Merge pull request #4 from majensen/main

Minor copy edits for JOSS paper

osspaper/paper.bib

@@ -1185,7 +1185,7 @@ @article{ohnSmoothFunctionApproximation2019
 }
 
 @article{okabeMathematicalModelEpidemics2020,
-  title = {A {{Mathematical Model}} of {{Epidemics}}\textemdash{{A Tutorial}} for {{Students}}},
+  title = {A {{Mathematical Model}} of {{Epidemics}}---{{A Tutorial}} for {{Students}}},
   author = {Okabe, Yutaka and Shudo, Akira},
   year = {2020},
   month = jul,

osspaper/paper.md

@@ -33,7 +33,7 @@ model in Facebook's Prophet model for time-series growth-forecasting
 at scale [@taylorForecastingScale2018] on big data. 
 The scientific basis for this prevalence is given in [@bejanConstructalLawOrigin2011]. 
 Such growth-processes can be viewed as complex input--output systems that involve 
-multiple peak inflection phases with respect to time. An idea that 
+multiple peak inflection phases with respect to time, an idea that 
 can be traced back in the crudest sense to [@reedSummationLogisticCurves1927]. A modern definition for the logistic-sigmoid growth which considers restricted growth from  a two-dimensional perspective is the nlogistic-sigmoid function (`NLSIG`) [@somefunLogisticsigmoidNlogisticsigmoidModelling2020] 
 or logistic neural-network (`LNN`) pipeline. 
 
@@ -43,37 +43,37 @@ of the COVID-19 epidemic growth in each affected country of the world and the wo
 
 # Statement of need
 
-Admittedly, epidemiological models such as the SEIRD variants 
-[@leeEstimationCOVID19Spread2020;@okabeMathematicalModelEpidemics2020] are just another form of representing sigmoidal growth [@xsRichardsModelRevisited2012]. It has been noted in 
+Epidemiological models such as the SEIRD variants 
+[@leeEstimationCOVID19Spread2020;@okabeMathematicalModelEpidemics2020] are just another form of representing sigmoidal growth [@xsRichardsModelRevisited2012]. However, it has been noted 
 [@christopoulosNovelApproachEstimating2020] that the SEIRD-variant models yield largely exaggerated forecasts. 
-Observing the current state of the COVID-19 pandemic, this is also true, as regards, 
+Observing the current state of the COVID-19 pandemic, this is concern is borne out, in 
 the results of various applications of logistic modelling [@batistaEstimationStateCorona2020;@wuGeneralizedLogisticGrowth2020]
-which have largely resulted in erroneous identification of the epidemic's progress and its future projection, hence leading policymakers astray [@matthewWhyModelingSpread2020]. 
+which have largely led to erroneous assessments of the epidemic's progress and its future projection, leading policymakers astray [@matthewWhyModelingSpread2020]. 
 
-Notably, two recurring limitations of the logistic definitions in the literature and other software packages exist. These two limitations are trends that have persisted since the first logistic-sigmoid function introduction [@bacaerVerhulstLogisticEquation2011]. 
+Notably, two recurring limitations of the logistic definitions in the literature and other software packages exist. These two limitations are trends that have persisted since the first introduction of the logistic-sigmoid function [@bacaerVerhulstLogisticEquation2011]. 
 
 First is that, the co-domain of logistic function is assumed to be infinite. This assumption violates the natural principle of finite growth. 
 Second is that, during optimization, estimation of the logistic hyper-parameters  for the individual logistic-sigmoids that make the multiple logistic-sigmoid sum is computed separately, instead of as a unified function. The effect of this, is that, as the number of logistic-sigmoids 
-considered in the sum increases, regression analysis becomes more cumbersome and complicated as can be observed in these works [@leeEstimationCOVID19Spread2020;@batistaEstimationStateCorona2020;
+considered in the sum increases, regression analysis becomes more cumbersome and complicated as can be observed in a number of works [@leeEstimationCOVID19Spread2020;@batistaEstimationStateCorona2020;
 @hsiehRealtimeForecastMultiphase2006;@wuGeneralizedLogisticGrowth2020;
 @chowellNovelSubepidemicModeling2019;@taylorForecastingScale2018]. 
 
