A Crop Modelling Strategy to Improve Cacao Quality and Productivity

Cacao production systems in Colombia are of high importance due to their direct impact in the social and economic development of smallholder farmers. Although Colombian cacao has the potential to be in the high value markets for fine flavour, the lack of expert support as well as the use of traditional, and often times sub-optimal technologies makes cacao production negligible. Traditionally, cacao harvest takes place at exactly the same time regardless of the geographic and climatic region where it is grown, the problem with this strategy is that cacao beans are often unripe or over matured and a combination of both will negatively affect the quality of the final cacao product. Since cacao fruit development can be considered as the result of a number of physiological and morphological processes that can be described by mathematical relationships even under uncontrolled environments. Environmental parameters that have more association with pod maturation speed should be taken into account to decide the appropriate time to harvest. In this context, crop models are useful tools to simulate and predict crop development over time and under multiple environmental conditions. Since harvesting at the right time can yield high quality cacao, we parameterised a crop model to predict the best time for harvest cacao fruits in Colombia. The cacao model uses weather variables such as temperature and solar radiation to simulate the growth rate of cocoa fruits from flowering to maturity. The model uses thermal time as an indicator of optimal maturity. This model can be used as a practical tool that supports cacao farmers in the production of high quality cacao which is usually paid at a higher price. When comparing simulated and observed data, our results showed an RRMSE of 7.2% for the yield prediction, while the simulated harvest date varied between +/−2 to 20 days depending on the temperature variations of the year between regions. This crop model contributed to understanding and predicting the phenology of cacao fruits for two key cultivars ICS95 y CCN51.

Linguistic Mathematical Relationships Saved or Lost in Translating Texts: Extension of the Statistical Theory of Translation and Its Application to the New Testament

The purpose of the paper is to extend the general theory of translation to texts written in the same language and show some possible applications. The main result shows that the mutual mathematical relationships of texts in a language have been saved or lost in translating them into another language and consequently texts have been mathematically distorted. To make objective comparisons, we have defined a “likeness index”—based on probability and communication theory of noisy binary digital channels-and have shown that it can reveal similarities and differences of texts. We have applied the extended theory to the New Testament translations and have assessed how much the mutual mathematical relationships present in the original Greek texts have been saved or lost in 36 languages. To avoid the inaccuracy, due to the small sample size from which the input data (regression lines) are calculated, we have adopted a “renormalization” based on Monte Carlo simulations whose results we consider as “experimental”. In general, we have found that in many languages/translations the original linguistic relationships have been lost and texts mathematically distorted. The theory can be applied to texts translated by machines. Because the theory deals with linear regression lines, the concepts of signal-to-noise-ratio and likenss index can be applied any time a scientific/technical problem involves two or more linear regression lines, therefore it is not limited to linguistic variables but it is universal.

Creation of a Program for Finding an Approximating Function of the Obtained Experimental Results by the Method of Least Squares

When solving engineering and economic problems, it is often necessary to obtain mathematical relationships between various parameters characteristic of a given problem. As a rule, all physical experiments are reduced to measuring the dependence of a certain quantity u on one or several other quantities z1, z2,…, zn. The main task of using the least squares method as an approximation method from the point of view of approximate recovery of a function from its known values at a number of points is the selection of empirical formulas that allow an analytical presentation of the obtained experimental measurement data. This article discusses the problems of obtaining data and approximating a function by the least squares method using OOP.

Fuel Consumption of Wheeled Vehicle and Transportation Costs during Highway Construction/Reconstruction

A method is proposed for determining the fuel consumption of a wheeled vehicle depending on its speed, road surface flatness and road slope in the longitudinal direction. The purpose of the research is to derive mathematical relationships for calculating the fuel consumption of vehicles, which is one of the transport cost factors during the construction/reconstruction or overhaul of a highway. The proposed polynomial dependencies for calculating fuel in addition to vehicle speed, road surface flatness and its longitudinal slope take into account the mass-dimensional parameters of vehicles involved in road traffic. New mathematical relationships between the speed of wheeled vehicles, road surface flatness and longitudinal road slope allow to simulate the change in the value of fuel consumption of a wheeled vehicle when the speed of traffic flow or the slope of the road surface changes in the forward or reverse direction of the vehicle. In a graphic way, the influence of the pavement slope on the value of fuel consumption, both loaded and unloaded wheeled vehicle is presented. When determining transport costs associated with the highway construction, reconstruction or overhaul it is proposed to use empirical mathematical relationships, which make it possible to obtain fuel consumption with an accuracy of 5 % and save up to 15 % of budget (private) investments. The analysis of scientific publications of the existing approach determine the transport costs associated with highway construction, reconstruction or overhaul. The presented method for determining the fuel consumption of wheeled vehicles with small and large loading capacity increases the accuracy of determining transportation costs and reduces the level of financial costs for highway construction, reconstruction or overhaul.

