The uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

In this paper, a new approach to retrieve semantic images based on shape and geometric features of image in conjunction with multi-class support vector machine is proposed. Zernike moment as shape feature is to verify the invariance of objects for silhouette image. In addition, a set of geometrical features is to explore the objects shape using two features of rectangularity and circularity. Then the extracted features are normalized and employed for multi-class support vector machine either for learning or retrieving processes. The retrieving process relies on three main tasks which namely Query Engine, Matching Module and Ontology Manger, respectively. Query Engine is to build the input text or image query using SPARQL language. The matching module extracts the shape and geometric features of image’s objects and employ them to Ontology Manger which in turn inserts them in ontology knowledge base. Benchmark mammals have been conducted to empirically conclude the outcome of proposed approach. Our experiment on text and image retrieval yields efficient results to problematic phenomena than previously reported.

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

In this paper, we present an experimental procedure to enhance the dimensional accuracy of fabrication via Stereolithography (SLA) of features at the micro-scale. Using a custom benchmark part, deviations in feature dimensions (micro-pores diameters and depths) were detected and measured by confocal microscopy. Samples characterization and experimental observations allowed the identification of inaccuracy sources, mainly due to the laser beam scanning strategy and to the incomplete removal of uncured liquid resin in post-processing (i.e., IPA washing). As a technology baseline, the measured dimensional errors on pores diameters were up to -46%. A compensation method of the nominal laser spot diameter (85m) was defined and implemented resulting in relevant improvements in dimensional accuracy of 9.8% and 11.3% on full-open pores diameter and depth, respectively. Further investigation was performed on a customized test part to adjust the calibration procedure. The measurements revealed that the estimate of the laser beam spot size is 968m. Measurements on micro-pores having different sizes revealed that a constant compensation parameter (i.e., C=85, 96, 120m) is not fully effective at the micro-scale, where average errors still remain at -24%, -18.8%, and -16% for compensations equals to 85, 96 and 120m, respectively. A further experimental campaign allowed the identification of an effective nonlinear compensation law where the compensation parameter depends on the micro-feature size C= f (D). Results show a sharp improvement in dimensional accuracy on micro-pore fabrication, with errors consistently below +8.2%. The proposed compensation method can be extended for the fabrication of any micro-features without restrictions on the specific technology implementation. Concerning the inaccuracy introduced by the laser path, experimentation with a customized part allowed the optimization of the part orientation to reduce the errors and their differences along the X and Y machine axes.

Hypersonic aircraft focuses more on the integration of aircraft and engine than ordinary aircraft owing to high performance requirements, and the nozzle design is reflected in the required large area ratio of nozzle inlet and outlet and the compactness of the overall size of the aircraft. In this study, the height constraint is directly introduced into the maximum thrust nozzle design method. A new method for designing nozzles under the height constraints that consults the maximum thrust theory is proposed. Initially, the condition that the nozzle reaches the maximum thrust under the height constraint is deduced mathematically. Then, a nozzle design method satisfying the height constraint is computed using the method of characteristics (MOC). Subsequently, the influence of the design parameters on the design method is studied parametrically. Results show that Mach number scale and asymmetrical factors can affect ramp length and flap length of the nozzle, respectively. These factors great influence the axial thrust performance and lift under a specific height constraint. Compared with the traditional truncation design method, the thrust coefficient and lift increased by 11.93% and 138.45% respectively.

Aging rate differs greatly between species, indicating that the process of senescence is largely genetically determined. Senescence evolves in part due to antagonistic pleiotropy (AP), where selection favors gene variants that increase fitness earlier in life but promote pathology later. Identifying the biological mechanisms by which AP causes senescence is key to understanding the endogenous causes of aging and its attendant diseases. Here we argue that the frequent occurrence of AP as a property of genes reflects the presence of constraint in the biological systems that they specify. This arises particularly because the functionally interconnected nature of biological systems constrains the simultaneous optimization of coupled traits (interconnection constraints), or because individual traits cannot evolve (impossibility constraints). We present an account of aging that integrates AP and biological constraint with recent programmatic aging concepts, including costly programs, quasi-programs, hyperfunction and hypofunction. We argue that AP mechanisms of costly programs and triggered quasi-programs are consequences of constraint, in which costs resulting from hyperfunction or hypofunction cause senescent pathology. Impossibility constraint can also cause hypofunction independently of AP. We also describe how AP corresponds to Stephen Jay Gould’s constraint-based concept of evolutionary spandrels, and argue that pathologies arising from AP are bad spandrels. Biological constraint is a missing link between ultimate and proximate causes of senescence, including diseases of aging. That this was not realized previously may reflect a combination of hyperadaptationism among evolutionary biologists, and the erroneous assumption by biogerontologists that molecular damage accumulation is the principal primary cause of aging.

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

The technology for determining the point’s coordinates on the earth’s surface using the global navigation satellite system (GNSS) is becoming the norm along with ground-based methods. In this case, determining coordinates does not cause any particular difficulties. However, to identify normal heights using this technology with a given accuracy, special research is required. The fact is that satellite determinations of geodetic heights (h) over an ellipsoid surface differ from ground-based measurements of normal height (HN) over a quasi-geoid surface by a certain value called quasi-geoid height or height anomaly (ζ). In relation to determining heights of a certain territory, the concept of geoid height (N) is usually operated when dealing with a geoid model. In this work, geodetic and normal heights are determined for 5 control points in three different regions in Lebanon, where measurements are carried out using GNSS technology and geometric levelling. The obtained quasi-geoid heights are compared with geoid heights derived from the global Earth model EGM2008. The results obtained showed that, in the absence of gravimetric data, the combination of global Earth model data, geometric levelling for selected areas and satellite determinations allows the creation of a high accurate altitude network for mountainous areas.

Semiconductor nanowhiskers, in particular, nanostructured whiskers based on zero-dimensional (0D) C70 fullerene, are being actively discussed due to the great potential of their application in modern electronics. For the first time, we proposed and implemented a method for the synthesis of nanostructured C70 fullerene whiskers based on the self-organization of C70 molecules during thermal evaporation of C70 droplets on the substrate surface. We found that the onset of the synthesis of C70 nanowhiskers upon evaporation of drops of a C70 solution in toluene on the substrate surface depends on the substrate temperature. We have provided experimental evidence that an increase in both the C70 concentration in the initial drop and the substrate temperature leads to an increase in the geometric dimensions of C70 nanowhiskers. The obtained results provide useful vision on the role of solute concentration and substrate temperature in the synthesis of one-dimensional materials.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

The foot-mounted inertial navigation system is an important application of pedestrian navigation as it in principle does not rely any external assistance. A real-time range decomposition constraint method is proposed in this paper to combine the information of dual foot-mounted inertial navigation systems. It is well known that low-cost inertial sensors with ZUPT (zero-velocity update) and range decomposition constraint perform better than in either single way. This paper recommends that the distance of separation between the position estimates of feet-mounted inertial navigation systems be restricted in the ellipsoidal constraint which relates to the maximum step and leg height. The performance of the proposed method is studied utilizing experimental data. The results indicate that the method can effectively correct the dual navigation systems’ position over the existing spherical constraint.

