Deep neural networks with powerful auto-optimization tools have been widely applied in various research fields, e.g., NLP and computer vision. However, existing neural network architectures typically are constructed using different inductive biases, e.g., preconceptions, expecting to decrease parameter search space during training, reduce computational cost or introduce expert knowledge in the neural network design. As an alternative, Multilayer Perceptron (MLP) provides much better freedom for exploration, has a lower inductive bias than convolutional neural networks (CNNs), and offers good flexibility in learning complex patterns. Even though, such neural architectures are commonly built in a flat Euclidean space, which is not necessarily the optimal space for any data, and is especially not good for modeling hierarchical correlations. Hyperbolic neural networks (HNNs) have gained attention for their ability to capture hierarchical structures present in complex data types like graphs. Recently, there has been an increasing interest to extend HNNs to computer vision tasks, motivated by the observations that images possess rich hierarchical relations. However, this is generally applied by employing a Euclidean backbone for learning higher-level semantic representations and only incorporating a hyperbolic classifier for classification, which, we argue, does not make full use of the advantage of hyperbolic space. Considering the recovery of the attention-free Multilayer Perceptron(MLP), in this paper, we extend it to non-Euclidean space and propose a novel architecture, named Hyperbolic Res-MLP (HR-MLP), that leverages fully hyperbolic layers to learn feature embeddings and perform image classification in an end-to-end fashion. With the help of the proposed Lorentz cross-patch and cross-channel layers, we can directly perform operations in the hyperbolic domain with fewer parameters, making it faster to train and providing comparatively better performance than its Euclidean counterpart. Experiments on CIFAR10, CIFAR100, and MiniImageNet demonstrate a comparable and superior performance when compared to Euclidean baselines. Our code is available at (https://github.com/Ahmad-Omar-Ahsan/HR-MLP)

We examine here the conductance changes associated with the change in spin state in a variety of different structures, using the example of the spin crossover complex [Fe(H2B(pz)2)2(bipy)] (pz= (pyrazol-1-yl)-borate and bipy = 2,2’-bipyridine) and [Fe(Htrz)2(trz)](BF4)] (Htrz = 1H-1,2,4-triazole) thin films . This conductance change is highly variable depending on the mechanism driving the change in spin state, the substrate and the device geometry. Simply stated, the choice of spin crossover complex used to build a device is not the only factor in determining the change in conductance with the change in spin state.

Central to an understanding of the physical nature of biosystems is an apprehension of their ability to control entropy dynamics in their environment.  To achieve ongoing stability and survival, living systems must adaptively respond to incoming information signals concerning matter and energy perturbations in their biological continuum (biocontinuum).  Entropy dynamics for the living system are then determined by the natural drive for reconciliation of these information divergences in the context of the constraints formed by the geometry of the biocontinuum information space.  The configuration of this information geometry is determined by the inherent biological structure, processes and adaptive controls that are necessary for the stable functioning of the organism.  The trajectory of this adaptive reconciliation process can be described by an information-theoretic formulation of the living system’s procedure for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback Principle of Minimum Information Discrimination (a derivative of Jaynes’ principle of maximal entropy). Utilizing relative information for entropic inference provides for the incorporation of a background of the adaptive constraints in biosystems within the operations of Fisher biologic replicator dynamics.  This mathematical expression for entropic dynamics within the biocontinuum may then serve as a theoretical framework for the general analysis of biological phenomena.

The dynamic factors in the environment violate the static environment assumption of the SLAM algorithm, leading to a decrease in the accuracy of camera positioning. In recent years, many studies have attempted to address dynamic objects by combining semantic constraints and geometric constraints, but issues such as poor real-time performance, the potential for mistakenly treating humans as rigid objects, and subpar performance in high-dynamic scenes still persist. This paper proposes a dynamic scene visual SLAM algorithm called Dynamic SLAM based on target tracking and multi-view geometry (TKG-SLAM), based on object detection, Kalman filters, and multi-view geometry. This algorithm takes into consideration both real-time performance and algorithm accuracy. It combines semantic constraints and multi-view geometry constraints, selectively running the algorithm in different scenarios, filtering and preserving static points for camera pose estimation. Experimental results demonstrate that, compared to current state-of-the-art dynamic SLAM methods, our approach achieves optimal performance in some scenarios and exhibits stronger real-time capabilities.

