Mohamed Ali

Ben Halima Bassem

Ben Halima
email: benhalima@gate.cnrs.fr

The determinants for labour contract length A French micro-econometric study

Keywords: contract length, duration model, selection bias, unobservable heterogeneity Classification JEL : J41, C41

Two types of analyses are conducted to explain the determinants of labour contracts length. The first analysis emphasizes on the contracting costs and the level of uncertainty. The second analysis focuses on the incentive and selection effect of the contract length. This paper test the determinants for contract duration by means of econometric duration models. The estimates are carried out from French data (TDE). An econometric treatment of the endogeneity of the labour contract status and unobservable heterogeneity is carried out. Our results show that wages positively affect employment duration. This confirms the positive effect of contracting costs reported.

Introduction:

The recent period is characterized by an evolution of the working relationship in the industrialized countries. Indeed, many studies highlight an increase in the proportion of shortterm contracts. There is a growth in these temporary forms of employment compared to longer contracts in France as well as in the other European countries.

The literature about contract duration can be classified in two distinct categories. A first type of analysis [START_REF] Canzoneri | Labor Contracts and Monetary Policy[END_REF][START_REF] Dye | Optimal Length of Labor Contracts[END_REF]Danziger, 1988) considers the duration of contracts from an external point of view. By external we mean that the temporary dimension of the employment relationship between an employer and one or more workers results from a search for a structure which can efficiently adapt to uncertainty affecting the external environment of the firm represented by real and monetary shocks. A second type of analysis [START_REF] Cantor | Firm-Specific Training and Contract Length[END_REF][START_REF] Jovanic | Job Matching and the Theory of Turnover[END_REF][START_REF] Lazear | Why is There Mandatory Retirement?[END_REF][START_REF] Loh | Employment Probation as a Sorting Mechanism[END_REF] apprehends the duration of employment according to the internal environment of the firm. It is the search for performance in personnel management, selection of skilled workers, and control of the input of work which generates the duration of the relation between the employer and the employee.

To do so, firms have to incite, control and organize these human resources by means of contract duration.

The early theoretical contributions emphasize that uncertainty and volatility are negatively related to contract length, whereas contracting costs positively affect duration. [START_REF] Gray | On Indexation and contratct length[END_REF] argues that contract length should be positively related to transactions costs and inversely related to uncertainty, regardless of whether the uncertainty pertains to real or nominal shocks. These implications arise from two basic ingredients: a transaction-cost argument and an efficient-production argument. The former emphasizes that longer contracts lower the losses due to transaction costs. The latter stresses that shorter contracts reduce the expected losses due to inefficient production and employment. This is true because the expected losses increase with the deviation of the actual real wage from the real wage that would equate the demand and supply of labour, and such a deviation is greater for more distant periods as uncertainty rises over time. [START_REF] Dye | Optimal Length of Labor Contracts[END_REF] builds a model which tries to overcome some of the limitations of Gray's approach, finding the same theoretical implications about uncertainty and contracting costs.

More recent models, however, stress that uncertainty and volatility may have a positive effect on contract length under some circumstances. Danziger (1988) develops an implicit contract model where workers are risk averse and firms are risk neutral. Within this framework, contracts allow for efficient-risk-sharing between parties and provide workers with a means of insuring against income fluctuations due to aggregate productivity shocks. As a consequence, greater real uncertainty causes workers to seek increased insurance through longer contracts.

In the following analysis, we will limit ourselves to an internal analysis about personnel management: the role short-terms contracts can play in the policy of incentive and control of employees. Studies in labour microeconomics based on game theory implicitly point out this principle again since they stress the importance of the temporary framework on the behaviours adopted by the agents and the results of game. In the same way, [START_REF] Lazear | Why is There Mandatory Retirement?[END_REF] like [START_REF] Cantor | Work Effort and Contract Length[END_REF][START_REF] Cantor | Firm-Specific Training and Contract Length[END_REF] proposed a dynamic approach of personnel management. [START_REF] Cantor | Work Effort and Contract Length[END_REF][START_REF] Cantor | Firm-Specific Training and Contract Length[END_REF] highlights a certain number of determinants of the optimal contract duration: this tends to decrease when the present preferential rate increases, or if the cost in term of utility associated with the same effort is higher. On the other hand this duration lengthens when the share of the quasi rent allocated to the employee increases.

In the next part, we will study shorter contracts as a probationary stage, in a context where optimal matching is not immediate and where dismissal costs dissuade firms to break contract relations. We will also point out how temporary contracts can be stepping stones to permanent employment. Recent studies dispute the common view that fixed-term contracts actually offer firms increased flexibility due to restrictions that typically apply to the rolling over of these contracts [START_REF] Hunt | Firing Costs, Employment Fluctuations and Average Employment: An Examination of Germany[END_REF]. However, firms have a number of reasons to use fixedterm contracts or temporary contracts. First, temporary workers may be preferred because they are less costly to employ. Second, fixed-term contracts, like other temporary contractual types, are preferred alternatives when temporary or temporarily vacant positions need to be filled. Third, in the case where there is uncertainty about the value of the match. The theory of the matching suggested by Jovanovic (1979), constitutes the model of reference integrating this dimension of the labour market. According to these authors, it is necessary to install a mechanism making it possible to produce an optimal pairing in order to reach an efficient production. Firms view the initial fixed-term contracts as a probationary stage. Depending on the job performance and labour demand, workers will move into permanent employment within the firm. As pointed out by [START_REF] Loh | Employment Probation as a Sorting Mechanism[END_REF]), Rosen (1994) and [START_REF] Lazear | Hiring Risky Workers[END_REF] probationary periods may induce self-selection of those workers with higher ability because they have a higher probability to obtain permanent contracts. Temporary contracts with lower wages are therefore a sorting instrument for firms. Low wages during the temporary contract period will be compensated for by higher future wages at the same employer [START_REF] Lazear | Why is There Mandatory Retirement?[END_REF].

This paper use the French data to investigate the external and internal determinants of the contract length evoked in the literature analyses. In the next section we highlight the econometric problems encountered to test the micro-economic determinants of the duration of the contracts. In the third section, data used for this study is examined. Estimation results are reported in the forth section. Finally, a synthesis of the main results is given as a conclusion.

The econometric model

The econometric evaluation of the determinants of the labour contract duration encounters a basic problem, ie the endogeneity of the labour contract status. Indeed, the employment duration on the labour market varies according to the contract status. Since the selection into longer or shorter contracts is not random, it is important to account for the selection mechanism in order to estimate the determinants of contract duration in an unbiased way and this was demonstrated through some empirical studies which investigate the endogeneity of the contractual status on the employment duration (Booth and Al, 2002b).

Moreover, [START_REF] Hagen | Do fixed term contracts increase the long-term employment opportunities of the unemployed?[END_REF] stresses that it is necessary to take the mechanism of selection into account to estimate unbiased effect of fixed-term contracts (FTC) on wages.

According to the econometric model, the duration of survival in employment has to be estimated with the various labour contract statuses. In the sample, the distribution of the individuals between the different classes of employment contracts is not random but raises an endogenous selection mechanism. We propose a model representing three types of labour contract market: Indefinite-Term Contract (ITC), Fixed-Term Contract (FTC), Temporary Contract (TC).

The issue of selecting individuals is made clearer if the individuals' specific characteristics determine the choice of the contract. We can suppose that some of these determinants also have an influence on the duration of survival in employment. The problem which we encounter is to isolate the real effect of the labour contract status. It is therefore necessary to determine the elements which influence the duration of the employment contract and we will adopt the method suggested by [START_REF] Heckman | Alternative Methods for Evaluating the Impact of Interventions : an Overview[END_REF] for that purpose. The advantage of this method is that it offers a very vast choice of duration models. However, if we adopted the Heckman's method (1979)1 , we would had to restrict ourselves to normal distribution.

Our approach initially consists in instrumenting the probability whether the individual has an indefinite-term contract (ITC) or a fixed-term contract (FTC), or a temporary contract (TC) by a multinomial logit model2 . The predicted probabilities are then integrated for final estimation in the parametric duration model in order to control for the endogeneity of the labour contract status. The econometric model is introduced in the following way :

First step: selection model               (TC) contract
* j ij ij ij P N i TC FTC ITC j Z P   Second step: duration model ) 2 ( 3 1 ' i ij j j i i P X DE         1 ( '
We estimate i DE , the employment duration, according to the individual characteristics i X and the estimated probabilities for the labour contract status. The parametric estimation of the duration model under this specification makes it possible to obtain unbiased estimators.

Data

We

Estimation results:

Multinomial logit estimation of labour contract status:

In this section, the determinants of the labour contract status (ITC, FTC, TC) are analysed by the estimation of the logit multinomial model (see table 2). This corresponds to the estimation of the sample selection of our model.

The fixed-term contract (FTC) concerns especially workers aged 16-34, relative to the base of individuals over 50 years old. Since the majority of young people have no professional experience on the labour market, they accept even precarious working conditions. This result is confirmed by Booth, Francesconi and Frank (2002a) on English data. However, it is noticed that workers aged 34-50 are granted indefinite-term contracts (ITC). [START_REF] Lazear | Male-female wage differentials in job ladders[END_REF] and Booth and al. (2002a) show that women more often hold temporary contracts. This result confirms that being a man has a positive and significant probability of getting an ITC. The chances of having an established position under indefinite contract duration are higher for Europeans than for non-European people.

