Geometry Of Connections Research Articles

Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces

We classify equivariant harmonic maps of the complex projective spaces CPm into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective line, we have one parameter family of those maps. (This result is already shown in [2] and [4] in other ways). However, when m≧2, we will obtain the rigidity results.

Unraveling the unknown: Adaptive spatial planning to enhance climate resilience for the endangered Swamp Grass-babbler (Laticilla cinerascens) with habitat connectivity and complexity approach

The endangered and poorly known Swamp Grass-babbler, Laticilla cinerascens (Passeriformes: Pellorneidae), confronts critical threats and vulnerability due to its specific habitat requirements and restricted populations in the northeastern region of the Indian Subcontinent. This study investigates the distribution of the species, habitat quality, geometry and shape complexity of connectivity among the protected areas (PAs), and responses to climate change in Northeast India under different climate change pathways by utilizing ensemble distribution models, and ecological metrics. From the total distribution extent (1,42,000 km2), approximately 9366 km2 (6.59 %) is identified as the suitable habitat for this threatened species. Historically centered around Dibru Saikhowa National Park (DSNP), the species faced a drastic decline due to anthropogenic activities and alteration in land use and lover cover. The study also reveals a significant decline in suitable habitat for L. cinerascens in future climate scenarios, with alarming reductions under SSP126 (>10 % in the timeframe 2041–2060 and > 30 % from 2061 to 2080), SSP245 (>90 % in both time periods), and SSP585 (>90 % in both timeframes) from the present scenario. At present, DSNP has the most suitable habitat within the distribution range but is projected to decline (>90 %) under more severe climate change scenarios, as observed in other PAs. Landscape fragmentation analysis indicates a shift in habitat geometry, highlighting the intricate impact of climate change. It predicts a substantial 343 % increase (in the SSP126) in small habitat patches in the future. Connectivity analysis among PAs shows a significant shift, with a decline exceeding 20 %. The analysis of shape complexity and connectivity geometry reveals a significant increase of over 220 % in the fragmentation of connectivity among PAs between 2061 and 2080 under the SSP585 climate change scenario compared to the present conditions. The study underscores the urgent need for conservation actions, emphasizing the complex interplay of climate change, habitat suitability, and fragmentation. Prioritizing PAs with suitable habitats and assessing their connectivity is crucial. Adaptive management strategies are essential to address ongoing environmental changes and safeguard biodiversity. Future research in critical areas is needed to establish long-term monitoring programs to lead/extend effective conservation strategies.

Line Drawing Vectorization via Coarse‐to‐Fine Curve Network Optimization

AbstractVectorizing line drawings is a fundamental component of the workflow in various applications such as graphic design and computer animation. A practical vectorization tool is desired to produce high‐quality curves that are faithful to the original inputs and close to the connectivity of human drawings. The existing line vectorization approaches either suffer from low geometry accuracy or incorrect connectivity for noisy inputs or detailed complex drawings. We propose a novel line drawing vectorization framework based on coarse‐to‐fine curve network optimization. Our technique starts with an initial curve network generated by an existing tracing method. It then performs a global optimization which fits the curve network to image centrelines. Finally, our method performs a finer optimization in local junction regions to achieve better connectivity and curve geometry around junctions. We qualitatively and quantitatively evaluate our system on line drawings with varying image quality and shape complexity, and show that our technique outperforms existing works in terms of curve quality and computational time.

Numerical Analysis of Masonry-Infilled RC-CLT Panel Connections

CLT panels have been investigated for reinforcement of existing masonry-infilled RC framed buildings through the increase of the overall lateral stiffness of the structure, thus reducing the story drift demand. The contribution of CLT panels depends on the connection to the RC frame elements. This paper evaluates the role of connectors by which CLT is attached to RC frames for capacity, ductility, and energy dissipation of the structure and its elements separately using different kinds of RC-CLT connections, and ultimately finds and compares the optimum number and arrangement of connectors. The results show that the geometry of connections plays a greater seismic role in RC frames than their mechanical properties. Regarding masonry infills, they allow a higher strength capacity but reduce the efficacy of CLT strengthening. However, strong connectors decrease the ability of infills in dissipation. Finally, in the optimum arrangement of connectors, they are distributed equally along the upper and lower beams at equal spacing, where CLT is added, starting in the middle of the beams and moving to the frame corners.

