Space Of Connections Research Articles

Langevin dynamic for the 2D Yang–Mills measure

We define a natural state space and Markov process associated to the stochastic Yang–Mills heat flow in two dimensions.To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric.To construct the Markov process we show that the stochastic Yang–Mills heat flow takes values in our space of connections and use the “DeTurck trick” of introducing a time dependent gauge transformation to show invariance, in law, of the solution under gauge transformations.Our main tool for solving for the Yang–Mills heat flow is the theory of regularity structures and along the way we also develop a “basis-free” framework for applying the theory of regularity structures in the context of vector-valued noise – this provides a conceptual framework for interpreting several previous constructions and we expect this framework to be of independent interest.

Two Invariants for Geometric Mappings

Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection.

‘What matters what makes us gay?’ Affective failure in a social justice classroom

ABSTRACT This article focuses on the dynamics at play in a challenging lesson observed during the LGBTQ unit in a social justice-focused high school course. On the surface, the lesson was a chaotic struggle involving a tense intergenerational clash between the teacher and an outspoken group of students. Young people interrupted and refused the teacher’s lesson plan. In response, the teacher raised his voice and consistently tried to redirect the students back to his priorities for the unit. In this article, I am interested in how the teacher and the students were limited in their engagement with each other by the distances imposed by the adult/youth binary that remains so central to schooling. This constraint participated in the failure of this lesson and, most importantly, the failure to communicate across divided understandings of queerness. Drawing on Quinlivan’s framework of affective failure, I rethink the possibilities of this lesson, and the teacher/student relationship involved, through the three facets of affective failure: the queer art of failure; affective silences; and engaging otherwise. I seek to explore what relationships, pedagogical and otherwise, could become possible if we reject imposed hierarchies and make space for affective connection in the classroom.

Tangible and intangible spaces of community connectivity

This forum is dedicated to exploring the notion of meaningfulness in design processes, taking the perspectives of community groups, nongovernmental organizations, and those who are marginalized in society as starting points. Authors will reflect conceptually and methodologically on practical engagements. --- Rosanna Bellini and Angelika Strohmayer, Editors

Experimental investigation and design considerations on cold-formed steel built-up​ I-section columns subjected to interactive buckling modes

An experimental investigation into the behavior of cold-formed steel (CFS) built-up column assembly compressed between fixed ends is presented in this paper. The built-up column assembly is designed to be doubly symmetric and locally slender to study the interactive buckling mode of failures. A total of forty-one columns were tested including different cross-section dimensions, lengths, intermediate connection spacing, and slendernesses. It is experimentally shown that the back-to-back connected doubly symmetric built-up cross-section assembly columns fail predominantly in interactive local and flexural–torsional buckling due to the shift in the line of action of the internal force caused by local buckling deformations. The influence of intermediate fastener spacing was also prevalent in the failure modes of the doubly symmetric CFS built-up columns. The appropriateness of the AISI’s maximum intermediate connection spacing limitation is verified to prevent global instability failures. The test and design results comparison indicated that the current AISI’s DSM design curve for interactive buckling is unconservative for the CFS built-up columns with predominant interactive local–global failure mode vulnerability. Therefore, a modified design curve for interactive buckling is suggested based on the test results with reliability analysis.

Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

In this paper, we treat moduli spaces of parabolic connections. We take an affine open covering of the moduli spaces, and we construct a Hamiltonian structure of an algebraic vector field determined by the isomonodromic deformation for each affine open subset.

