Action Of Group Research Articles

Non-Virtually Abelian Discontinuous Group Actions vs. Proper SL(2,ℝ) -Actions on Homogeneous Spaces

We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions on homogeneous spaces which do not admit proper SL ( 2 , R ) -actions.

𝐾𝐾-duality for self-similar groupoid actions on graphs

We extend Nekrashevych’s K K KK -duality for C ∗ C^* -algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a graph, removing the recurrence condition entirely and generalising from a finite alphabet to a finite graph. More precisely, given a regular and contracting self-similar groupoid ( G , E ) (G,E) acting faithfully on a finite directed graph E E , we associate two C ∗ C^* -algebras, O ( G , E ) \mathcal {O}(G,E) and O ^ ( G , E ) \widehat {\mathcal {O}}(G,E) , to it and prove that they are strongly Morita equivalent to the stable and unstable Ruelle C*-algebras of a Smale space arising from a Wieler solenoid of the self-similar limit space. That these algebras are Spanier-Whitehead dual in K K KK -theory follows from the general result for Ruelle algebras of irreducible Smale spaces proved by Kaminker, Putnam, and the last author.

Enhancing plant fiber antibacterial and antiviral performance through synergistic action of amino and sulfonic acid groups

As the most abundant renewable resource, cellulose fibers are potential candidates for use in health-protective clothing. Herein, we demonstrate a novel strategy for preparing cellulose fiber with prominent antibacterial and antiviral performance by the synergistic effect of amino groups and sulfonic acid groups. Specifically, guanylated chitosan oligosaccharide (GCOS) and N-sulfopropyl chitosan oligosaccharide (SCOS) were synthesized and chemically grafted onto cellulose fibers (CFs) to endow the fibers with antibacterial and antiviral properties. Moreover, a compounding strategy was applied to make the fibers with simultaneously high antibacterial and antiviral activity, especially in short contact time. The bacteriostatic rate (against S. aureus: 95.81 %, against E. coli: 92.07 %, 1 h) of the compounded fibers improved substantially when a few GCOS-CFs were mixed with SCOS-CFs; especially, it was much higher than both the individual GCOS-CFs and SCOS-CFs. By contrast, the improvement of the antiviral properties was less dramatic; however, even a few SCOS-CFs was mixed, the antiviral properties increased pronouncedly. Although the electrostatic interaction between SCOS and GCOS can make the SCOS-GCOS mixture lose some extent of antibacterial activity, the long chains of cellulose restrain the electrostatic interaction between sulfonic and amino groups, leading to their synergistic action and eventually superior antibacterial and antiviral effects.

Influence of bottom protection structures group on the hydraulic characteristics in sharp bends

Bottom protection (BP) is a commonly used engineering measure in river training. A 3D hydrodynamic numerical model is established to study the influence of the overall arrangements of BP structures on the hydraulic characteristics of the sharp bends. Under the action of the BP structures group, the maximum longitudinal flow velocity is closer to the water surface vertically and closer to the concave bank laterally compared with no BP. The high shear stress zones on the riverbed at the exit straight section of the bend do not occur. The so-called primary circulation after the apex of the bend gradually weakens and disappears. If the coverage rate of BP is increased to 1.5 times that of the sequential BP, the average longitudinal flow velocity near the bottom of BP decreases by 10% and the average bed shear stress at the outlet section of the bend decreases by 35%. In the staggered BP condition, the average bed shear stress at the outlet section of the bend is reduced by 23% compared with the sequential BP. Moreover, the results show that the protection effects of the dense BP and the staggered BP are better than that of sequential BP.

Narrative as active inference: an integrative account of cognitive and social functions in adaptation.

While the ubiquity and importance of narratives for human adaptation is widely recognized, there is no integrative framework for understanding the roles of narrative in human adaptation. Research has identified several cognitive and social functions of narratives that are conducive to well-being and adaptation as well as to coordinated social practices and enculturation. In this paper, we characterize the cognitive and social functions of narratives in terms of active inference, to support the claim that one of the main adaptive functions of narrative is to generate more useful (i.e., accurate, parsimonious) predictions for the individual, as well as to coordinate group action (over multiple timescales) through shared predictions about collective behavior. Active inference is a theory that depicts the fundamental tendency of living organisms to adapt by proactively inferring the causes of their sensations (including their own actions). We review narrative research on identity, event segmentation, episodic memory, future projections, storytelling practices, enculturation, and master narratives. We show how this research dovetails with the active inference framework and propose an account of the cognitive and social functions of narrative that emphasizes that narratives are for the future-even when they are focused on recollecting or recounting the past. Understanding narratives as cognitive and cultural tools for mutual prediction in social contexts can guide research on narrative in adaptive behavior and psychopathology, based on a parsimonious mechanistic model of some of the basic adaptive functions of narrative.

