A Zarragoitia
email: alain.zarragoitia@cqf.sld.cu

S Schetrite

U Jáuregui-Haza

O Lorain

) C Albasi

OPTIMIZATION OF WASTEWATER FILTRATION PROCESS IN SUBMERGED MEMBRANE BIOREACTORS: APPLICABILITY OF A DYNAMIC MODEL TO SCALE UP

Keywords: Biological wastewater treatment, Submerged Membrane Bioreactor (SMBR), modelling, optimization

The application of a hybrid mathematical model, which takes into account the effect of main variables in Submerged Membrane Bioreactor (SMBR) systems, was established in order to simulate and optimize the FILTRATION process into SMBR, on the base of experimental data performed on a bench and pilot scale bioreactors. The validity of the numerical process in the scale up of the water treatment process was checked. Numerical simulations of the wastewater treatment process were performed in order to find the optimal filtration conditions for both different scale bioreactors. Various operating conditions (idlefiltration time, aeration intensity, solids retention time, hydraulics retention time, and total suspended solids concentration) were tested. Different optimization criteria were considered to minimize the transmembrane pressure and energy consumption, and to maximize filtrate flow.

The wastewater treatment using a submerged membrane bioreactor (SMBR) allows obtaining a quite constant filtrate quality after biological degradation process and physical separation. The membrane bioreactor technology has been improved, and research on SMBR technology has increased significantly, particularly in the last 5 years 1 . The advantages of the SMBR system over conventional biological treatment processes leads to a growing interest in MBR technology for water and wastewater treatment. MBR treatment of municipal wastewater yields high-quality water with reported removal percentages of 95%, 98%, and 99% (or greater) for chemical oxygen demand (COD), biochemical oxygen demand (BOD), and suspended solids (SS), respectively 2 . Nevertheless, the filtration process is disturbed by the influence of complex factors that cause the membrane fouling.

On the other hand, mathematical modelling and simulation are powerful tools with which the specialists can predict the performances of potential systems under different operating conditions. For this reason, it is interesting to use models that can accurately describe the SMBR process for the design, and optimization of these systems.

The objective of this work is to show the practical application of a hybrid mathematical model, developed in a previous work [START_REF] Alain | Modelling of Submerged Membrane Bioreactor: Conceptual Study About Link Between Activated Slugde Biokinetics, Aeration and Fouling Process[END_REF] for optimizing the operation of two SMBRs using different optimization criteria to minimize the transmembrane pressure and energy consumption, and to maximize filtrate flow. The model was established considering Soluble Microbial Products (SMP) formation-degradation kinetic based on modified published models [4][5][6] . A modification of Li and Wang's model 7 allows to calculate the increase of the TMP evaluating, at the same time, the influence on fouling control of an intermittent aeration of coarse bubbles synchronized with the filtration cycles, and to analyze the effects of shear intensity on sludge cake removal. In order to describe the biological system behaviour a modified ASM1 model was developed to estimate the optimal operating conditions related to a specific bioreactor condition. The validation of the model was carried out using the data from an experimental SMBR installed in a real domestic wastewater treatment plant.

EXPERIMENTAL PART

Two different SMBRs were studied. In the first (bench scale), a U-shaped, hollow-fiber membrane module with area of 0.3 m2 (provided by Polymem, Toulouse, France), was immersed in a bioreactor of 10.5 L of working volume. Hollow fibres were made of polysulfone with a pore size of 0.1 µm, and internal/external diameter of 0.4/0.7 mm. The SMBR was initially filled with activated sludge from the Brax wastewater treatment plant (2000 eq inhabitants, only domestic wastewater). The municipal wastewater was continuously introduced. The influent flow rate was controlled by the liquid level in the reactor. Filtration was operated in an intermittent sequence of filtration-relaxation. The TMP was continuously monitored as an indicator of membrane fouling (Sensor Keller). Filtrate flow was measured with an electromagnetic flow meter (Rosemount), a temperature sensor (PT 100; -50 to 250 °C) and a Mettler Toledo pH meter were utilized. The pH was maintained between 6.5 and 7.5 by adding a Na 2 SO 4 solution (10 g/L). PC-based real time data acquisition hardware (IOTECK) and the software DASYLAB have been used for acquiring all data.

The second bioreactor has four hollow-fibre membrane modules with an area of 2.5 m 2 (10 m 2 of total filtration area) and a bioreactor tank of 1 m 3 (Polymem, Labège, France). The membrane material is the same as the previous one. This bioreactor is operated in a largest plant, collecting wastewater from domestic area as well as industrial one. In this case, different simulations were carried out in order to estimate the optimal values of the operating conditions using the approach of the experimental design. The model was established in order to simulate and optimize the filtration process into SMBR, on the base of experimental data performed on a laboratory scale bioreactor, with 10 litres of mixed liquor. Numerical simulations of the wastewater treatment process were performed in order to find the optimal filtration conditions for two different scale bioreactors.

The bench scale bioreactor was operated with two types of aeration flows. An intermittent coarse bubbles flow injected closed to the fibres, providing a tangential liquid movement, to avoid the membrane fouling by reduction of cake formation (reversible fouling), and a constant fine bubbles flow injected through a perforated membrane at the bottom of the reactor, providing mixing and biomass oxygenation. The membrane module was isolated to the contact with fine bubbles; thus, membrane fibers movement is only produced by the flow of coarse bubbles. The operation was stopped at 12 days of filtration or when the TMP reached 60 kPa under atmospheric pressure, and a chemical cleaning was applied, using solutions of 2 M chlorine for 2 h, and 0.1 N NaOH for 24 h.

Analytical methods

The Total Suspended Solids (TSS) concentration was determined by centrifugation at 5000 rpm for 10 min and drying at 105°C using a PRECISA HA60 moisture analyzer. The activated sludge flocs size distribution was estimated with a laser granulometer (Mastersizer 2000, Malvern Instruments). Deadend filtration tests were performed to estimate the specific filtration resistance (α = rsc = rdc). The filtration index measurements were performed in a special cell. The experimental filtration device was a Sartorius filtration pressured cell, with a working volume of 50 mL on a plane organic membrane of cellulose acetate (47 mm diameter, filtration area 0.17 cm2 and pore size 0.2 µm). The quantification of Extracellular Polymeric Substances (EPS) was made on the sludge supernatant that had been obtained by centrifugation at 5000 rpm for 20 min, and on the suspended solid. The EPS from the suspended solid were extracted by addition of 2 N NaOH at 4°C for 4 h. The extracted solutions were then centrifuged at 20000 rpm for 20 min and filtrated on a 0.2 µm membrane. Soluble EPS were quantified in influent and permeate samples. Proteins and polysaccharides were measured by spectrophotometric methods. The Lowry method modified by Frolund was used for the quantification of proteins and humics with bovine serum albumin as standard 8 . For quantitative analysis of carbohydrates, the modification of the anthrone method described by Raunkjaer et al 9 was used with glucose as standard.

The composition of municipal wastewater is highly variable. For this reason, average influent composition values were used during calculation. These estimated values were determined by different batch procedures. Respirometric measurements were used for the determination of readily and slowly biodegradable substrates considering Y H = 0.67 gCOD / gCOD. The reactor of 1.5 L used for the oxygen uptake measurement was constantly aerated and stirred. A water bath was used to keep the temperature of the liquid constant at 25 °C. Allylthiourea (ATU) (2 mg/l) was added to reactor to inhibit the nitrifying microorganisms. An S/X ratio of 1.2 was used, and these enabled the areas under the Oxygen Uptake Rate (OUR) curve to be distinguished. Dissolved oxygen was measured in the reactor by means of an oxygen meter (YSI-51). The readily biodegradable substrates (S S ) and the slowly biodegradable substrates (X S ) were estimated following a published procedure 10 .

Simulation conditions and optimization procedure

A numerical simulation of the membrane fouling was performed using a program that was written in Berkeley Madonna programming language, run on a PC in the Windows XP environment. Membrane fouling development was simulated by numerical iterations, which produces the overall TMP increase and the evolution in the distribution of the flux and the sludge cake layer across the membrane surface sections (time step = 1 s). The intermittent process of filtration and coarse bubbles injection were simulated by means of periodic functions implemented in Berkeley Madonna V 8.3.9. When the simulation results were compared with experimental data a good agreement was observed, thus, a D-Optimal Experimental Design (DOED) matrix was used for the optimization of the operating conditions for both SMBRs (Tables 1 and2). The values of the response variables in each experiment were estimated "in-silico" using our model, then, the optimal values were founded using the mathematical tools included in the software Design-expert v7. This procedure allows a quickly estimation of the optimal values, that is important when the physical experiments are time-consuming, expensive and difficult to carry out 11 . Finally, the predicted optimal operating conditions were validated by experimental way for bench scale SMBR. The validation of the optimum for the pilot scale SMBR is under study.