The results show that workers with low human capital (primary education, general education and techniques) hold more temporary contracts than the workers with university degree. People who undertook university studies have a higher probability to obtain indefinite contract duration.

We use the occupation of the individuals' father as a proxy for permanent income.

Social origin variables indicate that children of executive or intermediary professions have a higher probability of holding indefinite-term contracts relative to children of workmen. On the other hand, children of farmers hold fixed-term contracts whereas temporary contracts meet more success with children of workmen.

Relative to resignation, individuals entering unemployment at the end of their FTC have a lower probability to obtain an ITC than dismissed individuals and those who left their last employment for others causes (such as end of the probationary period or end of military service). This result highlights the significance of the status when recruiting and selecting on the labour market. These results are consistent with Waldman's hypothesis (1990) Individuals with unemployment benefit are more likely to reach fixed-term contracts or temporary contracts than indefinite-term contracts. The local rate of unemployment tends to increase the probability of precarious employment (FTC-TC). Persistence of unemployment obviously makes the recourse to this type of employment much more frequent.

Analysis of the results of parametric estimation:

In this section, various parametric estimates were carried out while controlling the endogeneity of labour contract statuses (see table 3). In order to compare the various specifications (Weibull, Log normal, Log logistic), the Akaike information criterion is used. It is the model minimizing the function of the information criteria which is chosen, i.e. the Weibull distribution model. The hazard rate of leaving employment is thus monotonous. In order to reinforce the robustness of the econometric estimate of the Weibull specification, we estimated this duration model by introducing a correction for unobserved heterogeneity by the Gamma distribution [START_REF] Lancaster | The Economic Analysis of Transition Datas[END_REF]. In the next part, we will interpret the results relative to this distribution duration in table 3. The significant character of the associated coefficient of heterogeneity (theta) indicates the relevance of the use of the Weibull model with correction of the unobservable individual effects.

The respective coefficients of variables PITC, PFTC, PTC indicate the predicted probability value for an indefinite-term contract, fixed-term contract and temporary contract.

These variables control the endogeneity of the labour contract status over employment duration. The coefficients of PITC, PFTC, and PTC are very significant. Indeed, it is noticed that individuals under an ITC or a FTC have employment duration significantly longer than those under a temporary contract. Therefore, individuals under an ITC or a FTC improve their chances of stabilization in an employment position compared to people with other contractual statuses.

Concerning the age of individuals, compared to individuals in the first age class (16-25 years), individuals in the second and the third classes have significantly longer employment periods. The introduction of interacted variables (status of contracts × Female) enables us to conclude that the fact of being a woman under a ITC or a FTC reduces the employment duration, although being under these contracts has a significant and positive effect over the employment duration. That confirms the effect of discrimination according to gender evoked by Booth et al. (2002a) and [START_REF] Lazear | Male-female wage differentials in job ladders[END_REF].

The individual employment history seems to be very important. Individuals with the latest employment duration (from 2 to 5 years) and a long duration (from 5 years and +) have a significant and positive effect over the duration of new employment than people with a latest employment of shorter duration (from 0 to 2 years). This result is in conformity with those of the [START_REF] Spence | Job Market Signaling[END_REF]), Looh (1994), Rosen (1994) and [START_REF] Lazear | Hiring Risky Workers[END_REF] theory. The employment history may also capture characteristics like ability or motivation which cannot be observed. A further explanation suggests that employers hesitate to hire workers with an unstable labour market history under indefinite contract duration. Employment duration varies according the size of firms. Compared to firms employing over 200 employees, workers in firms with 49 to 200 employees have longer employment spells.

The introduction of the wage variable into the duration equation confronts us with a possible problem of endogeneity. For this reason, the difference in actual wages and predicted wages resulting from the estimate of Mincer equation of (1974) 3 has to be introduced. The individuals having a wage belonging to the third and fourth quartile have longer employment 3 The results of the estimate of the equation of wages are presented in table 4. This method consists in introducing the estimated residual (real wages -predicted wages) of the duration equation in order to detect the endogeneity of wages. The non-significativity of the coefficient allows us to deduce that there is no correlation between the residue of wages and employment duration.

spell than those of the first quartile. That confirms the positive effect of the contracting costs evoked by Gray and Canzoneri over the contract length.

Location in the CERGY, MANTES POSSY, and ROUBAIX labor-market employment areas has a negative and significant effect over employment duration compared to AIX and MARSEILLES. This can be due to the fact that these areas are characterized by more uncertainty on the job supply.

Conclusion:

The microeconomic analysis of contract lengths proposed in this article highlights several stylized facts. On the one hand, the analyses of [START_REF] Gray | On Indexation and contratct length[END_REF], [START_REF] Canzoneri | Labor Contracts and Monetary Policy[END_REF]Danziger (1988) argues that contract length should be positively related to transactions costs and inversely related to uncertainty, regardless of whether the uncertainty pertains to real or nominal shocks. The second analysis of contract length as an internal mechanism of personal management shows the influence of time-limited contracts on the incentive with the effort, and the selection of the skilled workers.

The contract length has to be estimated with the various labour contract statuses. In the sample, the distribution of the individuals between the different classes of employment contracts is not random but raises from an endogenous selection mechanism. The estimates were carried out starting from French data called 'Trajectoires des Demandeurs d'Emploi'

(TDE), conducted by the Research Direction of Employment Ministry (DARES). An econometric treatment of the endogeneity of the labour contract status (indefinite-term contract (ITC), fixed-term contract (FTC), temporary contract (TC)) by [START_REF] Heckman | Alternative Methods for Evaluating the Impact of Interventions : an Overview[END_REF] method and unobservable heterogeneity [START_REF] Lancaster | The Economic Analysis of Transition Datas[END_REF]) was carried out.

The results of the estimate of a duration model by introducing a correction of unobserved heterogeneity by the Gamma distribution conclude that there is an endogeneity of the labour contract status. Besides, employment duration is all the more large as wages are high. This confirms the positive effect of the contracting costs evoked by Gray and Canzoneri over the contract length. Moreover, the fact of having a latest labour contract of over two years of time can explain the increase in the duration of the recent contract, which is close to the theoretical results of the Rosen and Lazear models. (***) significant at 1%, (**) significant at de 5%, (*) significant at 10%.

Table 4 : Estimate of Mincer equation (MCO)

In order to determine the earning of education, [START_REF] Mincer | Schooling, Experience, and Earnings[END_REF] (***) significant at 1%, (**) significant at de 5%, (*) significant at 10%.

  exploit data from a French survey called Trajectoires des Demandeurs d'Emploi (TDE), conducted by the Research Direction of Employment Ministry (DARES). It deals with people who became unemployed in 1995 and were interviewed each year until 1998. This survey provides large information both on individual characteristics, type of labour contracts and employment duration. The sample includes 2289 individuals. All individuals have returned to employment after a period of unemployment. The average unemployment duration is about 10 months. Information on the length of new labour contracts after unemployment periods until the survey was completed concerns the types of contract and the size of firms of the new positions, the individual characteristics, the search strategies for the new labour contract, the causes for unemployment and the duration of the latest labour contract. Table1 reports the means of various variables in the sample.

  in an "upor-out contract" environment and Spence's signal theory(1973) on the labour market. If employers are uncertain about the unobservable characteristics of employees like ability or motivation, the individuals employment history may serve as a signal. References from previous employers and the causes of entry in unemployment may include information on the unobservable characteristics of workers. If the previous employment history involves bad signals and there are no alternative applicants available, the employer will hire the worker on a shorter contract.Examining the significance of the search strategy for employment enables us to classify a grid of research for each type of labour contract. Indeed, using market methods (reference: schools) increases the probability of getting an ITC or FTC. The probability of holding a fixed-term contract is greater when individuals use a local employment agency as well as the market method for search in new employment.

Table 1 : Descriptive statistic

 1 Notes: Data from a French survey called Trajectoires des Demandeurs d'Emploi (TDE), conducted by the Research Direction of Employment Ministry (DARES). It deals with people who became unemployed in 1995 and were interviewed each year until 1998.