Application of solid-state NMR techniques for structural characterization of metal-organic frameworks

Solid-state NMR can afford the structural information about the chemical composition, local environment, and spatial coordination at the atomic level, which has been extensively applied to characterize the detailed structure and host-guest interactions in metal-organic frameworks (MOFs). In this review, recent advances for the structural characterizations of MOFs using versatile solid-state NMR techniques were briefly introduced. High-field sensitivity-enhanced solid-state NMR method enabled the direct observation of metal centers in MOFs containing low-γ nuclei. Two-dimensional (2D) homo- and hetero-nuclear correlation MAS NMR experiments provided the spatial proximity among linkers, metal clusters and the introduced guest molecules. Moreover, quantitative measurement of inter-nuclear distances using solid-state NMR provided valuable structural information about the connectivity geometry as well as the host-guest interactions within MOFs. Furthermore, solid-state NMR has exhibited great potential for unraveling the structure property of MOFs containing paramagnetic metal centers.

On the geometry of lift metrics and lift connections on the tangent bundle

We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection.

Do Impulsive Solar-Energetic-Electron (SEE) Events Drive High-Voltage Charging Events on the Nightside of the Moon?

When the Earth’s moon is in the supersonic solar wind, the darkside of the Moon and the lunar plasma wake can be very dangerous charging environments. In the absence of photoelectron emission (dark) and in the absence of cool plasma (wake), the emission or collection of charge to reduce electrical potentials is difficult. Unique extreme charging events may occur during impulsive solar-energetic-electron (SEE) events when the lunar wake is dominated by relativistic electrons, with the potential to charge and differentially charge objects on and above the lunar surface to very-high negative electrical potentials. In this report the geometry of the magnetic connections from the Sun to the lunar nightside are explored; these magnetic connections are the pathways for SEEs from the Sun. Rudimentary charging calculations for objects in the relativistic-electron environment of the lunar wake are performed. To enable these charging calculations, secondary-electron yields for impacts by relativistic electrons are derived. Needed lunar electrical-grounding precautions for SEE events are discussed. Calls are made 1) for future dynamic simulations of the plasma wake in the presence of time-varying SEE-event relativistic electrons and time-varying solar-wind magnetic-field orientations and 2) for future charging calculations in the relativistic-electron wake environment and on the darkside lunar surface.

Computing Temporal Sequences Associated With Dynamic Patterns on the C. elegans Connectome.

Understanding how the structural connectivity and spatial geometry of a network constrains the dynamics it is able to support is an active and open area of research. We simulated the plausible dynamics resulting from the known C. elegans connectome using a recent model and theoretical analysis that computes the dynamics of neurobiological networks by focusing on how local interactions among connected neurons give rise to the global dynamics in an emergent way. We studied the dynamics which resulted from stimulating a chemosensory neuron (ASEL) in a known feeding circuit, both in isolation and embedded in the full connectome. We show that contralateral motorneuron activations in ventral (VB) and dorsal (DB) classes of motorneurons emerged from the simulations, which are qualitatively similar to rhythmic motorneuron firing pattern associated with locomotion of the worm. One interpretation of these results is that there is an inherent—and we propose—purposeful structural wiring to the C. elegans connectome that has evolved to serve specific behavioral functions. To study network signaling pathways responsible for the dynamics we developed an analytic framework that constructs Temporal Sequences (TSeq), time-ordered walks of signals on graphs. We found that only 5% of TSeq are preserved between the isolated feeding network relative to its embedded counterpart. The remaining 95% of signaling pathways computed in the isolated network are not present in the embedded network. This suggests a cautionary note for computational studies of isolated neurobiological circuits and networks.

