Action Of Group Research Articles

INDIVIDUAL SPONTANEITY AND THE POSSIBILITY OF COMMUNITY IN MEAD’S SOCIAL PSYCHOLOGY

The central question of the present study is how to understand the spontaneity of the social self in George H. Mead’s account of the genesis and structure of the self. Its argument develops in three stages. First, I provide a brief discussion of the notion of the self in relation to social existence in Hegel in order to highlight some salient features that will prefigure some of the claims that Mead makes. Second, I discuss Mead’s theory in greater detail in order to emphasize the role of communication and ‘attitude-taking’ in the constitution of the self. These factors comprise what is particularly original in Mead’s account. Finally, I offer an evaluation of Mead’s key claims in the context of certain questions concerning the relationship between the individual and community. I think that Mead provides a sound scheme by means of which we can understand the constitution of the self as a social phenomenon and communities as dynamic systems susceptible to transformation in response to individual and/or group action, i.e., without reifying communities. However, the dynamics of social change, for the most part in terms of ‘adaptation’ in Mead’s account, needs some modification, if we want to understand those periods of social upheaval during which the continuity between the ‘old’ and the ‘new’ seems minimal.

Construction of first-order invariant differential operators

The paper considers the problem of constructing systems of vector fields that are invariant under the action of the local Lie group of transformations. It is shown that there exists a special class of Lie groups for which this problem can be solved elementarily.

SICs and the Triangle Group (3,3,3)

The problem of existence of symmetric informationally-complete positive operator-valued measures (SICs for short) in every dimension is known as Zauner's conjecture and remains open to this day. Most of the known SIC examples are constructed as an orbit of the Weyl-Heisenberg group action. It appears that in these cases SICs are invariant under the so-called canonical order-three unitaries, which define automorphisms of the Weyl-Heisenberg group. In this note, we show that those order-three unitaries appear in projective unitary representations of the triangle group $(3,3,3)$. We give a full description of such representations and show how it can be used to obtain results about the structure of canonical order-three unitaries. In particular, we present an alternative way of proving the fact that any canonical order-three unitary is conjugate to Zauner's unitary if the dimension $d>3$ is prime.

Can Orbital-Selective Néel Transitions Survive Strong Nonlocal Electronic Correlations?

Spin- or orbital-selective behaviors in correlated electron materials offer rich promise for spintronics or orbitronics phenomena and applications deriving from them. Strong local electronic Coulomb correlations might lead to an orbital-selective Mott state, characterized by the coexistence of localized electrons in some orbitals with itinerant electrons in others. Nonlocal electronic fluctuations are much more entangled in orbital space than the local ones. For this reason, finding orbital-selective phenomena related to nonlocal correlations, such as orbital-selective magnetic transitions, is a challenge. In this Letter, we investigate possibilities to realize an orbital-selective Néel transition (OSNT). We illustrate that stabilizing this state requires a decoupling of magnetic fluctuations in different orbitals, which can only be realized in the absence of Hund's exchange coupling. On the basis of two-orbital calculations for a Hubbard model with different bandwidths we show that the proposed OSNT can be found all the way from the weak to the strong coupling regime. In the weak coupling regime the transition is governed by a Slater mechanism and thus occurs first for the narrow orbital. At strong coupling a Heisenberg mechanism of the OSNT sets in, and the transition occurs first for the wide orbital. Remarkably, at intermediate values of the interaction we find a nontrivial regime of the OSNT, where the Slater mechanism leads to a Néel transition occurring first for the wide orbital. Our work suggests strategies for searching for orbital-selective Néel ordering in real materials in view of possible spin-orbitronics applications.

Partially hyperbolic endomorphisms with expanding linear part

Abstract In this paper, we study transitivity of partially hyperbolic endomorphisms of the two torus whose action in the first homology group has two integer eigenvalues of moduli greater than one. We prove that if the Jacobian is everywhere greater than the modulus of the largest eigenvalue, then the map is robustly transitive. For this, we introduce Blichfedt’s theorem as a tool for extracting dynamical information from the action of a map in homology. We also treat the case of specially partially hyperbolic endomorphisms, for which we obtain a complete dichotomy: either the map is transitive and conjugated to its linear part, or its unstable foliation must contain an annulus which may either be wandering or periodic.

Situated Learning for Community Engagement: Chinese and Chinese Americans Transformative Action for Identity Reformation in the Context of the Politicalized COVID-19 Pandemic

This qualitative case study examines the learning experiences of self-organized Chinese and Chinese American adults from the X Care Group amid the political repercussions of the COVID-19 pandemic. The findings revealed how care group members created meaning in their daily life experiences, reformed their identity, and increased their Chinese and Chinese American visibility. Situated learning is employed to understand participants’ transformative actions through learning in their social engagement through their community of practice. These findings indicate that situated learning can lead to collective transformative action, personal and group growth in identity formation, and community engagement and social development through communities of practice. Subsequently, this study demonstrated how the X group learned to reform their new identities and respond to changes in their social environment. This study contributes to the collective dimension of situated learning theory and has implications for adult educators, researchers, and policymakers interested in fostering social change through community-based, situated learning.