Table 1-Summary of the DOED used during the optimization of the operating conditions for the bench scale SMBR * Design Model (quadratic), Experiments= 26, qa = 9 (L/(m 2 s)), J T =0.24 (m 3 /(m 2 day)). Where qa= aeration intensity, tf= filtration time, tid= idle time, Int CB = time interval between two coarse bubbles injection, t CB = coarse bubbles injection time, SRT=solids retention time, J T = Overall flux Table 2-Summary of the DOED used during the optimization of the operating conditions for the pilot scale SMBR * Design Model (quadratic), Experiments= 30, qa = 1 (L/(m 2 s)), J T = 0.24 (m 3 /(m 2 day)) Where qa= aeration intensity, tf= filtration time, tid= idle time, Int CB = time interval between two coarse bubbles injection, t CB = coarse bubbles injection time, tbw=backwashing time, J T = Overall flux

RESULTS AND DISCUSSION

Optimization of the operating conditions for the bench scale SMBR

During the optimization, different criteria were considered, to minimize the transmembrane pressure and energy consumption, and to maximize filtrate flow (figs. 3-4). The equation 1 shows the objective function used to calculate and to minimize the energy consumption. On the other hand, Table 3 shows a summary of the measured influent characteristics and initial operating conditions used during simulation. The table 4 shows the optimization results estimated by simulation as well as the predicted values of the optimized response variables (after 12 days of filtration using the optimized operating conditions). (Superscript 0, R0 expresses in "influent", "initial value in the bioreactor" respectively), X TSS = Total suspended solids in the mixed liquor (mg/l), X S = slowly biodegradable products (mgCOD/l), X I = inert organic materials (mgCOD/l), S S = soluble biodegradable substrate (mgCOD/l), S I = soluble inert matters (mgCOD/l), S SMP =soluble microbial products (mgCOD/l) Table 4-Optimization results calculated by simulation and the DOED for bench scale SBMR.

During the optimization, only five factors were considered in the DOE. Figures 12show different examples of the optimization results, but considering only the values of tid and tf in the axis. The other factors values could be calculated in the same way, once a specific optimization criterion is chosen. Table 4 points out the existence of differences in the tf and SRT values for the case A and B, but it also suggests that different filtration-idle time cycles may lead in both cases to work in optimal conditions, this also change the synchronization between the filtration and the intermittent aeration. This result is reasonable and may find explanation in the fact that the cases A and B have different influent characteristics and biomass concentration (Table 3). These differences modify the behavior of the system due to the presence of different F/M ratios, different sludge viscosities (that are function of the X TSS concentration), and biological variables. The same observations can be made for the composition of mixed liquors, which are not the same between case A and B, and modifying the value of the specific filtration resistance of the sludge cake layer, and consequently the fouling rate. In the experiments ran "in silico", the EC values were found between 0.15-0.96 kW/m 3 h and the FV values between 432-800 l, therefore, the estimated optimal conditions facilitated, in both cases, to operate the bioreactor for an adequate volume of produced water with a reasonable energy consumption (Table 4).

h A-1 A-2 B-2 B-1

Optimization of the operating conditions for the pilot scale SMBR

In the case of the pilot scale SMBR, the optimization study was carried out with the objective of modifying the usual values of the operating variables, in order to improve the operation efficiency of the SMBR. The results are shown in table 5. The analysis of the simulation-optimization results (Table 6) suggests that for a better utilization of the SMBR it would be convenient to increase the filtration time almost of 30% of its current value. In relation to the injection cycles of the coarse bubbles, the idle time between every injection could be increased in 80%, but at the same time, it is necessary to double the length of the aeration time. This operating way is more efficient because it decreases the energy consumption due to the aeration flow used to remove the sludge deposited on the membrane. Although, a higher idle time allows some temporary deposition of the sludge on the membrane, the simulation estimates that the increase of the injection time get possible to later efficiently the deposition of the sludge and the formation of the filtration cake on the membrane. On the other hand, a higher filtration time facilitates the production if a higher filtrate volume (increase of 11%) during the considered time, which decreases the estimated value of energy consumption by m 3 of treated water (decrease of 56%). In relation to the value of the backwashing time, the model considers that the current value is correct (0.5 min). To evaluate the validity of the simulations and the quality of the model prediction, all results have still to be validated in the bench scale SMBR. Some simplifications have been made during the modelling of the system; therefore, it is necessary to characterize the influence of the assumptions and the limitations of the model on the optimization results. The optimization procedure presupposes the existence of a model calibrated to the real system, an accurate process of prediction by simulation is only possible after tuning the parameters of the model to a given plant. Therefore, the more sensible parameters must be recalibrated if the influent conditions and the biomass characteristics change considerably. Before the optimization evaluation, the quality of the model prediction is a very important key to guarantee the quality of the optimization process.

CONCLUSIONS

An optimization study to improve the filtration process on two different SMBRs at different scales has been successfully developed. For this task, a recent developed model was used. A DOED was carried out "in silico" in order to optimize some operating variables. This simple optimization procedure improves the operating conditions for two different optimization criteria: minimizing energy consumption and minimizing TMP. Subsequently, the experimental verification process of the optimized operating conditions for the bench scale is in good agreement with the model predictions. Future tasks will focus on the system optimization, but, also including the aeration intensity and the filtration flux as factors to consider in the design of experiments. However, for better results a special attention is needed during parameters model calibration.

Figure 1 -

 1 Figure 1-Optimization of operating conditions for the bench scale SMBR. Case A: Minimizing energy consumption [A-1: Contour graph obtained during the optimization of the operating conditions (minimizing the energy consumption). A-2: Experimental validation of the optimized values of the operating conditions].

Figure 2 -

 2 Figure 2-Optimization of operating conditions for the bench scale SMBR. Case B: Minimizing TMP [B-1: Contour graph obtained during the optimization of the operating conditions (minimizing the transmembrane pressure). B-2: Experimental validation of the optimized values of the operating conditions].The same observations can be made for the composition of mixed liquors, which are not the same between case A and B, and modifying the value of the specific filtration resistance of the sludge cake layer, and consequently the fouling rate. In the experiments ran "in silico", the EC values were found between 0.15-0.96 kW/m 3 h and the FV values between 432-800 l, therefore, the estimated optimal conditions facilitated, in both cases, to operate the bioreactor for an adequate volume of produced water with a reasonable energy consumption (Table4).

Table 5 -

 5 Current and optimized values of the studied operating values for the pilot scale SMBR. In brackets are shown the values used during the simulation with the optimized values of the operational variables.

Figure 3 -

 3 Figure 3-Examples of the contour graphs obtained during the optimization of the operating conditions for the pilot scale SMBR.

Table 3 -

 3 Where: EC= Energy consumption (kW/m3h), FV= Filtrate volume (l), TMP= Transmembrane pressure (kPa), Qair= aeration flow (l/h), Qfilt= Filtration Flow (l/h), ∆Pair= aeration drop pressure (bar) Summary of the measured influent and initial conditions used during simulation.

	EC	=	  	. 0	tf Qfil FV ( * * ( 666	tid TMP +	) *	tf	)	+	t Qair FV CB ( * * ( 666 . 0	Int Pair CB * ) t + ∆	CB	)	  	time	kW/m	3	h	(eq. 1)

Table 6 -

 6 Influence of the optimized operating variables on the response variables for the pilot scale SMBR.

			Reponse variables (at 15 days)
		TMP (kPa)	VPacum (L)	EC (kW/hm 3 )
	Results with the current values of	43.6	24000	0.055
	the operating variables
	Results with the optimized values	25	27160	0.024
	of the operating variables
	TMP reduction	42.6 %	-	-
	Volume increase	-	11.6 %	-
	Energy consumption reduction	-	-	56.4 %

ACKOWLEDGEMENT

This study was supported by the European Community in the framework of the program ALPHA II-400-FA. The authors gratefully acknowledge the material support from Mr. Olivier Lorain, POLYMEM SA, (Toulouse, France).


Mujtaba H Agha
email: mujtabahassan.agha@ensiacet.fr

Raphaele Thery
email: raphaele.thery@ensiacet.fr

Gilles Hetreux
email: gilles.hetreux@ensiacet.fr

Alain Hait
email: alain.hait@isae.fr

Jean Marc Le Lann
email: jeanmarc.lelann@ensiacet.fr

INTEGRATED PRODUCTION AND UTILITY SYSTEM APPROACH FOR OPTIMIZING INDUSTRIAL UNIT OPERATIONS

Keywords: Short-term scheduling, CHP plant, Utility management, Energy cost, MILP

Energy intensive industrial units use onsite utility system to meet their utility requirements. However emphasis in these industrial units is placed on manufacturing (production) schedule while the aspect of operational planning of utility system is largely ignored. In this article an integrated approach is presented that simultaneously undertakes shortterm scheduling of a multipurpose batch plant and operational planning of utility system. This approach is formulated using multi-period mixed-integer linear programming (MILP). Results indicate that integrated approach leads to significant reduction in energy costs and at the same time reduces emission of harmful gases.

The issue of energy has emerged as one of the greatest challenges facing the mankind. Ever since replacing less efficient sources, like water-driven mills and burning of timber, fossil fuels (oil, coal and gas) have been the primary source of energy. However, the extensive use of fossil fuels has not only resulted in depletion of the fossil fuel reserves but there also has been huge negative consequence on the ecological system of the planet. Intergovernmental Panel on Climate Channel 1 has identified the emissions of harmful gases (released during burning of fossil fuels) as the chief cause for the phenomenon of global warming.

In this context, there is increased emphasis on finding the alternative sources of energy, especially renewable sources like wind, solar, hydrogen, etc. There is no doubt that the alternative energy sources are the answer to the energy issue but it is also a reality that no such alternatives are available in immediate future. In fact projections of Environmental Information Agency [START_REF]Annual energy outlook 2007[END_REF] show that even in the year 2030 fossil fuels will remain as the primary source of energy. Hence, optimizing the utilization of energy generated by fossil fuels is perhaps just as important as finding the alternative sources of energy.

