Action Of Group Research Articles

Non-existence of a universal zero-entropy system via generic actions of almost complete growth

Abstract We prove that a generic probability measure-preserving (p.m.p.) action of a countable amenable group G has scaling entropy that cannot be dominated by a given rate of growth. As a corollary, we obtain that there does not exist a topological action of G for which the set of ergodic invariant measures coincides with the set of all ergodic p.m.p. G-systems of entropy zero. We also prove that a generic action of a residually finite amenable group has scaling entropy that cannot be bounded from below by a given sequence. In addition, we show an example of an amenable group that has such a lower bound for every free p.m.p. action.

Binding Profiles of Human and Mouse Complement Component 8γ to Trisubstituted Organometallic Compounds

Complement component 8gamma (C8γ), a member of the lipocalin protein family, is suggested to act as a carrier protein for various chemicals. Although C8γ has been identified in both humans and rodents for some time, our understanding of the species differences in its chemical binding properties remains limited. In the present study, with the aim to elucidate the potential role of C8γ as a carrier protein in both humans and mice, we conducted a radioligand binding assay to examine the chemical binding properties of human C8γ (hC8γ) and mouse C8γ (mC8γ). Scatchard analysis revealed that [14C]TPT bound to hC8γ with an equilibrium dissociation constant (Kd) of 64.2 ± 32.4 nM, comparable to that of [14C]TPT to mC8γ. Competitive ligand-binding assays demonstrated binding of TPT and TBT to hC8γ, while diphenyltin, dibutyltin, monophenyltin, monobutyltin, and tetrabutyltin did not exhibit binding. These results suggest that for effective binding to C8γ, chemicals must possess substituents of appropriate bulkiness. Further analyses with other group 14 compounds with triphenyl substituents revealed that a central metal atom, rather than a central non-metal or semi-metal atom, is crucial for specific binding to both hC8γ and mC8γ. Overall our findings imply that C8γ may play a role in the physiological or toxicological actions of group 14 metal compounds with tributyl or triphenyl substituents by binding to these chemicals in both humans and mice.

Representations of groups on Banach spaces

We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let G \mathcal {G} be a topological group, and A \mathcal {A} a unital symmetric C ∗ C^* -subalgebra of U C ( G ) \mathrm {UC}(\mathcal {G}) , the algebra of bounded uniformly continuous functions on G \mathcal {G} . Generalizing the notion of a stable metric, we study A \mathcal {A} -metrics δ \delta , i.e., the function δ ( e , ⋅ ) \delta (e, \cdot ) belongs to A \mathcal {A} ; the case A = W A P ( G ) \mathcal {A}=W\hskip -0.7mm A\hskip -0.2mm P(\mathcal {G}) , the algebra of weakly almost periodic functions on G \mathcal {G} , recovers stability. If the topology of G G is induced by a left invariant metric d d , we prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if d d is uniformly equivalent to a left invariant A \mathcal {A} -metric. As an application, we show that the additive group of C [ 0 , 1 ] C[0,1] is not reflexively representable; this is a new proof of Megrelishvili [Topological transformation groups: selected topics, Elsevier, 2007, Question 6.7] (the problem was already solved by Ferri and Galindo [Studia Math. 193 (2009), pp. 99–108] with different methods and later the results were generalized by Yaacov, Berenstein, and Ferri [Math. Z. 267 (2011), pp.129–138]). Let now G \mathcal {G} be a metric group, and assume A ⊆ L U C ( G ) \mathcal {A}\subseteq \mathrm {LUC}(\mathcal {G}) , the algebra of bounded left uniformly continuous functions on G \mathcal {G} , is a unital C ∗ C^* -algebra which is the uniform closure of coefficients of representations of G \mathcal {G} on members of F \mathscr {F} , where F \mathscr {F} is a class of Banach spaces closed under ℓ 2 \ell _2 -direct sums. We prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if G \mathcal {G} embeds into the isometry group of a member of F \mathscr {F} , equipped with the weak operator topology. As applications, we obtain characterizations of unitary and reflexive representability.

Simple Two-Message OT in the Explicit Isogeny Model

In this work we study algebraic and generic models for group actions, and extend them to the universal composability (UC) framework of Canetti (FOCS 2001). We revisit the constructions of Duman et al. (PKC 2023) integrating the type-safe model by Zhandry (Crypto 2022), adapted to the group action setting, and formally define an algebraic action model (AAM). This model restricts the power of the adversary in a similar fashion to the algebraic group model (AGM). By imposing algebraic behaviour to the adversary and environment of the UC framework, we construct the UC-AAM. Finally, we instantiate UC-AAM with isogeny-based assumptions, in particular the CSIDH action with twists, obtaining the explicit isogeny model, UC-EI; we observe that, under certain assumptions, this model is "closer" to standard UC than the UC-AGM, even though there still exists an important separation. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure oblivious transfer protocol described by Lai et al. (Eurocrypt 2021), hence providing the first concretely efficient two-message isogeny-based OT protocol in the random oracle model against malicious adversaries.

