Action Of Group Research Articles

Generic Stabilizers in Actions of Simple Algebraic Groups

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception, there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.

On reversible automata generating lamplighter groups

For any nontrivial abelian group X we construct a reversible automaton such that its set of states and alphabet are identified with X, transition and output functions are defined via the left regular action and its group splits into the restricted wreath product X≀Z, i.e. is a lamplighter group.

Repelling Planet Pairs by Ping-pong Scattering

The Kepler mission reveals a peculiar trough-peak feature in the orbital spacing of close-in planets near mean-motion resonances: a deficit and an excess that are, respectively, a couple of percent interior to and wide of the resonances. This feature has received two main classes of explanations: one involving eccentricity damping and the other scattering with small bodies. Here, we point out a few issues with the damping scenario and study the scattering scenario in more detail. We elucidate why scattering small bodies tends to repel two planets. As the small bodies random-walk in energy and angular momentum space, they tend to absorb fractionally more energy than angular momentum. This, which we call “ping-pong repulsion,” transports angular momentum from the inner to the outer planet and pushes the two planets apart. Such a process, even if ubiquitous, leaves identifiable marks only near first-order resonances: diverging pairs jump across the resonance quickly and produce the mean-motion resonance asymmetry. To explain the observed positions of the trough-peaks, a total scattering mass of order a few percent of the planet masses is required. Moreover, if this mass is dominated by a handful of Mercury-sized bodies, one can also explain the planet eccentricities as inferred from transit-time variations. Last, we suggest how these conditions may have naturally arisen during the late stages of planet formation.

A Cortical-Inspired Contour Completion Model Based on Contour Orientation and Thickness.

An extended four-dimensional version of the traditional Petitot-Citti-Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M=SIM(2). The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication. The sub-Riemannian distance is proportional to the energy expended in interneuron activation between two excited border neurons. According to the model, the damaged image contours are restored via sub-Riemannian geodesics in the space M of positions, orientations and thicknesses (scales). We study the geodesic problem in M using geometric control theory techniques. We prove the existence of a minimal geodesic between arbitrary specified boundary conditions. We apply the Pontryagin maximum principle and derive the geodesic equations. In the special cases, we find explicit solutions. In the general case, we provide a qualitative analysis. Finally, we support our model with a simulation of the association field.

Augmented reality and optical navigation assisted orbital surgery: a novel integrated workflow

Abstract Objectives Due to the close topographical relationship of functional relevant anatomic structures, limited space and cosmetic aspects orbital surgery will remain a challenging discipline. Therefore, novel technical capabilities are necessary for further surgical progress. We here tested the integration of augmented reality and optical navigation in one workflow for interdisciplinary decision-making, feasibility and intraoperative guidance. Methods High-resolution contrast-enhanced MRI and CT scans were automated and manual-assisted segmented to achieve a detailed three-dimensional (3D) model of the individual patho-anatomical relationships. Augmented reality was used for interdisciplinary preoperative planning and intraoperative intuitive navigation. Mayfield clamp head holder in combination with optical surface matching registration assured navigation assisted microsurgery. Results Combinations of different MRI-sequences and CT-scans were necessary for detailed 3D-modeling. Modeling was time consuming and only viable in the hands of medical, surgical and anatomical trained staff. Augmented reality assured a quick, intuitive interdisciplinary orientation. Intraoperative surface matching registration enabled precise navigation in the orbital space. Conclusions Optical Navigation and microscope integration achieved a straightforward microsurgical workflow and should be implemented regularly. Augmented reality represented a useful tool for preoperative interdisciplinary planning and intraoperative intuitive orientation. It further stated an excellent educational tool.

Primes and almost primes on orbits of group actions

Primes and almost primes on orbits of group actions

Agroenergy Policies and the Influence of Interest Groups – the Case of Polo Agroindustrial e Bioenergético do Médio São Francisco in Bahia, Brasil