	List of variable	Means	Observations
	Age
	CLASSE1 : [ 16 ; 25[	25.1	2289
	CLASSE2 : [ 25 ; 34[	38.0	2289
	CLASSE2 : [ 34 ; 50 [	33.2	2289
	CLASSE2 : [ 50 ; +[	3.7	2289
	Female	45.1	2289
	Nationality
	EUROP : european	94.3	2289
	NOEUR : not european	5.7	2289
	Skill level
	ETPRI : primary education	7.4	2289
	CYEG : general education.	20.5	2289
	ENTC : technical education	52.1	2289
	ENSUP : university degree	20.0	2289
	Socio professional category of father :
	AGRIP : agricultural	2.1	2289
	TRINP : independent worker	9.2	2289
	CPPLP : executive or professional	9.5	2289
	PIITP : intermediary profession	14.6	2289
	EMPYP : employee	10.6	2289
	OUVRP : workman	53.2	2289
	INACP : non participant	0.1	2289
	Reason of leaving previous occupation:
	LICEN : dismissal	33.2	2289
	DEMIS : resignation	13.4	2289
	PRECA : end of contract	49.0	2289
	OTHER	4.4	2289
	Search strategy of new employment :
	RESEAU : social and professional network	43.0	2289
	PROMAR : market, spontaneous appliances	31.6	2289
	INTPUB : ALE	12.3	2289
	ECOCON : schools ,examinations	13.1	2289
	INDEMCHO : unemployment benefits	58.0	2289
	Labour contract status of new employment:
	FTC : fixed-term contract	44.8	2289
	ITC : indefinite-term contract	32.3	2289
	TC : temporary contract	22.9	2289
	Size firms:
	T1 : [ 0 ; 49 [	60.8	2289
	T2 : [ 49 ; 99 [	10.7	2289
	T3 : [ 99 ; 200 [	7.5	2289
	T4 : [ 200 ; + [	21.0	2289

Table 2 : Estimation results of Multinomial Logit

 2

	ITC	FTC

Table 3 : Estimation results of the Weibull duration model with Gamma correction

 3 Data from a French survey called Trajectoires des Demandeurs d'Emploi (TDE).

	Variable		coefficient	T -Student
	One		1.571	8.181***
	PITC : probability of ITC	1.701	16.416***
	PFTC : probability of FTC	2.439	20.061***
	PTC : probability of TC	Base	Base
	CLASSE1 : [ 16 ; 25[	Base	Base
	CLASSE2 : [ 25 ; 34[	0.121	3.344***
	CLASSE3 : [ 34 ; 50 [	0.162	4.020***
	CLASSE4 : [ 50 ; + [	0.047	0.698
	MEN		Base	Base
	FEMME		-0.144	-5.202***
	PCDI * FEMME		-1.108	-3.611***
	PCDD * FEMME	-1.503	-3.955***
	EUROP : european	-0.043	-0.844
	NOEUR : not european	Base	Base
	ETPRI : primary education	Base	Base
	CYEG : general education.	0.216	4.080***
	ENTC : technical education	0.217	6.953***
	ENSUP : university degree	0.217	6.967***
	Duration of latest employment (years)
	DURCTE : [ 0 ; 2[	Base	Base
	DURMOY : [ 2 ; 5[	0.127	3.927***
	DURLONG : [ 5 ; +[	0.155	4.069***
	Size firms:
	T1 : [ 0 ; 49 [		0.085	2.562**
	T2 : [ 49 ; 99 [		0.129	2.718***
	T3 : [ 99 ; 200 [		0.137	2.552**
	T4 : [ 200 ; + [		Base	Base
	Monthly wage of new employment :
	First quartile	[591, 3900[	Base	Base
	Second quartile [3900, 7000[	0.036	0.985
	Third quartile [7000, 33600[	0.126	3.446***
	Fourth quartile [33600, 56000]	0.198	5.077***
	Job areas
	CERGY		-0.076	-1.911**
	MANTES		-0.157	-3.591***
	POSSY		-0.141	-3.370***
	ROUBAIX		-0.300	-6.631***
	LENS		-0.030	-0.688
	AIX / MARSEILLE	Base	Base
	ETANG		-0.01	-0.303
	Sigma		0.274	17.943***
	Thêta		1.653	9.619***
	Log Likelihood		-3453.545
	Number of observations	2289
	Notes :

  estimates a wage equation : AGE , age and squared age of individuals, S, number of years of education. A quadratic form is introduced to represent the concavity of earning education due to investment in human capital. X, a vector of individual and parental characteristics, c, the constant term which is interpreted as the basic wage without human capital, and u is a stochastic term of mean 0, representing the unobserved factors affecting wages. Data from a French survey called Trajectoires des Demandeurs d'Emploi (TDE).

	ln	  Y i		c		a	1	AGE		a	2	AGE	2		r 1	S		r 2	S	2		dX		u
	with i Y , the individual income,
	AGE,					2
	Thus,		  S Y i ln 		r 1		2	r 2	S	corresponds to the marginal earning rate of education in which 2 r is
	supposedly negative, showing decreasing marginal earnings,
		Variable																		coefficient	T -Student
		One																				-1.023	-6.251***
		AGE (AGE) 2																		0.238 -0.003	19.420*** -17.360***
		EDUCATION YEARS (EDUCATION YEARS) 2							0.507 -0.015	17.039*** -14.455***
		EUROP : european										Base	Base
		NOEUR : not european							-0.089	-1.827**
		Married																		0.025	1.122
		ETPRI : primary education							Base	Base
		CYEG : general education.							0.217	2.774***
		ENTC : technical education							-2.013	-0.257
		ENSUP : university degree							0.146	1.845**
		Socio professional category of father :
		AGRIP : agricultural									0.241	2.131***
		TRINP : independent worker							-0.106	-1.812**
		CPPLP : executive or professional				0.189	3.085***
		PIITP : intermediary profession					-0.002	-0.056
		EMPYP : employee										-0.058	-1.035
		OUVRP : workman										Base	Base
		INACP : non participant							-0.038	-1.286
		R 2 corrected (Adjusted)							58.62
		Log Likelihood													-2371.34
		Number of observations							2289
		Notes :

Heckman's approach (1979) suggests introducing the Mill's ratio in a duration equation. In order to correctly estimate this approach, the residuals in both equations (selection and duration models) have to follow normal distribution, which restricts the approach for the duration model.

In order to ease the interpretation of the estimated parameters, we choose the temporary contract as the reference.


Giuseppe Riccardo Leone

Andrea Carboni

Simone Nardi
email: simone.nardi@eikontech.it

Davide Moroni

Toward Pervasive Computer Vision for Intelligent Transport System

Keywords: Intelligent Transport System, pervasive computing, edge computing, privacy-by-design, multiple people tracking

The Smart Passenger Center (SPaCe) is a fully integrated platform that aims to overcome the complexity of centralized management of public transport infrastructure and vehicles. The SPaCe artificial intelligence engine predicts threats and critical events and proposes countermeasures by examining the daily flows of people and correlating different data and events, thanks to machine learning and big data analytics. All this massive data comes from a pervasive smart camera network that constantly monitors activities in stations, trains, buses and other places of interest. In this work, we present the idea of this computer vision distributed sub-system, the state of the art of the techniques involved and the advanced functionalities that this intelligent surveillance system offers to the upper layers. Everything is developed following the privacy-by-design paradigm; namely, no real image is recorded or transmitted, but all the elaborations take place on the edge nodes of the system.

I. INTRODUCTION

With public transport (trains, planes, buses, trams and ships) increasingly accessible to a more significant number of people, public transport operators are facing the dual challenge of meeting the growing demand for ever-increasing passenger flows by ensuring at the same time high levels of quality and security. To meet this challenge, infrastructures and vehicles must be safe and protected from different points of view. Today, areas of interest are fully monitored with closed-loop video systems. However, security operators must monitor and verify the video stream, around the clock, to identify anomalies and manually generate alarms.

Currently available systems, such as the one already present in the public transport vehicles, are used only for security purposes and only by law enforcement agencies. However, the potential of a closed-circuit control system for confined environments, such as a vehicle, is manifold if analyzed through modern automatic detection and classification systems. A modern video surveillance system should be designed to allow transport service operators to prevent, manage and post-analyze unexpected events. To the author best knowledge, there are two most important examples in this sector: the NAIA system [START_REF] Thalesgroup | Tha NAIA homepage[END_REF], and the MASTRIA system [START_REF] Alstom | The MASTRIA homepage[END_REF]. Both systems are considered experimental solutions not yet tested in the real environment. Those solutions provide suggestions on the state of the environment by examining the flows of people in transit in critical infrastructures. The objectives of such systems are: optimize public transport assets, react to incidents across a city, incorporate all stakeholders in decision-making and execution, deliver smoother journeys and predict and adapt to ridership variations. The Smart Passenger Center (SPaCe) system [START_REF] Mermec | The SPaCe project[END_REF], that we present, allows public transport operators to overcome the complexity of centralized management of infrastructure and vehicles and to meet the safety and security requirements of all interested parties. Thanks to the artificial intelligence engine of the SPaCe integration platform, service managers will be able to improve the efficiency of their operations by drastically reducing the impact of security events. Furthermore, SPaCe enables significant cost savings by providing operators with the ability to focus on critical events rather than micro-management. Moreover, SPaCe enables the transition from the traditional subsystem approach, where a dedicated team is needed to constantly monitor activities, towards a smarter integrated approach that proactively treats an increasing volume of information available in security control rooms. The new platform, which correlates different data and events by crossing them thanks to machine learning and data mining, makes it possible to predict threats with discernment and propose countermeasures. Thanks to SPaCe, it is possible to reduce the costs of personnel and vehicles, optimizing their Fig. 1. Privacy by design: the video streams are processed on edge and no image is stored permanently in all operations involving sensitive personal data such as seat counts or passenger analytics presence only in places and moments of actual need. SPaCe allows passengers to reduce delays caused by unforeseen events, allowing a predictive variation of passenger flows. In this work, we focus on the SPaCe computer vision subsystem that constantly monitors activities in stations, trains, buses and other places of interest: it is a pervasive smart camera network whose main task is people counting and passenger's journey tracking; it also supports the service operators with a number of event notifications such as unattended objects or damage detection, smoke and fire alarm and dirt and waste report. In the following sections, we present the state of the art of basic computer vision techniques involved and the advanced functionalities that the system offers to the upper layers.

