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Understanding the growth patterns of genotypes optimizes their selection and management. The objective of this study is to investigate the seasonal variations in the morphology and biochemistry of Coffea canephora clone leaves, considering climatic conditions and the maturation cycle. Morphological characteristics and carbohydrate contents of the leaves were analyzed throughout the growth cycle. A nonlinear logistic model was applied, and critical points of the leaf emission rates of plagiotropic branches were determined. Leaf growth was greater at higher temperatures during the rainy periods and lower at milder temperatures during the dry season. Genotype 143 exhibited the largest leaf width in spring, while 104, A1, and P2 had the largest leaf width in summer. The logistic model was suitable for describing leaf emission, with the critical points of genotype 143 being earlier, while P2 displayed a longer leaf emission cycle. The peak growth period influenced the quantities of starch and total soluble sugars in the leaves. The dormancy period showed a higher availability of reducing sugars. Pearson correlation indicated significant coefficients between temperature, precipitation, photoperiod, and foliar characteristics. The results obtained serve as a reference for future investigations, particularly in response to environmental challenges. [ABSTRACT FROM AUTHOR]

This paper investigates various aspects of the distribution of roots and critical points of a complex polynomial, including their variance and the relationships between their moduli using an inequality due to de Bruijn. Making use of two other inequalities-again due to de Bruijn-we derive two probabilistic results concerning upper bounds for the average moduli of the imaginary parts of zeros and those of critical points, assuming uniform distribution of the zeros over a unit disc and employing the Markov inequality. The paper also provides an explicit formula for the variance of the roots of a complex polynomial for the case when all the zeros are real. In addition, for polynomials with uniform distribution of roots over the unit disc, the expected variance of the zeros is computed. Furthermore, a bound on the variance of the critical points in terms of the variance of the zeros of a general polynomial is derived, whereby it is established that the variance of the critical points of a polynomial cannot exceed the variance of its roots. Finally, we conjecture a relation between the real parts of the zeros and the critical points of a polynomial. [ABSTRACT FROM AUTHOR]

In the theory of gene networks, the mathematical apparatus that uses dynamical systems is fruitfully used. The same is true for the theory of neural networks. In both cases, the purpose of the simulation is to study the properties of phase space, as well as the types and the properties of attractors. The paper compares both models, notes their similarities and considers a number of illustrative examples. A local analysis is carried out in the vicinity of critical points and the necessary formulas are derived. [ABSTRACT FROM AUTHOR]

In this paper, the precise design of a high-power amplifier (HPA) is shown, along with the problems associated with the stability of "on-wafer" measurements. Here, techniques to predict possible oscillations are discussed to ensure the stability of a monolithic microwave-integrated circuit (MMIC). In addition, a deep reflection is made on the instabilities that occur when measuring both on wafer and using a mounted chip. Stability techniques are used as tools to characterize measurement results. Both a precise design and instabilities are shown through the design of a three-stage X-band HPA in gallium nitride (GaN) from the WIN Semiconductors Corp. foundry. As a result, satisfactory performance was obtained, achieving a maximum output power equal to 42 dBm and power-added efficiency of 32% at a 20 V drain bias. In addition to identifying critical points in the design or measurement of the HPA, this research shows that the stability of the amplifier can be verified through a simple analysis and that instabilities are often linked to errors in the measurement process or in the characterization of the measurement process. [ABSTRACT FROM AUTHOR]

The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in studying the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where these two situations happen simultaneously. The rational map obtained by applying a method in the Chebyshev–Halley family to a polynomial has both super-attracting extraneous fixed points and super-attracting cycles different from the roots of the polynomial. [ABSTRACT FROM AUTHOR]