-These limitations are efficiently overcome by the nlogistic-sigmoid function `NLSIG` (or logistic neural-network pipeline) for describing logistic growth. We note that the `NLSIG` is a logistic neural-network machine-learning tool under active development. The benefits it provides at a functional level:
+These limitations are efficiently overcome by the nlogistic-sigmoid function `NLSIG` (or logistic neural-network pipeline) for describing logistic growth. We note that the `NLSIG` is a logistic neural-network machine-learning tool under active development. The benefits it provides at a functional level are:
 
- - unified function definition
+ - unified function definition,
 
- - functional simplicity and efficient computation
+ - functional simplicity and efficient computation,
 
- - improved nonlinear modelling power
+ - improved nonlinear modelling power.
 
-Ultimately, the development of the `NLSIG-COVID19Lab` was motivated by research needs, in that, it 
-illustrates the power of the nlogistic-sigmoid neural pipeline. `NLSIG-COVID19Lab` provides an optimization workflow with functions to make modelling and monitoring the COVID-19 pandemic easier and reliable. Notably, on the contrary, instead of engaging in false prophecy 
+Ultimately, the development of the `NLSIG-COVID19Lab` was motivated by research needs, in that it 
+illustrates the power of the nlogistic-sigmoid neural pipeline. \linebreak `NLSIG-COVID19Lab` provides an optimization workflow with functions to make modelling and monitoring the COVID-19 pandemic easier and reliable. Notably, instead of engaging in false prophecy 
 or predictions on the cumulative growth of an ongoing growth phenomena, whose source is both uncertain and 
-complex to be encoded in current mathematical models [@christopoulosEfficientIdentificationInflection2016;@matthewWhyModelingSpread2020], this software package makes projections by means of:
+complex to encode in current mathematical models [@christopoulosEfficientIdentificationInflection2016;@matthewWhyModelingSpread2020], this software package makes projections by means of:
 
-- two-dimensional perspective metrics: Y-to-Inflection Ratio (YIR, Here Y = Infections or Deaths); X-to-Inflection Ratio (XIR, Here X = Time in Days) for robust monitoring of the growth-process being modelled in an area or locale of interest. 
+- two-dimensional perspective metrics: Y-to-Inflection Ratio (YIR, here Y = Infections or Deaths); X-to-Inflection Ratio (XIR, here X = Time in Days) for robust monitoring of the growth-process being modelled in an area or locale of interest, and
 
-- adaptation of the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality for the Kolmogorov–Smirnov (KS) test to construct a non-parametric confidence interval of uncertainty on the nlogistic-sigmoid model with a 99% probability ($\alpha=0.01$) by default. 
+- an adaptation of the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality for the Kolmogorov–Smirnov (KS) test to construct a non-parametric confidence interval of uncertainty on the nlogistic-sigmoid model with a 99% probability ($\alpha=0.01$) by default. 
 
 `NLSIG-COVID19Lab` is useful as a quick real-time monitoring tool for the COVID-19 pandemic. It was designed to be used by humans: both researchers and non-researchers. 
 
@@ -89,7 +89,7 @@ In this case, the growth-process is the time-series COVID-19 pandemic growth fro
 
 
 ### Core Data Source
-As at the time of writing. The COVID-19 Database of `NLSIG-COVID19Lab` is sourced from the:
+At the time of writing, the COVID-19 database of `NLSIG-COVID19Lab` is sourced from the:
 
 * World Health Organization
 
@@ -116,7 +116,7 @@ and refer to \autoref{eq:fourier] from text.
 
 # Related research and software
 
-To the best of knowledge, we are unaware of any other software packages or tool providing a similar purpose or functionality for describing the logistic growth of the COVID-19 pandemic from a realistic finite two-dimensional perspective of natural growth.
+To the best of our knowledge, we are unaware of any other software packages or tool providing a similar purpose or functionality for describing the logistic growth of the COVID-19 pandemic from a realistic finite two-dimensional perspective of natural growth.
 
 This application of the `NLSIG` to modelling the COVID-19 pandemic was selected as the best paper at the *2nd African Symposium on Big Data, Analytics and Machine Intelligence and 6th TYAN International Thematic Workshop, December 3-4, 2020*.
 
@@ -125,4 +125,4 @@ This application of the `NLSIG` to modelling the COVID-19 pandemic was selected
 
 This work received no funding. 
 
-# References
+# References