Energy optimization is particularly important for energy intensive industrial units as they consume large quantities of energy in shape of utilities. A utility can be defined as any quantity having high energy and which can be useful to industrial unit in manufacturing the finished product. In industrial unit the utility can be in shape of electricity, steam (at various pressure levels), hot/cold water and hot air. There are two possible ways of energy optimization in industrial units -firstly, by technological advances in machinery which enhance efficiency of individual industrial equipments and secondly use of methodologies like process integration 3 that improve the operational efficiency of the industrial unit as a whole.

In this study the operational efficiency of an industrial unit is enhanced using mathematical modeling. A multi-period mixed-integer linear programming (MILP) model is used to develop a utility management for the industrial unit. The scope of this study is limited to only altering operating conditions and no structural changes are made to the industrial unit.

PROBLEM STATEMENT

Energy intensive industrial units normally fulfill their utility demands including that of electricity by employing an onsite utility system. Thus, these industrial units comprises of two distinct units -a utility system that generates utilities and a manufacturing unit that consumes utilities to produce the final product. Generally the emphasis is placed on the manufacturing unit while the utility system is regarded as a support function whose objective is to meet the energy demands of manufacturing unit. Due to this biased outlook the short-term scheduling of the industrial unit is carried out by sequential resolution of three sub-problems: scheduling of the manufacturing unit by minimizing inventory, estimating the utility needs of manufacturing unit and finally operation planning of the utility system.

The sequential approach creates a master-slave relationship between manufacturing unit and utility system. The first step of manufacturing unit scheduling is carried out without taking into the operational constraints utility system. Consequently the utility system functions below its potential and sub-optimal energy solutions are attained for industrial unit operations. In this study an integrated approach is adopted which concurrently carries out manufacturing unit scheduling and operational planning of utility system. This integrated approach results in better utility management and leads to higher energy efficiency of industrial unit.

MATHEMATICAL MODELING

The problem is formulated using discrete-time based MILP model. The planning horizon is divided into T periods with each period having duration of one hour. The model constraints are provided by applying -mass and energy balances, production and capacity constraints, simplified assumptions to linearize non-linear equations and use of binary variables to resolve conflicts on whether or not particular equipment is operational during time period t.

Sequential Approach

Step 1 -Task scheduling of manufacturing unit: The manufacturing unit, following production recipe, ascertains a schedule that allocates limited resources to manufacture one or more products. The schedule determines the number of tasks k (k ε K) and batch size of each task that is carried out by processing equipment j (j ε J) in manufacturing unit. The scheduling model in this study uses same capacity limitation constraints and material balance constraints that were first developed by Kondili et al [START_REF] Kondili | A general algorithm for short-term scheduling of batch operations -I. MILP formulation[END_REF] . However, for allocation constraints "big M" equations are replaced by following equation which was used by Méndez et al [START_REF] Méndez | State-of-the-art review of optimization methods for short-term scheduling of batch processes[END_REF] :

∑ ∑ ∈ + - = = ∀ ∈ ∀ ≤ j k K k p t t t j k T t J j W ,.., 1 , 1 1 ' ' , , (1)
The optimization criterion for scheduling problem is based on tardiness (minimize inventory):

∑∑ = ∈ ⋅ = T t S s t s s stock S l C 1 , (2)
Step 2 -Estimation of utility requirements: Based on the task scheduling and the utility requirement of each task the overall utility demand for the manufacturing unit is estimated.

∑ ∑ ∈ + - = = ∀ ∈ ∀ = k k J j p T t j k t k T t K k B TBatch ,.., 1 , 1 , , , θ θ (3) K k TBatch Cop CGlob k t k k v t v ∈ ∀ ⋅ = ∑ , , , (4)
The utility requirements are classified as high pressure (HP), medium pressure (MP), low pressure (LP) steam and electricity demands based on following equation:

T t UTIL v CGlob Dem t v t v ,.., 1 , , , = ∀ ∈ ∀ = (5)
Step 3 -Operational planning of utility system: The final step of sequential approach is to carry out the operational planning of the utility system. This part of mathematical model is based on the work that was initially proposed by Soylu et al. [START_REF] Soylu | Synergy analysis of collaborative supply chain management in energy systems using multi-period MILP[END_REF] The initial model was further extended by Agha et al. [START_REF] Agha | Collaboration among companies for better energy management[END_REF] to include part load behavior of boiler as well as time delays and costs incurred during boiler shutdown and restart. A multi-objective criterion was used to optimize the operational planning of the utility system.

( ) ∑ ∑ ∑ ∑ ∑ ∑ ∈ ∈ ∈ ⋅ + ⋅ + + ⋅ = t BOIL j t BOIL j t FUEL i i j t i j t i CSOX XSOX CEL ELP SI I cf COST , , , , (6)
The operational planning of utility system minimizes the energy costs (fuel & electricity purchase) and penalty costs (for emission of harmful gases) while fulfilling the utility demands of manufacturing unit.

Integrated Approach

The sequential approach results in sub-optimal solution as unlike other resources classically considered in the scheduling problems (machinery or work force), utilities have special characteristics which must be taken into account. Utilities are not only present in many different forms (steam at different pressure levels, electricity, etc) but they are also a resource that can not be stored in its ultimate form. Hence unlike materials they must be consumed immediately at the time of their generation. This makes the operational planning aspect of utility system vitally important for overall energy efficiency of industrial unit.

The drawback of the preceding approach is removed in integrated approach where the task scheduling of manufacturing unit and operational planning of the utility system is simultaneously carried out. Integrated approach concurrently solves: -production and capacity constraints of manufacturing unit (Kondili et al. [START_REF] Kondili | A general algorithm for short-term scheduling of batch operations -I. MILP formulation[END_REF] ), -allocation constraints of manufacturing unit (equation 1), -utility estimation constraints (equations 3, 4 and 5) and operational planning constraints of utility system (Agha et al. [START_REF] Agha | Collaboration among companies for better energy management[END_REF] )

The optimization criterion used in the integrated approach is the minimization of equation 6, i.e., reducing the energy and emission penalty costs. Hence, at the time of task allocation the integrated approach cross checks for the availability of utilities based on the operational planning of the utility system. Trade-offs are made and a greater synchronization between the manufacturing unit and utility system is achieved. This results in an optimum operating condition for the industrial unit. To compare integrated approach with sequential approach an example was formulated and resolved using software XPRESS-MP release 2008A [START_REF]Xpress-Optimizer version[END_REF] . The problem was solved on an Intel(R) Core(TM) 2 Duo CPU @ 2.00 GHz and 1.00 GB of RAM. The industrial unit considered for this example is presented in the figure 1. The left hand side shows the Resource Task Network (RTN) representation of the manufacturing unit while the right hand side demonstrates a combined heat and power (CHP) based utility system. CHP plants are a popular choice as onsite utility system as they simultaneously generate steam (at different pressure levels) and electricity.

EXAMPLE S1 T1 (1)
The manufacturing unit undertakes eleven tasks (K) using six processing equipments (J) to convert four raw materials (S1, S2, S8 and S11) into two finished products (S12 and S13). The industrial unit is supposed to be operating around the clock (planning horizon T =24) and after every eight hours the manufacturing unit must meet certain product demands. The utilities consumed (Cop v,k ) by each task in manufacturing unit are also given in figure 1.

Scenario 1: Reduction in energy costs and diminution in emissions of harmful gases

The demand for product1 (S12) at time period t = 8, t = 16 & t = 24 is 0, 80 & 100 tons respectively. The demand for product 2 (S13) at same time periods is 0, 40 and 80 tons respectively. Figure 2 presents the short-term scheduling of manufacturing unit and operational planning of utility system for both the sequential and integrated approaches. It is clear that in the case of the integrated approach the tasks in manufacturing unit are arranged in such a manner that their utility demands are synchronized with the utilities being generated in utility system. This not only results in fewer variations in steam load curves of utility system but also minimizes the wastage of utilities. For example, during period 19-21 in the sequential approach manufacturing unit does not undertake any tasks that consume electricity. This is in spite of the fact that MP steam demands can be met by expanding HP steam in turbines and simultaneously generating electricity. Such opportunities are not missed in integrated approach where tasks that consume electricity are always aligned with tasks that consume MP and LP steam. There by, reducing the need for electricity purchase from external source. Figure 2: Results for scenario 1 Table 1 represents the comparison between sequential and integrated approach based on the energy costs and gas emissions. The use of integrated approach results in 13 % reduction in overall energy costs. The higher energy efficiency of integrated approach not only leads to lesser quantity of fuel being burnt in boiler but it also eliminates the need for electricity purchase from external source. Moreover it results in 30 % reduction in SO x emissions and 13 % reduction in green house gas emissions. In this scenario the product demands are increased by roughly 60%. Hence demand of product 1 (S12) at time period t = 8, t = 16 & t = 24 is 0, 130 & 160 tons respectively. The demand for product 2 (S13) at same time periods is 0, 65 & 130 tons respectively. Figure 3 presents the short-term scheduling of manufacturing unit and operational planning of utility system for both the sequential and integrated approaches. The sequential approach fails to fulfill the product demands as the utility system is unable to meet the utility requirements of the manufacturing unit. The net steam requirements (at t = 20) surpass the maximum steam generation capacity of the boilers. In contrast, the integrated approach shifts and rearranges tasks in manufacturing unit in such a manner that utility requirements never exceed the capacity of utility system. Hence, higher productivity in the manufacturing unit can be achieved by using integrated approach.

