Projective Space Research Articles

Point cloud registration method for indoor depth sensor acquisition system based on dual graph computation with irregular shape factors

AbstractThe registration performance determines the widespread indoor application of 3D models acquired by depth sensors. Many advanced registration methods lack comprehensive feature aggregation and poor generalization capabilities, which improves the mismatching ratio. Here, a dual graph network is proposed by incorporating irregular shape factors to make point cloud features more expressive. At first, we transform point cloud sets into the stellar graph within the local neighbourhood of each point. The deep feature and shape factor of each point are combined in the directional‐connected irregular projection space. Subsequently, the combined features are modelled as the second graph. By the attention mechanism computation, feature information is continuously aggregated with intra‐graph and inter‐graph. Finally, a loss function is utilized to confirm point correspondence and perform the registration through singular value decomposition. Extensive experiments validate that the proposed point cloud registration method achieves state‐of‐the‐art performance.

Abstract LB252: iCellSight: An interactive tool for analyzing and visualizing in-situ high-plex cellular protein data

Abstract Introduction The increased use of tissue-based multiplex immunohistochemistry (mIHC) in cancer research has significantly enhanced the generation of spatial hyper-plex images, crucial for understanding complex tumor-immune microenvironments. This advancement has led to a growing demand for spatial data analysis tools that enable quick and insightful evaluation. While existing spatial analysis software like Steinbock and SPIAT offer foundational support, effectively managing the high-dimensional and voluminous cellular data to derive meaningful biological insights remains challenging. This is especially true for researchers lacking bioinformatics expertise who seek to conduct quick preliminary evaluations. To address this gap, we introduce iCellSight: a user-friendly, code-free interactive analysis and visualization tool tailored to empower researchers with rapid and intuitive interpretation of in-situ cellular data. Material and methods A formalin-fixed, paraffin-embedded colorectal carcinoma (CRC) patient tissue section was subjected to staining using COMET (Lunaphore, Switzerland), which automates sequential immunofluorescence staining and imaging of up to 40 protein markers. The stacked image file produced was analyzed with HALO (Indica Labs, USA), which generated cell-level data like cell coordinates, stain intensity values and user-defined cell types. We developed a Shiny App tool, using the Shiny R package, with key features for cell data interpretation: (1) user-input cell number subsampling; (2) dimensional reduction plots with PhenoGraph for unsupervised clustering, allowing a choice of UMAP or t-SNE, and neighbor number selection of 30, 50 or 150; (3) 2D tissue space mapping of PhenoGraph clusters; and (4) heatmap visualizations displaying cluster-wise biomarker expression (with customizable color schemes and scaling), biomarker co-expression, and cluster pair-wise distance. Results Using iCellSight, 297,000 cells were detected from the CRC sample, where 27 clusters were identified. We observed 3 distinct clusters from the t-SNE plot that consist of macrophages, granulocytes, and NK cells and monocytes respectively. From the cluster projection in 2D tissue space, the cluster of NK cells and monocytes was found to be densely populated in a particular area of the tumor nest. Conclusion We presented iCellSight, a code-free visualization and analysis tool which streamlines the semi-automated analysis of spatial hyper-plex protein data. Designed with an intuitive user interface, this app enables researchers to efficiently navigate its features without requiring any prior coding expertise. We anticipate that the visualizations and analysis provided by this tool will significantly assist researchers in their data analyses and facilitate the validation of experimental hypotheses. Citation Format: Yancun Zhu, Felicia Wee, Menaka Priyadharsani Rajapakse, Esther Gek Teo, Nicholas Ang, Solomonraj Wilson, Zheng Yi Ho, Willa Wen-You Yim, Li Yen Chong, Craig Ryan Joseph, Jeffrey Chun Lim, Zhen Wei Neo, Chwee Ming Lim, Bernett Lee, Olaf Rotzschke, Joe Yeong, Mai Chan Lau. iCellSight: An interactive tool for analyzing and visualizing in-situ high-plex cellular protein data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 2 (Late-Breaking, Clinical Trial, and Invited Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(7_Suppl):Abstract nr LB252.

QUASI-POSITIVE ORBIFOLD COTANGENT BUNDLES.: PUSHING FURTHER AN EXAMPLE BY JUNJIRO NOGUCHI

In this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category.