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the Friedmann equations of uniform space, we derive equations characterizing a $\Lambda$CDM model that describes a universe corresponding to current observational data. The equations take into account the effects of radiation and ultra-relativistic neutrinos. It is shown that the universe at very early and late stages can be described to sufficient accuracy by simple formulas. Certain important moments of cosmic evolution are determined: the times when densities of the gravitational components of the universe become equal, when they contribute equally to the gravitational force, when the accelerating expansion of space begins, and several others. The dependences of different distances on redshift and the scale factor of space are derived. The distance to the sphere that expands with the speed of light (the Hubble distance), and its current and future acceleration, are found. Concepts of a horizon, second inflation, and second horizon are discussed. We consider the remote future of the universe and the opportunity, in principle, of connection with extraterrestrial civilizations.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In this article it is shown, first, that a change of basis in Minkowski space is equivalent to a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. Second, that such mixed bases can be interpreted as a measurement system used by local, flat observers whose direct distance measurements are restricted to an (n−1)-dimensional submanifold in an n-dimensional Euclidean space. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean space measures a Minkowski spacetime. This interpretation could be useful for theories in special relativity and related fields that rely on spacetime concepts, as it offers a more intuitive geometric understanding of the Minkowski metric.

Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.

We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler’s substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.

In light of the self-simulation hypothesis, a simple form implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in context of geometric state sum models.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

Camera malfunctions or loss of storage elements in imaging devices may lead to loss of important image information or random impulse noise interference. Low rank is one of the important prior information in image optimization processing. This paper uses different low-rank constraint models of the image matrices to recover the impulse interference satellite images. Firstly, an overview of image inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F-norm is presented, and corresponding optimiza-tion iterative algorithms are provided. Then, we conducted experiments under three types of pulse interference and provided visual and numerical results. Finally, it is concluded that the WSVT_ADMM method based on the weighted nuclear norm can obtain the best image inpainting results; The UV_ADMM method based on F norm of matrix factorization has the least computa-tion time and can be used for large-scale low-rank matrix computation; The WSVT_ADMM method based on weighted nuclear norm and the TSVT_ ADMM method based on truncated nuclear norms can significantly improve the repair effect compared to the nuclear norm-based methods such as SVT, SVP, and n_ADMM.

In heterogeneous networks, the random walks based on meta-path requires prior knowledge and lacks flexibility. And the random walks based on non-meta-path only considers the number of node types, but does not consider the influence of schema and topology between node types in real networks. To solve the above problems, this paper proposes a novel model HNE-RWTIC (Heterogeneous Network Embedding Based on Random Walks of Type & Inner Constraint). Firstly, to realize the flexible walks, we design a Type strategy, which is the node type selection strategy based on the co-occurrence probability of node types. Secondly, to achieve the uniformity of node sampling, we design an Inner strategy, which is the node selection strategy based on the adjacency relationship between nodes. The Type & Inner strategy can realize the random walks based on meta-path, the flexibility of the walks, and can sample the node types and nodes uniformly in proportion. Thirdly, based on the above strategy, a transition probability model is constructed; then, we obtain the nodes embedding based on the random walks and Skip-Gram. Finally, in classification and clustering tasks, we conducted a thorough empirical evaluation of our method on three real heterogeneous networks. Experimental results shown that F1-Score and NMI of HNE-RWTIC outperform state-of-the-art approaches.

Microalgae biomass is a budding raw material for the origination of food, fuel, and other value-added products. However, bulk production of microalgal biomass at commercial level is a herculean task for the current microalgal mass production technologies due to the undesirable contaminations by biological pollutants. These contaminants hamstring the production of microalgae biomass by debilitating the growth of cultures, crumble the quality of biomass and sometimes may crash the whole culture. The best utilization of the microalgae biomass at industrial level could be attained by avoiding various possible biological contaminations in mass cultivation system, understanding the contamination mechanisms, and the complex interactions of algae with other microorganisms. This review explores the various types of biological pollutants, their possible mode of infection along with mechanisms, different controlling methods to maintain desired microalgae culture.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

We review a modern differential geometric description of the fluid isotropic motion and featuring it the diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. There is analyzed the adiabatic liquid dynamics, within which, following the general approach, there is explained in detail, the nature of the related Poissonian structure on the fluid motion phase space, as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product. We also present a modification of the Hamiltonian analysis in case of the isotermal liquid dynamics. We study the differential-geometric structure of the adiabatic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and invariant theory. In particular, we construct an infinite hierarchies of different kinds of integral magneto-hydrodynamic invariants, generalizing those before constructed in the literature, and analyze their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, some generalization of the canonical Lie-Poisson type bracket is obtained.

We propose versatile integrated polarizers based on geometric metasurfaces. Metasurface polarizer consists of L-shaped hole array etched on a silver film and it can generate simultaneously several polarization states including the linear polarization, circular polarization, elliptical polarization, or even hybrid polarization. Meanwhile, the combination of output polarization states changes with the illumination polarization type. The theoretical analysis provides the detail explanation for the generation of the integrated polarization states. The well-designed metasurface polarizers may generate more complex polarization modes including vector beams and vector vortex beams. The theoretical and simulated results confirm the polarization performance of the proposed integrated metasurface polarizers. The compact design of metasurface polarizers and the controllable generation of versatile polarization combinations are benefit to the applications of polarization light in optical imaging, biomedical sensing and material processing.

In this paper, we study the constrained minimization problem for an energy functional which is related to the following Kirchhoff type equation \begin{equation*} -\Big(\eta+b\big(\int_{\R^{3}}|\nabla u|^{2}dx\big)^{s}\Big)\Delta u+V(x)u=\mu u +\lambda|u|^{p}u,\end{equation*} where $b$ is a positive constant, parameters $\eta\geq0, \lambda>0$, exponents $s>0$, $0

Carbon nanotube (CNT) yarns are fiber-like materials that exhibit excellent mechanical, electrical and thermal properties. More importantly, they exhibit a piezoresistive response that can be tapped for sensing purposes. The objective of this study is to determine experimentally the piezoresistive response of CNT yarns that are embedded in a polymeric medium while subjected to either compression or tension, and compare it with that of the free or unconstrained CNT yarns. The rationale for this study is the need to know the response of the CNT yarn while in a medium, which provides a lateral constraint to the CNT yarn thus mimicking the response of integrated CNT yarn sensors. The experimental program will include the fabrication of samples and their electromechanical characterization. The CNT yarns are integrated in polymeric beams and subjected to four-point bending, allowing the determination of their response under tension and compression. The electrical resistance data from an Inductance-Capacitance-Resistance (LCR) device is used with the data acquired from the mechanical testing system to determine the piezoresistive response of the CNT yarns. This data and information will be used for future modeling efforts and to study the phenomena that occur when CNT yarns are integrated in polymeric and composite materials and structures.

Deep learning has achieved lots of successes in many fields, but when trainable sample are extremely limited, deep learning often under or overfitting to few samples. Meta-learning was proposed to solve difficulties in few-shot learning and fast adaptive areas. Meta-learner learns to remember some common knowledge by training on large scale tasks sampled from a certain data distribution to equip generalization when facing unseen new tasks. Due to the limitation of samples, most approaches only use shallow neural network to avoid overfitting and reduce the difficulty of training process, that causes the waste of many extra information when adapting to unseen tasks. Euclidean space-based gradient descent also make meta-learner's update inaccurate. These issues cause many meta-learning model hard to extract feature from samples and update network parameters. In this paper, we propose a novel method by using multi-stage joint training approach to post the bottleneck during adapting process. To accelerate adapt procedure, we also constraint network to Stiefel manifold, thus meta-learner could perform more stable gradient descent in limited steps. Experiment on mini-ImageNet shows that our method reaches better accuracy under 5-way 1-shot and 5-way 5-shot conditions.