Scheduling of manufacturing unit

CONCLUSION

Energy intensive industrial units normally generate their own utilities by using an onsite utility system. However even in these industrial units the emphasis is placed on production (manufacturing unit) and the utility system is treated as a subsidiary unit. This biased approach results in sub-optimal solutions as the utility system is never able to achieve its energy efficiency potential. This paper presents an integrated approach in which both the manufacturing unit scheduling and utility system operational planning are concurrently undertaken. The use of integrated approach not only displays energy cost reduction potential but it can also lead to significant decrease in emissions of harmful gases. Moreover, the multi-objective function (equation 6) can be used to simulate and develop scenarios in which emissions are more severely penalized, for example including a penalty cost for green house gas emission.

This study is a part of research being conducted at CNRS, whose objective is energy management solutions for mono and multi-sites. In future the discrete time model will be replaced by a continuous time formulation.

NOMENCLATURE

Figure 1 :

 1 Figure 1: An industrial unit comprising of two distinct units

Figure 3 :

 3 Figure 3: Results for scenario 2

Table 1 :

 1 Comparison between sequential and integrated approaches for scenario 1

	Approach	Fuel Cost (€)	Electricity Cost (€)	SOx Cost (€)	Energy Costs (€)	GHG emissions (tons)	SOx emissions (tons)
	Sequential	33,941.8	1,022.9	268.7	35,233.3	1,734.8	11.68
	Integrated	30,579.6	0	181.8	30,761.4	1,508.2	7.908
			Scenario 2: Attaining of higher productivity

  Amount of material being undertaken by task k in processing unit j at time period tCstockScheduling criterion used for minimizing inventory levelCGlobv,kOverall consumption of utility v during the time period t (tons/hr of steam and MWh/hr electricity) Demand of utility v from processing unit j in time period t (with v in tons for steam and MWh for electricity) Quantity of fuel i used in boiler j during time period t (tons) Quantity of fuel i used during the starting of boiler j from cold state in time period t (tons) Binary variable that determines if task k is being carried out in processing unit j in time period t XSOX Quantity of SOx released by boiler j during time period t (tons)

	Indices		Sets		Parameters
	i	fuels	BOIL	set of boilers	cfi	Cost of fuel
	k	tasks	J	set of processing	CEL	Cost of electricity
				equipments
	s	states	K	set of tasks	CSOX	Cost of emission of SOx gas
	t	time	S	set of states	Copv,k	Utility v consumed by task k for each ton of material
						processed
	v	utility	UTIL	set of utilities	ls	Inventory coefficient to obtain the tardiness starting
						date
	j	equipments		T	Time Horizon
	Variables
	Bk,j,t
	Demv,t
	ELPt	Electricity purchased during time period t
	It,j,i
	SIt,j,i
	Wk,j,t


Isariebel Quesada-Peñate

Carine Julcour-Lebigue

Ulises Javier

Jáuregui Haza

Anne-Marie Wilhelm

Henri Delmas
email: henri.delmas@ensiacet.fr

Ulises Jáuregui-Haza

Catalytic wet air oxidation of paracetamol on activated carbons: conversion, mineralization and stability

Keywords: catalytic wet air oxidation, activated carbon, paracetamol. 1. Introduction

come

Considering the potential impacts of pharmaceutical products on environment and human health, it is highly important to remove them from domestic and industrial wastewaters before discharge. It has been shown that many pharmaceuticals are not completely removed by conventional wastewater treatment and, as a result, their occurrence is being reported in sewage plant effluents, rivers and lakes, and more rarely in groundwater 1 . Then alternative methods, like catalytic wet air oxidation (CWAO) using activated carbon (AC) as catalyst 2 and sequential adsorption-oxidation processes with AC 3 , have to be evaluated. The aim of this work was to study the feasibility of paracetamol degradation by CWAO using different ACs.

Experimental

In a typical experimental run, 200-mL of 1g/L paracetamol aqueous solution and 1 g of AC were added in a stirred autoclave (Parr Instruments), operating at 150 °C and oxygen partial pressures of 3.5 bar (total pressure of air 20 bar). The experiments were performed batchwise for the liquid phase and were continuous for air at a flow rate of 60 L/h to ensure constant oxygen pressure. Prior to oxidation reactions, the ACs were saturated with paracetamol at 150°C under nitrogen atmosphere. The stirrer speed was set at 800 rpm to avoid catalyst attrition and prevent external mass transfer limitations. Liquid samples were analyzed via high-performance liquid chromatography, using a C18 reverse-phase column and a diode array detector at 254 nm. The closed reflux colorimetric method was used to determine COD values.

ACs from different source materials (carbon L27 from wood, S23 from coconut shell and C1 from casuarina) were characterised and then used as catalysts to compare their efficiency.

Table 1 shows the physical properties of ACs. The adsorption equilibrium on fresh AC particles sieved to 800-1000 µm was reached after 2 hours, showing an higher adsorption capacity of S23 and C1 than L27 (Fig. 1). Then, after AC saturation, the CWAO reaction was started, and the highest oxidation rate was obtained with fresh C1 and the lowest one with L27. Further, the stability of AC to recycling was studied, evaluating the total conversion (adsorption + CWAO) and mineralisation (Table 2). In all cases, both paracetamol degradation and mineralisation decrease when AC is recycled. A similar trend has been observed by other authors when CWAO of several substrates was studied, due to the blockage of micropores by some carbonaceous deposit, formed by oxidative coupling reactions and irreversibly adsorbed 4 . In our case, although L27 was less efficient in the first cycle, the best results were obtained for it after five CWAO cycles, which can be explained by its higher mesoporous/microporous ratio.

Conclusions

The degradation of paracetamol by CWAO using different ACs as catalysts is feasible. The best conversion and mineralization degree after five cycles was obtained for L27 AC, which has higher mesoporous/microporous ratio than others studied ACs.

Figure 1 .Figure 2 .

 12 Figure 1. Adsorption and CWAO of paracetamol on fresh ACs

Table 1 .

 1 Physical properties of the ACs (particle diameter 0.8-1 mm; r: mesoporous/microporous ratio)

	AC	BET surface area, m 2 .g -1	Microporous volume, cm³.g -1	Mesoporous volume, cm³.g -1	r	Average pore diameter, Å	Apparent particle density, g/L
	L27	1860	0.77	0.48	0.62	25	552
	S23	1234	0.49	0.04	0.08	17	1013
	C1	1304	0.53	0.26	0.49	22	799


Olivier Colliot
email: olivier.colliot@cnrs.fr

A non-technical introduction to machine learning

Keywords: machine learning, artificial intelligence, supervised learning, unsupervised learning

This chapter provides an introduction to machine learning for a nontechnical readership. Machine learning is an approach to artificial intelligence. The chapter thus starts with a brief history of artificial intelligence in order to put machine learning into this broader scientific context. We then describe the main general concepts of machine learning. Readers with a background in computer science may skip this chapter.

Introduction

Machine learning (ML) is a scientific domain which aims at allowing computers to perform tasks without being explicitly programmed to do so [START_REF] Samuel | Some studies in machine learning using the game of checkers[END_REF]. To that purpose, the computer is trained using the examination of examples or experiences. It is part of a broader field of computer science called artificial intelligence (AI) which aims at creating computers with abilities that are characteristic of human or animal intelligence. This includes tasks such as perception (the ability to recognize images or sounds), reasoning, decision making or creativity. Emblematic tasks which are easy to perform for a human and are inherently difficult for a computer are for instance recognizing objects, faces or animals in photographs, or recognizing words in speech. On the other hand, there are also tasks which are inherently easy for a computer and difficult for a human, such as computing with large numbers or memorizing exactly huge amounts of text. Machine learning is the AI technique that has achieved the most impressive successes over the past years. However, it is not the only approach to AI and conceptually different approaches also exist.

Machine learning also has close ties to other scientific fields. First, it has evident strong links to statistics. Indeed, most machine learning approaches exploit statistical properties of the data. Moreover, some classical approaches used in machine learning were actually invented in statistics (for instance linear or logistic regression). Nowadays, there is a constant interplay between progress in statistics and machine learning. ML has also important ties to signal and image processing, ML techniques being efficient for many applications in these domains and signal/image processing concepts being often key to the design or understanding of ML techniques. There are also various links to different branches of mathematics, including optimization and differential geometry. Besides, some inspiration for the design of ML approaches comes from the observation of biological cognitive systems, hence the connections with cognitive science and neuroscience. Finally, the term data science has become commonplace to refer to the use of statistical and computational methods for extracting meaningful patterns from data. In practice, machine learning and data science share many concepts, techniques and tools. Nevertheless, data science puts more emphasis on the discovery of knowledge from the data while machine learning focuses on solving tasks. This chapter starts by providing a few historical landmarks regarding artificial intelligence and machine learning (section 2). It then proceeds with the main concepts of ML which are foundational to understand other chapters of this book. proposed an artificial neuron model, which is a mathematical abstraction of a biological neuron [START_REF] Mcculloch | A logical calculus of the ideas immanent in nervous activity[END_REF], and showed that sets of neurons can compute logical operations. In 1948, the mathematician and philosopher Norbert Wiener coined the term "cybernetics" [START_REF] Wiener | Cybernetics or Control and Communication in the Animal and the Machine[END_REF] to designate the scientific study of control and communication in humans, animals and machines. This idea that such processes can be studied within the same framework in both humans/animals and machines is a conceptual revolution. In 1949, the psychologist Donald Hebb [START_REF] Hebb | The organization of behavior[END_REF] described a theory of learning for biological neurons which was later influential in the modification of the weights of artificial neurons.