II. SYSTEM DESIGN AND FUNCTIONALITIES

The system architecture follows the privacy-by-design paradigm: no real image is recorded or transmitted, but all the elaborations take place on the system's edges. Therefore we focus on the computer vision pipeline used on every smart sensor which is equipped with a stereo camera and a powerful NVIDIA Jetson AGX Xavier [START_REF]Jetson Embedded Systems[END_REF]; this AI embedded device has the computation and memory capabilities to run all the expected elaborations. As you can see in fig. 2 the first step is to classify and locate all elements in the image with object detection, which is useful to locate people and items in the scene. For passengers identification we relay on face recognition which is also useful to build the person model used in people tracking. For better estimations and measures, we use stereo cameras or depth sensors in combination with standard colour cameras. Let us see a brief review of the fundamental computer vision techniques heavily used in the images processing pipeline.

Object detection: The best results for this task are obtained with convolutional neural networks (CNNs) with supervised learning models. R-CNN (Region-Based Convolutional Network) [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF] allows to locate objects by training a model using a small amount of annotated data; SPP-net (Spatial Pyramid Pooling) [START_REF] He | Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition[END_REF] aims to eliminate the need to provide fixedsize images to the classifier and therefore to avoid cropping or resizing of the images; Fast R-CNN (Fast Region-Based Convolutional Network) [START_REF] Girshick | Fast R-CNN[END_REF] guarantees better mean average precision than the previous ones with single-stage learning. Faster R-CNN [START_REF] Ren | Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks[END_REF] generates region proposals in a less expensive way than both R-CNN and Fast R-CNN. R-FCN (Region-based Fully Convolutional Network) [START_REF] Dai | R-FCN: Object Detection via Region-based Fully Convolutional Networks[END_REF] is completely convolutional, and unlike other RPN-based methods, it replaces FC layers after ROI pooling with simple and low-cost computational operations. SSD (Single Shot Detector) [START_REF] Liu | SSD: Single Shot MultiBox Detector[END_REF] is an object detection method that makes use of a single deep neural network, ensuring a speed suitable for real-time video processing. YOLO (You Only Look Once) [START_REF] Redmon | You Only Look Once: Unified, Real-Time Object Detection[END_REF] as SSD is a regression-based method, which is computationally suitable for real-time (can even reach 155 fps) but behaves worse than SSD on small objects or near objects among them.

Face recognition: The main technique to identifying people is based on Facial Recognition (FR) [START_REF] Whitelam | IARPA Janus Benchmark-B Face Dataset[END_REF]; more specifically Fig. 2. All the elaborations take place on the edge nodes: after the object detection task the system performs face detection, tracking and counting with people and auxiliary functions with other items; these auxiliary functionalities are related to the detection of dirt and waste, unattended objects, damaged or missing equipment, smoke and fire. in the SPaCe system we are interested in Face Identification: given an image of a face, a numerical representation is generated, which is used to search within a database if the subject is known. The Deep Learning algorithms used for FR are generally trained through large datasets such as LFW [START_REF] Huang | Labeled Faces in the Wild: A Database for Studying Face Recognition in Unconstrained Environments[END_REF] and VGGFace2 [START_REF] Cao | VGGFace2: A Dataset for Recognising Faces across Pose and Age[END_REF]. There are many problems with the FR: quantization errors [START_REF] Wu | Rotation consistent margin loss for efficient low-bit face recognition[END_REF], unbalancing of the classes in the dataset [START_REF] Liu | AdaptiveFace: Adaptive Margin and Sampling for Face Recognition[END_REF], [START_REF] Yin | Feature transfer learning for face recognition with under-represented data[END_REF] and, above all, different resolutions [START_REF] Massoli | Cross-resolution learning for Face Recognition[END_REF]. The latter is because the datasets used in the training phase are composed of high resolution images while, in surveillance systems, you can have images with very low resolutions (up to 8x8 pixels). To face this problem we find the SuperResolution techniques [START_REF] Singh | Identity Aware Synthesis for Cross Resolution Face Recognition[END_REF], [START_REF] Kolouri | Transport-based single frame super resolution of very low resolution face images[END_REF], projections in a common space [START_REF] Li | On Low-Resolution Face Recognition in the Wild: Comparisons and New Techniques[END_REF] and Cross-Resolution training [START_REF] Massoli | Cross-resolution learning for Face Recognition[END_REF].

People tracking: Single-camera people tracking means assigning an identification number (ID) to all the people present in a given frame and recognizing the same subjects in the following frames by carrying forward the assigned IDs. If someone is no longer present, the ID is inserted in the list of disappeared; every time a new person appears, a new identification is assigned only after checking if the person is not in the list of missing. The problem just described goes under the name of person re-identification, and many approaches have been proposed in the literature [START_REF] Vezzani | People reidentification in surveillance and forensics: A survey[END_REF]. Deep Learning has made it possible to obtain great performances also in tracking [START_REF] Ciaparrone | Deep learning in video multi-object tracking: A survey[END_REF], [START_REF] Wojke | Simple online and realtime tracking with a deep association metric[END_REF]. A reference site that shows the results of the best algorithms is [START_REF]Multiple Object Tracking Benchmark[END_REF]: the winner of the CVPR19 competition proposed in [START_REF] Mykheievskyi | Learning Local Feature Descriptors for Multiple Object Tracking[END_REF] is still the top algorithm today. It uses a detection based on Faster R-CNN and a similarity estimation based on features of size 128 produced by the patches of the converted image in the HSV color space. In the second place, there is [START_REF] Zhou | Tracking Object as Points[END_REF] whose code in open-source format is freely usable and modifiable.

Relying on the previous computer vision techniques, the system implements both people-based and auxiliary functionalities. The first set involves people counting and multicamera passenger tracking, while the auxiliary one refers to the detection of "dirt and waste", "unattended objects", "damage or missing equipment" and "smoke and fire". Recent related works for these tasks will be presented in the following paragraphs.

People counting: A first implementation of this functionality is obtained by counting the instances of people found by an object detector. This approach works well for small to medium-sized, uncrowded spaces where people are distinct. In the case of large and crowded places, on the other hand, techniques based on the estimation of the density of [START_REF] Zhang | Single-Image Crowd Counting via Multi-Column Convolutional Neural Network[END_REF], [START_REF] Boominathan | CrowdNet: A Deep Convolutional Network for Dense Crowd Counting[END_REF] instances, achieves higher performance than the approach described above. Recently, methods based on self-supervised and unsupervised strategies have been proposed in the literature. In particular, in [START_REF] Liu | Leveraging Unlabeled Data for Crowd Counting by Learning to Rank[END_REF] the authors used a self-supervised approach exploiting the learning-to-rank paradigm, while in [START_REF] Sam | Almost Unsupervised Learning for Dense Crowd Counting[END_REF] a technique based on the winner-takes -all applied to the representations produced by a DCNN giving life to an unsupervised framework. Differently, the authors in [START_REF] Xiong | From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer[END_REF] have proposed a self-supervised approach based on the idea that the count can be decomposed along with the spatial components of the image by acting independently on their partitions. In [START_REF] Shen | Crowd Counting via Adversarial Cross-Scale Consistency Pursuit[END_REF] an adversarial learning approach is used to reduce the blurring effects typical of the estimation methods using density maps, again using a loss that guarantees spatial consistency of the count. Recently, some papers such as [START_REF] Lian | Density Map Regression Guided Detection Network for RGB-D Crowd Counting and Localization[END_REF]- [START_REF] Yuting | Towards Unsupervised Crowd Counting via Regression-Detection Biknowledge Transfer[END_REF] have successfully attempted to combine regression approaches with detection approaches in an attempt to make the most of the advantages of both methodologies.

Garbage, damages, unattended and missing objects: An efficient and precise object detector is the basis for the implementation of all these functionalities in conjunction with other space-time information (fig. 3). As far as the identification of dirt or abandoned objects is concerned, these checks will be made only in precise moments or at the end of the trip and in the absence of people; in this context, the correct classification is already the desired result. Damage can also be more easily identified when the vehicle is empty using a reference image. Implementation of these functions while passengers are on board will be studied.