Objective: The objective of this article was to investigate how public policies to promote productive activities can be influenced by the actions of interest groups, affect decision-making, and consequently increase the risks of failure and generate government failures. Theoretical Framework: The theoretical framework adopted is the theories of Public Choice and Strategic Public Management, which provided the basis for understanding the context of the investigation. Method: The methodology consisted of literature review, interviews, policy analysis methodology (PAM) and case study. Data was collected through bibliographic and documentary research, semi-structured interviews with public officials, business people and researchers, and field visits for direct observation. Results and Discussion: The findings revealed that interest groups opposed to stricter regulations on the occupation of territorial space for the exploitation of natural resources influenced the decision-making process for setting the policy agenda, formulating and implementing policies. It also revealed the "permeability" of the government to pressure from these groups, which resulted in the nonimplementation of the Polo. Research Implications: The practical and theoretical implications of this research provide insights into how the findings can influence practices in the fields of state theory, public policy formulation and management, and territorial development, as well as in the productive, social, and environmental sectors. Originality/Value: This study contributes to the literature by relating the adopted theories to a real case of public policy failure, so that public policy makers can develop mechanisms to curb or minimize the influence of these groups in governments.

Reflection length at infinity in hyperbolic reflection groups

Abstract In a discrete group generated by hyperplane reflections in the 𝑛-dimensional hyperbolic space, the reflection length of an element is the minimal number of hyperplane reflections in the group that suffices to factor the element. For a Coxeter group that arises in this way and does not split into a direct product of spherical and affine reflection groups, the reflection length is unbounded. The action of the Coxeter group induces a tessellation of the hyperbolic space. After fixing a fundamental domain, there exists a bijection between the tiles and the group elements. We describe certain points in the visual boundary of the 𝑛-dimensional hyperbolic space for which every neighbourhood contains tiles of every reflection length. To prove this, we show that two disjoint hyperplanes in the 𝑛-dimensional hyperbolic space without common boundary points have a unique common perpendicular.

The number of Hamiltonian cycles in groups of Symmetry

Groups are algebraic structures in Abstract Algebra comprised of a set of elements with a binary operation that satisfies closure, associativity, identity and invertibility. Cayley graphs serve as a visualization tool for groups, as they are capable of illustrating certain structures and properties of groups geometrically. In particular, each element in a group is assigned to a vertex in Cayley graphs. By the group action of left-multiplication, distinct elements in the generating sets can act on each element to create varied directed edges (Meier[1]). By contrast, the presence of a Hamiltonian cycles within a graph demonstrates its level of connectivity. In this research paper, utilizing directed Cayley graphs, we present a series of conjectures and theorems regarding the number and existence of Hamiltonian cycles within Dihedral groups, Symmetric groups of Platonic solids and Symmetric groups. By exploring the relationship between Abstract groups and Hamiltonian graphs, this work contributes to the broader field of research pertaining to Groups of Symmetry and Geometric Group Theory.

Group-Action-Based S-box Generation Technique for Enhanced Block Cipher Security and Robust Image Encryption Scheme

Data security is one of the biggest concerns in the modern world due to advancements in technology, and cryptography ensures that the privacy, integrity, and authenticity of such information are safeguarded in today’s digitally connected world. In this article, we introduce a new technique for the construction of non-linear components in block ciphers. The proposed S-box generation process is a transformational procedure through which the elements of a finite field are mapped onto highly nonlinear permutations. This transformation is achieved through a series of algebraic and combinatorial operations. It involves group actions on some pairs of two Galois fields to create an initial S-box Pr Sbox, which induces a rich algebraic structure. The post S-box Po Sbox, which is derived from heuristic group-based optimization, leads to high nonlinearity and other important cryptographic parameters. The proposed S-box demonstrates resilience against various attacks, making the system resistant to statistical vulnerabilities. The investigation reveals remarkable attributes, including a nonlinearity score of 112, an average Strict Avalanche Criterion score of 0.504, and LAP (Linear Approximation Probability) score of 0.062, surpassing well-established S-boxes that exhibit desired cryptographic properties. This novel methodology suggests an encouraging approach for enhancing the security framework of block ciphers. In addition, we also proposed a three-step image encryption technique comprising of Row Permutation, Bitwise XOR, and block-wise substitution using Po Sbox. These operations contribute to adding more levels of randomness, which improves the dispersion across the cipher image and makes it equally intense. Therefore, we were able to establish that the approach works to mitigate against statistical and cryptanalytic attacks. The PSNR, UACI, MSE, NCC, AD, SC, MD, and NAE data comparisons with existing methods are also provided to prove the efficiency of the encryption algorithm.

Domains of discontinuity of Lorentzian affine group actions

We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb R}^n$$\\end{document}.

