From cd88538a3cf9edca841a0225288b5c66571014ce Mon Sep 17 00:00:00 2001 From: "Mark A. Jensen" Date: Sat, 3 Apr 2021 18:22:52 -0400 Subject: [PATCH 1/3] JOSS Ed.: copyedit --- osspaper/paper.md | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/osspaper/paper.md b/osspaper/paper.md index 11626e5..1f25057 100644 --- a/osspaper/paper.md +++ b/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. @@ -43,14 +43,14 @@ 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 in [@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 resulted in erroneous assessment of the epidemic's progress and its future projection, hence 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 @@ -58,7 +58,7 @@ considered in the sum increases, regression analysis becomes more cumbersome and @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 @@ -66,10 +66,10 @@ These limitations are efficiently overcome by the nlogistic-sigmoid function `NL - 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. `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. @@ -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 @@ -125,4 +125,4 @@ This application of the `NLSIG` to modelling the COVID-19 pandemic was selected This work received no funding. -# References \ No newline at end of file +# References From 0bbabd811dba944910f983ddb8f7f8cdc0556a16 Mon Sep 17 00:00:00 2001 From: "Mark A. Jensen" Date: Sat, 3 Apr 2021 18:40:40 -0400 Subject: [PATCH 2/3] JOSS Ed.: smoothing out references --- osspaper/paper.bib | 2 +- osspaper/paper.md | 18 +++++++++--------- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/osspaper/paper.bib b/osspaper/paper.bib index fb8fcb4..4bd7f98 100644 --- a/osspaper/paper.bib +++ b/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, diff --git a/osspaper/paper.md b/osspaper/paper.md index 1f25057..861682f 100644 --- a/osspaper/paper.md +++ b/osspaper/paper.md @@ -44,34 +44,34 @@ of the COVID-19 epidemic growth in each affected country of the world and the wo # Statement of need Epidemiological models such as the SEIRD variants -[@leeEstimationCOVID19Spread2020;@okabeMathematicalModelEpidemics2020] are just another form of representing sigmoidal growth [@xsRichardsModelRevisited2012]. However, it has been noted in +[@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 concern is borne out, in the results of various applications of logistic modelling [@batistaEstimationStateCorona2020;@wuGeneralizedLogisticGrowth2020] -which have largely resulted in erroneous assessment 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 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 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, instead of engaging in false prophecy +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 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. - 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. @@ -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*. From b7f8e410a93cb222e82c65058c43beb6a75669c9 Mon Sep 17 00:00:00 2001 From: "Mark A. Jensen" Date: Sat, 3 Apr 2021 18:45:59 -0400 Subject: [PATCH 3/3] JOSS Ed.: tweak --- osspaper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/osspaper/paper.md b/osspaper/paper.md index 861682f..8b95041 100644 --- a/osspaper/paper.md +++ b/osspaper/paper.md @@ -71,9 +71,9 @@ illustrates the power of the nlogistic-sigmoid neural pipeline. \linebreak `NLSI or predictions on the cumulative growth of an ongoing growth phenomena, whose source is both uncertain and 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.