Smoke and fire detection: A comprehensive survey of traditional computer vision methods, including some considerations on detection using multi-view and multimodal systems, is presented in the book [START_REF] Cetin | Methods and techniques for fire detection: signal, image and video processing perspectives[END_REF]. Methods based on deep learning have proven to be good in detecting fires, especially to prevent the limitations of traditional methods due to the high false alarm rate and low precision in distinguishing smoke from the isolated haze. For a recent and complete review, we refer to [START_REF] Gaur | Video Flame and Smoke Based Fire Detection Algorithms: A Literature Review[END_REF], [START_REF] Khan | DeepSmoke: Deep Learning Model for Smoke Detection and Segmentation in Outdoor Environments[END_REF]. In [START_REF] Yin | A Deep Normalization and Convolutional Neural Network for Image Smoke Detection[END_REF] a new deep network with normalization (DNCNN) with 14 layers is proposed to implement automatic feature extraction and classification. The experimental results show that the proposed method achieves false alarm rates lower than 0.60% and detection rates higher than 96.37% on a reference dataset not freely available. Some datasets useful for benchmarking smoke detection algorithms are [START_REF] Toreyin | Sample Fire and Smoke Video Clips[END_REF] and [START_REF] Firesense | [END_REF].

Privacy-by-design passengers identification and tracking: The SPaCe system should be able to reconstruct the complete route taken by people during their daily journeys, from the departure to the arrival. Therefore, the system should implement a real-time tracking process of people through the network of cameras mounted on the vehicles and in the parking and transit areas. All this must be achieved in compliance with current legislation on privacy, i.e., no image with recognizable people must be stored on permanent media nor transmitted on the network. Light variations, crowded environments and the consequent partial or total occlusions, different views and angles of the cameras make this task particularly difficult compared to a small indoor space. To compare people in different frames of different sensors, we need an appearance model that allows for effective correlation. With a good facial image, the phenotype characteristics of the passenger such as gender and age can be inferred; the face, however, is not always clearly visible; it is necessary to consider the entire figure by extracting unique characteristics to create a robust appearance model: from the analysis of the silhouette the height and build of the person observed can be estimated, and appearance characteristics associated with clothing or accessories can also be taken into consideration (e.g., colour of the clothes, glasses, trolley, suitcases, backpacks). Based on the face, physical characteristics and appearance, the SPaCe system builds a Digital Footprint (DF) of the observed person, that is a mathematical model associated with that person, which is helpful for its recognition (re-identification) every time it is seen by a camera (fig. 4). The probability of success of this recognition is greatly influenced by the clarity of the image, the shot's perspective, and any occlusions present. In favourable frontal framing situations, the system guarantees a clear identification of the people observed.

An interesting starting point for the construction of a fast and reliable digital footprint is the one based on the deep features that we find described in [START_REF] Wojke | Simple online and realtime tracking with a deep association metric[END_REF]. To calculate these characteristics, a model trained on millions of human images is used; the main limitation of this approach is the case of a very large bounding box that includes too much background or information not relating to the person.

III. CONCLUSION

In this paper, we introduce the Smart Passenger Center (SPaCe), an integration platform for managing and supporting the operators of public transport systems. We focused on the Computer Vision Subsystem of SPaCe which leverages edge computing and smart cameras to offer advanced services in a robust, scalable and privacy-preserving way. Still in the design phase, the work in progress will explore the interplay between computer vision and pervasive technologies and will address challenging aspects related to inter-node communication and orchestration. Results will be demonstrated in a realistic experimental setup using an installation on test carriages to cope with and tackle the actual issues of the real world.

  This work is supported by Regione Toscana grant POR-FESR 2014-2020 axe 1 action 1.1.5, CUP: 3647.04032020.157000059 SPaCe

Fig. 3 .

 3 Fig. 3. Examples of auxiliary functionalities: supporting cleaning activities, reporting abandoned objects, identifying damage and vandalism, detecting fire or smoke.

Fig. 4 .

 4 Fig. 4. Digital footprint: It is a mathematical model associated with each person based on the face, physical characteristics and appearance; passenger recognition is based on this information every time it is seen by a camera.


Diego Nocetti
email: dnocetti@clarkson.edu

Elyès Jouini
email: jouini@ceremade.dauphine.fr

Clotilde Napp
email: clotilde.napp@dauphine.fr

Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience

Keywords: social discount rate, hyperbolic discounting, cost-benefit analysis _____________________________________________________________________________________

This paper derives the properties of the discount rate that should be applied to a public-sector project when the affected population has heterogeneous degrees of impatience. We show that, for any distribution of discount rates, the social discount rate has the following properties: it decreases over time, it is lower than the average of the discount rates in the population and, it converges to the discount rate of the most patient individual in the economy. These properties hold for both constant and decreasing individual discount rates. Finally, we evaluate how changes in the distribution of individual discount rates affect the social discount rate.

Introduction

The appropriate social discount rate (SDR) to apply in public-sector cost-benefit analyses is a contentious issue. As Weitzman (2001 p.261) states "There does not now exist, nor has ever existed, anything remotely resembling a consensus, even -or, perhaps one should say especially-among the 'experts' on this subject." Especially when the discount rates of the affected population are Nocetti, Jouini, Napp: Properties of the Social Discount Rate _____________________________________________________________________________________ 2 heterogeneous, social planners face the difficult problem of what weight to give to them. Of course, a straightforward solution would be to use a simple average of the discount rates. Although frequently applied in practice [START_REF] Bazerlon | Discounting inside the Washington D.C. beltway[END_REF], this method is, in general, incorrect. To see this, consider a project that provides a payoff of $200 in 50 years to two individuals ($100 each), Patience who has a discount rate of one percent and Impatience who has a discount rate of ten percent. Using the average of the discount rates (5.5 percent) the present value of the project would be $12.8. However, the present value of $100 is about $61 for Patience and $0.7 for Impatience, for a total present value of the project of $61.7 (which implies an SDR of about 2.4 percent). In this example, the average discount rate understates the present value of the project by a factor of about five.

Further complicating the aggregation of preferences, empirical evidence has shown systematic departures from the standard model in which all benefits and costs are discounted at the same rate. For instance, people discount outcomes in the near future at a higher rate than they do for more distant outcomes, i.e. hyperbolic discounting [START_REF] Ainslie | Picoeconomics[END_REF][START_REF] Cropper | Preferences for life saving programs: How the public discounts time and age[END_REF]. In addition, the discount rate may depend on the 'sign' (i.e. whether it is a cost or a benefit) and on the magnitude of the outcomes, with higher discount rates for gains (benefits) and small outcomes [START_REF] Thaler | Some empirical evidence on dynamic inconsistency[END_REF][START_REF] Benzion | Discount rates inferred from decisions: An experimental study[END_REF]. 1 Given these and other difficulties, it is not surprising that in practice government agencies use a wide variety of discount rates, ranging from zero to infinite percent, with little justification [START_REF] Bazerlon | Discounting inside the Washington D.C. beltway[END_REF]. The aim of this paper is to provide some guiding principles for the selection of the appropriate SDR. Specifically, we consider a social planner who gathers data on individual discount rates, which may be constant or decreasing with time, and uses a Benthamite social welfare function to aggregate them. Then, we ask: what are the properties of the SDR that she will obtain?

This problem has been analyzed before in the literature by assuming specific distributions of the individual discount rates across the affected population. For example, [START_REF] Reinschmidt | Aggregate social discount rate derived from individual discount rates[END_REF] showed that if 1 Frederick et al. (2002) present a review of the literature on hyperbolic discounting and other 'anomalies' usually observed in experimental studies of intertemporal choice.

Nocetti, Jouini, Napp: Properties of the Social Discount Rate _____________________________________________________________________________________ 3 the individual discount rates are constant over time and normally distributed over the population, the SDR should be lower than the average of the individual rates and decreasing in time. In particular, suppose that a public project provides aggregate net benefits at time t of t A and that the net benefits are divided equally among a population of size n. Further, suppose that individuals discount the net benefits with an exponential discount function, with heterogeneous discount rates i ρ . Then, the present value of the benefits received at time t is

1 i t t i A e n ρ -
⎛ ⎞ ⎛ ⎞ - - - - ⎜ ⎟ ⎜ ⎟ - ⎝ ⎠ ⎝ ⎠ = = . It follows that the SDR is 2 2 soc t ρ μ σ = - .
Based on this result, Reinschmidt (2002, p.311) argues that "The aggregate social discount rate ( )

2 2 t t ρ μ σ = -
which decreases with time and variance, can be used for evaluating public-sector projects even when individual discount rates are considered to be constant in time." Two linked problems arise from this suggestion. First, a crucial assumption of the model (that some individuals in the population have constant and extremely large negative discount rates) seems insufficiently plausible to justify placing serious reliance on the derived SDR. Second, and more important, the SDR decreases linearly with the project's horizon and, as a result, is negative for sufficiently long horizons. Although declining discounts seem to be an empirical regularity in public-sector projects (e.g., Henderson andBateman, 1995, Bazerlon and[START_REF] Bazerlon | Discounting inside the Washington D.C. beltway[END_REF], a discount rate that goes to negative infinity as the project's horizon lengthens makes little sense. In order to deal with this issue Reinschmidt proposes: "To assure that ( ) 0 t ρ ≥ , Equation ( 14) -the SDR-is used only in the range Not only is constraining the time difficult to justify on any grounds, but also, the large heterogeneity in discount rates usually found in the data limits the applicability of the derived SDR to analyze any kind of project. For instance, in the fairly homogeneous population (economics and finance students) analyzed by [START_REF] Benzion | Discount rates inferred from decisions: An experimental study[END_REF], across the multiple treatments 2 2μ σ was never larger that twenty and usually much smaller. [START_REF] Henderson | Cross-disciplinary evidence for hyperbolic social discount rates[END_REF] and [START_REF] Weitzman | Gamma discounting[END_REF] show that a hyperbolic social discounting function can also be obtained by assuming a gamma distribution of the individual discount rates. 23 Yet, although the gamma distribution is a more sensitive choice to model the distribution of individual rates, an important question remains: is hyperbolic discounting a general property of social discounting when the affected population has heterogeneous discount rates? The same question regards the other properties derived (e.g. the SDR decreases with the variance of the individual discount rates). The main contribution of this paper is to characterize the properties of the SDR for any distribution of discount rates.