Neural networks are usually trained with different variants of gradient descent-based optimization algorithms such as the stochastic gradient descent or the Adam optimizer. Recent theoretical work states that the critical points (where the gradient of the loss is zero) of two-layer ReLU networks with the square loss are not all local minima. However, in this work, we will explore an algorithm for training two-layer neural networks with ReLU-like activation and the square loss that alternatively finds the critical points of the loss function analytically for one layer while keeping the other layer and the neuron activation pattern fixed. Experiments indicate that this simple algorithm can find deeper optima than stochastic gradient descent or the Adam optimizer, obtaining significantly smaller training loss values on four out of the five real datasets evaluated. Moreover, the method is faster than the gradient descent methods and has virtually no tuning parameters. [ABSTRACT FROM AUTHOR]

Cholic acid is a trihydroxy bile acid with a nice peculiarity: the average distance between the oxygen atoms (O7 and O12) of the hydroxy groups located at C7 and C12 carbon atoms is 4.5 Å, a value which perfectly matches with the O/O tetrahedral edge distance in Ih ice. In the solid phase, they are involved in the formation of hydrogen bonds with other cholic acid units and solvents. This fact was satisfactorily used for designing a cholic dimer which encapsulates one single water molecule between two cholic residues, its oxygen atom (Ow) being exactly located at the centroid of a distorted tetrahedron formed by the four steroid hydroxy groups. The water molecule participates in four hydrogen bonds, with the water simultaneously being an acceptor from the 2 O12 (hydrogen lengths are 2.177 Å and 2.114 Å) and a donor towards the 2 O7 (hydrogen bond lengths are 1.866 Å and 1.920 Å). These facts suggest that this system can be a nice model for the theoretical study of the formation of ice-like structures. These are frequently proposed to describe the water structure found in a plethora of systems (water interfaces, metal complexes, solubilized hydrophobic species, proteins, and confined carbon nanotubes). The above tetrahedral structure is proposed as a reference model for those systems, and the results obtained from the application of the atoms in molecules theory are presented here. Furthermore, the structure of the whole system allows a division into two interesting subsystems in which water is the acceptor of one hydrogen bond and the donor of another. The analysis of the calculated electron density is performed through its gradient vector and the Laplacian. The calculation of the complexation energy used correction of the basis set superposition error (BSSE) with the counterpoise method. As expected, four critical points located in the H...O bond paths were identified. All calculated parameters obey the proposed criteria for hydrogen bonds. The total energy for the interaction in the tetrahedral structure is 54.29 kJ/mol, while the summation obtained of the two independent subsystems and the one between the alkyl rings without water is only 2.5 kJ/mol higher. This concordance, together with the calculated values for the electron density, the Laplacian of the electron density, and the lengths of the oxygen atom and the hydrogen atom (involved in the formation of each hydrogen bond) to the hydrogen bond critical point, suggests that each pair of hydrogen bonds can be considered independent of each other. [ABSTRACT FROM AUTHOR]

Since the year 2012, nationwide monitoring of erosion on agricultural land has been carried out in the Czech Republic with more than 2,300 cases of erosion events recorded so far. The evaluation of the relationships between the actual manifestation of erosion and the characteristics of the 5600 erosion enclosed areas (EEAs), on which surface runoff develops after erosion-forming rainfall, are presented in this contribution. Most frequently grown crops during an erosion event include maize (49.8% of cases), rapeseed (13.7%), potatoes (8.1%) and sugar beets (2.1%). The distributions of affected erosion enclosed areas (EEAs) in terms of shares of soils with low susceptibility and medium susceptibility to compaction, drainage systems and contributing areas of critical points are bimodal; the low percentage (<10%) being more prominent than the high one (>90%). The percentage of hydrologic soil group B in EEA has the high share dominant over the low one. Unsurprisingly, erosion events have been recorded predominantly in EEAs with low forest cover and on arable land (share >90%). The distribution of EEAs across altitudes corresponds with the relief of the country. Obtained results will be used to validate the implementation of erosion-monitoring systems and for the adaptation of soil erosion prevention and mitigation measures in the sustainable land use policy. [ABSTRACT FROM AUTHOR]

