Search Results (209)

We explore a new approach for the parsimonious, generalizable, efficient, and potentially automatable characterization of spectral diversity of sparse targets in spectroscopic imagery. The approach focuses on pixels which are not well modeled by linear subpixel mixing of the Substrate, Vegetation and Dark (S, V, and D) endmember spectra which dominate spectral variance for most of Earth’s land surface. We illustrate the approach using AVIRIS-3 imagery of anthropogenic surfaces (primarily hydrocarbon extraction infrastructure) embedded in a background of Arctic tundra near Prudhoe Bay, Alaska. Computational experiments further explore sensitivity to spatial and spectral resolution. Analysis involves two stages: first, computing the mixture residual of a generalized linear spectral mixture model; and second, nonlinear dimensionality reduction via manifold learning. Anthropogenic targets and lakeshore sediments are successfully isolated from the Arctic tundra background. Dependence on spatial resolution is observed, with substantial degradation of manifold topology as images are blurred from 5 m native ground sampling distance to simulated 30 m ground projected instantaneous field of view of a hypothetical spaceborne sensor. Degrading spectral resolution to mimicking the Sentinel-2A MultiSpectral Imager (MSI) also results in loss of information but is less severe than spatial blurring. These results inform spectroscopic characterization of sparse targets using spectroscopic images of varying spatial and spectral resolution. Full article

Background: Alzheimer’s disease is a progressive neurological condition marked by a decline in cognitive abilities. Early diagnosis is crucial but challenging due to overlapping symptoms among impairment stages, necessitating non-invasive, reliable diagnostic tools. Methods: We applied information geometry and manifold learning to analyze grayscale MRI scans classified into No Impairment, Very Mild, Mild, and Moderate Impairment. Preprocessed images were reduced via Principal Component Analysis (retaining 95% variance) and converted into statistical manifolds using estimated mean vectors and covariance matrices. Geodesic distances, computed with the Fisher Information metric, quantified class differences. Graph Neural Networks, including Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and GraphSAGE, were utilized to categorize impairment levels using graph-based representations of the MRI data. Results: Significant differences in covariance structures were observed, with increased variability and stronger feature correlations at higher impairment levels. Geodesic distances between No Impairment and Mild Impairment (58.68, $p<0.001$) and between Mild and Moderate Impairment (58.28, $p<0.001$) are statistically significant. GCN and GraphSAGE achieve perfect classification accuracy (precision, recall, F1-Score: 1.0), correctly identifying all instances across classes. GAT attains an overall accuracy of 59.61%, with variable performance across classes. Conclusions: Integrating information geometry, manifold learning, and GNNs effectively differentiates AD impairment stages from MRI data. The strong performance of GCN and GraphSAGE indicates their potential to assist clinicians in the early identification and tracking of Alzheimer’s disease progression. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

Designing waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typically involve model-based approaches with relaxation and data-driven Deep Neural Networks (DNNs) methods, which face the challenge of dataimitation. We observe that the Complex Circle Manifold (CCM) naturally satisfies the CMC. By projecting onto the CCM, the problem is transformed into an unconstrained minimization problem that can be tackled using the CCM gradient descent model. Furthermore, we observe that the gradient descent model over the CCM can be unfolded as a Deep Learning (DL) network. Therefore, byeveraging the powerfulearning ability of DL and the CCM gradient descent model, we propose a Model-Adaptive Learned Network (MAL-Net) method without relaxation. Initially, we reformulate the problem as an Unconstrained Quartic Problem (UQP) on the CCM. Then, the MAL-Net is developed toearn the step sizes of allayers adaptively. This is accomplished by unrolling the CCM gradient descent model as the networkayer. Our simulation results demonstrate that the proposed MAL-Net achieves superior STAF performance compared to existing methods. Full article

After almost a century of global generational IQ test score gains, the Flynn effect has, in the past decades, been observed to show stagnation and reversals in several countries. Tentative evidence from academic achievement data has suggested that these trajectory changes may be rooted in a decreasing strength of the positive manifold of intelligence due to increasing ability differentiation and specialization in the general population. Here, we provide direct evidence for generational IQ test score and positive manifold strength changes based on IQ test standardization data from 1392 Austrian residents between 2005 and 2018. Our analyses revealed positive Flynn effects across all domains of the IQ test (Cohen’s d from 0.21 to 0.91) but a trend toward decreasing strength in the positive manifold of intelligence (R² from .908 to .892), though these changes were not statistically significant. Our results are consistent with the idea that increasingly inconsistent Flynn effect trajectories may be attributed to increasing ability differentiation and specialization in the general population over time. Full article