A bit of history

In 1950, Alan Turing, one of the founders of computer science, introduced a test (the famous "Turing test") for deciding if a machine can think [START_REF] Turing | Computing machinery and intelligence[END_REF]. Actually, since the question can a machine think? is ill-posed and depends on the definition of thinking, Turing proposed to replace it with a practical test. The idea is that of a game in which an interrogator is given the task of determining which of two players A and B is a computer and which is a human (by using only responses to written questions). In 1956, the mathematician John McCarthy organized what remained as the famous Darmouth workshop and which united ten prominent scientists for two months (among which Marvin Minsky, Claude Shannon, Arthur Samuel and others). This workshop is more important by its scientific programme than by its outputs. Let us reproduce here the first sentences of the proposal written by McCarthy et al. [START_REF] Mccarthy | A proposal for the dartmouth summer research project on artificial intelligence[END_REF] as we believe that they are particularly enlightening on the prospects of artificial intelligence:

We propose that a 2 month, 10 man study of artificial intelligence be carried out during the summer of 1956 at Dartmouth College in Hanover, New Hampshire. The study is to proceed Colliot on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it. An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves. We think that a significant advance can be made in one or more of these problems if a carefully selected group of scientists work on it together for a summer.

There was no major advance made at the workshop, although a reasoning program, able to prove theorems was presented by Allen Newell and Herbert Simon [START_REF] Newell | The logic theory machine-a complex information processing system[END_REF] at this occasion. This can be considered as the start of symbolic AI (we will come back later on the two main families of AI: symbolic and connexionist). Let us end the 1950s with the invention, in 1958, of the perceptron by Frank Rosenblatt [START_REF] Rosenblatt | The perceptron: a probabilistic model for information storage and organization in the brain[END_REF], whose work was built upon the ideas of McCulloch, Pitts and Hebb. The perceptron was the first actual artificial neuron. It was able to recognize images. This is an important landmark for several reasons. The perceptron, with some modifications, is still the building block of modern deep learning algorithms. To mimic an artificial neuron (Figure 2), it is composed of a set of inputs (which correspond to the information entering the synapses) x i , which are linearly combined and then go through a non-linear function g to produce an output y. This was an important advance at the time but it had strong limitations, in particular its inability to discriminate patterns which are not linearly separable. More generally, in the field of AI as a whole, unreasonable promises had been made and they were not delivered: newspapers were writing about upcoming machines that could talk, see, write and think; the US government funded huge programs to design automatic translation programs, etc. This led to a dramatic drop in research funding and, more generally, in interest in AI. This is often referred to as the first AI winter (Figure 3).

Even though research in AI continued, it was not before the early 1980s that real-world applications were once again considered possible. This wave was that of expert systems [START_REF] Buchanan | Rulebased expert systems: the MYCIN experiments of the Stanford Heuristic Programming Project[END_REF], which are a type of symbolic AI approach but with domain-specific knowledge. Expert systems led to commercial applications and to a real boom in the industry. A specific programming language, called LISP [START_REF] Mccarthy | Recursive functions of symbolic expressions and their computation by machine, part I[END_REF], became dominant for the implementation of expert systems. Companies started building LISP machines, which were dedicated computers with specific architecture tailored to execute LISP efficiently. One cannot help thinking of a parallel with current hardware dedicated to deep learning. However, once again, expectations were not met. Expert systems were very large and complex Machine Learning for Brain Disorders, Chapter 1 sets of rules. They were difficult to maintain and update. They also had poor performances in perception tasks such as image and speech recognition. Academic and industrial funding subsequently dropped. This was the second AI winter.

At this stage, it is probably useful to come back to the two main families of AI: symbolic and connexionist (Figure 4). They had important links at the beginning (see for example the work of McCulloch and Pitt aiming to perform logical operations using artificial neurons) but they subsequently developed separately. In short, these two families can be described as follows. The first operates on symbols through sets of logical rules. It has strong ties to the domain of predicate logic. Connexionism aims at training networks of artificial neurons. This is done through the examination of training examples. More generally, it is acceptable to put most machine learning methods within the connexionist family, even though they don't rely on artificial neuron models, because their underlying principle is also to exploit statistical similarities in the training data. For a more detailed perspective on the two families of AI, the reader can refer to the very interesting (and even entertaining!) paper of Cardon et al [START_REF] Cardon | Neurons spike back[END_REF].

Let us come back to our historical timeline. The 1980s saw a rebirth of connexionism and, more generally, the start of the rise of machine learning. Interestingly, it is at that time that two of the main conferences on machine learning started: the International Conference on Machine Learning (ICML) in 1980 and Neural Information Processing Systems (NeurIPS, formerly NIPS) in 1987. It had been known for a long time that neural networks with multiple layers (as opposed to the original perceptron with a single layer) (Figure 5) could solve non-linearly separable problems but their training remained difficult. The back-propagation al-

Artificial intelligence

Connexionism

-Neural networks -More generally: machine learning

Symbolic AI

Operates on symbols through logical rules gorithm for training multilayer neural networks was described by David Rumelhart, Geoffrey Hinton and Ronald Williams [START_REF] Rumelhart | Learning representations by backpropagating errors[END_REF] in 1986, as well as by Yann Le Cun in 1985 [START_REF] Cun | Une procédure d'apprentissage pour réseau à seuil assymétrique[END_REF], who also refined the procedure in his PhD thesis published in 1987. This idea had actually been explored since the 1960s but it was only in the 1980s that it was efficiently used for training multilayer neural networks. Finally, in 1989, Yann Le Cun proposed the convolutional neural network [START_REF] Lecun | Backpropagation applied to handwritten zip code recognition[END_REF], an architecture inspired by the organization of the visual cortex, whose principle is still at the core of state-of-the-art algorithms for many image processing and recognition tasks. Multilayer neural networks demonstrated their utility in several real-world applications such as digit recognition on checks and ZIP codes [START_REF] Matan | Reading handwritten digits: A zip code recognition system[END_REF]. Nevertheless, they would not become the dominant machine learning approach until the 2010s. Indeed, at the time, they required considerable computing power for training and there was often not enough training data.

During the 1980s and 1990s, machine learning methods continued to develop. Interestingly, connections between machine learning and statistics increased. We are not going to provide an overview of the history of statistics, but one should note that many statistical methods such as linear regression (Legendre, 1805 [17]), principal component analysis (Pearson, 1901 [18]), discriminant analysis [START_REF] Fisher | The use of multiple measurements in taxonomic problems[END_REF] [START_REF] Fisher | The use of multiple measurements in taxonomic problems[END_REF] or decision trees [START_REF] Loh | Fifty years of classification regression trees[END_REF] can actually be used to solve machine learning tasks such as automatic categorization of objects or prediction. In the 1980s, decision trees witnessed important developments (see for example the ID3 [START_REF] Quinlan | Induction of decision trees[END_REF] and CART [START_REF] Quinlan | Induction of decision trees[END_REF] algorithms). In the 1990s, there were important advances in Colliot

! ! ! " ! # & $ & " & ! & % ! ' " ! ' " "

Outputs Inputs Hidden

Figure 5: A multilayer perceptron model (here with only one hidden layer, but there can be many more).

the statistical theory of learning (in particular the works of Vladimir Vapnik [START_REF] Vapnik | The nature of statistical learning theory[END_REF]). A landmark algorithm developed at that time was the support-vector machine (SVM) [START_REF] Boser | A training algorithm for optimal margin classifiers[END_REF] which worked well with small training data sets and could handle non-linearities through the use of kernels.

The machine learning field continued to expand through the 2000s and 2010s, with new approaches but also more mature software packages such as scikit-learn [START_REF] Pedregosa | Scikit-learn: Machine learning in python[END_REF]. More generally, it is actually important to have in mind that what is currently called AI owes more to statistics (and other mathematical fields such as optimization in particular) than to modeling of brain circuitry and that even approaches that take inspiration from neurobiology can actually be viewed as complex statistical machineries. 2012 saw the revival of neural networks and the beginning of the era of deep learning. It was undoubtedly propelled by the considerable improvement obtained on the ImageNet recognition challenge which contains 14 million natural images belonging to 20,000 categories. The solution, proposed by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], was a convolutional neural network with a large number of layers, hence the term deep learning. The building blocks of this solution were already present in the 1980s but there was not enough computing power nor large training datasets for them to work properly. In the interval, things had changed. Computers had become exponentially more powerful and, in particular, the use of Graphical Processing Units (GPU) considerably sped up computations. The expansion of the Internet had provided massive amounts of data of various sorts such as texts and images. In the subsequent years, deep learning [START_REF] Lecun | Deep learning[END_REF] approaches became increasingly sophisticated. In parallel, efficient and mature software packages including TensorFlow [START_REF] Abadi | Ten-sorFlow: Large-scale machine learning on heterogeneous systems[END_REF], PyTorch [START_REF] Paszke | Pytorch: An imperative style, highperformance deep learning library[END_REF] or Keras [START_REF] Chollet | Keras[END_REF], whose development is supported by major companies such as Google and Facebook, enable deep learning to be used more easily by scientists and engineers.