Compressing animated meshes with fine details using local spectral analysis and deformation transfer

Geometry-centric shape animation, usually represented as dynamic meshes with fixed connectivity and time-deforming geometry, is becoming ubiquitous in digital entertainment and other relevant graphics applications. However, digital animation with fine details, which requires more diversity of texture on meshed geometry, always consumes a significant amount of storage space, and compactly storing and efficiently transmitting these meshes still remain technically challenging. In this paper, we propose a novel key-frame-based dynamic meshes compression method, wherein we decompose the meshes into the low-frequency and high-frequency parts by applying piece-wise manifold harmonic bases to reduce spatial-temporal redundancy of primary poses and by using deformation transfer to recover high-frequency details. First of all, we partition the animated meshes into several clusters with similar poses, and the primary poses of meshes in each cluster can be characterized as a linear combination of manifold harmonic bases derived from the key-frame of that cluster. Second, we recover the geometric details on each primary pose using the deformation transfer technique which reconstructs the details from the key-frames. Thus, we only need to store a very small number of key-frames and a few harmonic coefficients for compressing time-varying meshes, which would reduce a significant amount of storage in contrast with traditional methods where bases were stored explicitly. Finally, we employ the state-of-the-art static mesh compression method to store the key-frames and apply a second-order linear prediction coding to the harmonics coefficients to further reduce the spatial-temporal redundancy. Our comprehensive experiments and thorough evaluations on various datasets have manifested that, our novel method could obtain a high compression ratio while preserving high-fidelity geometry details and guaranteeing limited human perceived distortion rate simultaneously, as quantitatively characterized by the popular Karni–Gotsman error and our newly devised local rigidity error metrics.

Some recent progress in non-Kähler geometry

In this paper, we discuss some recent progress in the study of non-Kahler manifolds, in particular the Hermitian geometry of flat canonical connections and Kahler-like connections. We also discuss a number of conjectures and open questions in this direction.

Conductance and Kondo Interference beyond Proportional Coupling.

The transport properties of nanostructured systems are deeply affected by the geometry of the effective connections to metallic leads. In this work we derive a conductance expression for a class of interacting systems whose connectivity geometries do not meet the Meir-Wingreen proportional coupling condition. As an interesting application, we consider a quantum dot connected coherently to tunable electronic cavity modes. The structure is shown to exhibit a well-defined Kondo effect over a wide range of coupling strengths between the two subsystems. In agreement with recent experimental results, the calculated conductance curves exhibit strong modulations and asymmetric behavior as different cavity modes are swept through the Fermi level. These conductance modulations occur, however, while maintaining robust Kondo singlet correlations of the dot with the electronic reservoir, a direct consequence of the lopsided nature of the device.

Combining global and local scaling methods to detect soil pore space

Computed tomography (CT) images provide very useful information to characterize the pore space structure in different porous materials. Being a non-destructive technique, it allows preserving the real characteristics of the analysed samples. Moreover, providing 3 dimensional (3D) information, it also allows making more exhaustive studies on other characteristics of pore space such as connectivity or pore geometry. However, this technique also has drawbacks such as the insertion of errors and distortions from CT reconstruction that could drive to low contrast greyscale images hindering the detection of solid-void interface.The Singularity-CA (S-CA) binarization method has already proven to be an efficient method when detecting the pore space in CT soil images. This method is primarily based on the existence of self-similar properties in the singularity value (SV) spatial distribution. These self-similar properties derive to thresholds in the singularity map which are used to delimit the pore space. This method detects the medium and large pore sizes with an excellent fit. However, due to its high sensibility to low fluctuations in the greyscale images, some small pores are incorrectly detected and therefore its amount is overestimated.This work attempts to solve this drawback introducing a new approach named the Combining Singularity-CA (CS-CA) method. This improved method is based on the combination of a global thresholding method, the Maximum Entropy method, and the S-CA method. The CS-CA methodology is fully automatic and did not require human adjustment. A set of soil synthetic images with porosities from 3% to 25% were used to validate the new approach. These images were constructed using the Truncated Multifractal (TM) method, especially useful to simulate CT soil images. Based on parameters such as porosity, relative error and misclassification error, CS-CA method gave better pore detection than the S-CA and the Maximum Entropy method applied individually to the images.Finally, it was compared the two main methods used to detect slope-change points in plots with several linear segments: the linear regression (LR) method and the wavelet transform modulus maxima (WTMM) method. These methods are very important in the S-CA methodology since they are responsible of defining the threshold in the binarization step. The WTMM method proved to be easier to deal with when using by the new CS-CA method.