This paper presents an alternative constraint handling approach within a specialized genetic algorithm (SGA) for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a nonlinear single-objective optimization problem aiming to minimize power losses while keeping network constraints. The proposed constraint handling approach is based on a product of sub-functions that represents permissible limits on system variables and that includes a specific goal on power loss reduction. The main advantage of this approach is the fact that it allows a straightforward verification of both feasibility and optimality. The SGA is examined and tested with the proposed constraint handling approach and the traditional penalization of deviations from feasible solutions. Several tests are run in the IEEE 30, 57, 118 and 300 bus test power systems. The results obtained with the proposed approach are compared to those offered by other metaheuristic techniques reported in the specialized literature. Simulation results indicate that the proposed genetic algorithm with the alternative constraint handling approach yields superior solutions when compared to other recently reported techniques.

In order to understand the hot deformation behavior of novel Cu/Al laminated composites, isothermal hot compression tests were conducted by Gleeble-1500D thermo-mechanical simulator. And the effect of bonding interface, deformation temperature and strain rate on the deformation behavior was analyzed. Results show that under the interface constraint effect, soft Al layer trends to flow synchronously with hard Cu layer. And further microstructure examinations indicate the cooperative deformation capability of Cu/Al composites increases with increasing stain rate and decreasing deformation temperature. Strain hardening exponent, calculated based on the true stress-true strain data, also proves the effect of deformation temperature and strain rate on the cooperative deformation behavior. Meanwhile, unique composites structure allows the Al matrix to exhibit the characteristic of dynamic recrystallization during the hot deformation process. Lastly, strain compensated Arrhenius-type constitutive equation was employed to describe the coupling effect of temperature, strain rate and strain on the flow stress.

Electricity distribution network operators face several operational constraints in the provision of safe and reliable power given that investments for network area reinforcement must be commensurate with improvements in network reliability. This paper provides an integrated approach for assessing the impact of different operational constraints on distribution network reliability by incorporating component lifetime models, time-varying component failure rates as well as the monetary cost of customer interruptions in an all-inclusive probabilistic methodology that applies a time-sequential Monte Carlo simulation. A test distribution network based on the Roy Billinton test system is modelled to investigate the system performance when overloading limits are exceeded as well as when preventive maintenance is performed. Standard reliability indices measuring the frequency and duration of interruptions, and the energy not supplied are complemented with a novel monetary reliability index. The comprehensive assessment includes not only average indices but also their probability distributions to adequately describe the risk of customer interruptions. Results demonstrate the effectiveness of this holistic approach as the impacts of operational decisions are assessed from both reliability and monetary perspectives. This informs network planning decisions through optimum investments and consideration of customer outage costs.

: Following the phenomenal growth of and competition among coffee chain retailers, the coffee chain market has expanded substantially thanks to rising income levels, the increasing young population, and rapidly changing lifestyles. Attracting consumers’ attention and enhancing their loyalty behaviors have become very difficult for coffee chain retailers. This study seeks to understand the mechanisms through which emotions and the dedication-constraint model lead to brand loyalty and willingness to pay more to certain coffee chain retailers. Emotions and the dedication-constraint model are major factors in the research, but few studies have combined them to examine the formation of loyalty behaviors. This study synthesizes emotional responses and the dedication-constraint model to develop a theoretical model. Based on the ambivalent view of emotions, it also examines how positive and negative emotions affect the combination of brand loyalty and willingness to pay more to certain coffee chain retailers. Moreover, it identifies the antecedents of affective and calculative commitments in the context of coffee chain retailers. Our findings indicate that loyalty behaviors (dedication- and constraint-based mechanisms from brand loyalty and willingness to pay more to certain coffee chain retailers), emotional responses, and affective and calculative commitments significantly affect brand loyalty directly and indirectly through both positive and negative emotions. Furthermore, service quality, physical environment quality, and price fairness significantly affect affective commitments, while price fairness significantly affects both affective and calculative commitments. Finally, affective and calculative commitments significantly affect willingness to pay more, both directly and indirectly, through positive emotions and affect it directly through negative emotions. The results’ theoretical and managerial implications and possible future research directions are discussed.

With the renewed interest for lunar surface exploration, the European Space Agency envisions to stimulate the creation of lunar communications and navigation services (LCNS) to enable, among others, autonomous navigation capabilities for lunar rovers. As the number of satellites foreseen in such a service is much smaller compared to Earth based global navigation satellite systems (GNSS), different complementary technologies are pursued to improve the attainable navigation accuracy for lunar rovers. One way to improve the position accuracy provided by the LCNS satellites is to constrain the vertical position using a high resolution digital elevation model (DEM). This article presents the results of a variance covariance analysis of an extended Kalman filter (EKF) implementation in which the LCNS ranging measurements are used together with DEM from the LRO LOLA instrument. Assuming a realistic orbit determination and time synchronization (ODTS) accuracy of the LCNS satellites, the usage of a navigation grade IMU and an oven controlled crystal oscillator (OCXO), a 3-sigma position accuracy of less than 10 meters can be obtained. Furthermore, the availability is substantially improved as the DEM aided solution enables a position solution in case of only 3 visible satellites.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.

In this paper, we investigate how Rindler observer measures the universe in the ADM formalism. We compute his measurements in each slice of the space-time in terms of gravitational red-shift which is a property of general covariance. In this way, we found special relativity preferred frames to match with the general relativity Rindler frame in ADM formalism. This may resolve the widely known incompatibility between special relativity and general relativity on how each theory sees the red-shift. We found a geometric interpretation of the speed of light and mass.

High-precision dynamic positioning of highway vehicles is the foundation and prerequisite for achieving intelligent connected transportation. For the shortcomings of GNSS/INS combination and GNSS/INS/OD combination in tunnel vehicle positioning, this paper proposes a tunnel vehi-cle positioning method of GNSS/INS/OD combination based on lateral distance measurement and lane constraint. Firstly, lateral distance measurement of vehicles inside the tunnel is conducted based on laser radar point cloud data. Secondly, map matching positioning is performed based on lateral distance measurement, odometer, and lane markings. Experimental results demonstrate that for a 4.6 km tunnel, the average absolute error of lateral positioning is 0.294 meters, and the longitudinal positioning error is no more than 0.6 meters, which can effectively meet practical operational requirements.

Abstract Although we know something about single cell neuromuscular junction, It is still mysterious how multiple skeletal muscle cells coordinate to complete the intricate spatial curve movement. Here I propose a hypothesis that skeletal muscle cell populations with action potentials are alligned according to a curved manifolds on space(a curved shape on space) and the skeletal muscle also moves according to this corresponding shape(manifolds) when an specific motor nerve impulses are transmitted. the action potential of motor nerve fibers has the characteristics of time curve manifold and this time manifold curve of motor nerve fibers come from visual cortex in which a spatial geometric manifolds are formed within the synaptic connection of neurons. This spatial geometric manifolds of the synaptic connection of neurons orginate from spatial geometric manifolds in outside nature that are transmitted to brain through the cone cells and ganglion cells of the retina.Further,the essence of life is that life is an object that can move autonomously and the essence of life's autonomous movement is the movement of proteins. theoretically, due to the infinite diversity of geometric manifold shapes in nature, the arrangement and combination of 20 amino acids should have infinite diversity, and the geometric manifold formed by protein three-dimensional spatial structure should also have infinite diversity.