This short reading is an extraction from our previous work (Nyambuya 2020), the purpose of which is to make clear that it is very much possible to use Weyl (1918)'s idea of a conformal metric to achieve tensorial affinities. We are of the strong view that this is very important as it is predominantly assumed that this not possible. We want to dispel this myth once and for al-time.

The purpose of the investigation was to determine the relationship between rotary kiln liner loss and steel structure ovality. As measurement apparatus, a terrestrial laser scanner was used. The interior and exterior of the rotary kiln were measured. The primary focus object was inner-lining loss and the geometric characteristics of cylindrical shells. The research uncovered significant disparities in inner lining loss between sections. A correlation was found between ovality and elimination of inner lining. Due to the hypothesis of constant inner linig loss from the middle of the rotary kiln, the investigation found that the loss of brick lining was less than the value reported from the boreholes. The study offers significant information on maintenance and repair strategies for rotary kilns, which have the potential to increase their efficiency and useful life.

This research delves into the intricate challenges confronting the agricultural sector, with a specialized focus on mitigating infections in tomato crops, particularly powdery mildew induced by the Leveillula Taurica pathogen. Tomatoes, renowned for their nutritional richness, are vital to global food security. However, conventional methodologies for disease detection exhibit both laborious processes and limited accuracy. In response to these challenges, this study advocates for an innovative fusion of hyperspectral imaging and deep learning methodologies to detect crop disease and its severity. The systematic workflow commenced with the curation of a dataset, involving the acquisition of live images through OpenCV, followed by conversion to RGB format and subsequent feature extraction utilizing a pre-trained visual geometry group (VGG-16) model for enhanced analysis. Sequentially, RGB images were transformed into simulated hyperspectral images (SHSI) leveraging a Neural Network generator model, offering a distinctive viewpoint on spectral information. This novel approach transcends conventional constraints by delivering a three-dimensional perspective, seamlessly integrating spatial and spectral dimensions for holistic data acquisition. The SHSI is further transmuted into a 3D visualization cube comprehensive grasp of spatial and spectral aspects encompassing spectral, spatial, and Haralick features. The research concludes with severity detection, categorized as low, moderate, or high, employing a Gaussian Mixture Model (GMM) and K-means for visualization.

The present paper provides a new definition for dual spline curves in a geometric intuitive way based on adaptive curve refinement techniques. The dual spline is an implementation of the interpolatory subdivision scheme for curve modeling, which is comprised of polynomial segments of different degrees. Specially, the dual spline curves are mainly aims to solve the difficult geometry defeaturing problems in the existing computer-aided technology. Dual spline curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, continuous and discontinuous boundary approximation. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual spline is flexible and convenient for approximating a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of approximating the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

During few last years, climate change including global warming which is attributed to human activities and also its long-term adverse effects on the planet’s functions have been identified as the most challenging discussion topics which have arisen many concerns and efforts to find the possible solutions. Since the warmth arising from Earth’s landscapes affects the world’s weather and climate patterns, we decided to study the changes in the Land Surface Temperature (LST) patterns in different seasons through non-linear methods. Here, we particularly want to estimate the non-integer dimension and fractal structure of the land surface temperature. For this study, the (LST) data has been obtained during the daytime by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Depending on what time of the year data has been collected, temperatures change in different ranges. Since equatorial regions remain warm, and Antarctica and Greenland remain cold, and also because altitude affects temperature, we selected Riley County in the U.S. state of Kansas, which does not belong to any of this type locations and we are interested to observe the seasonal changes in temperature in this county. The results of the present study show that the Land Surface Temperature (LST) belongs to the class of fractal process with non-integer dimension.

