Projective Space Research Articles

Idaho libraries to provide private spaces for SUD telehealth treatment

Called the “Third Space Project,” Idaho libraries will provide space for telehealth treatment for substance use disorders (SUDs), with an emphasis on serving rural and high‐need communities. The state Division of Behavioral Health Substance Use Disorder Unit is leading the project in partnership with the Idaho Commission for Libraries (ICfL), with funding by a $500,000 grant from the American Rescue Plan Act's 2021 Substance Use Prevention, Treatment, and Recovery Services Block Grant supplemental.

Transarterial embolization for anterior cranial fossa dural arteriovenous fistula based on multi-modal three-dimensional imaging

Background: Dural arteriovenous fistula (DAVF) in the anterior cranial fossa (ACF) is known to show a high risk of intracranial hemorrhage. Recently, multi-modal fusion imaging with computed tomography angiography, computed tomography venography, and three-dimensional (3D) rotation angiography have been used preoperatively to ensure anatomical safety. We report on endovascular treatment as a first-line approach for ACFDAVF based on the understanding of vascular anatomy obtained from multi-modal fusion imaging. Methods: All patients with ACF-DAVF treated endovascularly as a first-line approach were included in this study. Analyses took into account complications (particularly visual function), immediate angiographic outcomes, and follow-up findings in consecutive patients with ACF-DAVF treated with interventional treatment based on multi-modal fusion imaging. Results: Five patients with ACF-DAVF underwent six sessions of transarterial embolization (TAE) in our institution. The five male patients (mean age, 74.5 years; range, 60–84 years) were treated with liquid embolic agents (Onyx, four procedures; n-butyl 2-cyanoacrylate, two procedures). No difference was seen between preoperative image evaluation and image evaluation during the endovascular procedure, and in all cases, a microcatheter was navigated into a target artery assumed from preoperative multi-modal imaging, allowing treatment completion in a single procedure. In all cases, the shunt disappeared completely and visual function after procedure was maintained. At the last follow-up, all patients showed a modified Rankin scale score of 0 or 1 with no recurrences. Conclusion: Multi-modal fusion imaging facilitates a 3D understanding of the vascular anatomy, allowing TAE as the first-line treatment for ACF-DAVF.

New curvature characterizations for spherical space forms and complex projective spaces

In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space C P n \mathbb {C}\mathbb {P}^n .

Tangent space functional reconfigurations in individuals at risk for alcohol use disorder

Abstract Human brain function dynamically adjusts to ever-changing stimuli from the external environment. Studies characterizing brain functional reconfiguration are nevertheless scarce. Here we present a principled mathematical framework to quantify brain functional reconfiguration when engaging and disengaging from a stop signal task (SST). We apply tangent space projection (a Riemannian geometry mapping technique) to transform functional connectomes (FCs) of 54 participants and quantify functional reconfiguration using the correlation distance of the resulting tangent-FCs. Our goal was to compare functional reconfigurations in individuals at risk for alcohol use disorder (AUD). We hypothesized that functional reconfigurations when transitioning to/from a task would be influenced by family history of alcohol use disorder (FHA) and other AUD risk factors. Multilinear regression models showed that engaging and disengaging functional reconfiguration were associated with FHA and recent drinking. When engaging in the SST after a rest condition, functional reconfiguration was negatively associated with recent drinking, while functional reconfiguration when disengaging from the SST was negatively associated with FHA. In both models, several other factors contributed to the functional reconfiguration. This study demonstrates that tangent-FCs can characterize task-induced functional reconfiguration, and that it is related to AUD risk.

A remarkable class of elliptic surfaces of amplitude 1 in weighted projective spaces

A remarkable class of elliptic surfaces of amplitude 1 in weighted projective spaces

Roto-Cyclization of 4-Bromopicene in On-Surface Synthesis.

Progress toward single-molecule electronics relies on a thorough understanding of local physico-chemical processes and development of synthetic routines for controlled hetero-coupling. We demonstrate a structurally unexpected ring closure process for a homo-coupled 4,4'-bipicenyl, realized in on-surface synthesis. An initial covalent C-C coupling of 4-bromopicene locks at lower temperatures the position and geometrically shields part of 4,4'-bipicenyl. Employing this effect of shielding might offer a path toward controlled stepwise hetero-coupling. At higher temperatures, a thermally activated three-dimensional rotation upon hydrogen dissociation, a dehydrogenative roto-cyclization, lifts the surface-dimensionality restriction, and leads to the formation of a perylene. Thereby, the shielded molecular part becomes accessible again.