On codimension one holomorphic distributions on compact toric orbifolds

The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we provide a classification for regular distributions on rational normal scrolls and weighted projective spaces. Additionally, under specific conditions, we prove that the singular set of a codimension one holomorphic foliation on a compact toric orbifold admits at least one irreducible component of codimension two, and we also present a Darboux–Jouanolou type integrability theorem for codimension one holomorphic foliations. Our results are exemplified through various illustrative examples.

Roudneff’s Conjecture in Dimension 4

J.-P. Roudneff conjectured in 1991 that every arrangement of n ≥ 2 d + 1 ≥ 5 pseudohyperplanes in the real projective space P d has at most ∑ i = 0 d − 2 ( n − 1 i ) complete cells (i.e., cells bounded by each hyperplane). The conjecture is true for d = 2, 3 and for arrangements arising from Lawrence oriented matroids. Our main contribution is to show the validity of Roudneff’s conjecture for d = 4. Moreover, based on computational data we show that for d ≤ 4 and n ≤ 2 d + 1 the maximum number of complete cells is only obtained (up to isomorphism) by cyclic arrangements.

Tropical graph curves

We study tropical line arrangements associated to a three-regular graph $G$ that we refer to as tropical graph curves. Roughly speaking, the tropical graph curve associated to $G$ , whose genus is $g$ , is an arrangement of $2g-2$ lines in tropical projective space that contains $G$ (more precisely, the topological space associated to $G$ ) as a deformation retract. We show the existence of tropical graph curves when the underlying graph is a three-regular, three-vertex-connected planar graph. Our method involves explicitly constructing an arrangement of lines in projective space, i.e. a graph curve whose tropicalization yields the corresponding tropical graph curve and in this case, solves a topological version of the tropical lifting problem associated to canonically embedded graph curves. We also show that the set of tropical graph curves that we construct are connected via certain local operations. These local operations are inspired by Steinitz’ theorem in polytope theory.

Integrating Artificial Intelligence in Interior Design Education: Concept Development

This article aims to explore the integration of artificial intelligence (AI) as a design tool in interior design education. The research examines the students' interior design studio project outcomes over the usage of AI in creating conceptual images, and the implementation of the AI-created concept to the overall space. In the research, students' projects are divided into two groups of 5 according to sufficient or insufficient prompts for the "AI generated" conceptual images. Barnard's (1992) CAIDC (Consensual Assessment of Interior Design Creativity) scale was used for the assessment. Mann-Whitney U Test was conducted for the results. We understand that there is no significant difference between writing sufficient or insufficient prompts in the concept development phase of interior design projects according to the Barnard (1992)’s design merits. It has been confirmed that the main factor that influences this regard is the need for an appropriate "concept analysis" to adapt the concept generated with AI to the specified project spaces.

Geometry of certain foliations on the complex projective plane

Let $d\geq2$ be an integer. The set $\mathbf{F}(d)$ of foliations of degree $d$ on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension $d^2+4d+2$ on which $\mathrm{Aut}(\mathbb P^2_{\mathbb C})$ acts. We show that there are exactly two orbits $\mathcal{O}(\mathcal{F}_{1}^{d})$ and $\mathcal{O}(\mathcal{F}_{2}^{d})$ of minimal dimension $6$, necessarily closed in $\mathbf{F}(d)$. This generalizes known results in degrees $2$ and $3.$ We deduce that an orbit $\mathcal{O}(\mathcal{F})$ of an element $\mathcal{F}\in\mathbf{F}(d)$ of dimension $7$ is closed in $\mathbf{F}(d)$ if and only if $\mathcal{F}_{i}^{d}\not\in\overline{\mathcal{O}(\mathcal{F})}$ for $i=1,2.$ This allows us to show that in any degree $d\geq3$ there are closed orbits in $\mathbf F(d)$ other than the orbits $\mathcal{O}(\mathcal{F}_{1}^{d})$ and $\mathcal{O}(\mathcal{F}_{2}^{d}),$ unlike the situation in degree $2.$ On the other hand, we introduce the notion of the basin of attraction $\mathbf{B}(\mathcal{F})$ of a foliation $\mathcal{F}\in\mathbf{F}(d)$ as the set of $\mathcal{G}\in\mathbf{F}(d)$ such that $\mathcal{F}\in\overline{\mathcal{O}(\mathcal{G})}.$ We show that the basin of attraction $\mathbf{B}(\mathcal{F}_{1}^{d})$, resp. $\mathbf{B}(\mathcal{F}_{2}^{d})$, contains a quasi-projective subvariety of $\mathbf{F}(d)$ of dimension greater than or equal to $\dim\mathbf{F}(d)-(d-1)$, resp. $\dim \mathbf{F}(d)-(d-3)$. In particular, we obtain that the basin $\mathbf{B}(\mathcal{F}_{2}^{3})$ contains a non-empty Zariski open subset of $\mathbf{F}(3)$. This is an analog in degree $3$ of a result on foliations of degree $2$ due to Cerveau, D\'eserti, Garba Belko and Meziani.