This paper presents a nonlinear velocity observer of tether deployment using the immersion and invariance technique, and the velocity observer design problem is recast as a problem of designing an attractive and invariant manifold inside the Hamiltonian framework. The passivity-based control theory is used to define an expected Hamiltonian function, and the stability of the designed velocity observer is addressed by using the passivity-based methodology. Finally, a simple tension control law with measurable and unmeasurable states is employed for controlling the tether deployment, where the unmeasurable states use the proposed velocity observer. Numerical simulations demonstrate that the proposed velocity observer is working successfully. Sensitivity analyses are conducted to test the effectiveness and robustness of the proposed velocity observer. Full article

The design and calculation of nonlinear observers for parameter estimation in multi-time-scale nonlinear systems present significant challenges due to the inherent complexity and stiffness of such systems. This study proposes a framework for designing observers for two-time-scale nonlinear systems, with the objective of overcoming the aforementioned challenges. The design procedure involves reducing the original two-time-scale nonlinear system to a lower-dimensional model that captures only the slow dynamics while approximating the fast states through the use of an algebraic slow motion invariant manifold function. Subsequently, an exponential observer can be devised for this reduced system, which is valid for both state and parameter estimation. By employing the output from the original system, this observer can be adapted for online state and parameter estimation for the detailed two-time-scale system. The challenges associated with estimating parameters in two-time-scale nonlinear systems, the complexities of designing observers for such systems, and the computational burden associated with computing observers for ill-conditioned systems can be effectively addressed through the application of this design framework. A rigorous error analysis validates the convergence of the proposed observer towards the states and parameters of the original system. The viability and necessity of this observer design framework are demonstrated through a numerical example and an anaerobic digestion process. This study presents a practical approach for state and parameter estimation with observers for two-time-scale nonlinear systems. Full article

A disaffinity vector on a Riemannian manifold $(M,g)$ is a vector field whose affinity tensor vanishes. In this paper, we observe that nontrivial disaffinity functions offer obstruction to the topology of M and show that the existence of a nontrivial disaffinity function on M does not allow M to be compact. A characterization of the Euclidean space is also obtained by using nontrivial disaffinity functions. Further, we study properties of disaffinity vectors on M and prove that every Killing vector field is a disaffinity vector. Then, we prove that if the potential field $\zeta$ of a Ricci soliton $\left(M,g,\zeta ,\lambda \right)$ is a disaffinity vector, then the scalar curvature is constant. As an application, we obtain conditions under which a Ricci soliton $\left(M,g,\zeta ,\lambda \right)$ is trivial. Finally, we prove that a Yamabe soliton $\left(M,g,\xi ,\lambda \right)$ with a disaffinity potential field $\xi$ is trivial. Full article

This study proposes a dual-fuel approach combining diesel and ammonia in a single-cylinder compression ignition engine to reduce harmful emissions from internal combustion. Diesel is directly injected into the combustion chamber, while ammonia is introduced through the intake manifold with intake air. In this study, injection timing and the percentage of ammonia energy fraction was varied. A computational fluid dynamics (CFD) model simulates the combustion and emission processes to assess the impact of varying diesel injection timings and ammonia energy contributions. Findings indicate that as ammonia content increases, the engine experiences reductions in peak in-cylinder pressure, temperature, heat release rate, as well as overall efficiency and power output. Emission results suggest that greater ammonia usage leads to a reduction in soot, carbon monoxide, carbon dioxide, and unburned hydrocarbons, though a slight increase in nitrogen oxides emissions is observed. This analysis supports ammonia’s potential as a low-emission alternative fuel in future compression ignition engines. Full article

The utilization of 20CrNiMo/Incoloy 825 composite materials as high-pressure pipe manifold steel can not only improve the strength and hardness of the steel, but also improve its corrosion resistance. However, research on the heat treatment of 20CrNiMo/Incoloy 825 composite materials is still scarce. Thus, the aim of this study was to investigate the influence of solid solution treatment on the microstructure and properties of 20CrNiMo/Incoloy 825 composite materials. Firstly, the composite materials were subjected to solid solution treatment at temperatures ranging from 850 to 1100 °C with varied holding times of 1 h, 4 h, and 6 h. Microstructural analysis revealed that the solid solution treatment temperature had a more pronounced effect than the treatment time on the interface decarburization layer, carburization layer, and grain size. It was observed that the carburized layer thickness decreased while the decarburized layer thickness increased with an increase in the solid solution treatment temperature, oil cooling was found to enhance the hardness of the base layer of the composite materials, and the size of the original austenite grains of 20CrNiMo steel and Incoloy 825 increased with an increase in the solid solution treatment temperature. Secondly, the tensile properties, microhardness, and fracture morphology were evaluated after the composite materials underwent solid solution treatment at temperatures between 950 °C and 1100 °C for 1 h. The results indicated that increasing the solution temperature initially led to an increase in tensile strength and elongation after fracture, followed by a decrease; furthermore, the hardness of Incoloy 825 exhibited a declining trend, while the hardness of 20CrNiMo first decreased then increased. Thirdly, the shear properties and interfacial element diffusion of the composite materials were analyzed following solid solution treatment in a temperature range of 950 °C to 1100 °C for 1 h. The findings demonstrated that higher solid solution treatment temperatures induced full diffusion of Cr, Ni, and Fe atoms at the interface and softened the matrix, leading to an increase in the thickness of the diffusion layer and toughening of the composite interface. Therefore, the shear strength increased with an increase in the solid solution treatment temperature. Finally, the optimal solid solution treatment process for 20CrNiMo/Incoloy 825 composite materials was determined to be 1050 °C/1 h oil cooling, following which the composite materials had good comprehensive mechanical properties. Full article