Strong equivalence of graded algebras

We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. As to a more general idempotent graded algebra B, we point out that the Cohen-Montgomery duality holds for B, and B is graded-equivalent to a global skew group algebra. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that any product partial group action α is globalizable up to Morita equivalence; if such a globalization β is minimal, then the skew group algebras by α and β are graded-equivalent; moreover, β is unique up to Morita equivalence. Finally, we show that strongly-graded-equivalent partially-strongly-graded algebras with orthogonal local units are stably isomorphic as graded algebras.

With sensitive eyes: ECEC teachers’ visual gaze and related reflections on pedagogical actions in toddler groups using eye-tracking glasses

This study explored early childhood education and care (ECEC) teachers’ visual gaze and related reflections on pedagogical actions during pedagogical activities in groups of children under three years of age in Finland. The data were collected from play and teacher-guided activities using mobile eye-tracking glasses, the retrospective thinking aloud (RTA) method, and semi-structured interviews. The results showed that even though the teachers were surprised about some aspects of the visual gaze metrics, they reflected on and gave reasons for their visual gazes on children. When observing gaze data from play, teachers explained the high amount of gaze by citing children’s particular needs. When observing gaze data from guided activities, teachers reflected on children’s unpredictable behavior and noted that the children’s need for support in concentration was linked to more gazes by the teacher. The findings showed that both during play and guided activities, children seeking a gaze and the position of children in the classroom influenced the number of teachers’ gazes. In the teachers’ explanations of their visual gaze and related pedagogical actions, five categories were identified: protection; physical and emotional availability, teaching and learning; facilitation; and initiatives. This explorative study showed that teachers utilize their knowledge concerning children’s individuality, development, and learning when they explain their decisions concerning their visual gaze and pedagogical activities with toddlers. The use of mobile eye-tracking technology is relatively new; therefore, its applications to ECEC are pioneering for the development of the field in relation to the practices and research of toddlers’ groups and groups with older children in ECEC

Substructures of the Weyl group and their physical applications

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

Strengthening person-centered care through quality improvement: a mixed-methods study examining implementation of the Person-Centered Care Assessment Tool in Zambian health facilities

Introduction Person-centered care (PCC) is considered a fundamental approach to address clients’ needs. There is a dearth of data on specific actions that HIV treatment providers identify as priorities to strengthen PCC. Objective This study team developed the Person-Centered Care Assessment Tool (PCC-AT), which measures PCC service delivery within HIV treatment settings. The PCC-AT, including subsequent group action planning, was implemented across 29 facilities in Zambia among 173 HIV treatment providers. Mixed-methods study objectives included: (1) identify types of PCC-strengthening activities prioritized based upon low and high PCC-AT scores; (2) identify common themes in PCC implementation challenges and action plan activities by low and high PCC-AT score; and (3) determine differences in priority actions by facility ART clinic volume or geographic type. Methods The study team conducted thematic analysis of action plan data and cross-tabulation queries to observe patterns across themes, PCC-AT scores, and key study variables. Results The qualitative analysis identified 39 themes across 29 action plans. A higher proportion of rural compared to urban facilities identified actions related to stigma and clients’ rights training; accessibility of educational materials and gender-based violence training. A higher proportion of urban and peri-urban compared to rural facilities identified actions related to community-led monitoring. Discussion Findings provide a basis to understand common PCC weaknesses and activities providers perceive as opportunities to strengthen experiences in care. Conclusion To effectively support clients across the care continuum, systematic assessment of PCC services, action planning, continuous quality improvement interventions and re-measurements may be an important approach.

Anaerobic recovery of vivianite from waste-activated sludge through combined sludge pre-fermentation and agroforestry biomass-based biochar

The recovery of vivianite through the anaerobic digestion of waste-activated sludge has attracted considerable attention due to its operational simplicity and the high economic value of vivianite. This study concentrated on the recovery of vivianite from anaerobic fermentation systems through a strategy combining sludge pre-fermentation with the waste agricultural and forestry biomass-derived biochar (ZBC). In-depth analyses of the structure and functionality of ZBC were conducted using techniques such as Fourier-transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), and Raman spectroscopy. The sediment produced after the experiment and the changes in microbial community composition were characterized. The results indicated that pre-fermentation promoted phosphorus release, enhancing the synthesis of vivianite while selectively enriching respiratory and fermentative Fe (III)-reducing microorganisms. When FeOOH was used as the Fe (III) source, ZBC, through its dual action of redox functional groups and graphitization structure, increased the Fe2+ production by 243.6 % in the system dominated by respiratory Fe (III)-reducing bacteria. The optimal dosage of ZBC for the simultaneous recovery of vivianite resources and methane energy was 2.5 g/L. The combined application of pre-fermentation and ZBC provides a novel approach for the efficient recycling of vivianite and offers new insights into the reuse of agroforestry waste biomass resources.

