Projective Space Research Articles

Voxel Map to Occupancy Map Conversion Using Free Space Projection for Efficient Map Representation for Aerial and Ground Robots

Voxel Map to Occupancy Map Conversion Using Free Space Projection for Efficient Map Representation for Aerial and Ground Robots

Channel Estimation for RIS-Assisted Multiuser mmWave Systems With Direct Channels Based on a Novel Space Projection Approach

Channel Estimation for RIS-Assisted Multiuser mmWave Systems With Direct Channels Based on a Novel Space Projection Approach

Action of ℝ-Fuchsian groups on ℙℂn

Let [Formula: see text] be the group of orientation preserving isometries of the [Formula: see text]-dimensional real hyperbolic space [Formula: see text], and let [Formula: see text] be the group of holomorphic isometries of the [Formula: see text]-dimensional complex hyperbolic space [Formula: see text]. The group [Formula: see text] is naturally a subgroup of [Formula: see text], so it acts on [Formula: see text] preserving a ball that serves as a model for [Formula: see text]. We consider discrete subgroups of [Formula: see text] with limit set an [Formula: see text]-dimensional real sphere and we look at their action on [Formula: see text] for [Formula: see text] via the natural embedding of [Formula: see text] into [Formula: see text]. We describe the Kulkarni limit set of these set of these actions and show that this is a real semi-algebraic set in [Formula: see text]. We also show that the Kulkarni region of discontinuity can only have either one or three connected components. We use Sylvester’s law of inertia when [Formula: see text]. In the other cases, we use some suitable projections of the [Formula: see text]-dimensional complex projective space to the [Formula: see text]-dimensional complex projective space.

A Schmidt–Nochka theorem for closed subschemes in subgeneral position

Abstract In previous work, the authors established a generalized version of Schmidt’s subspace theorem for closed subschemes in general position in terms of Seshadri constants. We extend our theorem to weighted sums involving closed subschemes in subgeneral position, providing a joint generalization of Schmidt’s theorem with seminal inequalities of Nochka. A key aspect of the proof is the use of a lower bound for Seshadri constants of intersections from algebraic geometry, as well as a generalized Chebyshev inequality. As an application, we extend inequalities of Nochka and Ru–Wong from hyperplanes in 𝑚-subgeneral position to hypersurfaces in 𝑚-subgeneral position in projective space, proving a sharp result in dimensions 2 and 3, and coming within a factor of 3 / 2 3/2 of a sharp inequality in all dimensions. We state analogous results in Nevanlinna theory generalizing the second main theorem and Nochka’s theorem (Cartan’s conjecture).

Audiovisual project «Zvukoizolyatsia»: specifics of conceptual and spatial implementation of the compositional and technical principles