Subspace dual and orthogonal frames by action of an abelian group

Subspace dual and orthogonal frames by action of an abelian group

Exact FLRW cosmological solutions via invariants of the symmetry groups

Until now, various methods have been demonstrated to solve the Friedmann-Lamaítre-Robertson-Walker (FLRW) equations in the spatially flat (k = 0) cosmological model. In this study, in order to solve the field equations of the spatially flat FLRW cosmological model in the presence of Λ, a new method based on the invariants of the symmetry groups which we called ISG-method, is presented. This method is based on the extended Prelle-Singer (PS) method and it uses the Lie point symmetry, λ-symmetry and Darboux polynomials (DPs). We employ this method to extract systematically the two independent first integrals (or invariants) such as I1(a,ȧ)=c1 and I2(t,a,ȧ)=c2 associated to the group of the Lie point transformations keeping the Friedmann-Einstein dynamical equation (DE), ä=ϕ(t,a,ȧ) , invariant. The obtained solutions from solving the DEs of the FLRW cosmological model by the ISG-method are explicitly written, so that they are suitable for cosmological applications. Finally, as an application of the solutions we look at the age of universe in the presence of cosmological constant where the dominant matter of the Universe is considered to be fluid with the state parameter w. In this regard, we calculate the age of universe when the dominant matter is dust.

The Memeing Body: More-than-activism in the more-than-real

This article explores the ways that bodies are imagined and enrolled in a digital political project in the context of Bosnia and Herzegovina. Using data from online and in-person fieldwork over the course of 2020–22, I follow a small group of young people in Tuzla, Bosnia and Herzegovina, who spend their days running CAT (Citizens Against Terrorism), a self-described anti-fascist meme group active on platforms such as Twitter/X, Facebook, and Instagram, as well as their own website. Behind the seeming unseriousness of this endeavour is a deliberate approach, grounded in the view that Bosnian youth are not apathetic, but ignored; that they are actively being targeted by the far right through memes and other mirthful means; and that attempts to engage youth in left political action must meet them on their own turf. As they attempt to meet young people where they are, the CATs engage in what they call “more-than-activism”, a serendipitous nod to the more-than-real spaces they create through their digital and physical activities. Drawing on cyberfeminism and recent work in digital geography, the article argues for an approach to young people’s politics that is sensitive to their embodied experiences, including in the digital parts of their lives. Through a more-than-real approach, we can understand how seemingly ephemeral objects like memes come to matter in the making and unmaking of political projects.

Partial actions of groups on profinite spaces

We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG  : X → X / ∼G  of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.

Integrated Reporting and the experience of the Pilot Programme: perspective of an Italian pioneer company over ten years

Purpose This study aims to propose a longitudinal analysis of motivations for Integrated Reporting (IR) adoption, internal changes, the benefits of IR implementation and compliance challenges. Design/methodology/approach The authors analyse a longitudinal case study of an Italian-listed company (Eni) participating in the IR-Pilot Programme (PP) and covering 10 years of IR adoption. The analysis was based on a mixed-method approach that included semi-structured interviews, content analysis of annual reports and triangulation with other data sources. Results are discussed regarding institutional theory, legitimacy theory and diffusion of innovation theory. Findings The study suggests that motivations for adopting IR change over time and participation in the IR-PP helps Eni acquire a comprehensive and substantial integrated view of value creation over time, makes integrated culture a key factor for strategic business sustainability and confirms the readiness of early adopters to comply with the non-financial Directive (NFD). Originality/value This study, among the few longitudinal case studies, provides organisations, regulators and academics with insights into the motivations driving the successful adoption and implementation of IR and the NFD. The results may help companies consider one of the tools currently deemed to bring sustainability into action and participation in pilot groups.

MKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere

We investigate geometric evolution equations for Legendrian curves in the 3-sphere which are invariant under the action of the unitary group ${\rm U}(2)$. We define a natural symplectic structure on the space of Legendrian loops and show that the modified Korteweg-de Vries equation, along with its associated hierarchy, are realized as curvature evolutions induced by a sequence of Hamiltonian flows. For the flow among these that induces the mKdV equation, we investigate the geometry of solutions which evolve by rigid motions in ${\rm U}(2)$. Generalizations of our results to higher-order evolutions and curves in similar geometries are also discussed.