The outlet flow rates and changes in behaviors of five outlet ports where water and air–water (two-phase) mixtures pass horizontally in a manifold pipe system were investigated experimentally. The effects of different air-flow rates, vacuumed from the atmosphere with a Venturi device in the system, on the outlet flow rates and diameters of the manifold port outlets were compared by measuring the outlet jet lengths. The system performance provided homogeneity of manifold port outlet flows and was tested. As a result, it was observed that homogeneous jet lengths were obtained in both single and two-phase low main manifold flows and equal outlet port diameters. When the main manifold flow rate V is 1.5–2 m/s, the system is stable and produces high jet lengths. The manifold pipe systems used in the experimental setup provide suitable working conditions for d/D = 0.433. The system does not show a smooth flow pattern with Venturi devices for d/D < 0.433. The low flow rates in this study’s tests are key. They are vital for designing micro irrigation systems. This depends on the critical d/D ratio of the system. Full article

In this work, the influence of plenum and port geometry on the performance of the intake process in a four-stroke spark ignition engine for ultralight aircraft applications is analyzed. Three intake systems are considered: the so-called “standard plenum”, with a relatively small plenum volume, the “V1 plenum”, with a larger plenum volume, and the “standard plenum” equipped with a large curvature manifold called the “G2 port”. Both measurements and 3D CFD simulations, by using Ansys^® Academic Fluent, Release 20.2, are performed to characterize and analyze the steady-flow field in the intake system for selected valve lifts. The experimental data and the numerical results are in excellent agreement with each other. The results show that at the maximum valve lift, i.e., 12 mm, the V1 plenum allows an increase in the air mass flow rate of 9.1% and 9.4% compared to the standard plenum and the standard plenum with the “G2 port”, respectively. In addition, the volumetric efficiency has been estimated under unsteady-flow conditions for all geometries at relatively high engine rpms. The difference between numerical results and measurements is less than 1% for the standard plenum, thus proving the accuracy of the model, which is then used to study the other configurations. The V1 plenum shows a fairly constant volumetric efficiency as the engine speed increases, although such an efficiency is lower than that of the other two geometries considered in this work. Specifically, the use of the “G2 port” leads to an increase of 1.5% in terms of volumetric efficiency with respect to the configuration with the original manifold. Furthermore, for the “G2 port” configuration, higher turbulent kinetic energy and higher swirl and tumble ratios are observed. This is expected to result in an improvement of air–fuel mixing and flame propagation. Full article

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the “Swampland” program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not. Full article

After reviewing important historical and present day ideas about the concept of time, we develop some instances of mathematical examples where, from the interaction of concepts that model interactions of things in the observable world, time flow emerges in an intuitive and local interpretation. We present several instances of emergence of time flow in mathematical contexts, to wit, by specific parametrisation of deterministic and stochastic curves or of geodesics in Riemann manifolds. Full article

Voltage-dependent anion channels (VDACs) are important proteins of the outer mitochondrial membrane (OMM). Their beta-barrel structure allows for efficient metabolite exchange between the cytosol and mitochondria. VDACs have further been implicated in the control of regulated cell death. Historically, VDACs have been pictured as part of the mitochondrial permeability transition pore (MPTP). New concepts of regulated cell death involving VDACs include its oligomerisation to form a large pore complex in the OMM; however, alternative VDAC localisation to the plasma membrane has been suggested in the literature and will be discussed regarding its potential role during cell death. Very recently, a phospholipid scramblase activity has been attributed to VDAC dimers, which explains the manifold lipidomic changes observed in VDAC-deficient yeast strains. In this review, I highlight the recent advances regarding VDAC’s phospholipid scramblase function and discuss how this new insight sheds new light on VDAC’s implication in regulated cell death, autophagy, and ageing. Full article