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection as well as to distribute the computing load to edge devices. However, even though wireless communications is a essential part for implementing FL in edge networks, there have been a few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks, and it can be exploited as a guideline for designing the network facilitating the wireless FL.

Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic.

Robot workpiece machining is interesting in industry since it offers some advantages, such as higher flexibility in comparison with the conventional approach based on the CNC technology. However, in recent years we have been facing a strong progressive shift to custom based manufacturing and low volume/high mix production, which require a novel approach to automation by the employment of collaborative robotics. However, collaborative robots feature only limited motion capability, to provide safety in cooperation with human workers. Thus, it is highly necessary to perform more detailed robot task planning to ensure its feasibility and optimal performance. In this paper, we deal with the problem of studying kinematic robot performance in the case of such manufacturing tasks, where the robot tool is constrained to follow the machining path embedded on the workpiece surface at a prescribed orientation. The presented approach is based on the well-known concept of manipulability, although the latter suffers from physical inconsistency due to mixing different units of linear and angular velocity in a general 6 DOF task case. Therefore, we introduce the characteristics of the workpiece surface constraint in the robot kinematic analysis, that enables evaluation of its available velocity capability in a reduced dimension space. Such constrained robot kinematics transform the robot`s task space to a two-dimensional surface tangent plane, and the manipulability analysis may be limited to the space of linear velocity only. Thus, the problem of physical inconsistency is avoided effectively. We show the theoretical derivation of the proposed method, which was verified by numerical experiments.

This study aims to reveal the revolutionary Gamma Distribution Manifold (GDM) info-geometric analysis combined with potential Gamma distribution (GD) applications to advance Satellite Earth Observations (SEOs). An exposition of the GDM Fisher Information Matrix (FIM) was undertaken, together with the analytic investigation of the existence of FIM’s inverse. The derivation of GDM’s Geodesic Equations (GEs) is undertaken. The solution of the obtained Geodesic Equations is optimally complicated, and it provides more extensions to numerous open problems. Notably, the current paper provides a first-time unification between three multi-interdisciplinary fields, namely, information geometry theory, probability theory, and Satellite earth observations. Looking at the other side of the coin, the provided revolutionary approach in this current work reports the significant impact of info-geometric analysis on the probabilistic dynamics as well as the influential role of information geometry on satellite and space industry. This poses numerous open issues that initiates a new form of contemporary unification between these inter-disciplinaries to discover another visionary thinking out of traditional statistical frames. In other words, refraining ourselves from using classical statistical frames of thinking and delving into a new info-geometric vision of statistical distributions as well as examining real life applications of information geometry to advance satellite earth observations. The curtain is drawn on this paper by providing several challenging open problems in combination with a concluding remark and the next phase of research.

This article investigates on the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity.

We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from "atoms" of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences the phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the universe’s topology. The "foamy" structure, analogous to Wheeler’s "spacetime foam," significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the universe.

The research paper proposes an algorithm to find congruence criteria between two convex polygons in Euclidean Geometry. It begins with a review of triangles, then extends to quadrilaterals and eventually gener- alizes the case to n-sided polygons. It attempts to prove said algorithm using a method of induction and a case-by-case analysis. It also states a corollary to said algorithm

As a radiant light source within the dynamic range of most spacecraft payloads, the moon pro-vides an excellent reference for on-orbit radiometric calibration. This research hinges on the pre-cise simulation of lunar spectral irradiances and the Earth-based Moon observation geometry. The paper leverages the Hapke model to simulate the temporal changes in lunar spectral irradi-ances, utilizing datasets obtained from Lunar Reconnaissance Orbiter Camera (LROC). The re-search also details the transformation process from the lunar geographic coordinate system to the instantaneous projection coordinate system, thereby delineating the necessary observational geometry. The insights offered by this study have the potential to enhance future in-orbit space-craft calibration procedures, thereby boosting the fidelity of data gathered from satellite obser-vations.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

This paper considers the possibility that abstract thinking and advanced synthesis skills might be selection criteria for extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic structures of current physical theories: vector fields, 1-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission.