Quotients by parabolic groups and moduli spaces of unstable objects

Motivated by constructing moduli spaces of unstable objects, we use new ideas in non-reductive GIT to construct quotients by parabolic group actions. For moduli problems with semistable moduli spaces constructed by reductive GIT, we consider associated instability (or HKKN) stratifications, which are often closely related to Harder-Narasimhan stratifications, and construct quotients of the unstable strata under various stabiliser assumptions by further developing ideas of non-reductive GIT. Our approach is to construct parabolic quotients in stages, in order for the required stabiliser assumptions to be more readily verified. To illustrate these ideas, we construct moduli spaces for certain sheaves of fixed Harder-Narasimhan type on a projective scheme in cases where our stabiliser assumptions can be verified.

Evidence for the Existence and Early Origin of Genes Making Possible the Darwinian Evolution of Biogeochemical Homeostasis at a Planetary Scale

This paper uses empirical evidence to address the subject of when and how the processes for the homeostatic influence of the biota on planetary-scale biogeochemical processes first arose. From Lovelock (1972) this planetary-scale homeostatic influence has been referred to as Gaia and we also do so in this paper. To set the scene for the study, the paper first proposes three core necessary attributes for Gaia: (1) individual organisms possessing control systems using feedback loops to regulate their external environment (the _environmental regulation_ core attribute); (2) joint action of groups of such organisms leading to the achievement of larger scale environmental regulation (the_ joint action_ core attribute); and (3) such action occurring at a planetary scale. The paper next identifies representative examples in contemporary organisms of each of the two non-planetary core attributes of Gaia in operation. For each of these examples, genes making up part of the genetic specification of the example were identified. We then sought these same genes in the earliest examples of life that have been genetically characterised in empirical terms - the Last Universal Common Ancestor (LUCA) and the Last Bacterial Common Ancestor (LBCA). These arose respectively between 4 and 3.5 billion years ago. Examining both the pools of known modern genes and demonstrated LUCA and/or LBCA genes, a number of modern genes related to functionality analogous to that of Gaia core attributes were also found likely to be in LBCA and/or LUCA. In other words, the potentiality for the eventual evolution of Gaia arose between 3.5 to 4 billion years ago. The paper also provides case studies showing similar results at increasing scales of organismal aggregation over the intervening period to the present. Doolittle (1981) and Dawkins (1982) stated, in essence, that it was impossible for them to imagine any evolutionary way by which Gaia could have arisen. Dawkins (1982) defined Gaia as was at the time predominantly done in terms of its planetary attribute. This posits that there is _one _Gaia on Earth. Dawkins pointed out that neo-Darwinian natural selection requires competition between _multiple _units of selection. Given the absence of such multiple units of selection, Dawkins proposed that Gaia could not come into being by neo-Darwinian natural selection. The Doolittle and Dawkins positions were influential and interpreted by some as evidence that Gaia could not exist at all. The evidence of the present study is that genes for processes analogous to the non-planetary core attributes of Gaia have been available from near the start of life. With such genes being units of selection, planetary Gaia could come about by a series of developments commencing near the start of life, each involving standard gene-based Darwinian natural selection. We consider these results to resolve the issue raised by Doolittle (1981) and Dawkins (1982).

Valuations, completions, and hyperbolic actions of metabelian groups

AbstractActions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobounded hyperbolic actions of many abelian‐by‐cyclic groups associated to expanding integer matrices. Each such action is equivalent to an action on a tree or on a Heintze group (a classically studied class of negatively curved Lie groups). Our investigations incorporate number systems, factorization in formal power series rings, completions, and valuations.

A conjecture of Zagier and the value distribution of quantum modular forms

In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modular group on their arguments. More precisely, when J_{K,0} denotes the colored Jones polynomial of a knot K , Zagier’s modularity conjecture describes the asymptotics of the quotient J_{K,0}(e^{2 \pi i \gamma(x)}) / J_{K,0}(e^{2 \pi i x}) as x \to \infty along rationals with bounded denominators, where \gamma \in \mathrm{SL}(2,\mathbb{Z}) . This problem is most accessible for the figure-eight knot 4_{1} , where the colored Jones polynomial has a simple explicit expression in terms of the q -Pochhammer symbol. Zagier also conjectured that the function h(x) = \log (J_{4_1,0}(e^{2 \pi i x}) / J_{4_1,0}(e^{2 \pi i /x})) can be extended to a function on \mathbb{R} which is continuous at irrationals. In the present paper, we prove Zagier’s continuity conjecture for all irrationals for which the sequence of partial quotients in the continued fraction expansion is unbounded. In particular, the continuity conjecture holds almost everywhere on the real line. We also establish a smooth approximation of h , uniform over all rationals, in accordance with the modularity conjecture. As an application, we find the limit distribution (after a suitable centering and rescaling) of \log J_{4_1,0}(e^{2 \pi i x}) , when x ranges over all reduced rationals in (0,1) with denominator at most N , as N \to \infty , thereby confirming a conjecture of Bettin and Drappeau.