Partial actions on quotient spaces and globalization

Given a partial action of a topological group G on a space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable, and having invariantmetric. Further, for a normal subgroup H, we introduce and study a partial action of G/H on the orbit space of X; applications to invariant metrics and inverse limits are presented.

Skew group categories, algebras associated to Cartan matrices and folding of root lattices

For an action of a finite group on a finite EI quiver, we construct its ‘orbifold’ quotient EI quiver. The free EI category associated to the quotient EI quiver is equivalent to the skew group category with respect to the given group action. Specializing the result to a finite group action on a finite acyclic quiver, we prove that, under reasonable conditions, the skew group category of the path category is equivalent to a finite EI category of Cartan type. If the ground field is of characteristic $p$ and the acting group is a cyclic $p$ -group, we prove that the skew group algebra of the path algebra is Morita equivalent to the algebra associated to a Cartan matrix, defined in [C. Geiss, B. Leclerc, and J. Schröer, Quivers with relations for symmetrizable Cartan matrices I: Foundations, Invent. Math. 209 (2017), 61–158]. We apply the Morita equivalence to construct a categorification of the folding projection between the root lattices with respect to a graph automorphism. In the Dynkin cases, the restriction of the categorification to indecomposable modules corresponds to the folding of positive roots.

Constructing amidoxime adsorption sites on the core-shell structured natural silk protein for uranium capture

Amidoxime-based fiber adsorbents hold significant promise for uranium extraction. However, a notable issue is that these adsorbents primarily originate from synthetic polymer materials, which, aside from providing good mechanical support, have no other functions. In recent study, we shifted our focus to silk fiber (SF), a natural protein fiber known for its unique core-shell structure and rich amino acids. The shell layer, due to its abundant functional groups, makes it easily modifiable, while the core layer provides excellent mechanical strength. Leveraging these inherent properties, an amidoxime-based fiber adsorbent was developed. This adsorbent utilizes amino and carboxyl groups for enhanced performance synergistically. This method involves establishing uranium affinity sites on the outer sericin layer of SF via chemical initiation of graft polymerization (CIGP) and amidoximation (SF-g-PAO). The water absorption ratio of SF-g-PAO is as high as 601.16 % (DG = 97.17 %). Besides, SF-g-PAO demonstrates an exceptional adsorption capacity of 15.69 mg/g in simulated seawater, achieving a remarkable removal rate of uranyl ions at 95.06 %. It can withstand a minimum of five adsorption-elution cycles. Over a 4-week period in natural seawater, SF-g-PAO displayed an adsorption capacity of 4.95 mg/g. Furthermore, SF-g-PAO also exhibits impressive uranium removal efficiency in real nuclear wastewater, with a removal rate of 63 % in just 15 min and a final removal rate of 90 %. It is hoped that this SF-g-PAO, prepared through this straightforward method and characterized by the synergistic action of amino and carboxyl groups, can offer innovative insights into the development of uranium extraction adsorbents.

Impact of virtual education based on health belief model on cervical cancer screening behavior in middle-aged women: A quasi-experimental study.

Cervical cancer is one of the most common cancers in women worldwide and a cause of high mortality among people. Pap smear screening is an appropriate method to prevent cervical cancer and reduce its mortality. This study aimed to determine the effect of web-based education based on the Health Belief Model (HBM) on cervical cancer screening behavior in middle-aged women. This study is a quasi-experimental interventional research that was conducted on 240 middle-aged women aged 40-59 years in Isfahan, Iran, in 2022. An online educational intervention based on the constructs of the Health Belief Model was conducted for the intervention group using the Triple-B platform. The information on the intervention and control groups was collected before, immediately after the intervention, and 2 months later using a valid questionnaire. The gathered Data was analyzed using ANOVA and LSD post-hoc, independent samples t test, chi-square, and MANCOVA statistical tests in SPSS 26 software. After the intervention, the mean scores of knowledge, perceived susceptibility, perceived severity, perceived benefits, self-efficacy, and internal cues to action in the intervention group increased and the mean score of perceived barriers decreased (p < .001). The mean score of the external cues to action did not show a significant difference between the intervention and control groups before, immediately, and 2 months after the intervention. Two months after the intervention, 32 women (26.2%) in the intervention group and two women (1.7%) in the control group performed the Pap smear test. Web-based educational intervention based on HBM using different strategies such as question and answer, presentation of infographics, lectures, brainstorming, showing videos and numerous educational images can be an effective way for increasing knowledge and cognitive variables of women and doing Pap smear test.