Penguatan Profil Pelajar Pancasila (P5) Pada Kurikulum Merdeka di Sekolah Dasar

The introduction of the Merdeka Curriculum resulted in a significant shift in focus towards the character of education, creating space for learning projects aimed at strengthening the profile of Pancasila (P5) students. Learning projects inspired by strengthening the Pancasila student profile (P5) are an important strategy in achieving the goals of character education at the elementary school level. This research aims to strengthen the profile of Pancasila students (P5) in the independent curriculum in elementary schools. Research Method This research adopts a qualitative approach as the main methodological framework, enabling an in-depth investigation of the Strengthening Pancasila Student Profile (P5) project in the Merdeka Curriculum. In identifying the project's impact, SDN Surgery 1 Depok was chosen as the research sample to represent various educational contexts and realities at the elementary level. Data collection was carried out using several methods including direct observation, interviews, and document analysis. Research Results The research results show that the Strengthening the Pancasila Student Profile (P5) learning project in the Independent Curriculum makes a positive contribution to the development of student character at the elementary school level

Dialogic space: An introduction

ABSTRACT Communicating in dialogic space in our classrooms prepares us to participate in a democratic, inclusive, and civil society. Dialogic space is that elusive shared space of possibilities that exists among participants as we commit to engaging in ways that new knowledge can be created, presented, questioned, and developed as interpretations of our realities are in conversation with those of others. We agree to be open, yet remain in dialogue, and to welcome different and conflicting ideas and perspectives. In other words, dialogic space carries a particular set of values about how differences are brought into relationship, how people are addressed, and who we can become. Teachers can communicate that dialogic space is an achievable communal aspiration, but it is up to students to participate. In this introduction to a special issue on dialogic space, we discuss challenges as well as discourse conditions and practices that signal investment in the project of dialogic space. In dialogic space, a classroom community embraces its potential as an environment for intellectual curiosity that invites courage and patience in students.

Scalable and Inductive Semi-supervised Classifier with Sample Weighting Based on Graph Topology

Recently, graph-based semi-supervised learning (GSSL) has garnered significant interest in the realms of machine learning and pattern recognition. Although some of the proposed methods have made some progress, there are still some shortcomings that need to be overcome. There are three main limitations. First, the graphs used in these approaches are usually predefined regardless of the task at hand. Second, due to the use of graphs, almost all approaches are unable to process and consider data with a very large number of unlabeled samples. Thirdly, the imbalance of the topology of the samples is very often not taken into account. In particular, processing large datasets with GSSL might pose challenges in terms of computational resource feasibility. In this article, we present a scalable and inductive GSSL method. We broaden the scope of the graph topology imbalance paradigm to extensive databases. Second, we employ the calculated weights of the labeled sample for the label-matching term in the global objective function. This leads to a unified, scalable, semi-supervised learning model that allows simultaneous labeling of unlabeled data, projection of the feature space onto the labeling space, along with the graph matrix of anchors. In the proposed scheme, the integration of labels and features from anchors is applied for the adaptive construction of the anchor graph. Experimental results were performed on four large databases: NORB, RCV1, Covtype, and MNIST. These experiments demonstrate that the proposed method exhibits superior performance when compared to existing scalable semi-supervised learning models.