Mechanical behavior of GFRP-bamboo composite shear connections

Sustainable development has become an important and urgent topic for civil engineering. More and more green and renewable materials, like engineered bamboo, have been designed to work with other traditional building materials to utilize the ecological benefit and mechanical advantages. Nonetheless, few researches investigated the mechanical performance of the composite structure made of fiber-reinforced polymer and engineered bamboo. A new composite connection made of pultruded H-section glass fiber-reinforced polymer (GFRP) profile and engineered bamboo was proposed and studied by push-out tests to assess the shear performance. A total of 46 specimens with bolted, glue or hybrid connectors were tested to investigate the influence of the connection type, bolt diameter and spacing, as well as the bamboo thickness, on the strength and stiffness of GFRP-bamboo connections. The load-carrying capacity and shear stiffness were analyzed, and three types of failure modes were identified. When the bamboo thickness was 17 mm and 20 mm, a single plastic hinge was formed in the shear connectors, and the bamboo panels performed splitting and edge crushing failures. When the bamboo thickness was 34 mm and 40 mm, two plastic hinges formed in the connectors with embedment failure in the bamboo panels. Nonetheless, when using glue connection, brittle and undesirable failure occurred. When increasing the bamboo thickness from 17 mm to 34 mm, the average peak load increased from 67.52 kN to 100.64 kN, and the yield and ultimate loads both increased by about 49%. In addition, the results showed that hybrid connections were more effective than bolted and glue connections. The average peak load of hybrid connections increased by 42.72% and 13.16% compared to that connected with glue and bolts, respectively. The experimental results were compared with those calculated according to Eurocode 5-1995 and GB/T50005-2017, and it could be concluded that the formulas of the codes were not suitable for such shear connections due to the conservative design. To predict the nonlinear behavior of the specimens, the theoretical model based on Foschi formula was built. The analytical predictions showed good agreement with the test results in case of bolted connections. In a word, the shear performance and theoretical model of the proposed composite shear connections make it possible to predict the bending strength and stiffness of GFRP-bamboo composite beams, but the sharp drop of load-carrying capacity induced by the failure of glue connection needs more consideration and research.

Line bundles on the moduli space of parabolic connections over a compact Riemann surface

Let X be a compact Riemann surface of genus g≥3 and S a finite subset of X. Let ξ be fixed a holomorphic line bundle over X of degree d. Let Mpc(r,d,α) (respectively, Mpc(r,α,ξ)) denote the moduli space of parabolic connections of rank r, degree d and full flag rational generic weight system α, (respectively, with the fixed determinant ξ) singular over the parabolic points S⊂X. Let Mpc′(r,d,α) (respectively, Mpc′(r,α,ξ)) be the Zariski dense open subset of Mpc(r,d,α) (respectively, Mpc(r,α,ξ)) parametrizing all parabolic connections such that the underlying parabolic bundle is stable. We show that there is a natural compactification of the moduli spaces Mpc′(r,d,α), and Mpc′(r,α,ξ) by smooth divisors. We describe the numerically effectiveness of these divisors at infinity. We determine the Picard group of the moduli spaces Mpc(r,d,α), and Mpc(r,α,ξ). Let C(L) denote the space of holomorphic connections on an ample line bundle L over the moduli space M(r,d,α) of parabolic bundles. We show that C(L) does not admit any non-constant algebraic function.

Deformation Theory of Deformed Hermitian Yang–Mills Connections and Deformed Donaldson–Thomas Connections

A deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a $G_2$-manifold $X$ satisfying a certain nonlinear PDE. This is considered to be the mirror of a (co)associative cycle in the context of mirror symmetry. The dDT connection is an analogue of a deformed Hermitian Yang-Mills (dHYM) connection which is extensively studied recently. In this paper, we study the moduli spaces of dDT and dHYM connections. In the former half, we prove that the deformation of dDT connections is controlled by a subcomplex of the canonical complex, an elliptic complex defined by Reyes Carri\'on, by introducing a new coclosed $G_2$-structure. If the deformation is unobstructed, we also show that the connected component is a $b^{1}$-dimensional torus, where $b^{1}$ is the first Betti number of $X$. A canonical orientation on the moduli space is also given. We also prove that the obstruction of the deformation vanishes if we perturb the $G_2$-structure generically under some mild assumptions. In the latter half, we prove that the moduli space of dHYM connections, if it is nonempty, is a $b^{1}$-dimensional torus, especially, it is connected and orientable. We also prove the existence of a family of moduli spaces along a deformation of underlying structures if some necessary conditions are satisfied.

The Winter Garden: Sarah Ruhl's In the Next Room and the Dialectic Deconstruction of Separate Spheres

Sarah Ruhl's In the Next Room (2009) breaks down the nineteenth-century dichotomy of public and private spheres. Catherine Givings exists in her parlor, which is separated from her husband's operating theatre where he treats hysteria patients by inducing orgasms with electric vibrators. Following much feminist dramatic precedent, Catherine is trapped in the domestic sphere, unable to make meaningful relationships. The private space of the parlor and the public (in its association with medical science) operating theatre interpenetrate one another, compromising the ideology of nineteenth-century gendered spaces. However, only when Catherine and Dr. Givings are transported to the winter garden—a third space outside the normal bounds of the public/private binary—can they connect emotionally. Ruhl's play models this alternative space of human connection to advocate breaking down of contemporary gendered binaries and hierarchies.