Opinion formation over dynamic hierarchical networks with acquaintances and strangers: A genetic variation based double-mechanism framework

Inspired by the psychological phenomenon that agents generally adopt different opinions or action-update mechanisms when faced with different types of neighbors, we propose a novel double-mechanism framework over dynamic hierarchical networks to fill this gap. First, a novel multi-attribute genetic variation-based leader-influencer-follower (LIF) dynamic hierarchical network is developed. Second, we propose a double-mechanism framework in which a synchronous asymmetric Deffuant–Weisbuch model with opinion memory effect (MSADW) and a continuous opinion and discrete action (CODA) model with action memory effect (MCODA) are built, achieving the co-evolution of the agent’s attribute and the social network with acquaintances and strangers, respectively. Finally, the experimental results show that the memory effect can effectively weaken the bounded confidence rule and behavioral preference, accelerating the consensus of group opinions or actions. In addition, all agents attempt to obtain a higher out-degree during the co-evolution process to realize the hierarchical transition. The fitted hierarchical partition functions provide a basis for adjusting social structure from the inverted T-shaped to the pyramid-shaped structure and finally to the olive-shaped structure, which has insightful social interpretations.

Radiant toric varieties and unipotent group actions

We consider complete toric varieties X such that a maximal unipotent subgroup U of the automorphism group Aut(X) acts on X with an open orbit. It turns out that such varieties can be characterized by several remarkable properties. We study the set of Demazure roots of the corresponding complete fan, describe the structure of a maximal unipotent subgroup U in Aut(X), and find all regular subgroups in U that act on X with an open orbit.

All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces

We demonstrate that the linear quotient singularity for the exceptional subgroup G G in S p ( 4 , C ) \mathrm {Sp}(4,\mathbb {C}) of order 32 is isomorphic to an affine quiver variety for a 5-pointed star-shaped quiver. This allows us to construct uniformly all 81 projective crepant resolutions of C 4 / G \mathbb {C}^4/G as hyperpolygon spaces by variation of GIT quotient, and we describe both the movable cone and the Namikawa Weyl group action via an explicit hyperplane arrangement. More generally, for the n n -pointed star shaped quiver, we describe completely the birational geometry for the corresponding hyperpolygon spaces in dimension 2 n − 6 2n-6 ; for example, we show that there are 1684 projective crepant resolutions when n = 6 n=6 . We also prove that the resulting affine cones are not quotient singularities for n ≥ 6 n \geq 6 .

Valence-Dependent Implicit Action Generalization Among Group Members.

People implicitly generalize the actions of known individuals in a social group to unknown members. However, actions have social goals and evaluative valences, and the extent to which actions with different valences (helpful and harmful) are implicitly generalized among group members remains unclear. We used computer animations to simulate social group actions, where helping and hindering actions were represented by aiding and obstructing another's climb up a hill. Study 1 found that helpful actions are implicitly expected to be shared among members of the same group but not among members of different groups, but no such effect was found for harmful actions. This suggests that helpful actions are more likely than harmful actions to be implicitly generalized to group members. This finding was replicated in Study 2 by increasing the group size from three to five. Study 3 found that the null effect for generalizing harmful actions among group members is not due to the difficulty of detecting action generalization, as both helpful and harmful actions are similarly generalized within particular individuals. Moreover, Study 4 demonstrated that weakening social group information resulted in the absence of implicit generalization for helpful actions, suggesting the specificity of group membership. Study 5 revealed that the generalization of helping actions occurred when actions were performed by multiple group members rather than being repeated by one group member, showing group-based inductive generalization. Overall, these findings support valence-dependent implicit action generalization among group members. This implies that people may possess different knowledge regarding valenced actions on category-based generalization.

Variational principle of higher dimension weighted pressure for amenable group actions

Let r≥2 and (Xi,G)(i=1,⋯,r) be topological dynamical systems with an infinite countable discrete amenable phase group G. Suppose that πi:(Xi,G)→(Xi+1,G) are factor maps, a={a1,⋯,ar−1}∈Rr−1 is a vector with 0≤ai≤1 and (w1,⋯,wr)∈Rr is a probability vector associated with a. In this paper, given f∈C(X1), we introduce the weighted topological pressure Pa(f,G). Moreover, by using measure-theoretical theory, we establish a variational principle:Pa(f,G)=supμ∈MG(X1)⁡(∑i=1rwihμi(Xi,G)+w1∫X1fdμ), where h{⋅}(⋅,G) is the Kolmogorov-Sinai entropy of the systems acted by the amenable group G and μi=πi−1∘⋯∘π1μ is the induced G-invariant measure on Xi.

Corrigendum: Model theory of fields with virtually free group actions

AbstractThere is an irreparable error in the proof of Theorem 3.26 in the above‐mentioned paper and we withdraw the claim of having proved that theorem. In fact, that theorem is false in a very strong sense.