Artificial intelligence in medicine as a research field is about 50 years old. In 1975, an expert system, called MYCIN, was proposed to identify bacteria causing various infectious diseases [START_REF] Shortliffe | Computer-based medical consultations: MYCIN[END_REF]. More generally, there was a growing interest in expert systems for medical applications. Medical image processing also quickly became a growing field. The first conference on Information Processing in Medical Imaging (IPMI) was held in 1977 (it existed under a different name since 1969). The first SPIE Medical Image Processing conference took place in 1986 and the Medical Image Computing and Computer-Assisted Intervention conference (MICCAI) started in 1998. Image perception tasks, such as segmentation or classification, soon became among the key topics of this field, even though the methods came in majority from traditional image processing and not from machine learning. In the 2010s, machine learning approaches became dominant for medical image processing and more generally in artificial intelligence in medicine.

To conclude this part, it is important to be clear about the different terms, in particular those of artificial intelligence, machine learning and deep learning (Figure 6). Machine learning is one approach to artificial intelligence and other radically different approaches exist. Deep learning is a specific type of machine learning approach. It has recently obtained impressive results on some types of data (in particular images and text) but this does not mean that it is the universal solution to all problems. As we will see in this book, there are tasks for which other types of approaches perform best.

Main machine learning concepts

As aforementioned, machine learning aims at making a computer capable of performing a task without explicitly being programmed for that task. More precisely, it means that one will not write a sequence of instruc-

Colliot

Artificial intelligence

Machine learning

Deep learning

Figure 6: Artificial intelligence, machine learning and deep learning are not synonymous. Deep learning is a type of machine learning which involves neural networks with a large number of hidden layers. Machine learning is one approach to artificial intelligence, but other approaches exist.

tions that will directly perform the considered task. Instead, one will write a program that allows the computer to learn how to perform the task by examining examples or experiences. The output of this learning process is a computer program itself that performs the desired task, but this program was not explicitly written. Instead, it has been learned automatically by the computer.

In 1997, Tom Mitchell gave a more precise definition of a well-posed machine learning problem [START_REF] Mitchell | Machine learning[END_REF]:

A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance at task T, as measured by P, improves with experience E. He then provides the example of a computer that learns to play checkers: task T is playing checkers, performance measure P is the proportion of games won and the training experience E is playing checker games against itself. Very often, the experience E will not be an actual action but the observation of a set of examples, for instance a set of images belonging to different categories such as photographs of cats and dogs, or medical images containing tumours or without lesions. Please refer to Box 1 for a summary.

Box 1: Definition of machine learning

Machine learning definition (Mitchell, 1997 [31]):

• "a computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance at task T, as measured by P, improves with experience E."

Example: learning to detect tumours from medical images

• Task T: detect tumours from medical image

• Performance measure P: proportion of tumours correctly identified

• Experience E: examining a dataset of medical images where the presence of tumours has been annotated examples for which the output that we are trying to learn is known.

Types of learning

-Example 1. The task is computer-aided diagnosis (a classification problem), the label can be the diagnosis of each patient, as defined by an expert physician.

-Example 2. The task is the prediction of the age of a person from a set of biological variables (for example a brain MRI). This is a regression problem. The label is the true age of a given person in the training set.

• Unsupervised learning. Learns from unlabelled examples.

-Example 1. Given a large set of newspapers articles, automatically cluster them into groups dealing with the same topic based only on the text of the article. The topics can for example be economics, politics, international affairs. The topics are not known a priori.

-Example 2. Given a set of patients with autism spectrum disorders, the aim is to discover cluster of patients that share the same characteristics. The clusters are not known a priori. Examples 1 and 2 will be referred to as clustering tasks.

-Example 3. Given a large set of medical characteristics (various biological measurements, clinical and cognitive tests, medical images), find a small set of variables that best explain the variability of the dataset. This is a dimensionality reduction problem.

• Reinforcement learning. Learns by iteratively performing actions to maximize some reward.

-Classical approach used for learning to play games (chess, go. . . ) or in the domain of robotics.

-Currently few applications in the domain of brain diseases. Colliot amples of common regression methods include simple or multiple linear regression, penalized regression, and random forest regression. Finally, there are many other tasks that can be framed as a supervised learning problem, including for example data synthesis, image segmentation and many others which will be described in other chapters of this book.

Unsupervised learning

In unsupervised learning, the examples are not labeled. The two most common tasks in unsupervised learning are clustering and dimensionality reduction (Figure 8). Clustering aims at discovering groups within the training set but these groups are not known a priori. The objective is to find groups such that members of the same group are similar while members of different groups are dissimilar. For example, one can aim to discover disease subtypes which are not known a priori. Some classical clustering methods are k-means or spectral clustering for instance. Dimensionality reduction aims at finding a space of variables (of lower dimension than the input space) that best explain the variability of the training data, given a larger set of input variables. This produces a new set of variables that, in general, are not among the input variables but are combinations of them. Examples of such methods include principal component analysis, Laplacian eigenmaps or variational autoencoders.

Reinforcement learning

In reinforcement learning, the machine will take a series of actions in order to maximize a reward. This can for example be the case of a machine learning to play chess, which will play games against itself in order to maximize the number of victories. These methods are widely used for learning to play games or in the domain of robotics. So far, they have had few applications to brain diseases and will not be covered in the rest of this book.

Discussion

Unsupervised learning is obviously attractive because it does not require labels. Indeed, acquiring labels for a training set is usually timeconsuming and expensive because the labels need to be assigned by a human. This is even more problematic in medicine because the labels must be provided by experts in the field. It is thus in principle attractive to adopt unsupervised strategies, even for tasks which could be framed as supervised learning problems. Nevertheless, up to now, the performances of supervised approaches are often vastly superior in many Colliot applications. However, in the past years, an alternative strategy called self-supervised learning, where the machine itself provides its own supervision, has emerged. This is a promising approach which has already led to impressive results in different fields such as natural language processing in particular [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF][START_REF] Radford | Improving language understanding by generative pre-training[END_REF][START_REF] Devlin | Bert: Pre-training of deep bidirectional transformers for language understanding[END_REF].

Clustering

Overview of the learning process

In this section, we aim at formalizing the main concepts underlying most supervised learning methods. Some of these concepts, with modifications, also extend to unsupervised cases.

The task that we will consider will be to provide an output, denoted as y, from an input given to the computer, denoted as x. At this moment, the nature of x does not matter. It can for example be any possible photograph as in the example presented in Figure 9. It could be also be a single number, a series of numbers, a text . . . For now, the nature of y can also be varied. Typically, in the case of regression, it can be a number. In the case of classification, it corresponds to a label (for instance the label "cat" in our example). For now, you do not need to bother about how these data (images, labels . . . ) are represented in a computer. For those without a background in computer science, this will be briefly covered in subsection 3.3.

Learning will aim at finding a function f that can transform x into y, that is such that y = f (x). For now, f can be of any type, just imagine it as an operation that can associate a given x with a given y. In chapter 3, the functions f will be artificial neural networks. Learning aims at finding a function f which will provide the correct output for each given input. Let us call the loss function and denote ℓ a function that measures the error that is made by the function f . The loss function takes two arguments: the true output y and the predicted output f (x). The lower the loss function value, the closer the predicted output is to the true output. An example of loss function is the classical least squares loss ℓ(y, f (x)) = (yf (x)) 2 but many others exist. Ideally, the best function f would be the one that produces the minimal error for any possible input x and associated output y, not only those which we have at our disposal, but any other possible new data. Of course, we do not have any possible data at our disposal. Thus, we are going to use a set of data called the training set. In supervised learning, this set is labelled, i.e. for each example in this set, we know the value of both x and y. Let us denote as (x (1) , y (1) ), . . ., (x (n) , y (n) ) the n examples of the training set which are n pairs of inputs and outputs. We are now going to search for the function f that makes the minimum error over the n samples of The aim is to be able to recognize the content of a photograph (the input x) which amounts to assigning it a label (the output y). In other words, we would like to have a function f that transforms x into y. In order to find the function f , we will make use of a training set (x (1) , y (1) ), . . ., (x (n) , y (n) ) (which in our case is a set of photographs which have been labelled). All images come from https://commons.wikimedia.org/ and have no usage restriction. Colliot the training set. In other words, we are looking for the function which minimizes the average error over the training set. Let us call this average error the cost function:

J(f ) = 1 n n i=1 ℓ y (i) , f (x (i) )
Learning will then aim at finding the function f which minimizes the cost function:

f = arg min f ∈F 1 n n i=1 ℓ y (i) , f (x (i) )
In the above equation, arg min indicates that we are interested in the function f that minimizes the cost J(f ) and not in the value of the cost itself. F is the space that contains all admissible functions. F can for instance be the set of linear functions or the set of neural networks with a given architecture.

The procedure that will aim at finding f that minimizes the cost is called an optimization procedure. Sometimes, the minimum can be find analytically (i.e. by directly solving an equation for f ) but this will rarely be the case. In other cases, one will resort to an iterative procedure (i.e. an algorithm): the function f is iteratively modified until we find the function which minimizes the cost. There are cases where we will have an algorithm that is guaranteed to find the global minimum and others where one will only find a local minimum.

Minimizing the errors on the training set does not guarantee that the trained computer will perform well on new examples which were not part of the training set. A first reason may be that the training set is too different from the general population (for instance, we have trained a model on a dataset of young males and we would like to apply it to patients of any gender and age). Another reason is that, even if the training set characteristics follow those of the general population, the learned function f may be too specific to the training set. In other words, it has learned the training set "by heart" but has not discovered a more general rule that would work for other examples. This phenomenon is called overfitting and often arises when the dimensionality of the data is too high (there are many variables to represent an input), when the training set is too small or when the function f is too flexible. A way to prevent overfitting will be to modify the cost function so that it not only represents the average error across training samples but also constrains the function f to have some specific properties.