As a first step a unification of the gravitational with the electromagnetic interaction within a classical framework is proposed. It is based on a V₅-geometry, with x₅ = q/m. The sole source term is mechanical stress energy, positioned along x₅. The trajectories of test-bodies are placed in V₄ (x₅ = const)-slices. The resulting field equation couples a geometric G-tensor to mechanical stress energy, its momentum with respect to V₅ and the change of this momentum with proper time τ. The following step proceeds to the quantization of space-time to enable the formalization of elementary particles und strong interaction. This is complimented by the inclusion of spin and the weak force, leading finally to a grand total equation, the stationary version of which corresponds to Schroedinger´s equation, the instationary version to the Einstein equation of General Relativity.

We review the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. As an example of practical worth, we consider the Drell-Yan process and discuss the gauge invariance of the corresponding hadron tensor. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in SU(3) gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

Having garnered significant attention in the scientific community over the past decade, Wire Arc Directed Energy Deposition (arc-DED) technology is at the heart of this investigation into additive manufacturing parameters. Singularly focused on invar as the selected material, the primary objective revolves around devising an indirect cord height measurement approach. This innovative methodology involves the seamless integration of internal signals and sensors, enabling the derivation of crucial measurements sans the requirement for direct physical interaction or conventional measurement methodologies. Through the course of this research, meticulous alteration of deposition parameters is undertaken to thoroughly scrutinize their influence on the ultimate cord dimensions. The fusion of cutting-edge manufacturing techniques with advanced sensor technology constitutes the essence of this endeavor, offering substantial potential to augment precision and efficiency in additive manufacturing processes. Remarkably cost-effective, this solution circumvents the need for intricate measurements and significantly contributes to the proper layer-by-layer growth process.

In this study, the unsteady Reynolds-averaged Navier-Stokes (URANS) equations are employed in conjunction with the Menter Shear Stress Transport (SST)-Scale-Adaptive Simulation (SAS) turbulence model in compressible flow, unstructured mesh and complex geometry. Whereas, other scale-resolving approaches in space and time, such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES), supply more comprehensive information about the turbulent energy spectra of the fluctuating component of the flow; however, previously mentioned avenues imply computationally intensive situations, usually performed over structured meshes and relatively simply geometries. In contrast, the SAS approach is designed according to “physically” prescribed length scales of the flow. More precisely, it operates by locally comparing the length scale of the modelled turbulence to the von Karman length scale (which is prescribed according to local fluid velocity derivatives and depends on the grid point distribution in the computational domain). This length scale ratio allows the flow to dynamically adjust the local eddy viscosity in order to better capture the large scale motions (LSM) in unsteady regions of URANS simulations. While SAS may be constrained to model only low flow frequencies or waivenumbers (i.e., LSM), its versatility and computational low-cost make it attractive to obtain a quick first insight of the flow physics; particularly, in those situations dominated by strong flow unsteadiness. The selected numerical application is the well-known M219 three-dimensional rectangular acoustic cavity from the literature at two different freestream Mach numbers, M∞ (0.85 and 1.35) and a length-to-depth ratio of 5:1. Thus, we consider the “deep configuration" in experiments by Henshaw. The SST-SAS model has demonstrated a satisfactory compromise between simplicity, accuracy and flow physics description.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Triangles are an ever present feature in nature, which the building construction industry duly echoes. However, an exact expression intended to offer the radiant field due to any triangle in an upright or inclined position had not been identified by previous research. In this case, the author has been able to solve by direct integration, the canonical expression of radiative transfer. This result alone confers a myriad of possibilities that had been inconceivable before, for studying in detail the three-dimensional heat transfer behavior of volumes and figures in which triangles do manifest, such as fins, windows, roof-gables and louvers of various kinds. Typically, shading devices, when tilted, give rise in their extremes to rhomboidal shapes which were difficult to take into account or had to be subject to discretization and subsequent Monte Carlo methods in order to perform an approximate calculation of their emission. This implied a lengthy and inexact procedure that induced many errors and consumed computing time. We can now avoid all the former downsides due to the advances hereby presented. As the novel expression can be converted into an algorithm it will be advantageously employed for simulation. This significant finding dovetails in the intricate puzzle of radiated heat and we believe that their consequences will greatly affect the conception and design of HVAC devices, aircraft manufacturing and specifically building or lighting industries among others.