New Zealand Building Code Clause G7 Compliance Assessment Tool: Development and Implementation

<p>The New Zealand Building Code Clause G7 (NZBC G7) minimum requirement for natural light is not being met in around half of New Zealand apartments post-construction. The main reasons for this are an acceptable solution that is not effective for apartment buildings and a lack of tools for Territorial Authorities to assess accurately whether an apartment will meet the minimum requirement. This report outlines the process involved in developing a simplified tool to assess quickly natural light compliance in apartments and preparing it for implementation. The tool was developed through simulation of factors that affect daylight performance at the point in the room specified in the Code: the back of habitable rooms. From these simulations statistical analysis was used to develop mathematical relationships between building features and light levels. These relationships were used to create a tool that specifies whether an apartment would require simulation to prove compliance with NZBC G7. Calibration measurements were performed, comparing simulated and real measurements in 97 apartments with the predictions of the tool. These demonstrated that the tool provides reliable results, hence determining the accuracy of the predictions provided by the tool. The final step in the research was for potential end-user groups to evaluate the usability and functionality of the tool. The conclusion of this process is that a tool has been developed that is simple and easy to use, is sufficiently accurate for application by Territorial Authorities as a decision tool and can be easily implemented.</p>

New Zealand Building Code Clause G7 Compliance Assessment Tool: Development and Implementation

<p>The New Zealand Building Code Clause G7 (NZBC G7) minimum requirement for natural light is not being met in around half of New Zealand apartments post-construction. The main reasons for this are an acceptable solution that is not effective for apartment buildings and a lack of tools for Territorial Authorities to assess accurately whether an apartment will meet the minimum requirement. This report outlines the process involved in developing a simplified tool to assess quickly natural light compliance in apartments and preparing it for implementation. The tool was developed through simulation of factors that affect daylight performance at the point in the room specified in the Code: the back of habitable rooms. From these simulations statistical analysis was used to develop mathematical relationships between building features and light levels. These relationships were used to create a tool that specifies whether an apartment would require simulation to prove compliance with NZBC G7. Calibration measurements were performed, comparing simulated and real measurements in 97 apartments with the predictions of the tool. These demonstrated that the tool provides reliable results, hence determining the accuracy of the predictions provided by the tool. The final step in the research was for potential end-user groups to evaluate the usability and functionality of the tool. The conclusion of this process is that a tool has been developed that is simple and easy to use, is sufficiently accurate for application by Territorial Authorities as a decision tool and can be easily implemented.</p>

Analysis of Static Molecular Gradients in a High-Throughput Drug Screening Microfluidic Assay

In this study, we thoroughly analyzed molecular gradient generation, its stability over time, and linearity in our high-throughput drug screening microfluidic assay (HTS). These parameters greatly affect the precision and accuracy of the device’s analytical protocol. As part of the research, we developed a mathematical model of dependence of the concentration profile on the initial concentrations of active substances in reservoirs and the number of tilts, as well as the dependence of the active substance concentration profiles in the culture chambers on the concentration profile of the reference dye in the indicator chamber. The mean concentration prediction error of the proposed equations ranged from 1.4% to 2.4% for the optimized parameters of the procedure and did not increase with the incubation time. The concentration profile linearity index, Pearson’s correlation coefficient reached −0.997 for 25 device tilts. The observed time stability of the profiles was very good. The mean difference between the concentration profile after 5 days of incubation and the baseline profile was only 7.0%. The newly created mathematical relationships became part of the new HTS biochip operating protocols, which are detailed in the article.

Computation of Vertex-Based Topological Descriptors of Organometallic Monolayers of TM 3 C 12 S 12

Topological descriptors are mathematical values related to chemical structures which are associated with different physicochemical properties. The use of topological descriptors has a great contribution in the field of quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) modeling. These are mathematical relationships between different molecular properties or biological activity and some other physicochemical or structural properties. In this article, we calculate few vertex degree-based topological indices/descriptors of the organometallic monolayer structure. At present, the numerical programming of the biological structure with topological descriptors is increasing in consequence in invigorating science, bioinformatics, and pharmaceutics.

Calculating the Inrush Current of Superconducting Transformers

Under certain circumstances, after connecting a superconducting transformer to the power network, a high value current may flow through its windings. This current can exceed the critical value of the superconductor many times and cause the windings to lose their superconductive state. Loss of superconductive state of the windings may result in thermal interruption of their continuity as a result of conduction of a current of very high density. The mathematical relationships used to calculate the inrush current of conventional transformers do not work well for the calculation of superconducting transformers. This is due to the properties of superconducting materials used in the windings, first of all to the stepwise changes of the windings’ resistance when exiting the superconducting state and when returning to this state. The article presents the mathematical dependencies allowing to calculate the pulse waveforms of the inrush current of these transformers are derived. Basic electrical circuit sizes are used in the calculations, making the calculations quick and easy. Using the formulas, calculations of the inrush current of 8.5 kVA and 13.5 kVA superconducting transformers. The results were verified with the results of the inrush current measurements, achieving good compliance.

Feasibility conditions of ecological models: Unfolding links between model parameters

Over more than 100 years, ecological research has been striving to derive internal and external conditions compatible with the coexistence of a given group of interacting species. To address this challenge, numerous studies have focused on developing ecological models and deriving the necessary conditions for species coexistence under equilibrium dynamics, namely feasibility. However, due to mathematical limitations, it has been impossible to derive analytic expressions if the isocline equations have five or more roots, which can be easily reached even in 2-species models. Here, we propose a general formalism to obtain the set of analytical conditions of feasibility for any polynomial population dynamics model of any dimension without the need to solve for the equilibrium locations. We additionally illustrate the application of our methodology by showing how it is possible to derive mathematical relationships between model parameters, while maintaining feasibility in modified Lotka-Volterra models with functional responses and higher-order interactions (model systems with at least five equilibrium points)—a task that is impossible to do with simulations. This work unlocks the opportunity to increase our systematic understanding of species coexistence.