The Living CV project: a model of collaborative learning in third space

The Living CV project is a collaborative initiative launched at a south coast university in the UK, which aims to help students develop their employability skills and evidence their learning outcomes. The project is delivered university-wide from a third space hub, where people from different disciplines and backgrounds come together to work on shared goals. It has therefore provided a way for colleagues across the university to collaborate within third space. In this study we focus on the role of the departmental Living CV Champions and their pivotal role in driving forward this third space project. These champions are situated across the university – in academic departments, in the university’s central Learning and Teaching service and in its career service – but all are working across boundaries and drawing collaborators into the third space of the project. We suggest that the Living CV Champions are also collaboration champions for the institution, in the way in which they support the development of staff networks and knowledge sharing, and therefore the collaborative capital of the institution as a whole. We find that third space projects such as the Living CV can contribute to the development of collaborative capital, act as a gateway for staff to wider communities of practice and build confidence for those engaged in them. In this case study we illustrate one route to achieving this, through a champions model which breaks down traditional academic silos and encourages wider collaboration.

Cyber Resilience Limitations in Space Systems Design Process: Insights from Space Designers

Space technology is integral to modern critical systems, including navigation, communication, weather, financial services, and defence. Despite its significance, space infrastructure faces unique cyber resilience challenges exacerbated by the size, isolation, cost, persistence of legacy systems, and lack of comprehensive cyber resilience engineering standards. This paper examines the engineering challenges associated with incorporating cyber resilience into space design, drawing on insights and experiences from industry experts. Through qualitative interviews with engineers, cybersecurity specialists, project managers, and testers, we identified key themes in engineering methodologies, cybersecurity awareness, and the challenges of integrating cyber resilience into space projects. Participants emphasised the importance of incorporating cybersecurity considerations from the earliest stages of design, advocating for principles such as zero-trust architecture and security by design. Our findings reveal that experts favour Model-Based Systems Engineering (MBSE) and Agile methodologies, highlighting their synergy in developing flexible and resilient systems. The study also underscores the tension between principles-based standards, which offer flexibility but can lead to inconsistent implementation, and compliance-based approaches, which provide clear measures but may struggle to adapt to evolving threats. Additionally, the research recognises significant barriers to achieving cyber resilience, including insider threats, the complexity of testing and validation, and budget constraints. Effective stakeholder engagement and innovative funding models are crucial for fostering a culture of cybersecurity awareness and investment in necessary technologies. This study highlights the need for a comprehensive cyber resilience framework that integrates diverse engineering methodologies and proactive security measures, ensuring the resilience of space infrastructure against emerging cyber threats.

Choosing a promotion channel for a startup project in the modern media space

Relevance. The startup market is becoming increasingly saturated. Effective promotion channels allow you to stand out from the competition and attract the attention of the target audience. Startups often work with a limited budget. Optimizing the choice of promotion channels is critical to maximizing the return on investment. Modern media management covers many platforms (social networks, blogs, video hosting, etc.). Choosing the right channel helps to optimally use resources and ensure maximum visibility. Different channels are suitable for different target groups. An effective choice of promotion channel helps to more accurately reach the desired audience, taking into account its preferences and behavior. Consumers are increasingly paying attention to digital communication channels. Taking into account current trends and preferences allows you to improve interaction with the audience. The influence of social networks and bloggers is becoming an important mechanism for creating trust among consumers. This can significantly increase the recognition of a startup. All this emphasizes the importance of a strategic approach to choosing promotion channels for a successful launch and sustainable growth of a startup project in the modern media landscape.The purpose of the study is to choose a promotion channel for a startup project in the modern media space.Objectives: to substantiate the relevance of choosing a promotion channel for a startup in the modern media space; to study the demand and effectiveness of modern promotion channels; to use in practice the method of multicriteria selection of promotion channels for a startup project; to substantiate the results obtained.Methodology. The research methodology is based on the methods of comparison and comparison, deduction and induction, qualitative and quantitative analysis, as well as the Churchman-Ackoff multi-criteria assessment method.Results. The study substantiates the relevance of choosing a promotion channel for a startup in the modern media space; the demand and effectiveness of modern promotion channels are studied; the method of multi-criteria selection of channels for promoting a startup project was used in practice; the obtained results were substantiated.Conclusions. The effectiveness of the selected channels for promoting a startup project in the modern media space was proven as conclusions.