The fossil record is notorious for being incomplete and distorted, frequently conditioning the type of knowledge that can be extracted from it. In many cases, this often leads to issues when performing complex statistical analyses, such as classification tasks, predictive modelling, and variance analyses, such as those used in Geometric Morphometrics. Here different Generative Adversarial Network architectures are experimented with, testing the effects of sample size and domain dimensionality on model performance. For model evaluation, robust statistical methods were used. Each of the algorithms were observed to produce realistic data. Generative Adversarial Networks using different loss functions produced multidimensional synthetic data significantly equivalent to the original training data. Conditional Generative Adversarial Networks were not as successful. The methods proposed are likely to reduce the impact of sample size and bias on a number of statistical learning applications. While Generative Adversarial Networks are not the solution to all sample-size related issues, combined with other pre-processing steps these limitations may be overcome. This presents a valuable means of augmenting geometric morphometric datasets for greater predictive visualization.

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.

Continuous Distributed Constraint Optimization Problem (C-DCOPs) are a powerful framework to model problems with continuous variables in multi-agent systems. Previous works about C-DCOP algorithms mainly use pseudo-trees to guarantee the anytime property or are without anytime property guarantees. However, there is a risk of privacy leakage in the pseudo-tree due to utility passing between agents. Therefore, based on the basic constraint graph instead of the pseudo-tree, we (i) extend the Maximum Gain Message (MGM) algorithm by combining the local search strategy to solve C-DCOPs, named Continuous MGM (C-MGM), and it’s able to guarantee the monotonicity of the solution quality; (ii) propose a Parallel C-MGM (C-PMGM) algorithm to improve the solution quality through parallel random search; and (iii) introduce the differential search into C-PMGM to design a Parallel Differential Search C-MGM (C-PDSM) algorithm, which constructs a heuristic method to speed up convergence and improve solution quality. Compared to other anytime C-DCOP algorithms using pseudo-trees, the proposed three algorithms can exhibit better performance in avoiding privacy violations. We theoretically prove that the proposed algorithms are the anytime algorithms and empirically demonstrate that our algorithms outperform the state-of-the-art C-DCOP algorithms.

Computers have evolved over the years and as the evolution continues, we have been ushered into an era where high-speed internet has made it possible for devices in our homes, hospital, energy and industry to communicate with each other. This era is what is known as the Internet of Things (IoT). IoT has several benefits in the health, energy, transportation and agriculture sectors of a country’s economy. These enormous benefits coupled with the computational constraint of IoT devices which makes it difficult to deploy enhanced security protocols on them make IoT devices a target of cyber-attacks. One approach that has been used in traditional computing over the years to fight cyber-attacks is Intrusion Detection System (IDS). However, it is practically impossible to deploy IDS meant for traditional computers in IoT environments because of the computational constraint of these devices. In this regard, this study proposes a lightweight IDS for IoT devices using an incremental ensemble learning technique. We used Gaussian Naive Bayes and Hoeffding tree to build our incremental ensemble model. The model was then evaluated on the TON IoT dataset. Our proposed model was compared with other state-of-the-art methods proposed and evaluated using the same dataset. The experimental results show that the proposed model achieved an average accuracy of 99.98\%. We also evaluated the memory consumption of our model which showed that our model achieved a lightweight model status of 650.11KB as the highest memory consumption and 122.38KB as the lowest memory consumption.

At present, indoor localization is one of the core technologies of location-based services (LBS), and there exist numerous scenario-oriented application solutions. Visual features, as the main semantic information to help people understand the environment and thus occupy the dominant part, many techniques about indoor scene recognition are widely adopted. However, the engineering application problem of cell phone indoor scene recognition and localization has not been well solved due to insufficient semantic constraint information of building map and the immaturity of building map location anchors (MLA) matching positioning technology. To address the above problems, this paper proposes a cell phone indoor scene recognition and localization method with building map semantic constraints. Firstly, we build a library of geocoded entities for building map location anchors (MLA), which can provide users with "immersive" real-world building maps on the one hand and semantic anchor point constraints for cell phone positioning on the other. Secondly, using the improved YOLOv5s deep learning model carried on the mobile terminal, we recognize the universal map location anchors (MLA) elements in building scenes by cell phone camera video in real-time. Lastly, the spatial location of the scene elements obtained from the cell phone video recognition is matched with the building MLA to achieve real-time positioning and navigation. The experimental results show that the model recognition accuracy of this method is above 97.2%, and the maximum localization error is within the range of 0.775 m, and minimized to 0.5 m after applying the BIMPN road network walking node constraint, which can effectively achieve high positioning accuracy in the building scenes with rich MLA element information. In addition, the building map location anchors (MLA) has universal characteristics, and the positioning algorithm based on scene element recognition is compatible with the extension of indoor map data types, so this method has good prospects for engineering applications.

A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based in principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (three to ten-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.

The fundamental objective is to study the application of multivariate sets of data in Gaussian distribution. This paper examines broad measurements of structure for both Gaussian and non-Gaussian distributions, which shows that they can be described in terms of the infor-mation-theoretic between the given covariance matrix and correlated random variables (in terms of relative entropy). In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion supported by illustrations, both technically and statistically. The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis based on differential equations, a wide range of information is addressed, including basic to application concerns.

Greenhouses are instrumental in the advancement of regions globally. The geometric arrangement of these structures plays a pivotal role in governing sunlight distribution, facilitating ventilation, and managing condensation. The roof's shape significantly affects energy efficiency and the accumulation of condensation water, which, when dripping onto crops, can induce diseases and diminish production. This study introduces a Matlab program designed for defining and analyzing greenhouse roof geometry, adaptable to both single-span and multi-span structures. Various roof shapes are examined, determining angles along their length to facilitate condensation droplet runoff. Furthermore, the greenhouse's energy efficiency is evaluated by analyzing diverse roof models, accounting for surface area and internal air volume. The results aim to aid in selecting the optimal greenhouse type based on climate and latitude. This study offers a valuable decision-making tool for the planning and design of agricultural structures, providing insights to enhance overall sustainability and performance in diverse environmental contexts.

The corrugated board is a versatile and durable material that is widely used in the packaging industry. Its unique structure provides strength and cushioning, while its recyclability and bio-degradability make it an environmentally friendly option. The strength of corrugated board depends on many factors, including the type of individual papers on flat and corrugated layers, the geometry of the flute, temperature, humidity, etc. This paper presents a new approach to analysis geometric features of corrugated boards based on the images. It allows for precise determination of the geometry of the corrugated layer, as well as the thickness of individual papers in all cardboard layers. The experimental set used in the work and the created software are characterized by high reliability and precision of measurement thanks to the use of an identification procedure based on image analysis and evolutionary algorithms. This allows to quickly find the main geometric characteristics of the corrugated board, which in turn leads to the possibility of performing numerical analyzes taking into account the real model of the corrugated board. Calculations made on a real (correctly mapped geometrically) model allow, for example, a more reliable analysis of the composition of the cardboard, and thus also to obtain greater savings in the optimization process.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.

Given the increase in consumers’ preferences for coffee, it is becoming important to understand their decision-making processes in the coffee chain context. To deepen the understanding of sustainable outcomes in this context, this study investigates the role of dedication- and constraint-based mechanisms in forming consumers’ repurchase and positive word-of-mouth (WOM) intentions, two critical sustainable outcomes. We examined the effects of coffee quality, the quality of the physical environment, and service quality in accelerating the formation of dedication-based factors. Moreover, this study offers an in-depth understanding of the enablers of perceived switching costs. Data collected from 238 university students that frequently visit coffee chains are empirically tested against the proposed theoretical framework by using structural equation modeling. The results confirm that both dedication- and constraint-based factors substantially predict consumers’ sustainable outcomes in the coffee chain context. Brand image and perceived switching costs play an important role in enhancing consumers’ repurchase and positive WOM intentions compared with customer satisfaction. Coffee quality is significantly associated with both customer satisfaction and brand image, whereas the quality of the physical environment and service quality are only significantly associated with brand image. Habit is found to be the key enabler of perceived switching costs, while loyalty programs have no significant impact on perceived switching costs.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

Based on a measuring system to determine the statistical heterogeneity of individual polygons we propose a method to use polygonal shape patterns as a source of data in order to determine the Shannon entropy of biological organizations. In this research, the term entropy is a particular amount of data related with levels of spatial heterogeneity in a series of different geometrical meshes and sets of random polygons. We propose that this notion of entropy is important to measure levels of information in units of bits, measuring quantities of heterogeneity in geometrical systems. In fact, one important result is that binarization of heterogeneity frequencies yields a supported metric to determine geometrical information from complex configurations. Thirty-five geometric aggregates are tested; biological and non-biological, in order to obtain experimental results of their spatial heterogeneity which is verified with the Shannon entropy parameter defining low particular levels of geometrical information in biological samples. Geometrical aggregates (meshes) include a spectrum of organizations ranging from cell meshes to ecological patterns. Experimental results show that a particular range (0.08 and 0.27) of information is intrinsically associated with low rates of heterogeneity. We conclude it as an intrinsic feature of geometrical organizations in multi-scaling biological systems.

Membrane materials are most widely applied in construction engineering with small mass and high flexibility, it presents strong geometric nonlinearity in the process of vibration. In the paper, an improved multi-scale perturbation method is used to solve the aeroelastic stability of closed and open membrane roofs for quantify the effect of geometric nonlinearity on the single-mode aeroelastic instability wind speed of membrane roofs. The results show that the critical wind speed values of the two models are small when the geometrical nonlinearity of membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of membrane on the aerodynamic stability of roof can be neglected, However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of membrane roof. The results obtained in this paper have important theoretical reference value for the design the membrane structures.

The Hubble parameter H(z), as a function of redshift, is modified by the presence of a new term originated from the extrinsic curvature in an embedded space-time. Assuming an asymptotic expansion factor $a\sim 0$ or, equivalently $z\rightarrow \infty$, it is obtained a nearly resemblance of the present model ($\beta$-model) with quintessence $w$CDM model with $H(z)\sim H_{wCDM}(z)$ at background level. In conjunction with $\Lambda$CDM, we test the models using a pack of recent datasets like that of the ``Gold 2018'' growth data, the best-fit Planck2018/$\Lambda$CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from $0.01 < z < 2.3$. Performing the Akaike Information Criterion (AIC) to ascertain the statistical viability of the model from Jeffreys' scale, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method. We find that the present model is in very good agreement with observations with a close statistical equivalence with the $\Lambda$CDM and $w$CDM cosmologies at 1-$\sigma$ level. We also show that a mild alleviation of the $\sigma$ tension between the growth amplitude factor and the matter content $(\sigma_8$-$\Omega_m)$ of the observations from CMB and Large Scale Structure (LSS) probes. A comparison of the aforementioned full pack of data in MCMC chains is made with the resulting MCMC from Pantheon SNIa+$H(z)$ in order to analyse the sensitivity of the models and how they respond to a cosmography analysis on the evolution of $H(z)$ and the deceleration parameter $q(z)$. In this sense, we find that only the $\beta$-model can be unaffected to the variations of the previous datasets due to its several minima in the likelihood (degeneracies) of the related parameters with an overall percentage relative difference only up to 4$\%$.

This article presents a methodology to process information from a Terrestrial Laser Scanner (TLS) from three dimensions (3D) to two dimensions (2D), and to two dimensions with a color value (2.5D), as a tool to document and analyze heritage buildings. Principally focused on the loss of material in stone, this study aims at creating an evaluation method for loss control, taking into account the state of conservation of the building in terms of restoration, from studying the pathologies, to their identification and delimitation. A case study on the Cathedral of the Seu Vella de Lleida was completed, examining the details of the stone surfaces. This cathedral was affected by military use, periods of abandonment, and periodic restorations.

In recent years, the abundance of streaming data has posed significant challenges for traditional machine learning algorithms due to the dynamic nature and high volume of data. To address these challenges, this paper presents an adaptive supervised learning framework designed for data streams, leveraging the power of reproducing kernel Hilbert spaces (RKHS) while incorporating a data sparsity constraint. The proposed framework aims to adaptively update the model to efficiently handle the continuous arrival of streaming data while ensuring accurate and reliable predictions. The primary objective is to exploit the RKHS framework, which provides a rich mathematical structure for learning in high-dimensional feature spaces. By utilizing RKHS, the model can capture complex patterns and nonlinear relationships in the streaming data. Furthermore, the framework incorporates a data sparsity constraint to address the issue of limited resources and computational efficiency. The constraint promotes the selection of a subset of relevant features, reducing the dimensionality of the problem and enhancing the scalability of the learning algorithm. This constraint not only improves computational efficiency but also mitigates the effects of noisy or irrelevant features, leading to more robust and accurate predictions. To achieve adaptability, the proposed framework employs an online learning approach that incrementally updates the model parameters as new data arrives. This allows the model to adapt to concept drift and changing data distributions, ensuring its relevance and effectiveness over time. The adaptation process is guided by a mechanism that balances the exploitation of current knowledge with the exploration of new information, enabling the model to gradually evolve and refine its predictions. Experimental evaluations on various benchmark datasets demonstrate the efficacy of the proposed framework in handling streaming data. The results indicate that the adaptive supervised learning approach in RKHS with a data sparsity constraint outperforms traditional batch learning methods and exhibits superior accuracy, scalability, and adaptability in dynamic data stream scenarios. Overall, this research contributes to the development of adaptive supervised learning methods for data streams, highlighting the effectiveness of RKHS and the significance of incorporating a data sparsity constraint. The proposed framework offers a promising solution to handle the challenges posed by streaming data, paving the way for real-time, efficient, and accurate learning in diverse application domains.

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

Information theory provides robust measures of multivariable interdependence, but classically does little to characterize the multivariable relationships it detects. The Partial Information Decomposition (PID) characterizes the mutual information between variables by decomposing it into unique, redundant, and synergistic components. This has been usefully applied, particularly in neuroscience, but there is currently no generally accepted method for its computation. Independently, the Information Delta framework characterizes non-pairwise dependencies in genetic datasets. This framework has developed an intuitive geometric interpretation for how discrete functions encode information, but lacks some important generalizations. This paper shows that the PID and Delta frameworks are largely equivalent. We equate their key expressions, allowing for results in one framework to apply towards open questions in the other. For example, we find that the approach of Bertschinger et al. is useful for the open Information Delta question of how to deal with linkage disequilibrium. We also show how PID solutions can be mapped onto the space of delta measures. Using Bertschinger et al. as an example solution, we identify a specific plane in delta-space on which this approach’s optimization is constrained, and compute it for all possible three-variable discrete functions of a three-letter alphabet. This yields a clear geometric picture of how a given solution decomposes information

Traditional underground pipeline inspection primarily relies on closed-circuit television (CCTV) systems, capturing visual data of deformations within sewer systems for manual assessment of their types and severity. However, these methods heavily rely on human expertise, which leads to subjective detection with limited accuracy. Moreover, they lack the capability for quantitative analysis of deformation extent, hindering accurate assessments and limiting overall inspection effectiveness. To address these challenges, this paper proposes a method for quantitatively detecting geometric deformations in underground pipe corridors using laser point cloud data. The approach, employing laser scanning with a 3D scanner, enables objective detection of internal pipeline deformations and quantitative assessment of blockage levels. In comparison to traditional CCTV-based methods, this approach offers advantages in objectivity and quantification, thereby improving detection reliability, accuracy, and overall efficiency.

The vocal folds are found in the larynx and their vibrations produce the voice. Little is known about morphology and the size of cattle larynx. The aim of the study was to quantify the shape asymmetry of the vocal folds in calves obtained post-mortem using a geometric morphometric approach. A sample of 14 larynges from calves (in an age range 335 to 625 days) belonging to “Bruna dels Pirineus” breed and its F1 crosses was obtained in an abattoir during the first semester of 2021. Landmark sets were superimposed on images of fixed transverse sections of larynges. Using geometric morphometric techniques, we analysed the presence of asymmetries. Results demonstrate differences between right and left vocal fold sides as directional asymmetry, at least in fixed structures. Our findings provide a foundation for quantifying the possible contribution of vocal organ asymmetry among cattle. This study can be considered the first to detect vocal fold asymmetries in cattle. Studies with a larger sample size are needed to validate the information in large populations. One limitation is that the present study does not have samples from adult animals, so it would be interesting to know if the results are similar among them.

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 find at least 4 quantum properties that are indeed universal in some number systems; and we can use them for quantum consciousness. Using the sets B={0,1}, N, Z, or Q has the +4 quantum properties that one can trust, as archetypes of easy communication to friends and foes, to ignoranti or cognoscenti, and for quantum computing. This paper proposes the use of Bayesian geometry to reduce the space of possible results, reducing or increasing initial beliefs by successive experimentation. This is exemplified in biology and mathematics, and can be applied to physics and other sciences. The conclusion is that an experimental fact can be absolutely verified. Any mathematical choice (as verified by computers) militating against R=Q, is under an absolutely low chance to succeed. Infinitesimals are denied based on 3^16 independent factors. This is not a probabilistic result, but based on reduction of the Bayes geometry for updating beliefs. This work applies to non-probabilistic and unknown phenomena, such as those found in oscillations (neutrino, health), evolution, and quantum computing, denies Gödel's uncertainty, and solves the liar's paradox by reflection. This connects different scientific fields with one another, in an internet, i.e., in a network of connections of multiple open networks, using the set Q, resembling a hologram, and includes entanglement.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

Complexity science studies physical phenomena that cannot be explained by the mere analysis of the single units of a system but requires to account for their interactions. A feature of complexity in connected systems is the emergence of mesoscale patterns in a geometric space, such as groupings in bird flocks. These patterns are formed by groups of points that tend to separate from each other, creating mesoscale structures. When multidimensional data or complex networks are embedded in a geometric space, some mesoscale patterns can appear respectively as clusters or communities, and their geometric separability is a feature according to which the performance of an algorithm for network embedding can be evaluated. Here, we introduce a framework for the definition and measure of the geometric separability (linear and nonlinear) of mesoscale patterns by solving the travelling salesman problem (TSP), and we offer experimental evidence on embedding and visualization of multidimensional data or complex networks, which are generated artificially or are derived from real complex systems. For the first time in literature the TSP’s solution is used to define a criterion of nonlinear separability of points in a geometric space, hence redefining the separability problem in terms of the travelling salesman problem is an innovation which impacts both computer science and complexity theory.

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

This study presents an extensive collection of data on the aerodynamic behavior at a low Reynolds number and geometric coefficients for 2900 airfoils obtained through the class shape transformation (CST) method. By employing a verified OpenFOAM-based CFD simulation framework, lift and drag coefficients were determined at a Reynolds number of 10^5. Considering the limited availability of data on low Reynolds number airfoils, this dataset is invaluable for a wide range of applications, including unmanned aerial vehicles (UAVs) and wind turbines. Additionally, the study offers a method for automating CFD simulations that could be applied to obtain aerodynamic coefficients at higher Reynolds numbers. The breadth of this dataset also supports the enhancement and creation of machine learning (ML) models, further advancing research into the aerodynamics of airfoils and lifting surfaces.

Although the similarity laws were widely used in impact fields, the scaling relations of anisotropic elastic structures often were broken when the geometric distortion (not equal scaling in different spatial directions) and the material distortion (different materials used for scaled model and full-size prototype) were considered. To overcome the difficulty of geometric and material distortion, a directional framework of similarity laws, termed as oriented-density-length-velocity (ODLV) system, is proposed for the anisotropic elastic structure under impact loads. Different from previous similarity law systems using scalar dimensional analysis, the directional similarity law framework mainly considers spatial anisotropy for structural geometry and material parameters. Based on the oriented dimensional analysis and the orthotropic Hooke's law, directional dimensionless numbers and directional scaling relations with geometric power properties for the elastic modulus and the Poisson's ratio are presented systematically. By selecting the dominant material parameters controlling similarity, three important scaling techniques with correction of geometric width and thickness are proposed to compensate for the difficulty of distortion. A clamped square plate with different anisotropic and isotropic elastic materials subjected to dynamic pressure pulse is verified numerically and discussed in detail. The results show that the thin square plate prototype must be scaled to be the thinner/thicker rectangular plate, and the components of displacement, stress and strain between scaled model and full-scale prototype behave good consistency in both spatial and temporal fields.

Today, mechanical tracking systems have been downsized to allow them to be used in the field of airborne laser communications and in the military domain. Risley systems are used for this purpose, which work by directing a beam of light to a given target point, this procedure is commonly known as the inverse problem. In this paper, an analytical method, the geometric method, has been designed and developed to determine the beam steering in a Risley system and solve the inverse problem. The method focuses on different geometric shapes, like circumference or ellipse, that are described when the beam passes through the second prism. The accuracy and efficiency of the geometric method has been analysed and found to be faster than the two-step method. Furthermore, the geometric method has been implemented in an iterative process and an accuracy of up to 1 pm has been achieved. This high accuracy would allow the geometric method to be applied in fields such as lithography, stereolithography or 3D printers.

Phlebotomus (Paraphlebotomus) sergenti Parrot, 1917, the proven vector of Leishmania tropica Wright, 1903, the causative agent of anthroponotic cutaneous leishmaniasis, is widely distributed in Morocco. Previous works using molecular markers (ITS2 rDNA and Cyt b mtDNA) have hy-pothesized the existence of multiple closely related populations of sandfly species (cryptic species) that would exhibit distinct vectorial capacities. In this work, descriptive characteristics of wings (size and shape of the right and left wings) were measured in samples collected from fourteen sta-tions in central Morocco. These analyses support the existence of distinct P. sergenti populations, enlightening significant phenotypic variations of P. sergenti’s wings, regarding their size and shape, depending on geographic origin. In addition, geomorphometric analyses of wing’s length, centroid size, alpha, and beta distances allowed clear discrimination of P. sergenti sub-populations. These data pinpoint the adaptative ability of P. sergenti to local environmental conditions. Additional studies are now required to further shed light on the genetic structure of P. sergenti populations in Morocco.

Scheduling and optimization have a central place in the research area of computing because it is increasingly important to achieve fully automated production processes to adjust manufacturing systems to the requirements of Industry 4.0. In this paper, we demonstrate how an automated wet-etch scheduling problem for a semiconductor industry can be solved by constraint answer set programming (CASP) and, its solver called clingcon. The considered scheduling problem includes a robot for lot transfers between the baths. CASP is a hybrid approach in automated reasoning that combines different research areas such as answer set programming, Constraint Processing and Satisfiability Modulo Theories. For a long time, exact methods such as constraint programming have displayed difficulties in solving real large-scale problem instances. Currently, the performance of state-of-the-art constrains solvers is comparatively better than a decade ago, and some complex combinatorial problems can be optimally solved. These theoretical and technical achievements open new horizons for declarative programming applications such as logistics. A successful solution to this problem is achieved and we found that in most cases tested, CASP is faster and obtains in most cases similar makespan values than solutions based on mixed integer linear programming and constraint paradigms.

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.

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 .

This article studies a class of pursuit problems admitting both a simple geometric solution as well as a more general analytic treatment. The results are specialized to demonstrate solutions to certain elementary problems typically posed to high schoolers, although a full analytic treatment, requiring some more comfort with geometry and calculus, is typically avoided at that stage.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Since large articulated vehicles have uncertainties in trailer articulation angle as well as dynamic complexity, it is not easy to accurately establish a reliable motion plan. In this paper, two geometric path plans constructed based on the empirical rules of driving experts are presented so that articulated vehicles can automatically perform perpendicular parking on a reverse path. By analyzing the empirical parking methods of professional drivers, these path plans were constructed by appropriately combining several standardized simple basic motions to facilitate implementation in real vehicles. In addition, path plans included appropriate complementary motions to effectively respond to uncertainties arising from articulation angles, etc. The complementary motions developed in this study are based on the results of qualitative analysis on the behavior of articulated vehicles. The usefulness of the proposed articulated vehicle parking method has been proven through hundreds of experimental tests using a 1:10 ratio model automated vehicle.

Laser metal deposition with wire (LMD-w) is a developing additive manufacturing (AM) technology that has a high deposition material rate and efficiency, and is suitable for fabrication of large aerospace components. However, control of material properties, geometry, and residual stresses is needed before LMD-w technology can be widely adopted for the construction of critical structural components. In this study, we investigated the effect of interlayer cooling time, clamp constraints, and tool path strategy on part distortion and residual stresses in large-scale laser additive manufactured Ti-6Al-4V components using finite element method (FEM). The simulations were validated with the temperature and the distortion measurements obtained from a real LMD-w process. We found that a shorter interlayer cooling time, full clamping constraints on the build plates, and a bidirectional tool path with 180⁰ rotation minimized part distortion and residual stresses and resulted in symmetric stress distribution.

The term Concept has been a prominent part of investigations in psychology and neurobiology where, mostly, it is mathematically or theoretically represented. The Concepts are also studied computationally through their symbolic, distributed and hybrid representations. The majority of these approaches focused on addressing concrete concepts notion, but the view of the abstract concept is rarely explored. Moreover, most computational approaches have a predefined structure or configurations. The proposed method, Regulated Activation Network (RAN), has an evolving topology and learns representations of Abstract Concepts by exploiting the geometrical view of Concepts, without supervision. In the article, the IRIS data was used to demonstrate: the RAN's modeling; flexibility in concept identifier choice; and deep hierarchy generation. Data from IoT's Human Activity Recognition problem is used to show automatic identification of alike classes as abstract concepts. The evaluation of RAN with 8 UCI benchmarks and the comparisons with 5 Machine Learning models establishes the RANs credibility as a classifier. The classification operation also proved the RAN's hypothesis of abstract concept representation. The experiments demonstrate the RANs ability to simulate psychological processes (like concept creation and learning) and carry out effective classification irrespective of training data size.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

Outliers seriously affect the accuracy in geometric model fitting. Previous works in coping with outliers involve threshold selection and scale estimation. However most scale estimators suppose the inlier distribution as a Gaussian model, which usually poorly meets the cases in geometric model fitting. Outliers, considered as the points with big residuals to all the true models, share common items with big values in quantized residual preferences, thus making the outliers gather away from the inliers in quantized residual preference space. In this paper we make use of this outlier consensus in quantized residual preference space by extending the usage of energy minimization to combine the model error and the spatial smoothness in quantized residual preference space for outlier detection. The energy minimization based outlier detection process follows an alternate sampling and labeling framework. After the outlier detection, an ordinary energy minimization method is employed to optimize the inlier labels, which also follows the framework of alternate sampling and labeling. The experimental results in this study show that the energy minimization based outlier detection method can detect most of the outliers in the data. Furthermore, the proposed energy minimization based inlier segmentation process segments the inliers into different models quite accurately. Overall, the performance of the proposed method is better than most of the state-of-the-art methods.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 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. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.

Reasonable trajectory planning is the precondition for the parafoil airdrop system to achieve autonomous accurate homing and safe landing. In order to successfully realize the self-homing of the parafoil airdrop system, a new trajectory optimization design scheme is proposed in this paper. The scheme is based on the parafoil's unique flight and control characteristics and adopts a segmented homing design. Compared with the current common trajectory design method, its core feature is to avoid the problem that the straight-line flight distance before landing is limited by the radius of the height-reducing area and ensure landing accuracy and safety. Firstly, the different starting states of the parafoil airdrop system and the landing requirements were comprehensively considered, and the homing trajectory is reasonably segmented. Based on the requirements of energy control, stable flight, and landing accuracy, the optimal objective function of the trajectory was established, and the trajectory parameters, calculation methods, and constraints were given. Secondly, the cuckoo search algorithm was applied to optimize the objective function to obtain the final home trajectory. Finally, the trajectory planning under different airdrop conditions was simulated and verified. The results showed that the planned trajectories could reach the target point accurately and meet the flight direction requirements, proving the proposed scheme's correctness and feasibility.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

This paper discusses how mathematical models are used to predict environmental conditions. While these models are successful for larger scale phenomena, it becomes more complex for local weather or wave processes. Several approaches have been proposed to address this problem, including neural networks and statistical and mathematical models. The novelty in this approach is the use of statistical manifolds, which provide a more accurate way to estimate distances and cost functions. This work focuses on advancements in differential and information geometry for creating different types of models that can be used for environmental simulation and forecasting. These fields are vital for many institutes and centres worldwide, as they help solve challenges in areas such as meteorology, renewable energy, and aviation safety. Some potential IG applications to advance energy were given. Closing remarks with new open problems combined with the next research phase are provided.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