This paper presents a novel real time control strategy on four-wheel independent steering system for electric vehicle with stepper motors using neural networks combined with fuzzy logic. The control of the four wheels is based on a variation of Hopfield Neural Network (VHNN) method, in which the input is the error of each steering motor and the output is processed by a hyperbolic tangent function (HTF) feeding the fuzzy logic controller (FLC), which ultimately drives the stepper motor. The whole system is made up of the four aforementioned blocks where they work in sync and inseparable from each other with the common goal of driving all the steering stepper motors at the same time. Simulation results demonstrate that the proposed control method has strong robustness and practicability under different angles and speeds.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm based on the Weyl Integrable Geometry (WIG) as an extension to the standard Einstein General Relativity (EGR). After a brief review of the mathematical framework, where we also highlight the connection between the weak-field SIV equations and the notion of un-proper time parametrization within the reparametrization paradigm, we continue with the main results related to early Universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. In the late time Universe the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth-Moon system.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

The dimethylaminophenyl-substituted silver phthalocyanine [dmaphPcAg] can be used as a UV-vis photoinitiator for in situ preparation of a silver/polymer nanocomposite. To verify early steps of the supposed mechanism of radical polymerization, we performed quantum chemical calculations of m[dmaphPcAg]q complexes with charges q = +1 to -2 in the two lowest spin states m, of a free ligand and its dehydrogenated/deprotonated products m[dmaphPcHn]q, n = 2 to 0, q= 0, -1 or -2, in the lowest spin states m. The calculated electronic structures and electron transitions of all the optimized structures in CHCl3 solutions are compared with experimental EPR and UV-vis spectra, respectively. The unstable 3[dmaphPcAg]+ species deduced only from previous EPR spin trap experiments was identified. In addition to 2[dmaphPcAg]0, our results suggest the coexistence of both reaction intermediates 1[dmaphPcAg]- and 3[dmaphPcAg]- in reaction solutions. Silver nanoparticle formation is a weak point of the supposed reaction mechanism from the energetic, stereochemistry, and electronic structure points of view.

A mixture of nonlabeled (14N2H4) and 15N labeled hydrazine (15N2H4) in an aqueous solution is oxidized to 15N2, 14N2, and 14N15N molecules, indicating the intermediate existence of the 14NH2-14NH-15NH-15NH2 with subsequent hydrogen transfers and splitting of side N-N bonds. Structures, thermodynamics, and electron characteristics of various N4H6 molecules in aqueous solutions are investigated using theoretical treatment at the CCSD/cc-pVTZ level of theory to explain the crucial part of the hydrazine oxidation reaction. Most N4H6 structures in aqueous solutions are decomposed during geometry optimization. Splitting the bond between central nitrogen atoms is the most frequent, but the breakaway of the side nitrogen is energetically the most preferred. The N-N fissions are enabled by suitable hydrogen rearrangements. Gibbs free energy data indicate the dominant abundance of NH3... N2... NH3 species. The side N atoms have very high negative charges, which should support hydrogen transfers in aqueous solutions. The only stable cyclo-(NH)4…H2 structure has a too high Gibbs energy and breaks the H2 molecule. The remaining initial cyclic structures are split into hydrazine and HN≡NH or H2N≡N species, and their relative abundance in aqueous solutions is vanishing.