Geometric decompositions of collective motion.

Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.

The Non-metricity Formulation of General Relativity

After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms for a class of cobase fields. Then we formulate a theory of gravitation (equivalent to General Relativity (GR)) which admits a geometrical interpretation in a flat torsionless space where the gravitational field is completely manifest in the non-metricity of a NM connection. We define and then apply the non-metricity gauge to a gravitational Lagrangian density discovered by Wallner and which is equivalent to the Einstein-Hilbert Lagrangian density. The Einstein equations coupled to the matter currents $\left( \mathcal{J}_{\alpha}\right) $ thus becomes $\delta dg_{\alpha}=\mathcal{T}_{\alpha}+\mathcal{J}_{\alpha}$, where $\left( \mathcal{T}_{\alpha}\right) $ is identified as the gravitational energy-momentum currents, to which we shall find a relatively simple and physically appealing form. It is also shown that in the gravitational analogue of the Lorenz gauge, our field equations can be written as a system of Proca equations, which may be of interest in the study of propagation of gravitational-electromagnetic waves.

Photoluminescence Imaging of Polyfluorene Surface Structures on Semiconducting Carbon Nanotubes: Implications for Thin Film Exciton Transport.

Single-walled carbon nanotubes (SWCNTs) have potential to act as light-harvesting elements in thin film photovoltaic devices, but performance is in part limited by the efficiency of exciton diffusion processes within the films. Factors contributing to exciton transport can include film morphology encompassing nanotube orientation, connectivity, and interaction geometry. Such factors are often defined by nanotube surface structures that are not yet well understood. Here, we present the results of a combined pump-probe and photoluminescence imaging study of polyfluorene (PFO)-wrapped (6,5) and (7,5) SWCNTs that provide additional insight into the role played by polymer structures in defining exciton transport. Pump-probe measurements suggest exciton transport occurs over larger length scales in films composed of PFO-wrapped (7,5) SWCNTs, compared to those prepared from PFO-bpy-wrapped (6,5) SWCNTs. To explore the role the difference in polymer structure may play as a possible origin of differing transport behaviors, we performed a photoluminescence imaging study of individual polymer-wrapped (6,5) and (7,5) SWCNTs. The PFO-bpy-wrapped (6,5) SWCNTs showed more uniform intensity distributions along their lengths, in contrast to the PFO-wrapped (7,5) SWCNTs, which showed irregular, discontinuous intensity distributions. These differences likely originate from differences in surface coverage and suggest the PFO wrapping on (7,5) nanotubes produces a more open surface structure than is available with the PFO-bpy wrapping of (6,5) nanotubes. The open structure likely leads to improved intertube coupling that enhances exciton transport within the (7,5) films, consistent with the results of our pump-probe measurements.

Anisotropic dissipation in lattice metamaterials

Plane wave propagation in an elastic lattice material follows regular patterns as dictated by the nature of the lattice symmetry and the mechanical configuration of the unit cell. A unique feature pertains to the loss of elastodynamic isotropy at frequencies where the wavelength is on the order of the lattice spacing or shorter. Anisotropy may also be realized at lower frequencies with the inclusion of local resonators, especially when designed to exhibit directionally non-uniform connectivity and/or cross-sectional geometry. In this paper, we consider free and driven waves within a plate-like lattice−with and without local resonators−and examine the effects of damping on the isofrequency dispersion curves. We also examine, for free waves, the effects of damping on the frequency-dependent anisotropy of dissipation. Furthermore, we investigate the possibility of engineering the dissipation anisotropy by tuning the directional properties of the prescribed damping. The results demonstrate that uniformly applied damping tends to reduce the intensity of anisotropy in the isofrequency dispersion curves. On the other hand, lattice crystals and metamaterials are shown to provide an excellent platform for direction-dependent dissipation engineering which may be realized by simple changes in the spatial distribution of the damping elements.