The relevance of the study is determined by the insufficient development of the stated problems, the lack of a systematic analysis of projects of electroacoustic and audiovisual synthesis in academic music. The introduction of technical materials from the private archives of the project authors into scientific circulation also seems important. Usually, such «internal» documents do not come to the attention of researchers due to their utilitarian nature in the organizational process of the implementation of a work/project, but sometimes they can open perspectives for the further study of similar artistic phenomena. Most often, large-scale projects, in particular audiovisual ones (requiring the involvement of significant resources to ensure technical organization), are performed «one time only»; mentions of them gradually disappear from the information space. The analysis of the peculiarities of the implementation of audiovisual projects contributes to the systematization and differentiation of existing and new perspectives of the study of this synthetic phenomenon in the modern art history discourse. The main objectives of the study are to reveal the specifics of the implementation of spatial compositional and technical principles and the peculiarities of the implementation of one of the landmark experiments in the field of electroacoustic and audiovisual synthesis, «ZvukoIzolyatsia» project (2011/2012), to understand its significance in the modern artistic space, to outline the particular features of reception of musical-spatial performance. The research methodology: historical and functional method to define and forecast the place and role of the project in the modern art space; analytical method to reveal the specifics of the embodiment of spatial compositional and technical principles; intent analysis to find the author's intentions; the method of theoretical generalization to summarize the results of the research. Results and conclusions. The first and second «ZvukoIzolyatsia» became one of the most daring and vivid experiments in the field of electroacoustic and visual synthesis. In the aesthetic search for musical expressiveness, in the logical regularity of the development of the art of the 21st century, the project covered the most important innovations of the compositional technique of the last century (in particular, the achievements of the electroacoustic avant-garde, the use of real-time sound processing technologies, the application of sonoristic principles that become a category of musical thinking, manipulation of objects which can make sounds, etc.). The expansion of the boundaries of the academic environment or a complete departure from it (in the 2012 project), as a desire to overcome the space of the concert hall, and the involvement of industrial spaces — conventionally marginal — forms a new type of aesthetic disposition (P. Bourdieu). The dialogue with the space is carried out as an action (artistic gesture) aimed at expanding the perception models of artistic expression, thanks to which the horizon of listening expectations is expanded. This leads to the formation of a new aesthetic experience in the recipient, which will potentially influence the reception of other works of modern academic practice. The involvement of VJ technologies creates a new communication situation, creating a fundamentally new conceptual field, which in some cases can act as a mechanism for destroying stereotypes of artistic thinking. Audiovisual synthesis in relation to musical art creates new perspectives for multifaceted work with audio and visual material. Researching the experience of using audio and video technologies, their interaction with the spatial factor contributes to the development of electroacoustic music. The proposed investigation can to some extent serve as a methodological aid in further art studies of audiovisual compositional projects.

Equivariant Holomorphic Hermitian Vector Bundles over a Projective Space

The aim here is to describe all isomorphism classes of SU(n+1)-equivariant Hermitian holomorphic vector bundles on the complex projective space CPn. If G⊂SU(n+1) is the isotropy subgroup of a chosen point x0∈CPn, and ρ:G⟶GL(V) is a unitary representation, we obtain SU(n+1)-equivariant holomorphic Hermitian vector bundles on CPn. Next, given any v∈End(Vρ)⊗(Tz00,1CPn)∗ satisfying certain conditions, a new structure of an SU(n+1)-equivariant holomorphic Hermitian vector bundle on this underlying C∞ holomorphic Hermitian bundle is obtained. It is shown that all SU(n+1)-equivariant holomorphic Hermitian vector bundles on CPn arise this way.

Mapping for Reconnection

Indigenous place names contain knowledge of the landscape and encode unique perceptions of landscapes with which Indigenous Peoples have interacted for hundreds, often thousands, of years. However, many Indigenous place names have been lost as a result of colonization. Furthermore, many of these have been replaced with colonial place names, and their loss contributes to overall language attrition. In turn, the loss of language makes it difficult, or even impossible, to understand the concepts embedded within Indigenous place names that do remain in use. The documentation and conservation of place names is thus an important aspect of Indigenous language preservation and revitalization that can help facilitate reconnection with the language and the land. This paper outlines the Atlas of Kanyen'kehá:ka Space digital atlas project, an initiative that uses digital mapping to aid in the documentation and revitalization of the Kanyen'kéha (Mohawk) language through community participatory mapping of Kanyen'kéha place names and landscape-related language. It describes the initial stages of the Atlas of Kanyen'kehá:ka Space project, including its theoretical framework, the O'nonna model, and its community-based participatory methodology for digital mapping. It reports on a series of mapping workshops within three Kanyen'kehá:ka communities and shares initial findings and future directions for the project.

CDVAE: VAE-guided diffusion for particle accelerator beam 6D phase space projection diagnostics

Imaging the 6D phase space of a beam in a particle accelerator in a single shot is currently impossible. Single shot beam measurements only exist for certain 2D beam projections and these methods are destructive. A virtual diagnostic that can generate an accurate prediction of a beam’s 6D phase space would be incredibly useful for precisely controlling the beam. In this work, a generative conditional diffusion- based approach to creating a virtual diagnostic of all 15 unique 2D projections of a beam’s 6D phase space is developed. The diffusion process is guided by a combination of scalar parameters and images that are converted to low-dimensional latent vector representation by a variational autoencoder (VAE). We demonstrate that conditional diffusion guided by a VAE (cDVAE) can accurately reconstruct all 15 of the unique 2D projections of a charged particle beam’s 6D phase space for the HiRES compact accelerator.

Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-dimensional domain extended in both the vertical and the transverse dimensions, Gao et al. (Phys. Rev. E, vol. 97, 2018, 053107) have observed a variety of convection patterns which are not described by linear stability analysis. We investigate the fully nonlinear dynamics of vertical convection using a dynamical-systems approach based on the Oberbeck–Boussinesq equations. We compute the invariant solutions of these equations and the bifurcations that are responsible for the creation and termination of various branches. We map out a sequence of local bifurcations from the laminar base state, including simultaneous bifurcations involving patterned steady states with different symmetries. This atypical phenomenon of multiple branches simultaneously bifurcating from a single parent branch is explained by the role of $D_4$ symmetry. In addition, two global bifurcations are identified: first, a homoclinic cycle from modulated transverse rolls and second, a heteroclinic cycle linking two symmetry-related diamond-roll patterns. These are confirmed by phase space projections as well as the functional form of the divergence of the period close to the bifurcation points. The heteroclinic orbit is shown to be robust and to result from a 1:2 mode interaction. The intricacy of this bifurcation diagram highlights the essential role played by dynamical systems theory and computation in hydrodynamic configurations.

Enhancing project success through value-creating social interactions: insights from project managers in Iranian governmental organizations

Purpose Despite significant advancements in project processes, tools and systems, overall project success rates have not markedly improved. Recent studies underscore the importance of “value creation” as a key factor in enhancing project outcomes, particularly through the interaction between project managers and employees. However, there remains a critical gap in understanding how project managers can effectively leverage daily social interactions to foster cooperation and create value in complex, temporary and high-pressure environments typical of project-based organizations. This study aims to address this gap by exploring the lived experiences of project managers in governmental project-based organizations, focusing on how they use social interactions as a strategic tool for value creation. Design/methodology/approach Semi-structured interviews were conducted with various groups of project managers using open-ended questions, selected through the snowball sampling method. The collected data were then analyzed qualitatively using grounded theory techniques. Findings The findings indicate that project managers can foster value creation in the minds of employees by employing a range of behavioral strategies in the workplace. The effectiveness of these strategies, however, is influenced by the prevailing social culture within the project implementation site. Originality/value Consequently, understanding and adopting the appropriate behavioral approaches depend on the project’s unique social context. In conclusion, this research sheds light on the most effective parameters for value creation through social interactions in project spaces.

Exploring the moderating effect of private green space on the relationship between density and housing prices

This study examines the impact of private green spaces on housing prices and their moderating effect on the relationship between housing density and prices in Seoul, South Korea. Our research finds a negative relationship between housing density and housing prices, suggesting that higher density typically depresses property values. The creation of private green spaces within residential complexes can generate an additional “green premium” when designed on a large scale with continuity and without the presence of automobiles. This study also suggests the potential of such green spaces in alleviating some of the negative effects of high density on housing prices. This research contributes to the discourse on sustainable and compact urban development, advocating for policy interventions that encourage the inclusion of private green spaces in high-density residential projects.

Transitive (q − 1)-fold packings of PGn(q)

A t-fold packing of a projective space PGn(q) is a collection P of line-spreads such that each line of PGn(q) occurs in precisely t spreads in P. A t-fold packing P is transitive if a subgroup of PΓLn+1(q) preserves and acts transitively on P. We give a construction for a transitive (q−1)-fold packing of PGn(q), where q=2k, for any odd positive integers n and k, such that n⩾3. This generalises a construction of Baker from 1976 for the case q=2.