Space‐Time Projection Enabled Ultrafast All‐Optical Diffractive Neural Network

AbstractAll‐optical neural networks have advantages in higher throughput, higher speed as well as lower energy consumption compared to electrical neural networks. Optical neural networks have already shown great potential in various applications; however, the operation speed of the network is limited by the 2D detector as most optical neural networks rely on space to space projection. Here, a space to time projection approach to build diffractive deep neural network (D2NN) is proposed, which can project spatial intensity distribution into time‐domain intensity variation, thus bypassing the detection speed limit of 2D imaging device. Based on this scheme, high‐speed all‐optical logic gates are theoretically analyzed and experimentally realized. In this case, the network's operation speed is only limited by the photodetector (PD), which can reach GHz levels. Moreover, the method will show great advantage when it comes to wavelengths where 2D detectors are not achievable easily such as infrared, terahertz or microwaves.

Chudnovsky's conjecture and the stable Harbourne-Huneke containment for general points

In our previous work with Grifo and Hà, we showed the stable Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal of sufficiently many general points in PN. In this paper, we establish the conjectures for all remaining cases, and hence, give the affirmative answer to Harbourne-Huneke containment and Chudnovsky's conjecture for the general points in PN for all N. Our new technique is to develop the Cremona reduction process that provides effective lower bounds for the Waldschmidt constant of the defining ideals of generic points in projective spaces.

On Stability Behaviors of 5D M-theory Black Objects

Abstract Using $N = 2$ supergravity formalism, we investigate certain behaviors of five dimensional black objects from the compactification of M-theory 
on a Calabi-Yau three-fold. The manifold has been constructed as the intersection of two homogeneous polynomials of degrees $ (\omega+2,1)$ and $ (2,1) $ in a product of two weighted projective spaces given by $ \mathbb{WP}^{4}(\omega,1,1,1,1) \times\mathbb{P}^{1}$. First, we determine the allowed electric charge regions of the BPS and non BPS black holes obtained by wrapping M2-branes on appropriate two cycles in such a proposed Calabi-Yau three-fold. After that, we calculate the entropy of these solutions which takes a maximal value corresponding to $\omega=1$ defining the ordinary projective space $\mathbb{P}^{4}$. For generic values of $\omega$, we show that the non BPS states are unstable. Then, we conduct a similar study of five dimensional black strings. Concerning the allowed magnetic charge regions of the BPS and non BPS black stringy solutions derived from M5-branes on dual divisors, we calculate the tension taking a minimal value for $\mathbb{P}^{4}$. By determining the recombination factor, we show that the non-BPS black string states are stable in the allowed regions in the magnetic charge space. 

Asymptotic syzygies for products of projective spaces

We study the asymptotic non-vanishing of syzygies for products of projective spaces. Generalizing the monomial methods of Ein, Erman, and Lazarsfeld we give an explicit range in which the graded Betti numbers of Pn1×Pn2 embedded by OPn1×Pn2(d1,d2) are non-zero.

LMD: Faster Image Reconstruction with Latent Masking Diffusion

As a class of fruitful approaches, diffusion probabilistic models (DPMs) have shown excellent advantages in high-resolution image reconstruction. On the other hand, masked autoencoders (MAEs), as popular self-supervised vision learners, have demonstrated simpler and more effective image reconstruction and transfer capabilities on downstream tasks. However, they all require extremely high training costs, either due to inherent high temporal-dependence (i.e., excessively long diffusion steps) or due to artificially low spatial-dependence (i.e., human-formulated high mask ratio, such as 0.75). To the end, this paper presents LMD, a faster image reconstruction framework with Latent Masking Diffusion. First, we propose to project and reconstruct images in latent space through a pre-trained variational autoencoder, which is theoretically more efficient than in the pixel-based space. Then, we combine the advantages of MAEs and DPMs to design a progressive masking diffusion model, which gradually increases the masking proportion by three different schedulers and reconstructs the latent features from simple to difficult, without sequentially performing denoising diffusion as in DPMs or using fixed high masking ratio as in MAEs, so as to alleviate the high training time-consumption predicament. Our approach allows for learning high-capacity models and accelerate their training (by 3x or more) and barely reduces the original accuracy. Inference speed in downstream tasks also significantly outperforms the previous approaches.