Sclerostin does not play a major role in the pathogenesis of skeletal complications in type 2 diabetes mellitus

SummaryIn contrast to previously reported elevations in serum sclerostin levels in diabetic patients, the present study shows that the impaired bone microarchitecture and cellular turnover associated with type 2 diabetes mellitus (T2DM)-like conditions in ZDF rats are not correlated with changes in serum and bone sclerostin expression.IntroductionT2DM is associated with impaired skeletal structure and a higher prevalence of bone fractures. Sclerostin, a negative regulator of bone formation, is elevated in serum of diabetic patients. We aimed to relate changes in bone architecture and cellular activities to sclerostin production in the Zucker diabetic fatty (ZDF) rat.MethodsBone density and architecture were measured by micro-CT and bone remodelling by histomorphometry in tibiae and femurs of 14-week-old male ZDF rats and lean Zucker controls (n = 6/group).ResultsZDF rats showed lower trabecular bone mineral density and bone mass compared to controls, due to decreases in bone volume and thickness, along with impaired bone connectivity and cortical bone geometry. Bone remodelling was impaired in diabetic rats, demonstrated by decreased bone formation rate and increased percentage of tartrate-resistant acid phosphatase-positive osteoclastic surfaces. Serum sclerostin levels (ELISA) were higher in ZDF compared to lean rats at 9 weeks (+40 %, p < 0.01), but this difference disappeared as their glucose control deteriorated and by week 14, ZDF rats had lower sclerostin levels than control rats (−44 %, p < 0.0001). Bone sclerostin mRNA (qPCR) and protein (immunohistochemistry) were similar in ZDF, and lean rats at 14 weeks and genotype did not affect the number of empty osteocytic lacunae in cortical and trabecular bone.ConclusionT2DM results in impaired skeletal architecture through altered remodelling pathways, but despite altered serum levels, it does not appear that sclerostin contributes to the deleterious effect of T2DM in rat bone.

Application of continuum percolation theory for modeling single- and two-phase characteristics of anisotropic carbon paper gas diffusion layers

Percolation theory is used to model intrinsic and relative permeabilities as well as tortuosity in anisotropic carbon paper gas diffusion layers (GDL) and compared with existing results from lattice-Boltzmann (LB) simulations and experimental measurements. Although single- and two-phase characteristics of the carbon paper GDL are mainly affected by medium geometrical and topological properties, e.g., pore-size distribution, connectivity, and pore geometry, analyzing capillary pressure curves implies that the pore-size distribution of the carbon paper GDL is very narrow. This suggests that its effect on tortuosity and wetting- and nonwetting-phase relative permeabilities is trivial. However, integrated effects of pore geometry, surface area, connectivity, and tortuosity on intrinsic permeability might be substantial. Universal power laws from percolation theory predict the tortuosity-porosity and relative permeability–saturation curves accurately, indicating both characteristics not affected by the pore-size distribution. The permeability–porosity relationship, however, conforms to nonuniversality.

A fast computational method for potential flows in multiply connected coastal domains

We present a fast and accurate numerical method for constructing incompressible, inviscid and irrotational flows in two-dimensional coastal domains, which are unbounded multiply connected domains above an infinitely long coastline boundary. In the numerical method, we utilize a numerical conformal mapping method based on a boundary integral equation with the generalized Neumann kernel in order to construct conformal mappings from coastal domains onto four of Koebe’s canonical domains. The numerical method is fast and accurate, since it just requires \(O((m+1)n\ln n)\) operations and it converges with \(O(e^{-cn})\) for coastal domains of connectivity \(m+1\), where \(n\) is the number of nodes in discretizing each smooth boundary component and \(c\) is a positive constant. With some examples, we also show that it is applicable to arbitrary coastal domains with high connectivity and complex geometry.

The geometry of tangent conjugate connections

The notion of conjugate connection is introduced in the almost tangent geometry and its properties are studied from a global point of view. Two variants for this type of connections are also considered in order to find the linear connections making parallel a given almost tangent structure. 2000 AMS Classification: 53C15; 53C05; 53C10; 53C07.