Robustly reusable fuzzy extractor from isogeny

Robustly reusable Fuzzy Extractor (rrFE) allows multiple extractions from the same fuzzy source in a reproducible way. The reusability of rrFE asks the pseudo-randomness of the extracted keys, while robustness of rrFE makes sure that active attacks can be detected during the reproduction of the extracted key. With rrFE, we are able to produce cryptographic keys for our cryptosystems from fuzzy sources, like biometrics, physical unclonable functions, etc. There are rrFE schemes from the DDH, LWE and LPN assumptions. However there is no rrFE scheme from isogeny-based assumptions up to now.In this paper, we construct the first rrFE from isogeny. To obtain such an rrFE, we propose a new framework for constructing rrFE with a core technical tool, named Enhanced Effective Group Action (EEGA). EEGA is built upon the basic Effective Group Action (EGA), and is equipped with a sampling algorithm and a derivation algorithm. With such an EEGA, the same random input can be derived to produce different pseudo-random and unpredictable outputs. The EEGA, together with other routine building blocks like secure sketch and extractor, leverages an FE to achieve reusability and robustness. We construct EEGA based on CSI-FiSh, which admits the first rrFE scheme from isogeny. Besides, we also propose another two EEGA instantiations from the DDH assumption, and this provides another approach to DDH-based rrFE, which may be of independent interest.

Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory

In this paper, we investigate a regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric and almost free action of a Hilbert Lie group whose orbits are minimal regularizable submanifolds. We prove that, if the initial invariant hypersurface satisfies a certain kind of horizontally convexity condition and some additional conditions, then it collapses to an orbit of the Hilbert Lie group action along the regularized mean curvature flow. In the final section, we state a vision for applying the study of the regularized mean curvature flow to the gauge theory.

Understanding Lorentz Utilizing Galilei: The Emergence of a Friendly Extended Special Relativity Theory that Admits Relativistic Multi-Particle Entanglement

Special relativity theory stems from the Lorentz transformation of signature (1,3). The incorporation into special relativity of the Lorentz transformations of signature (m,n) for all m,n∈ℕ (n = 3 in physical applications) enriches the theory. The resulting enriched special relativity is a friendly extended special relativity that admits multi-particle entanglement, as demanded by relativistic quantum mechanics. The Lorentz transformation of signature (m,n) admits a novel physical interpretation induced by the intuitively clear interpretation of the Galilei transformation of signature (m,n) for all m,n > 1. In this sense we understand Lorentz utilizing Galilei in m temporal and n spatial dimensions, resulting in the emergence of multi-particle entanglement that the enriched special theory of relativity admits. Remarkably, it turns out that, for any m,n∈ℕ, the group of Lorentz transformations of signature (m,n) is the symmetry group that underlies any multi-particle system that consists of m n - dimensional entangled particles.

Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets

A relaxation of the notion of invariant set, known as $k$-quasi-invariant set, has appeared several times in the literature in relation to group dynamics. The results obtained in this context depend on the fact that the dynamic is generated by a group. In our work, we consider the notions of invariant and 1-internally-quasi-invariant sets as applied to an action of a function $f$ on a set $I$. We answer several problems of the following type, where $k \in \{0,1\}$: what are the functions $f$ for which every finite subset of $I$ is internally-$k$-quasi-invariant? More restrictively, if $I = \mathbb{N}$, what are the functions $f$ for which every finite interval of $I$ is internally-$k$-quasi-invariant? Last, what are the functions $f$ for which every finite subset of $I$ admits a finite superset that is internally-$k$-quasi-invariant? This parallels a similar investigation undergone by C. E. Praeger in the context of group actions.

Non-Hausdorff germinal groupoids for actions of countable groups

We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a new criterion, which serves as an obstruction for the étale topology on the groupoid to be non-Hausdorff. We use this and other criteria to study the topology of germinal groupoids for a few classes of actions. In particular, we give examples of families of contracting and non-contracting self-similar groups, which are amenable and whose actions have associated germinal groupoids with non-Hausdorff topology.