General properties of the SDR

Imagine a decision maker who gathers data on individual discount rates and needs to evaluate the present value of a project providing a stream of net benefits t A for t=0,…,T. Consider a continuous population of measure one and suppose that fraction i

x of the population (group i) has a constant and 2 To be more precise, in [START_REF] Weitzman | Gamma discounting[END_REF] paper the underlying heterogeneity is among the recommendations of a group of experts that a government agency consults.

_____________________________________________________________________________________

5 non-negative discount rate [ ] 0 i m i n m a x , ρ ρ ρ ∈ ≥ (alternatively, i
x can be interpreted as the proportion of t A that group i receives).4

The present value of the stream of net benefits

0 i T t t i t i P A xe ρ - = = ∑ ∑ . ( 1
)
The social discount factor e -h(t) must satisfy, for every stream of net benefits ( t A ) t=0,…,T and for every horizon

T ( ) 0 0 . i T T t h t t t i t t i A e A xe ρ - - = = = ∑ ∑ ∑ (1')
Since (1') must always hold, it follows that we must also have

( ) . i t h t i i e xe ρ - - = ∑ (1'')
As in [START_REF] Weitzman | Why the Far Distant Future Should be Discounted at its Lowest Possible Rate[END_REF][START_REF] Weitzman | Gamma discounting[END_REF], we define the (instantaneous) SDR as '( )

i i t i i i soc t i i x e h t x e ρ ρ ρ ρ - - = = ∑ ∑ , ( 2
)
which is a weighted mean of the individual discount rates.

An alternative to this 'marginal' SDR would be to consider the 'average' SDR, defined as ( )

1 ln i t a i i h t t t x e ρ ρ - ⎛ ⎞ = =- ⎜ ⎟ ⎝ ⎠ ∑
. The relationship between the 'marginal' and the 'average' social discount rates is given by 0

1 ( ) t a s o c t s ds ρ ρ = ∫
. We choose to analyze the properties of the 'marginal' _____________________________________________________________________________________ 6 discount rate since it is easy to verify that all the properties of soc ρ presented in the paper carry over to a ρ (the converse is not true).

The following proposition characterizes the properties of soc ρ .

PROPOSITION 1. For any bounded distribution of the individual/group discount rates, the SDR is decreasing in t, it converges to min ρ as the horizon lengthens, and it is lower than the weighted average of the different groups' discount rates, (i.e.

i i soc x ∑ < ρ ρ ).
Although we relegate all formal proofs to a web appendix, the intuition is simple. As a payoff is delayed, its present value decreases more rapidly for the more impatient groups; therefore, the relative weights in the SDR of the more impatient people decrease with time. As a result, the social planner will use a lower SDR for net benefits that are further in the future and for benefits received in the very long-term she will only use the discount rate of the most patient group (since they are the only ones that give some value to the project).5 Furthermore, because the individual discount functions are convex in the discount rate, the appropriate SDR to use is lower than the case when the social planner simply averages the different groups' discount rates.

We also want to consider whether the properties derived above hold if, as suggested by experimental evidence from multiple fields, individual discount rates decline with the time horizon. Specifically, suppose that group i has a discount function of the form ( )

( ) i h t i D t e - =
. 6 It follows that the discount rate is ( ) ( )

i i t h t ρ ′ = , which obviously declines with time if ( ) i h t ′′ < 0 (i.e. ( ) i h t is concave in t).
The SDR is, as before, a weighted average of the groups' discount rates:

( ) ( ) ( ) i i h t i i i soc h t i i x h t e x e ρ - - ′ = ∑ ∑ ;
(3) in fact, the SDR with constant discount rates is just a special case in which ( )

i i h t t ρ = and i i h ρ ′ = .
What are the properties of the SDR when the individual discount rates decline with the project's horizon? As one would expect, in addition to aggregation issues that make social discounting hyperbolic even when individual discount rates are constant, the fact that individuals become 'more patient' over time gives an additional reason for the SDR to decline over time. Also, as long as the discount function is convex, the appropriate discount factor for a given horizon will be higher than that applied by a social planner who uses the average of the groups' discount rates in the same discount function. Finally, the SDR converges to the lower bound of the support of the discount rates' distribution that holds in the limit.

The intuition of this last result is as follows. When discount rates are constant, the weight that a given group receives in the SDR increases monotonically relative to the weights of the more impatient groups.

Instead, when discount rates vary over time, patience is defined relative to the payoff's horizon; therefore, the relative weights may be non-monotonic. For instance, suppose that group 'A' discounts the near future more heavily than group 'B', but the discount rate of the former declines to a lower limiting level.

Then, group A's relative weight will decline initially and, as they become more patient, it will eventually start to increase. In fact, the weight attached to the group with the lowest discount rate will converge to one.

In addition to establishing the properties of the SDR for a given population, we can evaluate how changes in the distribution of discount rates affect the SDR. Specifically, we want to determine conditions under which the SDR will unambiguously increase or decrease given a shift in the distribution of individual discount rates.

We begin by noting that, although first and second order stochastically dominated shifts in the distribution of discount rates increase the present value of the project, they are neither necessary nor sufficient to decrease the SDR for all horizons. Therefore, we need stronger notions of stochastic

( ) ( ) ' ( ) 0 ' ( ) 0 E u Z Z a E u Y Y a ⎡ ⎤ ⎡ ⎤ - = ⇒ - ≤ ⎣ ⎦ ⎣ ⎦
for any real number a and any non-decreasing and concave function u .

This concept has been introduced in the context of portfolio problems by [START_REF] Landsberger | Mean-preserving portfolio dominance[END_REF] and further studied by [START_REF] Gollier | A note on portfolio dominance[END_REF]. It characterizes the changes in the distribution of the returns of the risky asset that lead to an increase in demand for the risky asset irrespective of the risk-free rate. In the portfolio context, it is then related to the degree of riskiness of the assets returns. In our context, it is related to individual discount rates' heterogeneity. In particular a mean preserving PD dominated shift for a given distribution increases the variance [START_REF] Jouini | On Abel's concept of doubt and pessimism[END_REF].

7 More precisely, [START_REF] Landsberger | Demand for risky financial assets: A portfolio analysis[END_REF] showed that in the standard portfolio problem a MLR shift in the distribution of returns of the risky asset leads to an increase in demand for the risky asset for all agents with nondecreasing utilities.

Example

To provide a simple example of what our results mean in practice, we calculate the SDR (Equation 2) using the frequency distribution of discount rates obtained by [START_REF] Weitzman | Gamma discounting[END_REF] in a survey of economists. 9 Figure 1 illustrates the implied SDR for different horizons. Clearly, heterogeneity among the respondents in the survey makes the SDR decline substantially, from about 4 percent -the weighted mean in the sample-to 0 percent -the lowest discount rate-, and quite rapidly over the time horizon.

8 For example, suppose that in one population (say "A") we have three equally large groups with discount rates 2%, 4% and 6%. In a second population ("B"), there are three groups with the same discount rates but with proportions in the population equal to 0.1, 0.8 and 0.1 respectively. It follows that both populations have the same weighted average of discount rates (4%). However, because the distribution of discount rates in A is dominated in the sense of PD by the distribution of discount rates in B, the discount rate for the former is lower for all t. 9 The survey asked for the appropriate rate to discount long-term benefits and costs and not necessarily the respondents' rate of time preference. Our SDR was calculated 'as if' the response represented the individual's constant rate of time preference. See web appendix for further details.

Nocetti, Jouini, Napp: Properties of the Social Discount Rate _____________________________________________________________________________________ 10

The SDR obtained is, for most time horizons, lower than the sequence of declining rates suggested by [START_REF] Moore | Just Give Me a Number: Practical Values for the Social Discount Rate[END_REF]. Of course, a different population may lead to different results. For instance, Proposition 2 states that in a more homogeneous population the appropriate SDR would be higher. Yet, we suspect that, for the United States as a whole, heterogeneity of discount rates is larger than in the sample of economists, which implies even lower not higher discount rates. Therefore, although our framework is not inconsistent with [START_REF] Moore | Just Give Me a Number: Practical Values for the Social Discount Rate[END_REF], it does not provide strong support for the rates recommended.