Inputs and features

In the previous section, we made no assumption on the nature of the input x. It could be an image, a number, a text, etc.

The simplest form of input that one can consider is when x is a single number. Examples include age, clinical scores . . . However, for most problems, characterization of a patient cannot be done with a single number but requires a large set of measurements (Table 1). In such a case, the input can be a series of numbers x 1 , . . . , x p which can be arranged into a vector: However, there are cases where the input is not a vector of numbers. This is the case when the input is a medical image, a text or a DNA sequence for instance. Of course, in a computer, everything is stored as numbers. An image is an array of values representing the gray-scale intensity of each pixel (Figure 10). A text is a sequence of characters which are each coded as a number. However, unlike in the example presented in Table 1, these numbers are not meaningful by themselves. For this reason, a common approach is to extract features, which will be series of numbers that meaningfully represent the input. For example, if the input is a brain magnetic resonance image (MRI), relevant features could be the volumes of different anatomical regions of the brain (this specific process is done using a technique called image segmentation which is covered in another chapter). This would result in a series of numbers that would form an input vector. The development of efficient methods for extracting meaningful features from raw data is important in machine learning. Such an approach is often called feature engineering. Deep learning methods allow for avoiding extracting features by providing an end-to-end approach from the raw data to the output. In some areas, this has made feature engineering less important but there are still ap-Colliot plications where so-called "handcrafted features" are competitive with deep learning methods. 0 0 0 0 0 0 1 2 4 4 6 4 5 3 5 4 3 5 5 5 4 5 4 3 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 -1 -2 -1 -1 -1 -1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 -1 -2 0 7 16 20 24 29 30 32 33 25 14 3 -1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 0 14 33 50 49 44 42 38 38 35 34 33 37 45 47 27 1 0 1 1 1 1 1 1 1 1 1 0 1

x =    x 1 . . . x p   

Illustration in a simple case

We will now illustrate step-by-step the above concepts in a very simple case: univariate linear regression. Univariate means that the input is a single number as in the example shown in Figure 7. Linear means that the model f will be a simple line. The input is a number x and the output is a number y. The loss will be the least squares loss: ℓ(y, f (x)) = (y-f (x)) 2 . The model f will be a linear function of x i.e. f (x) = w 1 x + w 0 and corresponds to the equation of a line, w 1 being the slope of the line and w 0 the intercept. To further simplify things, we will consider the case where there is no intercept, i.e. the line passes through the origin. Different values of w 1 correspond to different lines (and thus to different functions f ) and to different values of the cost function J(f ), which can be in our case rewritten J(w 1 ) since f only depends on the parameter w 1 (Figure 11). The best model is the one for which J(w 1 ) is minimal.

How can we find w 1 such that J(w 1 ) is minimal? We are going to use the derivative of J: dJ dw 1 . A minimum of J(w1) is necessarily such that dJ dw 1 = 0 (in our specific case, the inverse is also true). In our case, it is

Machine Learning for Brain Disorders, Chapter 1

0 1 X X ! " # ! $(# ! ) 1 2 3 1 2 3
' " = 0.3" X ' " = 0.5"

' " = " possible to directly solve dJ dw 1 = 0. This will nevertheless not be the case in general. Very often, it will not be possible to solve this analytically. We will thus resort to an iterative algorithm. One classical iterative method is gradient descent. In the general case, f depends not on only one parameter w 1 but on a set of parameters (w 1 , . . . , w p ) which can be assembled into a vector w. Thus, instead of working with the derivative dJ dw 1 , we will work with the gradient ∇ w J. The gradient is a vector that indicates the direction that one should follow to climb along J. We will thus follow the opposite of the gradient, hence the name gradient descent. This process is illustrated in Figure 12, together with the corresponding algorithm.

Conclusion

This chapter provided an introduction to machine learning (ML) for a non-technical readership (e.g. physicians, neuroscientists . . . ). ML is an approach to artificial intelligence and thus needs to be put into this larger context. We introduced the main concepts underlying ML that will be further expanded in Chapters 2 to 6. The reader can find a summary of these main concepts, as well as notations, in Box 3. where the model f is defined using only one parameter w 1 . The w 1 is iteratively updated by following the opposite of the gradient method is gradient descent. In the general case, f depends not one parameter w 1 but on a set of parameters (w 1 , . . . w p ) which assembled into a vector w. Thus, instead of working with the de dJ dw 1 , we will work with the gradient r w J. The gradient is a vec indicates the direction that one should follow to climb along J. thus follow the opposite of the gradient, hence the name gradient This process is illustrated in Figure 12. The gradient descent al proceeds as follows:

repeat w 1 w 1 ⌘ dJ dw 1 until convergence;
where ⌘ is the learning rate, i.e. the speed at which w 1 will dated.

Conclusion

This chapter provided an introduction to machine learning (M non-technical readership (e.g. physicians, neuroscientists . . . ). M approach to artificial intelligence and thus needs to be put into th context. We introduced the main concepts underlying ML that further expanded in Chapters 2 to 6. The reader can find a sum these main concepts, as well as notations, in Box 3.

Machine Learning for Brain Disorders, Chapter 1 Figure 12: Upper panel: Illustration of the concept of gradient descent in a simple case where the model f is defined using only one parameter w 1 . The value of w 1 is iteratively updated by following the opposite of the gradient. Lower panel: gradient descent algorithm where η is the learning rate, i.e. the speed at which w 1 will be updated. • The training samples (x (1) , y (1) ), . . ., (x (n) , y (n) )

• The model: transforms the input into the output f such that y = f (x)

• The set of possible models F

• The loss: measures the error between the predicted and the true output, for a given sample ℓ(y, f (x))

• The cost function: measures the average error across the training samples J(f ) = 1 n n i=1 ℓ y (i) , f (x (i) ) • Learning process: finding the model which minimizes the cost function f = arg min f ∈F J(f )

Figure 1 :

 1 Figure 1: A brief timeline of AI with some of the landmark advances.

Figure 2 :

 2 Figure 2: (a) Biological neuron. The synapses form the input of the neuron. Their signals are combined and if the result exceeds a given threshold, the neuron is activated and produces an output signal which is sent through the axon. (b) The perceptron: an artificial neuron which is inspired by biology. It is composed of the set of inputs (which correspond to the information entering the synapses) x i , which are linearly combined with weights w i and then go through a non-linear function g to produce an output y. Image in panel (a) is courtesy of Thibault Rolland.

Figure 3 :

 3 Figure 3: Summers and winters of AI.

Figure 4 :

 4 Figure4: Two families of AI. The symbolic approach operates on symbols through logical rules. The connexionist family actually not only encompasses artificial neural networks but more generally machine learning approaches.

  One usually considers three main types of learning: supervised learning, unsupervised learning and reinforcement learning (Box 2). In both supervised and unsupervised learning, the experience E is actually the inspection of a set of examples, which will we refer to as training examples or training set.3.1.1. Supervised learningIn supervised learning, the machine learns to perform a task by examining a set of examples for which the output is known (i.e. the examples have been labelled). The two most common tasks in supervised learning are classification and regression (Figure7). Classification aims at assigning a category for each sample. The examples can for instance be different patients and the categories are the different possible diagnoses. The outputs are thus discrete. Examples of common classification algorithms include logistic regression (in spite of its name, it is a classification method), linear discriminant analysis, support vector machines, random forest classifiers and deep learning models for classification. In regression, the output is a continuous number. This can be for example the future clinical score of a patient that we are trying to predict. Ex-Colliot Box 2: Supervised, unsupervised and reinforcement learning • Supervised learning. Learns from labelled examples, i.e.

Figure 7 :

 7 Figure 7: Two of the main supervised learning tasks: classification and regression. The upper panel presents a classification task which aims at linearly separating the orange and the blue class. Each sample is described by two variables. The lower panel presents a linear regression task in which the aim is to predict the body mass index from the age of a person. Figure courtesy of Johann Faouzi.

Figure 8 :

 8 Figure 8: Clustering task. The algorithms automatically identifies three groups (corresponding to the red circles) from unlabelled examples (the blue dots). The groups are not known a priori. Figure courtesy of Johann Faouzi.

Figure 9 :

 9 Figure9: Main concepts underlying supervised learning, here in the case of classification. The aim is to be able to recognize the content of a photograph (the input x) which amounts to assigning it a label (the output y). In other words, we would like to have a function f that transforms x into y. In order to find the function f , we will make use of a training set (x(1) , y(1) ), . . ., (x (n) , y (n) ) (which in our case is a set of photographs which have been labelled). All images come from https://commons.wikimedia.org/ and have no usage restriction.

Figure 10 :

 10 Figure10: In a computer, an image is represented as an array of numbers. Each number corresponds to the gray-level of a given pixel. Here the example is a slice of an anatomical MRI which has been severely undersampled so that the different pixels are clearly visible. Note that an anatomical MRI is actually a 3D image and would thus be represented by a 3D array rather than by a 2D array. Image courtesy of Ninon Burgos.

Figure 11 :

 11 Figure 11: We illustrate the concepts of supervised learning on a very simple case: univariate linear regression with no intercept. Training samples correspond to the black circles. The different models f (x) = w 1 x correspond to the different lines. Each model (and thus each value of the parameter w 1 ) corresponds to a value of the cost J(w 1 ). The best model (the blue line) is the one which minimizes J(w 1 ), here it corresponds to the line with a slope w 1 = 1.