Concordance structure set of connected sum of projective spaces

Concordance structure set of connected sum of projective spaces

Speed excess and total acceleration: a kinematical approach to entanglement

Abstract The total variance of a spin state is defined as the average of the variances of spin projection measurements along three orthogonal axes. We show that this quantity also gives the squared rotational speed of the state in projective space, averaged over all rotation axes. We compute the addition law, under system composition, for this quantity and find that, in the case of separable states, it is of simple pythagorean form. In the presence of entanglement, we find that the composite state ‘rotates faster than its parts’, thus unveiling a kinematical origin for the correlation of total variance with entanglement. We analyze a similar definition for the acceleration of a state under rotations, for both pure and mixed states, and probe numerically its relation with a wide array of entanglement related measures.

Dual Contrastive Label Enhancement

Label Enhancement (LE) strives to convert logical labels of instances into label distributions to provide data preparation for label distribution learning (LDL). Existing LE methods ordinarily neglect to consider original features and logical labels as two complementary descriptive views of instances for extracting implicit related information across views, resulting in insufficient utilization of the feature and logical label information of the instances. To address this issue, we propose a novel method named Dual Contrastive Label Enhancement (DCLE). This method regards original features and logical labels as two view-specific descriptions and encodes them into a unified projection space. We employ dual contrastive learning strategy at both instance-level and class-level to excavate cross-view consensus information and distinguish instance representations by exploring inherent correlations among features, thereby generating high-level representations of the instances. Subsequently, to recover label distributions from obtained high-level representations, we design a distance-minimized and margin-penalized training strategy and preserve the consistency of label attributes. Extensive experiments conducted on 13 benchmark datasets of LDL validate the efficacy and competitiveness of DCLE.

Correlators of N=4 Supersymmetric Yang-Mills Theory on Real Projective Space at Strong Coupling.

We consider type IIB supergravity on a Z_{2} quotient of AdS_{5}×S^{5} as the holographic dual of strongly coupled 4D N=4 SYM on RP^{4} space with the gauging of charge conjugation. Using bootstrap techniques, we determine all two-point functions of 1/2-BPS operators of arbitrary weights at the leading order in the large central charge expansion.

Minimal Terracini loci in projective space

Minimal Terracini loci in projective space

Local complete intersections and Weierstrass points

This work presents a simple proof that the moduli space of complete integral Gorenstein curves with a prescribed symmetric Weierstrass semigroup becomes a weighted projective space, even for fields of positive characteristic, when the associated monomial curve is a local complete intersection.

Upper bounds for the number of substructures in finite geometries from the container method

We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial ovoids and EKR-sets of flags in polar spaces, line spreads in PG(2r−1,q) and plane spreads in PG(5,q), and caps in PG(3,q). The latter result extends work due to Roche-Newton and Warren [21] and Bhowmick and Roche-Newton [6].Finally, we investigate caps in p-random subsets of PG(r,q), which parallels recent work for arcs in projective planes by Bhowmick and Roche-Newton, and Roche-Newton and Warren [6,21], and arcs in projective spaces by Chen, Liu, Nie and Zeng [8].

Period integrals of smooth projective complete intersections as exponential periods

Let X be a smooth projective complete intersection over Q of dimension n−k in the projective space PQn defined by the zero locus of f_(x_)=(f1(x_),⋯,fk(x_)), for given positive integers n and k. For a given primitive homology cycle [γ]∈Hn−k(X(C),Z)0, the period integral is defined to be a linear map from the primitive de Rham cohomology group HdR,primn−k(X(C);Q) to C given by [ω]↦∫γω. The goal of this article is to interpret this period integral as Feynman's path integral of 0-dimensional quantum field theory with the action functional S=∑ℓ=1kyℓfℓ(x_) (in other words, the exponential period with the action functional S) and use this interpretation to develop a formal deformation theory of period integrals of X, which can be viewed as a modern deformation theoretic treatment of the period integrals based on the Maurer-Cartan equation of a dgla (differential graded Lie algebra).