An analytic application of Geometric Invariant Theory II: Coarse moduli spaces

In [5] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact Kähler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in the weakly normal category is a coarse moduli space in the sense of complex geometry when the topology is fixed as induced by the space of Hermite-Einstein connections modulo the group of unitary gauge transformations.

Rule-based generative design of translational and rotational interlocking assemblies

Despite being a notoriously difficult task, efficient design of interlocking assemblies could greatly impact the construction sector and reduce its environmental footprint by helping in the design of demountable buildings and the reuse of structural members. While a growing research effort in this direction is being undertaken by the computer graphics and structural engineering communities, most of the algorithms proposed so far imply restrictions on assembly directions or prior knowledge on the joint's geometry.While relevant, such tools do not fully explore the space of possible assemblies and often fail to produce surprising results. Moreover, these designs are always assembled through translational motions, and, to the best of our knowledge, very little research has been conducted to address the challenges of designing an assembly for rotation motions.Building on recent advances in assembly design, this study investigates the automatic generation, using a Markov process and turtle graphics, of 2D interlocking sequential assemblies that can be assembled for any prescribed combination of translations and rotations. This generative approach shall be an aid to the engineer to explore the space of geometrical form-fitting connections and represents a first step towards an end-to-end workflow to design interlocking assemblies.

Loneliness, coping practices and masculinities in later life: Findings from a study of older men living alone in England.

While much attention has been given to loneliness as a public health and societal problem less consideration has been given to men's experiences, particularly in later life, and there is a limited evidence based on what works with supporting older men to counteract the impact of loneliness on their mental and social wellbeing. In this paper, we focus on the experiences of older men living alone in the community. Between 2017–2018 72 men residing in England (65–95 years) took part in the study and shared their accounts of experiencing and addressing loneliness on an everyday basis. We generated qualitative data through semi‐structured interviews. Interview data were analysed thematically using the framework analysis approach. We present and discuss findings on the difficulties older men experience in responding to and discussing loneliness and the range of coping practices men applied within their home environments. Three core themes are presented: 1. Maintaining silence around loneliness and distress; 2. Getting on with it versus feeling stuck in loneliness and, 3. Temporary remedies and distractions from loneliness from within the home. Across men's accounts, ‘the home’ is constructed as a space of biographical connections with others as well as a restrictive environment of separation from others. In relation to help‐seeking and efforts to break silence surrounding loneliness, the findings speak to the ways in which masculinities and social expectations attached to male roles complicate older men's varying attempts at help‐seeking and underpin some of their everyday methods of coping with loneliness. The findings reiterate the importance of targeted individual support for older men, particularly for those feeling frozen in loneliness. Facilitators of group‐based support for older men need to recognise the different and potentially conflicting positions older male service users may adopt in relation to help‐seeking that are configured around masculine ideals but in diverging ways.

Non-standard colorimetry in ICC colour management

In ICC v4 colour management, data is exchanged between different colour encodings via a fixed Profile Connection Space (PCS), in which colorimetry is based on the D50 illuminant, and the CIE 1931 standard observer. According to the ICC specification, colorimetry that is based on a different illuminant, or observer should be transformed into the fixed PCS; however, while a chromatic adaptation method is specified for when illuminants are different, there is no method specified for differences in observer. The Waypoint method has been proposed as a means of transforming between different colorimetric data encodings. In this study a Waypoint-based method recommended by ICC was evaluated as a mechanism for transforming into the ICC PCS, as applied to a use case in digital textile printing in which source colorimetry is based on the D65 illuminant and the CIE 1964 observer. It was compared with an alternative approach in which a non-ICC PCS was used within a conventional ICC colour management framework. The results show that when both source and destination colorimetry are based on D65/10-degrees, both methods perform equally well. However, when the source and destination colorimetry do not match, the ICC approach of transforming via the standard PCS yields better results.

Institutional experiments in urban relationality: repairing the social bond in capitalist urbanism

ABSTRACT Isolation and loneliness have become characteristic of capitalist cities where spaces for sociality, connection, and togetherness are few and far between, supplanted by an abundance of artificial “pseudo-social spaces” mediated by capital. This social fracture at the heart of contemporary urbanism is an urban-spatial extension of sociality’s degradation and economic capture under capitalist production. For many urban Marxist scholars, urbanization is a process now characterized by the commons’ continuous appropriation and annihilation by private interests. Arguably, within this context, “experimental institutionalism” has aimed to reconfigure art institutions into sites for sociality, dialogue, care, and collaboration. Experimental institutionalism is a field of institutional reform, curatorial practice, and debate concerned with the art institution’s transformation into a socially responsible agent. In this paper, I summarize experimental institutionalism’s main dimensions, drawing on key examples from the field to explore the art museum’s capacity to repair the social bonds ruptured by capitalist urbanism.