Half-space results for generalized linear Weingarten hypersurfaces immersed in the real projective space

Half-space results for generalized linear Weingarten hypersurfaces immersed in the real projective space

Infinitely many exotic Lagrangian tori in higher projective spaces

In de Velloso Vianna (J Topol 9(2):535-551, 2016), Vianna constructed infinitely many exotic Lagrangian tori in P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^2$$\\end{document}. We lift these tori to higher dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula of Pascaleff and Tonkonog (Adv Math 361:106850, 2020).

Additive actions on projective hypersurfaces with a finite number of orbits

An induced additive action on a projective variety [Formula: see text] is a regular action of the group [Formula: see text] on [Formula: see text] with an open orbit, which can be extended to a regular action on the ambient projective space [Formula: see text]. In this work, we classify all projective hypersurfaces admitting an induced additive action with a finite number of orbits.

A cardiac audio classification method based on image expression of multidimensional features.

Heart sound auscultation plays a crucial role in the early diagnosis of cardiovascular diseases. In recent years, great achievements have been made in the automatic classification of heart sounds, but most methods are based on segmentation features and traditional classifiers and do not fully exploit existing deep networks. This paper proposes a cardiac audio classification method based on image expression of multidimensional features (CACIEMDF). First, a 102-dimensional feature vector is designed by combining the characteristics of heart sound data in the time domain, frequency domain and statistical domain. Based on the feature vector, a two-dimensional feature projection space is constructed by PCA dimensionality reduction and the convex hull algorithm, and 102 pairs of coordinate representations of the feature vector in the two-dimensional space are calculated. Each one-dimensional component of the feature vector corresponds to a pair of 2D coordinate representations. Finally, the one-dimensional feature component value and its divergence into categories are used to fill the three channels of a color image, and a Gaussian model is used to dye the image to enrich its content. The color image is sent to a deep network such as ResNet50 for classification. In this paper, three public heart sound datasets are fused, and experiments are conducted using the above methods. The results show that for the two-classification/five-classification task of heart sounds, the method in this paper can achieve a classification accuracy of 95.68%/94.53% when combined with the current deep network.

Some More Fano Threefolds with a Multiplicative Chow–Künneth Decomposition

We exhibit several families of Fano threefolds with a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain tautological subring of the Chow ring of powers of these threefolds injects into cohomology. As a by-product of the argument, we observe that double covers of projective spaces admit a multiplicative Chow–Künneth decomposition.

Comment on 'A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging'.

We read with great interest the paper by Limet al(2018Phys. Med. Biol.63035042) on bias reduction in Y-90 PET imaging. In particular, they proposed a new formulation of the tomographic reconstruction problem that enforces non-negativity in projection space as opposed to image space. We comment on the algorithm they derived from this formulation and bring some clarifications on the constraint that this algorithm respects.

Degenerations of the product geometries in projective space that contain Nil

This paper produces explicit conjugacy paths for the product geometries H2×R and S2×R whose limits contain the geometry of the Heisenberg group's action on itself. These are the first such conjugacy limits to any model of Nil, continuing the program of Daryl Cooper, Jeffrey Danciger, and Anna Wienhard to determine all possible degenerations between Thurston geometries in (PGL(4,R),RP3).

Dynamic analysis of six-bar tensegrity-based robot

Abstract The tensegrity-based robot is a hot research topic in the research field of robotics. The dynamics of the robot, describing the specific motion patterns under the influence of forces and torques, play an important role in the application of robotics. In addition, the dynamics should be considered when revealing the internal mechanisms of robots and predicting their dynamic behaviors. In this work, a dynamic model for a rolling six-bar tensegrity-based robot is established. In terms of kinematic representation, quaternions are chosen as the tool for attitude description, simplifying the derivation process of the complex three-dimensional rotational kinematics calculations. Quaternions play a crucial role in mathematical processing for robot attitude control and path planning due to their effective representation of three-dimensional space rotations. The classic Newton-Euler dynamic framework was adopted to conduct in-depth and detailed studies on the dynamic characteristics of the robot under various force conditions and motion states, with a particular focus on rolling dynamic analysis. Special attention was paid to the dynamic response mechanisms of each component of the robot under the combined action of internal and external forces and torques.

A Framework for Assessing Ocean Mixed Layer Depth Evolution

AbstractThe ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes (“restratification,” “stable,” “deepening,” and “strong deepening”) are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration.

Meromorphic mappings from a Kähler manifold into a projective space sharing different families of hyperplanes

Meromorphic mappings from a Kähler manifold into a projective space sharing different families of hyperplanes

A new class of distances on complex projective spaces

The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances.