fixing typos and minor english improvment

paper/paper.md

@@ -29,15 +29,15 @@ bibliography: paper.bib
 
 # Summary
 
-Insect pests are a major threat to agricultural systems [@oerkeCropLossesPests2006], leading to intensive use of pesticides for crop protection with non-sustainable drawbacks on environment, biodiversity and human health. Most insects produce pheromones for conspecific communication, making pheromone sensors a good tool for early specific detection of pests, in order to reduce pesticide use in a precision agriculture context [@gebbersPrecisionAgricultureFood2010].
+Insect pests are a major threat to agricultural systems [@oerkeCropLossesPests2006], leading to intensive use of pesticides for crop protection with unsustainable drawbacks on environment, biodiversity and human health. Most insects produce pheromones for conspecific communication, making pheromone sensors an effective tool for early specific detection of pests, in order to reduce pesticide use within the context of precision agriculture [@gebbersPrecisionAgricultureFood2010].
 
-`Pheromone-toolbox` is a Python package containing numerical tools for pheromone sensor data assimilation to infer the position of emitting pest insects. It contains specific tools to model pheromone propagation and solve the corresponding inverse problem to determine emitters' position taking into account the environmental context (wind, landscape, vegetation...). A specific focus is put on the integration of biological knowledge of pest behavior during inference. 
+`Pherosensor-toolbox` is a Python package containing numerical tools for pheromone sensor data assimilation to infer the position of emitting pest insects. It contains specific tools to model pheromone propagation and solve the corresponding inverse problem to determine emitters' position taking into account the environmental context (wind, landscape, vegetation...). A specific focus is put on the integration of biological knowledge of pest behavior during inference. 
 
 # Statement of need
 
-In the field of data assimilation for PDE and dynamic systems, existing packages provide tools to easily interface dynamic systems, observation models and a collection of data assimilation algorithms, such as DAPPER [@raanesDAPPERDataAssimilation2024], OpenDA [@ridlerDataAssimilationFramework2014] or PDAF [@nergerPDAFPARALLELDATA2005]. 
+In the field of data assimilation for PDE and dynamic systems, existing packages provide tools to easily interface dynamic systems, observation models and a collection of data assimilation algorithms, such as DAPPER [@raanesDAPPERDataAssimilation2024], OpenDA [@ridlerDataAssimilationFramework2014], or PDAF [@nergerPDAFPARALLELDATA2005]. 
 
-Unlike these generic packages, `Pherosensor-toolbox` is a context-specific application-oriented package specifically designed to solve the inverse problem of inferring the source term (i.e. pheromone emitters position and emission rates) within a Chemical-Transport Model (CTM) modeling pheromone propagation in an agricultural landscape. An additional feature is the possibility of informing the data assimilation with insect behavior, such as the population dynamics partial differential equations (PDE), to get Biology-Informed Data-Assimilation (BI-DA). BI-DA aims to counter-balance data scarcity with prior biological knowledge. Another additional feature to come is optimal sensor placement tools to find the most informative sensor placement for assimilating the sensor data and inferring the source term of the CTM. The target audience is then academic researchers interested in epidemiosurveillance for crops.
+Unlike these generic packages, `Pherosensor-toolbox` is a context-specific application-oriented package specifically designed to solve the inverse problem of inferring the source term (i.e. pheromone emitters position and emission rates) within a Chemical-Transport Model (CTM) modeling pheromone propagation in an agricultural landscape. An additional feature is the possibility of informing the data assimilation with insect behavior, such as population dynamics modeled by partial differential equations (PDEs), to get Biology-Informed Data-Assimilation (BI-DA). BI-DA aims to counter-balance data scarcity with prior biological knowledge. An other upcoming feature is optimal sensor placement tools to find the most informative sensor placement for assimilating the sensor data and inferring the source term of the CTM. The target audience is then academic researchers interested in epidemiosurveillance for crops.
 
 # Outlook
 
@@ -53,7 +53,7 @@ where $c(t,x,y)$ is the local pheromone concentration, $\mathbf{K}$ is a diffusi
 
 ## BI-DA to solve the inverse problem
 
-We define BI-DA with the following optimization problem: find the optimal quantity of pheromone emitted in time and space $s_a(t,x,y)$ such that
+We define BI-DA with the following optimization problem: find the optimal quantity of pheromone emitted over time and space $s_a(t,x,y)$ such that
 \begin{equation}\label{eq: VDA-probleme-optimisation}
         s_a(x,y,t)=\underset{s(x,y,t)}{\mathop{\mathrm{argmin}}}\text{~}j(s)\text{ with } j(s)=j_{obs}(s)+j_{reg}(s)
 \end{equation}
@@ -66,7 +66,7 @@ In the BI-DA framework, the term $j_{reg}$ involves biological priors including
 `Pherosensor-toolbox` provides gradient-based (gradient descent or proximal gradient) variational optimization methods to solve \autoref{eq: VDA-probleme-optimisation}, where the gradient $\nabla j_{obs}(s)$ is obtained by solving the adjoint model of the CTM. It also provides tools to implement the population dynamics PDE or ODE-based regularization.
 
 ## Postprocessing
-`Pherosensor-toolbox` has several plotting functions to display differences and benchmarks between ground truth and the estimate $s_a$ including spatial maps or pest presence maps defined with level sets. 
+`Pherosensor-toolbox` includes several plotting functions to display differences and benchmarks between ground truth and the estimate $s_a$ including spatial maps or pest presence maps defined with level sets. 
 
 # Related works
 `Pherosensor-toolbox` has been used in a publication introducing the BI-DA framework and assessing the impact of incorporating prior biological knowledge on the estimation accuracy [@malouBiologyInformedInverseProblems2024a]. This publication also incorporates mathematical developments to include any type of PDE-based population dynamics regularization. The optimal placement tools, which will be soon added to the `Pherosensor-toolbox`, will be used to study the optimal placement in the landscape of pheromone sensors in order to enhance the accuracy of pest localization, and to study methodologies of sensor placement and replacement.