Mathematical modeling has been used to describe the characteristics of crop growth. Establishing a growth model can help to better understand the responses of crops to their environment and improve the efficiency of agricultural production. This study establishes empirical growth models to predict the growth of greenhouse tomato. In this study, we collected beef tomato (Solanum lycopersicum cv. '993′) growth data over two crop seasons in Taiwan and established growth models by employing the commonly used Gompertz and Logistic curves. Days after transplanting (DAT) and growing degree-days (GDD) were introduced as independent variables and their relationships with five traits, i.e., plant height, leaf area index, stem dry matter, leaves dry matter, and fruits dry matter were determined. The performances of GDD models were slightly better than those of the DAT models. In addition, we inferred five critical points with biological meaning based on the proposed growth models. The critical points estimated by the Logistic model are closer to our expectation than those of the Gompertz model, and they were applicable for the '993′ tomato in Taiwan. These results can be used to predict tomato growth and adjust the fieldwork schedule to improve the efficiency of the greenhouse production of tomatoes. [ABSTRACT FROM AUTHOR]

To improve the resolution and accuracy of the high-order weighted compact nonlinear scheme (WCNS), a new ϵ -adaptive algorithm based on local smoothness indicators is proposed. The new algorithm introduces a high-order global smoothness indicator to adjust the value of ϵ according to the local flow characteristics. Specifically, the algorithm increases ϵ in smooth regions, which can help cover up the disparity in smoothness indicators of sub-stencils and make the nonlinear scheme approach the background linear scheme. As a result, optimal order accuracy can be achieved in smooth regions, including critical points. While near discontinuities, the algorithm decreases ϵ , thereby strengthening the stencil selection mechanism and further attenuating spurious oscillations. Meanwhile, the new algorithm makes nonlinear schemes scale-invariant of flow variables. The results of approximate dispersion relation (ADR) show that the new algorithm can greatly reduce spectral errors of nonlinear schemes in the medium and low wavenumber range without inducing instability. Numerical results indicate that the new algorithm can significantly improve resolution of small-scale structures and suppress numerical oscillations near discontinuities with only a minor increment in computational cost. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) printing technology enables the design of new drug delivery systems for personalised medicine. Polymers that can be molten are needed to obtain extruded filaments for Fused Deposition Modelling (FDM), one of the most frequently employed techniques for 3D printing. The aim of this work was to evaluate the extrusion process and the physical appearance of filaments made of a hydrophilic polymer and a non-molten model drug. Metformin was used as model drug and Affinisol™ 15LV as the main carrier. Drug-loaded filaments were obtained by using a single-screw extruder and, subsequently, their printability was tested. Blends containing up to a 60% and 50% drug load with 5% and 7.5% of auxiliary excipients, respectively, were successfully extruded. Between the obtained filaments, those containing up to 50% of the drug were suitable for use in FDM 3D printing. The studied parameters, including residence time, flow speed, brittleness, and fractal dimension, reflect a critical point in the extrusion process at between 30–40% drug load. This finding could be essential for understanding the behaviour of filaments containing a non-molten component. [ABSTRACT FROM AUTHOR]

The arrangement and form of the image sensor have a fundamental effect on any further image processing operation and image visualization. In this paper, we present a software-based method to change the arrangement and form of pixel sensors that generate hexagonal pixel forms on a hexagonal grid. We evaluate four different image sensor forms and structures, including the proposed method. A set of 23 pairs of images; randomly chosen, from a database of 280 pairs of images are used in the evaluation. Each pair of images have the same semantic meaning and general appearance, the major difference between them being the sharp transitions in their contours. The curviness variation is estimated by effect of the first and second order gradient operations, Hessian matrix and critical points detection on the generated images; having different grid structures, different pixel forms and virtual increased of fill factor as three major properties of sensor characteristics. The results show that the grid structure and pixel form are the first and second most important properties. Several dissimilarity parameters are presented for curviness quantification in which using extremum point showed to achieve distinctive results. The results also show that the hexagonal image is the best image type for distinguishing the contours in the images. [ABSTRACT FROM AUTHOR]