Conclusions

This paper provided a general characterization of the properties of the social discount rate when the discount rates of the affected population are heterogeneous and when using a Benthamite social welfare function. Importantly, we showed that the social discounting function should be hyperbolic when individual discount rates are declining or even constant. This is of great practical relevance since it implies that, for projects providing net benefits at different periods, decision-makers do not need to estimate the individual discount rates across time (a task that is likely to be very demanding) to justify Note. We employed the frequency distribution of discount rates obtained by [START_REF] Weitzman | Gamma discounting[END_REF] [Table 1, p. 268] to calculate the proportion x i of the sample with a given discount rate ρ i in Equation (2). See web appendix for further details. _____________________________________________________________________________________ 11 applying declining discounts. For instance, [START_REF] Henderson | Cross-disciplinary evidence for hyperbolic social discount rates[END_REF]p.1498-1499) state that "In practical terms the weight of evidence in favor of hyperbolic discounting must be particularly convincing if there is to be any likelihood of introducing its use in analyses by government agencies." Given the generality of our results, we believe that this paper provides such evidence.

Our results are particularly relevant for very long-term cost-benefit evaluations (e.g. those dealing with global climate change) that are especially sensitive to the selected discount rate. 10 We showed that, for those cases, the appropriate SDR should be equal to the discount rate of the most patient individuals which, in practice, is likely to be close to zero percent.

Proofs of Statements and Data for Numerical Example

EC.1. PROOF OF PROPOSITION

PROPOSITION 1. For any bounded distribution of the individual/group discount rates, the SDR is decreasing in t, it converges to min ρ as the horizon lengthens, and it is lower than the weighted average of the different groups' discount rates, (i.e.

EC.1.1. Proof that

0 soc t ρ ∂ ∂ < Denote i t i i x e ρ θ - =
. Taking the derivative of the SDR with respect to the project's horizon gives

2 2 2 2 2 * i i i i i i i i i i i i i soc i i i i i i i t ρ θ θ ρ θ ρ θ ρ θ ρ θ θ θ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ - + ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ∂ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎢ ⎥ = = - -⎜ ⎟ ⎢ ⎥ ∂ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎜ ⎟ ⎝ ⎠ ⎣ ⎦ ⎝ ⎠ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
. From Jensen's inequality we know that the second term in brackets must be equal or lower than the first term, proving the result that the sign of the derivative is non-positive (and negative when there is heterogeneity). Denote the (arbitrary) difference between the discount rate of the most patient group (with subscript min ) and any other group as i y (i.e., min i i y ρ ρ = -). Then, the SDR can be written as In the text we mentioned that the SDR for the discount function ( )

EC.1.2. Proof that

ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ - + - - ≠ - - - ≠ - ≠ ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ = = ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ ∑ ∑ ∑ ∑
( ) i h t i D t e - =
has three properties: it decreases with time, it converges to the lower bound of the support of the distribution of discount rates that holds in the limit, and it is lower than the average discount rate.

EC.2.1. Proof that

0 soc t ρ ∂ ∂ <
The derivative of the SDR with respect to the project's horizon is ( )

i i i i i i soc i i i i i i i i i h h h θ θ θ ⎛ ⎞ ′ ′ ′ ′ - ⎟ ⎜ ⎟ ∂ ⎜ ⎟ ⎜ ⎟ = + + ⎜ ⎟ ⎜ ⎟ ∂ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎝ ⎠ ∑ ∑ ∑ ∑ ∑ ∑ , where i h i i
x e θ -= and all the terms may be functions of time.

The first and third terms are isomorphic to the terms obtained in the case of constant discount rates. As before, by Jensen's inequality the sum of these terms is non-positive. The second term is new and results from the fact that the groups' discount rates change over time. Given our assumption that the discount rates decrease over time (i.e. ( ) , where we used the subscript min in the fraction x and the function ( ) , i.e., the most patient group would receive a weight of 1 (which provides an alternative proof to the second part of Proposition 1). When discount rates are not constant the ratio of the weights may be non-monotonic; yet, because by definition it will eventually be true that ( ) ( )

i h t ′′ < 0 ) it
min i h t h t ′ ′ <
, min z will approach 1 as in the case with constant discount rates.

EC.2.3. Proof that the SDR is lower that the weighted mean of discount rates

As long as the discount function is convex, by Jensen's inequality the appropriate discount factor will be higher than that applied by a social planner that uses the average of the groups' discount rates in the same discount function, i.e., ( ) ( )

EC.4. DATA FOR NUMERICAL EXAMPLE

To calculate the SDR in Figure 1 we used equation (2) in the text, soc i i i i i i

x ρ ρ θ θ = ∑ ∑ , together with the data collected by [START_REF] Weitzman | Gamma discounting[END_REF] in a survey of economists. In particular, he asked the question: [START_REF] Weitzman | Gamma discounting[END_REF]. Responses (3) with a negative discount rate were excluded.

  Figure 1. SDR for Different Horizons

  h is non-decreasing and where E exp is the expectation operator associated to the probability whose density with respect to the

  . For large n we can write this as , where E is the expectations operator over the distribution of discount rates. Assuming that the discount rates are sampled from a normal distribution (with a mean discount u and a variance 2

														t A Ee ρ	t
														σ ),	e ρ -	t	has a lognormal
	distribution and	Ee	ρ	t	e	1 2 t E t Var ρ	( ) ρ	e	t	μ	t	1 2	σ	2

-

  In other words, a MLR dominated shift for a given distribution puts less weight for higher values of ρ . When Y and Z have a finite common support 1 ......

	dominance.
	DEFINITION 1. Monotone likelihood ratio dominance (MLR). Let Y and Z denote two random
	variables with respective distribution functions F Y and F Z . We say that Z dominates Y in the sense of
	MLR (	Z		MLR	Y ) if there exist numbers -∞≤a≤b≤∞ and a non-decreasing function h:[a,b]→[0, ∞] such
	that Pr(Z<a)=0, Pr(Y>b)=0 and dF Z (x)=h(x) dF Y (x) on [a,b].
					ρ	<	<	ρ	n	with respective weights ( ) Y i i x = 1,.....,	n	and
	( ) Z i i x = 1,.....,	n	then Z dominates Y in the sense of MLR if and only if 1 1 Z Y x x	≤	.....	≤	Z n Y n x x

. This concept is widely used in the statistical literature and was first introduced in the context of portfolio problems by

Landsberger and Meilijson 7 (1990)

. MLR dominance is stronger than FSD and, in particular, a MLR dominated shift for a given distribution reduces the mean. DEFINITION 2. Portfolio Dominance (PD). Let Y and Z denote two random variables. We say that Z dominates Y in the sense of PD ( PD Z Y ) if we have

  Let us consider Y and Z two random variables with associated distribution functions Y and F Z such that Z≽ MLR Y. Without loss of generality, we may assume that Y and Z have the same support. By

	EC.3. PROOF OF PROPOSITION 2
		PROPOSITION 2. MLR and PD stochastically dominated shifts in the distribution of the individual
	discount rates reduce the SDR.
	definition, the social discount rates Z soc ρ	and Y soc ρ respectively associated to Z and Y are given by
	ρ	Z soc	Zt Zt --E Ze E e ⎡ ⎣ = ⎡ ⎤ ⎤ ⎦ ⎣ ⎦	and						ρ	Y soc	Yt Yt --E Ye E e ⎡ ⎣ ⎣ ⎦ ⎤ ⎦ = ⎡ ⎤	.	We	have	then
		Z soc	( ) ( ) Z e dF t t Z e dF	( ) e h dF t Y ( ) ( ) ( ) t Y e h dF		[ E Yh Y exp ( ) [ ] ] exp ( ) E h Y
			i ∑	i i x D t	,	ρ	i	t	i D t ⎛ ≥ ⎜ ⎝	,	i ∑	i i x ρ	( ) t	⎞ ⎟ ⎠	.

  Nocetti, Jouini, Napp: Properties of the Social Discount Rate _____________________________________________________________________________________ 18 "Taking all relevant considerations into account, what real interest rate do you think should be used to discount over time the (expected) benefits and (expected) costs of projects being proposed to mitigate the possible effects of global climate change?" The frequency distribution is reproduced in the following table.

	Discount rate (%)	Frequency*	x	i
	0	46	0.0213
	1	236	0.1094
	2	454	0.2105
	3	427	0.1980
	4	362	0.1678
	5	227	0.1052
	6	136	0.0631
	7	71	0.0329
	8	44	0.0204
	9	28	0.0130
	10	44	0.0204
	11	15	0.0070
	12	25	0.0116
	13	12	0.0056
	14	5	0.0023
	15	8	0.0037
	16	3	0.0014
	17	2	0.0009
	18	3	0.0014
	19	1	0.0005
	20	4	0.0019
	25	2	0.0009
	26	1	0.0005
	27	1	0.0005
	Total responses	2157
	*Source: Table 1 p.268

A declining SDR might also be justified if there is uncertainty about future discount rates (e.g.[START_REF] Newell | Discounting the Benefits of Climate Change Mitigation: How Much do Uncertain Rates Increase Valuations[END_REF] or about the state of the economy (e.g.,[START_REF] Gollier | Discounting an uncertain future[END_REF]. In a quite general setting with heterogeneous individual discounts,[START_REF] Gollier | Aggregation of Heterogeneous Time Preferences[END_REF] relate the term structure of the social discount rate with the shape of the individual utility functions.