Figure 12 :

 12 Figure 12: Illustration of the concept of gradient descent in a sim where the model f is defined using only one parameter w 1 . The w 1 is iteratively updated by following the opposite of the gradient

Box 3 :

 3 Summary of main concepts • The x • The output y

Table 1 :

 1 Example where the input is a series of number. Here each patient is characterized by several variables

		Age (years) Height (cm) Weight (kg)
	Patient 1	52.5	172	52
	Patient 2	75.1	182	78
	Patient 3	32.7	161	47
	Patient 4	45	190	92

O. Colliot (Ed.), Machine Learning for Brain Disorders, Springer, 2023

Machine Learning for Brain Disorders, Chapter 1

Acknowledgments

The author would like to thank Faouzi for his insightful comments. This work was supported by the French government under management of Agence Nationale de la Recherche as part of the "Investissements d'avenir" program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute) and reference ANR-10-IAIHU-06 (Institut Hospitalo-Universitaire ICM).


Sergio Magnani
email: semagnani@gmail.com

Modulo per proposta di presentazioni Form for Paper Proposal Nome(i) e affiliazioni dei proponenti

Panel nel quale si intende presentare Panel in which paper is proposed Panel 23 On the notion of crisis: what the Saharan-Sahelian case can teach us Abstract (max.300 parole/words)

In the last forty years Sahel has been depicted as a region in permanent 'crisis', environmental in the following of the 1970-80's droughts and security-driven with reference to the widespread insurgencies of the last decade. Within these frameworks, the notion of 'crisis' has been mobilized in a poorly analytical but highly performative way. Along with all-encompassing explanations like 'farmer-herder' conflict for scarce resources as well as religious radicalization driven by international jihadism, it has been used to justify a revival of problematic approaches and solutions. These dominant narratives depoliticise Sahelian societies and the historical and contemporary effects of development intervention on the society-environment relations.

Building on a systemic approach (Morin), this communication proposes to consider the current situation in the light of a 'crisis' of development, here intended as a specific form of public action 'under aid-regime' (Lavigne-Delville) characterised by high levels of extraversion and complexity. 'Crisis' takes here the meaning of a turningpoint where political and social critiques leading to multiple forms of active contestation become major trends that affect the whole system and produce significant changes. Drawing from a scientific literature review and an empirical research on vernacular perceptions of 'security crisis' in Burkina Faso (2019-20), the communication shall highlight through several examples how insurgencies embody contestation of agricultural and environmental development and of its effects on peasant and pastoral moral economies (i.e. long-term ill-adaptation of conceptual models and policy, extraversion and local power relationships…). The case of Burkina Faso is illustrative of the scarce visibility in public debates of heterodox analysis and political solutions based on social equality, entitlements and rebalancing of power relationships.

In conclusion, different potentially 'regressive' or 'progressive' scenarios of change at the interplay of international, national and local scales will be discussed.

Attenzione, la proposta di presentazione deve essere spedita alla email degli organizzatori del panel entro la data di scadenza del 3 marzo 2022.

Introduction

In this communication I want to question the central role that the notion of crisis plays in the mainstream narratives to explain the insurgencies and the political conflicts that have taken place in several Sahelian countries in the last decade.

I will build upon the work of Janet Roitman to show that common-sense definition of crisis as exceptional, turning-point events are ill-adapted to understand the current situation. In fact, "continuity" seems to be the mark of both development diagnosis and solutions, and of vernacular perceptions of the causes of conflict and of the insurgencies.

I will conclude by advancing the hypothesis that what could be possibly understood in terms of 'crisis' in the Sahelian rural areas are a specific form of public action and a set of power relationships under open and widespread contestation.

Even if this hypothesis needs to be verified in the medium term, it opens up new possibilities to renew development narratives and envision policy reforms at different scales, as well as to approach the notion of crisis in a more open way, as an object knowledge and an account for the emergent.

The Sahel, a space of "crisis"?

In the last 50 years, the Sahel has been described as a space of crisis: (i) "Environmental crisis" during the heavy droughts of the 70's and the 80's that became the first environmental problem to be managed by a global initiative within the network of the United Nations. (ii) As a space of "security" crisis since the last decade with regard the insurgencies which have progressively spread from the Sahel to the Gulf of Guinea.

In this context, the notion of crisis has been mobilized in a very performative but poorly analytical way. It has become an all-encompassing notion that undermines the understanding of field dynamics and of the social and political dimensions of insurgencies and conflicts.

A theoretical proposition

I took inspiration from the critical work of Janet Roitman on the notion of crisis, in particular from the paper Figures of the subject in times of crisis (1995)1 and the book Anti-crisis (2013)2 .

In the first, the author describes the subjectivation of crisis in Cameroon in the context of the structural adjustment programs of the 80's, 90's. The author shows how economic crisis has been experienced as an historical condition in the long term. Therefore, in this case, how what is supposed to be an exceptional event becomes a long lasting socially and culturally constructed condition (continuity).

In the second, through the analysis of the subprime crisis of 2008, the author proposes to consider the notion of crisis as a form of judgement and a diagnosis. She invites to ask: what legitimizes the qualification of a given situation as crisis? What are the implications of this qualification? What questions can be asked under such a diagnosis, and what others are overlooked?

By asking these questions through the Sahelian context allow us to envision the notion of "crisis" from different perspectives:

Crisis narratives as narratives of power

The effects of the heavy droughts of the 70's, 80's were interpreted as a trend of linear progressive aridification, and attributed to the practices of local societies. What was presumed to be environmental degradation was poorly defined and measured, mainly through ill-adapted concepts like capacity of charge and linear trends of evolution of vegetation.

Desertification theory misunderstood both the ecology of drylands, its strong structural variability, and local knowledge and socio-political institutions allowing local systems to work with rather than against variability. Nevertheless, desertification became a powerful framework for development interventions, driving to the implementation of problematic harmful solutions that have generated fragmentation of space and the uproot of local institutions: largescale irrigation, ranching, enclosures for environmental protection.

Present narratives of "security crisis" build on this body of knowledge. They associate environmental degradation, poverty with international jihad to explain dynamics of conflicts often in terms of "farmer-herder" conflict. These narratives ignore a large literature both from ecological and social sciences that shows, and produce a renewal of development intervention in continuity with the past (Great green wall…), while also promoting counterproductive security policies (forced closure of livestock markets, declaration of forests as no-man lands and military zones).

The ideas behind this revival are: (i) that there have been little development interventions in the Sahel, so poverty has spread; (ii) the present situation is the outcome of lack of governance.

But, to recall the analysis of Roitman on the crisis of subprime, what if the current situation is not the produce of lack of intervention but instead the outcome of the execution of development models in practice? What if, this is not the result of a lack of governance but rather of a specific form of governance?

In any case, if we look at development diagnosis and solutions we can't find traces of rupture or deep changes.

Continuity also emerges from vernacular perceptions of the causes of insurgencies and conflicts.

"Durable crisis"? Injustice and inequalities under development regimes

When I did fieldwork in Burkina Faso, in 2019 -2020, working on Pastoralist youth mobility to Cities 3 in a context of widespread violence and displacement, several actors (public officers, members of professional organizations, associations for civic rights…) put forward different explanations.

These insisted on two main long-time trends: (i) firstly, a despotic, predatory attitudes of public servants towards the rural poor and pastoralists in particular (illegal fines, taxes, unequal arbitration of local contentious); (ii) secondly, a trend of grab of land and resources driven by both international projects and national urban and rural elites, including religious and customary authorities.

This trend, occurring in several sectors (environmental conservation, agri-business, mining) were taught as problematic because it generates exclusion and ruptures in local moral economies.

These alternative views pointed at a set of power relationships within a specific framework of public action that with Lavigne-Delville (2017 4 ) we can define as under aid regime.

This definition refers to long and fragmented chains of public action connecting a wide range of actors on international, national and local scales. The main characteristic of this are: (i) the central role of diagnosis and development models elaborated by the international expertise for intervention in strategic sectors (land, agricultural and environmental policy) and then circulating across scales and contexts;

(ii) extraversion, the capacity to manipulate external resources to comfort specific sets of interests; (iii) a precarious and discretionary delivery of public services a low level of accountability to the citizens.

Recent research confirms that this set of connections and power relationships and the forms of exclusion it produces, perceived as unjust, are the object of open contestation and at the core of dynamics of insurgency in the Sahel.

Can we describe this situation in terms of crisis in the sense of rupture or radical change? In other terms, is this a moment bringing about durable changes in the forms of authority exerted over Sahelian rural areas by the State, international development and local and national elites? And in this case, how politics and policies are going to be reorganized?

The outcomes of these processes remain uncertain, but under this hypothesis the notion of 'crisis' is an entry point to account for the emergent and not as a decisive judgement.

If we take seriously into account this perspective, we can envision new levers of actions and opportunities for reform at different scales: (i) international -recognize scientific knowledge, change narratives and development models (deep reform of development cooperation, as well as trade and agricultural policies -i.e. Economic Partnership Agreements UE-ACP); (ii) national -question the nature of the presence of the State in rural areas, social, land, agricultural, environmental political orientations reversing the current trends of privatization/concentration of land and fragmentation of the space and the exclusion this creates); (iii) local -recognize the political dimensions underlying local conflicts, take power relations and changing balances into account, arbitrate local agreements with a clear and coherent objective of preserving political and moral institutions for cooperation, sharing and livelihood upholding for the most.

Mbembe, A., & Roitman, J. (1995). Figures of the Subject in Times of Crisis. Public culture, 7(2), 323-352.

Roitman, J. (2013). Anti-crisis. Duke University Press.