The pressure of intricacy and average sample complexity for amenable group actions

The pressure of intricacy and average sample complexity for amenable group actions

Accuracy of projected atomic virtual orbital space in embedding applications

ABSTRACT The performance of the recently suggested projected atomic orbitals (PAO) approach as the virtual space in excited state projection-based embedding applications is analysed. The role of the parameters in the PAO generation is discussed and the impact of different choices is evaluated on the ground state of the stacked formaldehyde and pyrrole dimers. A comparison of excitation energies obtained with PAOs and localised virtual orbitals is given and the role of diffuse basis functions is discussed using a benchmark set from previous studies.

Equivariant lattice bases

We study lattices in free abelian groups of infinite rank that are invariant under the action of the infinite symmetric group, with emphasis on finiteness of their equivariant bases. Our framework provides a new method for proving finiteness results in algebraic statistics. As an illustration, we show that every invariant lattice in Z ( N × [ c ] ) \mathbb {Z}^{(\mathbb {N}\times [c])} , where c ∈ N c\in \mathbb {N} , has a finite equivariant Graver basis. This result generalizes and strengthens several finiteness results about Markov bases in the literature.

Möbius homogeneous hypersurfaces in [formula omitted]

Let M(Sn+1) denote the Möbius transformation group of the (n+1)-dimensional sphere Sn+1. A hypersurface x:Mn→Sn+1 is called a Möbius homogeneous hypersurface if there exists a subgroup G of M(Sn+1) such that the orbit G⋅p=x(Mn),p∈x(Mn). In this paper, the Möbius homogeneous hypersurfaces are classified completely up to a Möbius transformation of Sn+1.

G-solid rational surfaces

We classify G-solid rational surfaces over the field of complex numbers for finite group actions.

Möbius group actions in the solvable chimera model

We study actions of Möbius group on two sub-populations in the solvable chimera model proposed by Abrams et al. Dynamics of global variables are given by two coupled Watanabe–Strogatz systems, one for each sub-population. At the first glance, asymptotic dynamics in the model seem to be very simple. For instance, in the stable chimera state distributions of oscillators perform a simple rotation after a certain (sufficiently large) moment. However, a closer look unveils that dynamics are subtler that what can be observed from evolution of densities of oscillators’ phases. In order to gain the full picture, one needs to investigate dynamics on the transformation group that acts on these densities. Such an approach emphasizes impact of the “hidden” variable that is not visible on macroscopic level. More precisely, we demonstrate that the chimera model is an intriguing example of the classical system that exhibits the holonomy in fiber bundles of the group of Möbius transformations.

Electrochemical γ-Selective Deuteration of Pyridines.

Herein, we first report a γ-selective deuteration reaction of pyridines via H/D exchange without the need for preinstalled directing groups and transformable functional groups. The electrochemical process offers an attractive approach to producing γ-deuterated pyridines under gentle conditions. The broad substrate scope, excellent deuterium incorporation, and remarkable selectivity of the electrochemical method make it applicable for the late-stage modification of pharmaceutical molecules.

The largest orbit sizes of linear group actions and abelian quotients

Let G be a finite group and let V be a finite and faithful G-module such that V is completely reducible, possibly of mixed characteristic, or V is a G-module over a field of characteristic p with Op(G)=1. Suppose that M is the largest orbit size in the action of G on V. It is known that the index of the commutator subgroup G′ in G is bounded by M, that is, |G:G′|≤M. In this paper, we classify all linear group actions in which |G:G′|=M. It turns out that our classification is a vast generalization of a classic 1967 result by D. Passman. We also include an application of the main results to Brauer's k(B)-problem.

Wedge product matrices and orbits of principal congruence subgroups

Following Bump and Hoffstein in [2], the orbits in Γ∞(3)﹨Γ(3) are in bijection with sets of invariants satisfying certain relations. We explain how wedge product matrices give an alternative definition of the invariants of matrix orbits. This new method provides the possibility of performing similar computations with other congruence subgroups and arbitrary n×n matrices. Using Steinberg's refined version of the Bruhat decomposition, we construct an explicit choice of coset representative for each orbit in the orbit space Γ∞(3)﹨Γ(3) of 3×3 matrices over the PID of Eisenstein integers.

Towards a bilipschitz invariant theory

Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.