) selectively induces inflammation and cellular immunity. These processes provide positive and negative angiogenic regulation, respectively. Together, new therapeutic approaches for selectively targeting pathological, but not physiological, retinal neovascularization are outlined

The UN Sustainable Development Goals (SDGs): Contributions from the Humanities

It is widely agreed that achieving the United Nations Sustainable Development Goals requires the insights, knowledge and comparative perspectives of Humanities disciplines. The UNESCO Hangzhou Declaration of 2013 highlighted the importance of culture as ‘an enabler and driver of sustainable development’. Yet the Humanities have so far featured relatively little in work on the SDGs

Counting the changes of random Δ20 sets

We study the number of changes of the initial segment Zs ↾n for computable approximations of a Martin-Löf random Δ02Δ20 set Z. We establish connections between this number of changes and various notions of computability theoretic lowness, as well as the fundamental thesis that, among random sets, randomness is antithetical to computational power. We introduce a new randomness notion, called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↾n changes more than c2n times. We establish various connections with ω-c.e. tracing and omega;-c.e. jump domination, a new lowness property. We also examine some relationships to randomness theoretic notions of highness, and give applications to the study of (weak) Demuth cuppability.Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hirschfeldt, Denis R.. University of Chicago; Estados UnidosFil: Miller, Joseph S.. University of Wisconsin; Estados UnidosFil: Ng, Keng Meng. Nanyang Technological University; SingapurFil: Nies, André. The University Of Auckland; Nueva Zeland

The lived experience of recovery in borderline personality disorder: a qualitative study

BackgroundThe concept of recovery in borderline personality disorder (BPD) is not well defined. Whilst clinical approaches emphasise symptom reduction and functioning, consumers advocate for a holistic approach. The consumer perspective on recovery and comparisons of individuals at varying stages have been minimally explored.MethodFourteen narratives of a community sample of adult women with a self-reported diagnosis of BPD, were analysed using qualitative interpretative phenomenological analysis to understand recovery experiences. Individuals were at opposite ends of the recovery continuum (seven recovered and seven not recovered).ResultsRecovery in BPD occurred across three stages and involved four processes. Stages included; 1) being stuck, 2) diagnosis, and 3) improving experience. Processes included; 1) hope, 2) active engagement in the recovery journey, 3) engagement with treatment services, and 4) engaging in meaningful activities and relationships. Differences between individuals in the recovered and not recovered group were prevalent in the improving experience stage.ConclusionRecovery in BPD is a non-linear, ongoing process, facilitated by the interaction between stages and processes. Whilst clinical aspects are targets of specialist interventions, greater emphasis on fostering individual motivation, hope, engagement in relationships, activities, and treatment, may be required within clinical practice for a holistic recovery approach