Image analysis is widely applied in plant science for phenotyping and monitoring botanic and agricultural species. Although a lot of software is available, tools integrating image analysis and statistical assessment of seedling growth in large groups of plants are limited or absent, and do not cover the needs of the researchers. In this study, we developed Morley, a free, open-source graphical user interface written in Python. Morley automates the following workflow: (1) group-wise analysis of a few thousand seedlings from multiple images; (2) recognition of seeds, shoots and roots in seedling images; (3) calculation of shoot and root lengths and surface areas, (4) evaluation of statistically significant differences between plant groups, (5) calculation of germination rates, (6) visualization and interpretation. Morley is designed for laboratory studies of biotic effects on seedling growth, when molecular mechanisms underlying morphometric changes are analyzed. Performance was tested using cultivars of T. aestivum, P. sativum on seedlings of up to 1 week old. Accuracy of the measured morphometric parameters was comparable with the ones obtained using ImageJ and manual measurements. Dose-dependent laboratory tests for germination affected by new bioactive compounds and fertilizers, assuming extraction of seedlings from a substrate and/or dissection are among the suggested applications.

This paper aims the automatic ball balancers (ABBs) used in passive balancing devices for suppressing vibration of the eccentric rotor. The system model describes which equipped with a skew-mounted ABB with angular deviation. The dynamic equilibrium equations of the system are deduced from the perspective of three-dimensional (3D) dynamics. The results obtained are consistent with those derived from the Euler-Lagrange equations. It is exciting that the spatial dynamics method reveals the spatial geometric characteristic of dynamic balance positioning of the balls when the system is balanced with vibration suppression. The spatial property emerges the perpendicular line from each ball to the rotating spindle of the system must pass through the central axis of the orbit perpendicular to the ABB plane. This characteristic is a general rule that can be used to explain the phenomenon of the stable equilibrium positions of the balls in all previously studied cases.

Background: Fold change is widely used in biomedical research to quantify the magnitude of group differences in omics variables. However, the exact calculation method is often not reported, leading to inconsistent results. This study re-evaluates different fold-change calculation methods and provides a clear preference. Methods: Data scenarios with different distributions of treatment/test and reference data were created to challenge the assumption of interchangeable calculation methods. The main difference lies in the definition of the expected values of the groups used to calculate the log ratio, which is the basis of the fold change calculation. In addition, a multi-omics biomedical dataset was analyzed. Results: Using the arithmetic mean as the expected value for the treatment and reference groups resulted in incorrect fold change values more frequently than other methods, especially when the standard deviations between subgroups differed widely. Conclusions: The inferior arithmetic mean method is often perceived as the standard, although mathematically different equations are possible that differ mainly in the estimation of the expected value. Alternatives that define expectation by median, geometric mean, or paired fold change combinations are less susceptible to violations of equal variances or similar treatment/reference distributions.

Information geometry is a mathematical framework that analyses the structure of statistical models using concepts from differential geometry. It treats families of probability distributions as manifolds, where the parameters of each model determine the coordinate charts. By applying info-geometric tools, we can gain insights into the characteristics of these models. The approach involves characterizing the queueing system's manifold using information geometry and presenting the exponential of the information matrix. This integration of information geometry with queueing theory provides a novel perspective for analyzing the dynamics of queueing systems, incorporating relativistic and Riemannian concepts. Some applications to E-health are highlighted. Finally, closing remarks and the next phase of research.

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

We introduce poly-symplectic extension of Souriau Lie groups Thermodynamics based on higher-order model of statistical physics introduced by R.S. Ingarden. This extended model could be used for small data analytics and Machine Learning on Lie groups. Souriau Geometric Theory of Heat is well adapted to describe density of probability (Maximum Entropy Gibbs density) of data living on groups or on homogeneous manifolds. For Small Data Analytics (Rarified Gases , sparse statistical survey,…), density of maximum entropy should consider Higher Order Moments constraints (Gibbs density is not only defined by first moment but fluctuations request 2nd order and higher moments) as introduced by R.S. Ingarden. We use Poly-sympletic model introduced by Christian Günther, replacing the symplectic form by a vector-valued form. The poly-symplectic approach generalizes the Noether theorem, the existence of momentum mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. The formalism is covariant, i.e. no special coordinates or coordinate systems on the parameter space are used to construct the Hamiltonian equations. We underline the contextures of these models, and the process to build these generic structures.

Non-pneumatic tires have gained a lot of attention due to their advantages, including not having to worry about getting a flat tire. In this type of tire, metamaterial cells replace the pneumatic part of the tire. In general, metamaterials are formed by stacking cells together. These cells are obtained by various methods including topology optimization. Therefore, in this research, to achieve a metamaterial cell suitable for a non-pneumatic tire with the objective function of increasing compressive strength and bending fatigue life, optimization for three types of geometry including (1) square plane, (2) rectangular plane, and (3) entire circumference of tire and three types of material including polylactic acid (PLA), thermoplastic polyurethane (TPU) and void have been done. Optimization has been implemented by using MATLAB code in 2D mode. The cubic cell is obtained from extruding the optimized response of the square plane. From the optimized response of the rectangular plane, the cylindrical cell and from extruding the optimized response of the entire circumference of tire to the tire cross-section size, the main geometry of the tire has been calculated. Finally, to check the quality of 3D printing in producing cells and how they are connected, the optimal cell fabricated by the fused deposition modeling (FDM) method has been observed using a field-emission scanning electron microscopy (FE-SEM). The results show that in the optimization of the square plane, the sample with the minimum remaining weight constraint equal to 40% and in the optimization of the rectangular plane and the entire circumference of tire, the sample with the minimum remaining weight constraint equal to 60% was selected as the optimal sample. From checking the quality of 3D printing, it has been concluded that PLA and TPU materials are completely connected.

Due to the vast conformational space proteins can adopt, accurate and efficient prediction of protein structure remains still a challenging task, coupled with the intricacies of interatomic interactions and the limitations of current computational models in effectively navigating this complex molecular landscape. Additionally, the lack of comprehensive experimental data for all protein structures further exacerbates the difficulty in reliable machine learning-based prediction of the three-dimensional conformations of the proteios building block of life. Geometrically, Cartesian coordinate system (CCS, X, Y and Z) and spherical coordinate system (SCS, ρ, θ and φ) are two interconvertible coordinate systems, and are like two sides of one coin. Since the beginning of Protein Data Bank (PDB) in 1971, CCS has been the default approach to specify atomic positions with X, Y and Z in PDB. In this manuscript, therefore, I present a novel method for the reversible spherical geometric conversion of protein backbone structure coordinate matrices to three independent vectors: ρ, θ and φ. This reversible conversion facilitates lossless extraction of essential structural features from protein backbone structural data, enabling the development of advanced novel algorithms for protein structure prediction in future. In short, this inter-atomic SCS approach offers a comprehensive yet efficient means of representing protein backbone geometry, leveraging spherical coordinates to capture spatial relationships in a compact and intuitive inter-atomic manner, and to provide a robust framework for reversible feature extraction for the ongoing efforts in advancing the field of protein structure prediction, the holy grail of computational structural biology.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

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 paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.