Raw GPS trajectory data are often very large and use up excessive storage space. The efficiency and accuracy of activity patterns analysis or individual-environment interaction modeling using such data may be compromised due to data size and computational needs. Line generalization algorithms may be used to simplify GPS trajectories. However, traditional algorithms focus on geometric characteristics of linear features. Trajectory data may record information beyond location. Examples include time and elevation, and inferred information such as speed, transportation mode, and activities. Effective trajectory simplification should preserve these characteristics in addition to location and orientation of spatial-temporal movement. This paper proposes an Enhanced Douglas-Peucker (EDP) algorithm that implements a set of Enhanced Spatial-Temporal Constraints (ESTC) when simplifying trajectory data. These constraints ensure that the essential properties of a trajectory be preserved through preserving critical points. Further, this study argues that speed profile can uniquely identify a trajectory and thus it can be used to evaluate the effectiveness of a trajectory simplification. The proposed ESTC-EDP simplification method is applied to two examples of GPS trajectory. The results of trajectory simplification are reported and compared with that from traditional DP algorithm. The effectiveness of simplification is evaluated. [ABSTRACT FROM AUTHOR]

This paper describes an efficient, decentralized algorithm to monitor qualitative spatial events in a dynamic scalar field. The events of interest involve changes to the critical points (i.e., peak, pits and passes) and edges of the surface network derived from the field. Four fundamental types of event (appearance, disappearance, movement and switch) are defined. Our algorithm is designed to rely purely on qualitative information about the neighborhoods of nodes in the sensor network and does not require information about nodes' coordinate positions. Experimental investigations confirm that our algorithm is efficient, with O(n) overall communication complexity (where n is the number of nodes in the sensor network), an even load balance and low operational latency. The accuracy of event detection is comparable to established centralized algorithms for the identification of critical points of a surface network. Our algorithm is relevant to a broad range of environmental monitoring applications of sensor networks. [ABSTRACT FROM AUTHOR]

We state the product formulae of the values of the levels of functions at critical points involved in asymptotic behaviors of hypergeometric integrals associated with symmetric arrangements of three-dimensional spheres. We show, in an explicit way, how the product of the Hessian, regarding the level functions at all critical points, is related to the behavior of its critical points. We also state two conjectures concerning the same problem associated with general hypersphere arrangements. [ABSTRACT FROM AUTHOR]

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and compact method to work the fractional calculus through the classification of fractional operators using sets. This new method of working with fractional operators, which may be called fractional calculus of sets, allows generalizing objects of conventional calculus, such as tensor operators, the Taylor series of a vector-valued function, and the fixed-point method, in several variables, which allows generating the method known as the fractional fixed-point method. Furthermore, it is also shown that each fractional fixed-point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed-point methods that generate convergent sequences. So, it is presented a method to estimate numerically in a region Ω the mean order of convergence of any fractional fixed-point method, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function. Finally, considering that the proposed method to classify fractional operators through sets allows generalizing the existing results of the fractional calculus, some examples are shown of how to define families of fractional operators that satisfy some property to ensure the validity of the results to be generalized. [ABSTRACT FROM AUTHOR]