Результаты определения профиля высот геоида и уклонения отвесной линии по сигналам ГНСС, отраженным от водной поверхности

The method for determining geoid elevations, based on the use of GNSS signals reflected from water surface, is called bistatic one. Its features are small dimensions and weight of the necessary on-board equipment, and that enables mounting them on a nano-satellite, as well as simultaneously determining several dozen geoid height profiles. It corresponds to the number of visible navigation satellites from among GLONASS, GPS, Galileo, BeiDou. Several space projects using the technology under description were implemented abroad, their analysis has shown the possibility of determining geoid heights with an error of 10–20 cm, as well as sea ice thickness. The authors provide a review of some similar projects, an assessment of the simultaneously determined number of geoid height profiles, and calculation of its elevations and deflection of vertical along a single profile based on primary measurements from the project of CYGNSS. To compensate for various interfering parameters when calculating geoid elevations, the following models were used

The RO(C4) cohomology of the infinite real projective space

The RO(C4) cohomology of the infinite real projective space

Leadership in Energy and Environmental Design Commercial Interior Version 4 (LEED-CI v4) Gold-Certified Office Space Projects: A Pairwise Comparative Analysis between Three Mediterranean Countries

Over the past five years, Leadership in Energy and Environmental Design Commercial Interior version 4 (LEED-CI v4)-certified office projects have been intensively studied in the USA and China, but they have not yet been studied in the Mediterranean region. The purpose of this study was to explore office building certification strategies for LEED-CI v4-certified projects in the Mediterranean region. The study design included pairwise comparative analyses between Spain (number of projects (n) n1 = 14), Türkiye (n2 = 13), and Israel (n3 = 11). Cliff’s δ and exact Wilcoxon–Mann–Whitney tests were used to process ordinal and discrete data, while the natural logarithm of the odds ratio and 2 × 2 Fisher’s exact tests were used to handle dichotomous data. It was found that Spain and Türkiye outperformed Israel in the Location and Transportation (LT) category due to their desire to reduce the use of private transport. Spain and Türkiye were ahead of Israel in the LTc5 “reduced parking footprint” credit (p = 0.008 and 0.0005, respectively). Israel outperformed Spain and Türkiye in the Energy and Atmosphere (EA) category due to the sum of all six EA credits (p = 0.086 and 0.010). Spain overtook Türkiye and Israel in the Materials and Resources (MRs) category due to Spain’s increased use of environmental product declarations. Spain and Türkiye were ahead of Israel in the following four MRs credits: MRc1 “long-term commitment” (p = 0.030), MRc2 “interiors life cycle impact reduction” (p = 0.037), MRc3 “building product disclosure and optimization—environmental product declarations” (p = 0.029), and MRc5 “building product disclosure and optimization—material ingredients” (p = 0.034). Spain, Türkiye, and Israel showed similarly low levels of achievement in the Indoor Environmental Quality (EQ) category (p ≥ 0.405). However, Spain and Türkiye outperformed Israel in the following two credits: EQc1 “enhanced indoor air quality strategies” and EQc2 “low-emitting materials” (p = 0.001 and 0.060, respectively). In parallel, Israel outperformed Türkiye in the EQc3 “construction indoor air quality management plan” (p = 0.026), and Israel outperformed Spain in the EQc8 “quality views” credit (p = 0.066). As a result, a pairwise comparison of the three Mediterranean countries showed that each country has a unique LEED certification strategy. Knowledge of the above green building strategies will be helpful for LEED professionals.

Behaviors of black holes and black strings in M-theory on Calabi–Yau manifolds

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by [Formula: see text]. Using the [Formula: see text] supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions by wrapping M-branes on appropriate cycles in such a Calabi–Yau geometry. For the black hole case, we compute certain thermodynamical quantities. In particular, we calculate the entropy taking a maximal value corresponding to the ordinary projective space [Formula: see text] with [Formula: see text]. Using extended black hole entropies, we evaluate the temperature involving a minimal value for [Formula: see text]. Then, we approach the stability of the non-BPS black holes via the recombination factor. In the allowed electric charge regions, we show that such states are unstable. For the black string solutions, we calculate the tension taking a minimal value corresponding to [Formula: see text]. Computing the recombination factor, we show that the associated non-BPS black string states are stable in the allowed magnetic charge regions of the moduli space.