Using the potent tools of information geometry (IG), the current research analyses the information geometrics of the five-dimensional HTBFC Manifold. By enabling a unique revolutionary analysis for the performance of Human-Trust Based Feedback Control (HTBFC), the integration of information geometry into HTBFC facilitates the relativistic analysis of the five-dimensional HTBFC manifold. Both the two- and three-dimensional manifold subcases are investigated. This work provides a ground-breaking approach to IG unification of Human- Machine Interactions (HMIs). Some potential applications of HTBFC to robotics are presented.Conclusions are provided, along with some emerging open problems and recommendations for future research.

The current letter complements my info-geometric discoveries, especially those provided from two papers of mine. Fundamentally, the statistical relativization of the Generalized Brownian Motion Manifold. Following this innovative and unprecedented track of research will open a plethora of numerous info-geometric investigations to many unexplored related phenomena in the hope to uncover more new interpretations for the Generalized Brownian Motion Manifold from an info-geometric perspective.

A cyclic antipodal points of a circle is a pair of points that are the intersection of the circle with a diameter of the circle. A recent proof of Ptolemy’s Theorem, simultaneously in both (i) Euclidean geometry; and (ii) the relativistic model of hyperbolic geometry (which is identified with the Klein model of hyperbolic geometry), motivates in this article the study of four cyclic antipodal points of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Formulas that extend the Pythagorean formula in both Euclidean and hyperbolic geometry are obtained as byproducts

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

Matrices and their inverses allow accurate calculations to be produced quickly and compactly and can be used to control any process represented by a system of equations. Singular matrices require extensive workarounds (costing time and money) to solve these systems of equations because they have no inverse. Finding their inverse involves division by zero. Nevertheless, recently a new number set called semi-structured complex numbers was developed to enable division by zero in algebraic equations. The aim of this research was to demonstrate that the inverse of a singular matrix can be found using semi-structured complex numbers. This research reveals (1) Singular matrices and their inverses can be used to find a unique solution to a pair of simultaneous equations that appear to have infinitely many solutions or appear to have no solution; (2) Singular matrices map coordinates in projective space to coordinates in Euclidean space and their inverse maps coordinates in Euclidean space to coordinates in projective space; (3) the inverse of a singular matrix proves that parallel lines in Euclidean space do not intersect but in projective space intersect at a “point at infinity” and (4) collinear lines that intersect at infinitely many points in Euclidean space only intersect at one point in projective space.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

Precise monitoring of individual crop growth and health status is crucial for precision agriculture practices. However, traditional manual inspection methods are time-consuming, labor-intensive, and often lack the spatial resolution required for detailed analysis. This research addresses the need for efficient and high-resolution crop monitoring by leveraging Unmanned Aerial Vehicle (UAV) imagery and advanced computational techniques. The primary objective was to develop a methodology for precise identification, extraction, and monitoring of individual corn crops throughout their growth cycle. This was achieved by integrating UAV-derived data with image processing, computational geometry, and machine learning techniques. UAV imagery was ac-quired bi-weekly at altitudes of 40m and 70m, capturing the entire growth cycle of a corn crop from planting to harvest. A time-series Canopy Height Model (CHM) was generated by analyzing the differences between the Digital Terrain Model (DTM) and the Digital Surface Model (DSM) derived from the UAV data. Local spatial analysis and image processing techniques were em-ployed to determine the local maximum height of each crop. Subsequently, a Voronoi data model was developed to delineate individual crop canopies, successfully identifying 13,000 out of 13,050 corn crops in the study area. For enhanced accuracy in canopy size delineation, vegetation indices were incorporated into the Voronoi model segmentation, refining the initial canopy area esti-mates by eliminating interference from soil and shadows. The proposed methodology enables precise estimation and monitoring of crop canopy size, height, biomass reduction, lodging, and stunted growth over time, providing valuable insights for precision agriculture practices. This work contributes to the scientific community by demonstrating the potential of integrating UAV technology, computational geometry, and machine learning for accurate and efficient crop mon-itoring at the individual plant level.