A Fruitful Interaction Between Algebra, Geometry, and Topology: Varieties Through the Lens of Group Actions

A Fruitful Interaction Between Algebra, Geometry, and Topology: Varieties Through the Lens of Group Actions

Brieskorn spheres, cyclic group actions and the Milnor conjecture

AbstractIn this paper we further develop the theory of equivariant Seiberg–Witten–Floer cohomology of the two authors, with an emphasis on Brieskorn homology spheres. We obtain a number of applications. First, we show that the knot concordance invariants defined by the first author satisfy for torus knots, whenever is a prime not dividing . Since is a lower bound for the slice genus, this gives a new proof of the Milnor conjecture. Second, we prove that a free cyclic group action on a Brieskorn homology 3‐sphere does not extend smoothly to any homology 4‐ball bounding . In the case of a non‐free cyclic group action of prime order, we prove that if the rank of is greater than times the rank of , then the ‐action on does not extend smoothly to any homology 4‐ball bounding . Third, we prove that for all but finitely many primes a similar non‐extension result holds in the case that the bounding 4‐manifold has positive‐definite intersection form. Finally, we also prove non‐extension results for equivariant connected sums of Brieskorn homology spheres.

Actions of Compact and Discrete Quantum Groups on Operator Systems

Abstract We introduce the notion of an action of a discrete or compact quantum group on an operator system, and study equivariant operator system injectivity. We then prove a duality result that relates equivariant injectivity with dual injectivity of associated crossed products. As an application, we give a description of the equivariant injective envelope of the reduced crossed product built from an action of a discrete quantum group on an operator system.

The Bolivian pluriverse: the Comuna Group, emerging subjects, and transformative political action against neoliberalism

ABSTRACT This article reviews an important experience of pluriversal political activity in Bolivia, through the prism of the theoretical and political contributions of Grupo Comuna, a local organization of scholar activists and public intellectuals. Comuna deployed Marxist categories to examine, and intervene upon, the dilemmas of the pluriverse and the social and political challenges facing Bolivia’s original peoples (pueblos originarios). The article examines publications of the Group and original interviews with its members. Bolivian social movements were partially successful defeating neoliberalism in the country, and Morales’ administrations transformed Bolivia. These successes were achieved in and through an innovative analysis, including the recognition of the pluriversal nature of the Bolivian political process. Almost uniquely among politically engaged academics, Comuna helped to develop a programme adapted to the country’s circumstances and addressing the challenges of intervention in pluriversal activity; in doing this, they supported mass organization and mobilization, and achieved strong political impact.

TWISTED ACTIONS ON COHOMOLOGIES AND BIMODULES

AbstractFor closed subgroups L and R of a compact Lie group G, a left L-space X, and an L-equivariant continuous map $A:X\to G/R$ , we introduce the twisted action of the equivariant cohomology $H_R^{\bullet }(\mathrm {pt},\Bbbk )$ on the equivariant cohomology $H_L^{\bullet }(X,\Bbbk )$ . Considering this action as a right action, $H_L^{\bullet }(X,\Bbbk )$ becomes a bimodule together with the canonical left action of $H_L^{\bullet }(\mathrm {pt},\Bbbk )$ . Using this bimodule structure, we prove an equivariant version of the Künneth isomorphism. We apply this result to the computation of the equivariant cohomologies of Bott–Samelson varieties and to a geometric construction of the bimodule morphisms between them.

Rotationally invariant translators of the mean curvature flow in Einstein's static universe

In this paper, we deal with non-degenerate translators of the mean curvature flow in the well-known Einstein's static universe. We focus on the rotationally invariant translators, that is, those invariant by a natural isometric action of the special orthogonal group on the ambient space. In the classification list, there are three space-like cases and five time-like cases. All of them, except a totally geodesic example, have one or two conic singularities. Also, we show a uniqueness result based on the behaviour of the translator on its boundary. As an application, we extend an isometry of the sphere to the whole translator under simple conditions. This leads to a characterization of a bowl-like example.

A Classification of Compact Cohomogeneity One Locally Conformal Kähler Manifolds

In this paper, we apply a result of the classification of a compact cohomogeneity one Riemannian manifold with a compact Lie group G to obtain a classification of compact cohomogeneity one locally conformal Kähler manifolds. In particular, we prove that the compact complex manifold is a complex one-dimensional torus bundle over a projective rational homogeneous, or cohomogeneity one manifold except of a class of manifolds with a generalized Hopf surface bundle over a projective rational homogeneous space. Additionally, it is a homogeneous compact complex manifold under the complexification GC of the given compact Lie group G under an extra condition that the related closed one form is cohomologous to zero on the generic G orbit. Moreover, the semi-simple part S of the Lie group action has hypersurface orbits, i.e., it is of cohomogeneity one with respect to the semi-simple Lie group S in that special case.

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.