Moms, Memes, and Mitigating Pandemic Stress: Exploring Themes and Implications in an Academic Mamas’ Facebook Group

This article pairs autoethnography with a thematic analysis of memes in a private Facebook group made up of academic mothers during the first year of the COVID-19 pandemic. The analysis illustrates the challenges members faced during the pandemic related to their roles as mothers, academics, caregivers, and partners and how they used memes as a mechanism for virtual support in 2020 and 2021. Group members used memes to communicate about four primary themes: the stress and humor that arose from pandemic conditions, mothering during the pandemic, work–life tensions, and pressures for research productivity. Throughout the themes, humor offered a foundation for support and connection. The analysis provides insights into the potential for professional support networks online and how humor, shared via social media, can create space for vulnerability and connection among colleagues. The authors also consider the ambivalent dynamics that online social support offers. While it may reduce tension and provide emotional comfort, it also has the potential to uphold gendered expectations at home and at work.

Performative Scores in Pandemic Times1

In this essay, we explore the performative score 'INviteME Online' and discuss how the method of scoring may create spaces of connection and collective care in pandemic times of uncertainty and restriction. The practice of scoring takes its point of departure in the performing arts, in particular the dance-practice Contact Improvisation. Here, scores are seen as a set of gentle instructions for a collective activity, which allows participants to explore and improvise within a certain framework. Situating the practice of performative scores within a framework of the biopolitics of COVID-19, we highlight how measures taken by the state to control the epidemic and uphold biological life, alter the way social life can unfold. With INviteME Online, we suggest ways of being together at a distance, while retaining some of the affective properties of physical closeness. Through interviews with 11 participants from the INviteME Online score, we find that the score engendered experiences of intimate togetherness and collectivity for those that took part. These experiences were based in introspective explorations and spatial attention, as the score guided the participants' attention from their own bodies, through the space around them and towards the other participants. With these findings, we argue that the method of scoring may act as an antidote to the social disconnection and anxiety caused by the biopolitics of pandemic measures, as it suggests a way to ensure physical distance while retaining social closeness.

Dirac structures on the space of connections

We shall give a twisted Dirac structure on the space of irreducible connections on a SU(n)-bundle over a three-manifold, and give a family of twisted Dirac structures on the space of irreducible connections on the trivial SU(n)-bundle over a four-manifold. The twist is described by the Cartan 3-form on the space of connections. It vanishes over the subspace of flat connections. So the spaces of flat connections are endowed with ( non-twisted ) Dirac structures. The Dirac structure on the space of flat connections over the three-manifold is obtained as the boundary restriction of a corresponding Dirac structure over the four-manifold. We discuss also the action of the group of gauge transformations over these Dirac structures.

Group Bundles and Group Connections

We consider smooth families of Lie groups (group bundles) and connections that are compatible with the group operation. We characterize the space of group connections on a group bundle as an affine space modeled over the vector space of $$1$$ -forms with values cocycles in the Lie algebra bundle of the aforementioned group bundle. We show that group connections satisfy the Ambrose–Singer theorem and that group bundles can be seen as a particular case of associated bundles realizing group connections as associated connections. We give a construction of the Moduli space of group connections with fixed base and fiber, as a space of representations of the fundamental group of the base.

Enhancing preschool–home collaboration: lessons from virtual home visit experiences during the COVID-19 outbreak in China

ABSTRACT In the midst of the COVID-19 worldwide pandemic, the virtual home visit became a key strategy among China’s multiple approaches to ensure children’s continuity of learning, sustain teacher-parent-child relationships, and promote home–preschool collaboration. In this study, using a small stories research narrative paradigm to analyze documented family engagement captured in social media data, we explore how early childhood educators relied on frequent, personal connections with children and families through virtual home visits to mitigate the negative effects of preschool closures in China. Results suggest that the exchange of information and socio-emotional supports during virtual home visits supported and enhanced home–preschool relationships. The virtual home visits evolved into a space for connection and collaboration between the educators and families. We use an ecological-exchange framework to discuss the implications of virtual home visit experiences across time and reflect on pedagogy and practice to enhance development of teachers in online interactions with children and families.