Finite group actions on abelian groups of finite Morley rank

Finite group actions on abelian groups of finite Morley rank

CSI-Otter: isogeny-based (partially) blind signatures from the class group action with a twist

In this paper, we construct the first provably-secure isogeny-based (partially) blind signature scheme. While at a high level the scheme resembles the Schnorr blind signature, our work does not directly follow from that construction, since isogenies do not offer as rich an algebraic structure. Specifically, our protocol does not fit into the linear identification protocol abstraction introduced by Hauck, Kiltz, and Loss (EUROCYRPT’19), which was used to generically construct Schnorr-like blind signatures based on modules such as classical groups and lattices. Consequently, our scheme is provably secure in the random oracle model (ROM) against poly-logarithmically-many concurrent sessions assuming the subexponential hardness of the group action inverse problem. In more detail, our blind signature exploits the quadratic twist of an elliptic curve in an essential way to endow isogenies with a strictly richer structure than abstract group actions (but still more restrictive than modules). The basic scheme has public key size 128 B and signature size 8 KB under the CSIDH-512 parameter sets—these are the smallest among all provably secure post-quantum secure blind signatures. Relying on a new ring variant of the group action inverse problem (rGAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{rGAIP}$$\\end{document}), we can halve the signature size to 4 KB while increasing the public key size to 512 B. We provide preliminary cryptanalysis of rGAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extsf{rGAIP}} $$\\end{document} and show that for certain parameter settings, it is essentially as secure as the standard GAIP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{GAIP}$$\\end{document}. Finally, we show a novel way to turn our blind signature into a partially blind signature, where we deviate from prior methods since they require hashing into the set of public keys while hiding the corresponding secret key—constructing such a hash function in the isogeny setting remains an open problem.

On symmetry adapted bases in trigonometric optimization

The problem of computing the global minimum of a trigonometric polynomial is computationally hard. We address this problem for the case, where the polynomial is invariant under the exponential action of a finite group. The strategy is to follow an established relaxation strategy in order to obtain a converging hierarchy of lower bounds. Those bounds are obtained by numerically solving semi-definite programs (SDPs) on the cone of positive semi-definite Hermitian Toeplitz matrices, which is outlined in the book of Dumitrescu Dumitrescu (2007). To exploit the invariance, we show that the group has an induced action on the Toeplitz matrices and prove that the feasible region of the SDP can be restricted to the invariant matrices, whilst retaining the same solution. Then we construct a symmetry adapted basis tailored to this group action, which allows us to block-diagonalize invariant matrices and thus reduce the computational complexity to solve the SDP.The approach is in its generality novel for trigonometric optimization and complements the one that was proposed as a poster at the ISSAC 2022 conference Hubert et al. (2022) and later extended to Hubert et al. (2024). In the previous work, we first used the invariance of the trigonometric polynomial to obtain a classical polynomial optimization problem on the orbit space and subsequently relaxed the problem to an SDP. Now, we first make the relaxation and then exploit invariance.Partial results of this article have been presented as a poster at the ISSAC 2023 conference Metzlaff (2023).

Research on the Motivation and Effect of Longfor Group's Transformation to Asset-light Operation Mode

Since the real estate marketization reform in 1998, China's real estate industry has continued to focus on asset operation mode, at that time in the golden period of the industry, real estate enterprises only need to hoard a lot of land, wait for the appreciation of the land and then resell, you can get considerable returns. However, in the context of the current slowdown in the economic growth of China's real estate industry, it is difficult for commercial real estate enterprises to continue to operate with heavy assets, so such enterprises begin to seek transformation, and want to change a profit model to match the current market. As a new way for enterprises to accumulate core competence and maximize value, "asset-light operation" model has been highly valued by the academic and business circles. This paper takes Longfor Group, a representative real estate enterprise, as the research object, and makes an in-depth analysis of the company's finance from the perspective of its financial characteristics and financial performance, in order to provide certain theoretical references for the successful application of the transformation and development of similar companies.