The urban water supply system environment is becoming more complicated and unpredictable than ever before in the context of global climate change and expanding urbanization. Existing studies have adopted either static or dynamic approaches to assess the resilience of water supply systems without combining the two. Previous literature mostly establishes rigid quantitative metrics for resilience assessment, often without depicting the dynamics and adaptability of system resilience. For example, these studies usually fail to provide a critical point for identifying system resilience. To accurately describe the dynamics and adaptability of water supply system resilience under uncertain scenarios, in this study, we constructed a comprehensive framework based on the qualitative assessment of the input parameters, combining static and dynamic assessment, with the latter playing a dominant role based on the system perspective of pressure-state-influence-response. Taking Qingdao as a case study, we combined this framework with the system resilience theory, and statically assessed the five types of capitals and three attributes of resilience with the capital portfolio approach (CPA). Then, we dynamically assessed the resilience of urban water supply systems and identified critical points with the dynamic socio-technical model coupled with system resilience and the fitting analysis method. The results are as follows: (1) the static assessment results demonstrate an imbalanced development in the levels of the five types of capitals (financial capital, management efficiency, infrastructure, available water resources, and adaptation) and three attributes (robustness, recoverability, and adaptability) in the water supply systems of Qingdao. (2) The dynamic assessment results show that the current resilience trajectory of the water supply systems in Qingdao is that of a city in transition. (3) The fitting analysis shows that robustness (RB) has a linear relationship with resilience, recoverability (RE) has a non-linear relationship with resilience, and the critical points are RB = 0.70 and RE = 1.20. The research findings provide a reference for studying resilience mechanisms, internal attribute relationships, and resilience enhancement measures of urban water supply systems. [ABSTRACT FROM AUTHOR]

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes. [ABSTRACT FROM AUTHOR]

This paper proposes a building façade contouring method from LiDAR (Light Detection and Ranging) scans and photogrammetric point clouds. To this end, we calculate the confidence property at multiple scales for an individual point cloud to measure the point cloud's quality. The confidence property is utilized in the definition of the gradient for each point. We encode the individual point gradient structure tensor, whose eigenvalues reflect the gradient variations in the local neighborhood areas. The critical point clouds representing the building façade and rooftop (if, of course, such rooftops exist) contours are then extracted by jointly analyzing dual-thresholds of the gradient and gradient structure tensor. Based on the requirements of compact representation, the initial obtained critical points are finally downsampled, thereby achieving a tradeoff between the accurate geometry and abstract representation at a reasonable level. Various experiments using representative buildings in Semantic3D benchmark and other ubiquitous point clouds from ALS DublinCity and Dutch AHN3 datasets, MLS TerraMobilita/iQmulus 3D urban analysis benchmark, UAV-based photogrammetric dataset, and GeoSLAM ZEB-HORIZON scans have shown that the proposed method generates building contours that are accurate, lightweight, and robust to ubiquitous point clouds. Two comparison experiments also prove the superiority of the proposed method in terms of topological correctness, geometric accuracy, and representation compactness. [ABSTRACT FROM AUTHOR]

We show the existence of at least one nontrivial solution for a nonlinear sixth-order ordinary differential equation is investigated. Our approach is based on critical point theory. [ABSTRACT FROM AUTHOR]

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications. [ABSTRACT FROM AUTHOR]

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors' groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair–π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors' groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP. [ABSTRACT FROM AUTHOR]

Retrofitting of industrial heat recovery systems can contribute significantly to meeting energy efficiency targets for industrial plants. One issue to consider when screening retrofit design proposals is that industrial heat recovery systems must be able to handle variations, e.g., in inlet temperatures or heat capacity flow rates, in such a way that operational targets are reached. Consequently, there is a need for systematic retrofitting methodologies that are applicable to multi-period heat exchanger networks (HENs). In this study, a framework was developed to achieve flexible and cost-efficient retrofit measures of (industrial) HENs. The main idea is to split the retrofitting processes into several sub-steps. This splitting allows well-proven (single period) retrofit methodologies to be used to generate different design proposals, which are collected in a superstructure. By means of structural feasibility assessment, structurally infeasible design proposals can be discarded from further analysis, yielding a reduced superstructure. Additionally, critical point analysis is applied to identify those operating points within the uncertainty span that determine necessary overdesign of heat exchangers. In the final step, the most cost-efficient design proposal within the reduced superstructure is identified. The proposed framework was applied to a HEN retrofit case study to illustrate the proposed framework. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the existence of solutions to a class of impulsive fractional differential equations with derivative dependence. The used technical approach is based on variational methods and iterative methods. In addition, an example is given to demonstrate the main results. [ABSTRACT FROM AUTHOR]