Students have historically fared poorly on the West African Examinations Council’s (WAEC) mathematics exam. This study investigated senior high school students’ difficulties with studying Geometry in the Cape Coast Metropolis, Central Region, Ghana. Using the descriptive survey design, data were collected from 300 Senior High School Two (SHS 2) students using simple random sampling. Students responded to the questionnaire and a 30-item multiple-choice achievement test on geometry. Four geometry concepts students perceived difficult to study are Circle theorems, Perpendicularity of Tangent and radius of a circle, Angle between Tangent and a chord and Tangents from an external point. The reasons for the difficulty in studying geometry topics are the unavailability of instructional materials, the geometry topics being complex, and teachers not teaching geometry concepts to the students’ understanding. Students’ gender did not influence the learning of concepts in geometry at a 0.05 level of significance. There was an insignificantly weak positive correlation between the students’ performance and their perceived difficult geometry concepts. It was concluded that the Ministry of Education does not provide relevant instructional materials to the various schools to teach geometry concepts. Schools do not organise workshops and seminars for teachers on effectively teaching geometry concepts in mathematics.

Advancements in computer vision are rapidly revolutionizing the way traffic agencies gather roadway geometry data, leading to significant savings in both time and money. Utilizing aerial and satellite imagery for data collection proves to be more cost-effective, more accurate, and safer compared to traditional field observations, considering factors such as equipment cost, crew safety, and data collection efficiency. Consequently, there is a pressing need to develop more efficient methodologies for promptly, safely, and economically acquiring roadway geometry data. While image processing has previously been regarded as a time-consuming and error-prone approach for capturing these data, recent developments in computing power and image recognition techniques have opened up new avenues for accurately detecting and mapping various roadway features from a wide range of imagery data sources. This research introduces a novel approach combining image processing with a YOLO-based methodology to detect turning lane pavement markings from high-resolution aerial images, specifically focusing on Florida's public roadways. Upon comparison with ground truth data from Leon County, Florida, the developed model achieved an average accuracy of 87% at a 25% confidence threshold for detected features. Implementation of the model in Leon County identified approximately 3,026 left turn, 1,210 right turn, and 200 center lane features automatically. This methodology holds paramount significance for transportation agencies in facilitating tasks such as identifying deteriorated markings, comparing turning lane positions with other roadway features like crosswalks, and analyzing intersection-related accidents. The extracted roadway geometry data can also be seamlessly integrated with crash and traffic data, providing crucial insights for policymakers and road users.

The authors undertook pilot studies to assess the accuracy of the reverse engineering process of worn nonstandard spur gears (non-standardized modulus value, unusual profile/pressure angle, high or low teeth), using conventional techniques and measuring instruments. Eight gears were tested, the module of which ranges from 1.020 to 4.98 mm and the number of teeth from 13 to 42. The key parameter, the basic pitch, was selected to estimate the accuracy of the process. The goal is to determine the value of the profile angle. Eleven models were proposed to estimate the nominal tolerance field, using various types of random data distribution. The tested gears were made in IT grade: 6, 7, 8 and 9 according to DIN 3961. Vernier disc micrometers with various measurement ranges were used for research. It has been shown that the nominal module does not have to be treated as a random variable in the population. EIG (Equation of Identity) was developed, allowing conversion of any gear with specific values of geometric parameters into an identical gear with alternative values of these parameters. The directions and degrees of shifts of the estimated tolerance fields relative to the nominal field were determined. The most effective estimating model was selected in the context of the percentage filling of the nominal tolerance field, taking into account the symmetric Student-Fisher distribution with a confidence level of 60%. Further directions of the research activities were described.