The results that follow do not depend on the assumption that the individual discount rates are non-negative. Yet, as we show in Proposition 1, this restriction guarantees that the SDR applied to very long-term payoffs is non-negative.

A similar result is obtained in a quite different setting in[START_REF] Weitzman | Why the Far Distant Future Should be Discounted at its Lowest Possible Rate[END_REF]. In fact, this is also the reason why[START_REF] Reinschmidt | Aggregate social discount rate derived from individual discount rates[END_REF]'s social discount rate tends to negative infinity, since in the case of a normal distribution the most patient individual has a constant discount rate of negative infinity.

The exponential form is assumed here for ease of comparison with the case of constant discount rates; the only requirement to obtain the results, however, is that the discount function is convex in time.

Acknowledgements

This paper heavily relies on a previous version by D. Nocetti alone. The authors thank the associate editor and three anonymous referees for many helpful comments and suggestions. The financial support of the GIP-ANR ("Croyances" project) and of the Risk Foundation (Groupama chair) is gratefully acknowledged by Jouini and Napp. 10 For instance, given the SDR estimated in the previous section, if one applies the short-term discount rate (4 percent) to a project that provides net benefits in say 300 years, the net benefits would be underestimated by a factor of about 80,000 (given an appropriate SDR of 0.24 percent).

Nocetti, Jouini, Napp: Properties of the Social Discount Rate _____________________________________________________________________________________


Hector Zenil

Genaro Martínez

Chiara Marletto

Samira El Yacoubi

Rodrigo Torres-Aviles

Martin Lind

Narsis A Kiani

Mariana González

Jan Baetens

Alonso Castillo-Ramírez

Alberto Dennunzio

Jarkko Kari

Gilles Dowek

Alonso Castillo-Ramirez

Enrico Formenti

Anahí Gajardo

Eric Goles

Andreas Malcher

David A Rosenblueth

Nicolas Ollinger

Ivan Rapaport

Jürgen Riedel

Andrew Adamatzky

Hernández -Quiroz

Fernando Soler-Toscano

Jesper Tegnér

M T I Mariana

G Castellón

Organization Steering Committee

Keywords: Controllability, Observability, Cellular Automata, Kalman condition

for Information Processing (IFIP), Working Group 5, on CA and DCS, of the Technical Committee 1, on Foundations of Computer Science.

AUTOMATA 2020 is part of an annual series established in 1995 as a collaboration forum between researchers in CA and DCS. Current topics of the conference include, but are not limited to, dynamical, topological, ergodic and algebraic aspects of CA and DCS, algorithmic and complexity issues, emergent properties, formal languages, symbolic dynamics, tilings, models of parallelism and distributed systems, timing schemes, synchronous versus asynchronous models, phenomenological descriptions, scientific modeling, and practical applications.

While AUTOMATA 2020 was innovating on several aspects, including remote attendance because of concerns around carbon footprint, due to the pandemic this is the first time AUTOMATA took place fully online.

AUTOMATA 2020 hosted seven invited speakers, including, Alyssa Adams,

The Role of Emergence in Open-Ended Systems

Alyssa Adams

University of Wisconsin-Madison, USA Biological systems are notorious for their complex behavior within short timescales (e.g., metabolic activity) and longer time scales (e.g., evolutionary selection), along with their complex spatial organization. Because of their complexity and their ability to innovate with respect to their environment, living systems are considered to be open-ended. Historically, it has been difficult to model open-ended evolution and innovation. As a result, our understanding of the exact mechanisms that distinguish open-ended living systems from non-living ones is limited. One of the biggest barriers is understanding how multiple, complex parts within a single system interact and contribute to the complex, emergent behavior of the system as a whole. In biology, this is essential for understanding systems such as the human gut, which contain multiple microbial communities that contribute to the overall health of a person. How do interactions between parts of a system lead to more complex behavior of the system as a whole? What types of interactions contribute to open-ended behavior? In this talk, two interacting cellular automata (CA) are used as an abstract model to address the effects of complex interactions between two individual entities embedded within a larger system. Unlike elementary CA, these CA are state-dependent because they change their update rules as a function of the system's state as a whole. The resulting behavior of the two-CA system suggests that complex interaction rules between the two CA have little to no effect on the complexity of each component CA. However, having an interaction rule that is random results in open-ended evolution regardless of the specific type of state-dependency. This suggests that randomness does indeed contribute to open-ended evolution, but not by random perturbations of the states as previously speculated.

Collision-Based Computing with Cellular Automata

Genaro J. In theoretical computer science there are several models of unconventional computing, which are based on processes in spatially extended non-linear media with different physics and non-classical logics. In this talk, we will discuss how a collision-based computer employs mobile compact finite patterns represented as mobile self-localized excitations (as particles, gliders, waves, signals) to represent quanta of information in an active non-linear medium. Information values are given by either absence or presence of the particles or other parameters of the localizations. The particles travel in space and when they collide the occuring result can be interpreted as a computation. In this way, any part of the medium space can be used as a wire, particles can collide anywhere within a space sample, there are no fixed positions at which specific operations occur, nor location specified gates with fixed operations. The particles undergo transformations and form bound states, annihilate, or fuse when they interact with other particles. Information values of particles are transformed as a result of the collision.

Particles in complex one-dimensional cellular automata are compact sets of non-quiescent patterns translating along evolution space. These non-trivial patterns can be coded as binary strings or symbols traveling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions and computation.

Typically, we can find all types of localizations manifested in cellular automata particles, including positive, negative, and with neutral displacements. This phenomenon can be found in an ample number of complex cellular automata rules. 1 The number of collisions between particles in complex cellular automata is determined by the their periods (phases) and a number of contact points. A lot of synchronized particles, packages of them or particles with capacity of extensions, are introduced to universes with an infinity of collisions.

A cellular automaton collider is a finite state machine built of rings of one-dimensional cellular automata. We will discuss how a computation can be performed on the collider by exploiting interactions between these particles. In 2002, Tommaso Toffoli introduced the basis of symbol super collider which synthesize the collision-based computing dynamics. In this way, we fuse this framework with the universality of the elementary cellular automaton rule 110 to show how a cellular automata collider works.

Some Control and Observation Issues in Cellular Automata

Samira El Yacoubi 1,2 , Sara Dridi 1,2 , and Théo Plénet This talk is based on some recent work carried out in collaboration with my PhD students Sara Dridi and Théo Plenet and other colleagues: Franco Bagnoli, Laurent Lefèvre, and Clément Raïevsky. It focuses on studying problems of observability and controllability of cellular automata (CA) considered in the context of control theory, an important feature of which is the adoption of a state space model. This model traditionally uses a set of partial differential equations (PDEs) in the description of system input-output dynamics. While the controllability concerns the ability to steer controlled evolution processes, observability deals with the capability to reconstruct the initial state of the system, taking into account sufficient knowledge of the system dynamics through certain output measurements. These two major concepts have already been studied for continuous systems described by PDEs as reported in the literature [3,7,[START_REF] Zerrik | Actuators and regional boundary controllability for parabolic systems[END_REF]]. In the case of deterministic linear systems analysis, the so-called Kalman condition [11,12] is essential and has been widely used to obtain the main characterization results according to the choice of actuator/sensor structures, locations, number, and types (mobile or fixed), see for example [7,8] and the references therein.

Our work first consists of generalizing the obtained results to systems described by CA considered as the discrete counterpart of PDEs, and exploring other suitable approaches to prove controllability and observability. CA are widely used mathematical models for studying dynamical properties of discrete systems and constitute very promising tools for describing complex natural systems in terms of local interactions [2,14,15]. After having introduced the notion of control and observation in CA, in a similar way to the case of discrete-time distributed parameter systems [10], we started to investigate these key concepts of control theory in the case of complex systems modeled by CA.

The case of Boolean CA has been particularly examined to investigate the special case of boundary regional controllability [4]. It consists of considering objectives to be achieved only on a subregion of the whole domain through the application of controls exerted on the boundary of the target region. The problem has been apprehended using several tools: Kalman theorem, Markov Chains, and graph theory [5,6]. The extension to non-linear CA has also been studied. For the problem of observability, we assume that the studied system is autonomous and we applied the tools mentioned above to prove observability. The first results for affine CA can be found in [13]. The non-linear case as well as the probabilistic case are currently under investigation.

Topological Dynamical Properties in Turing Machines

Rodrigo Torres-Aviles Universidad de Concepción, Chile

The goal of this talk is to review a non-exhaustive compilation of some of the work in topological properties in Turing machine Dynamical Systems. We follow two interesting lines, born in Kurka's seminal paper: Topological Entropy, where we talk about Jeandel's computability algorithm and undecidability of positivity; and Aperiodicity, where the existence of the property leads to the existence and undecidability of Topological Transitivity, Minimality, and Mixing, among others.

Isotropic Cellular Automata

Andrew Wuensche

Unconventional Computing Lab, University of the West of England, UK

To respect physics and nature, cellular automata (CA) models of self-organization, emergence, computation, and logical universality should be isotropic, having equivalent dynamics in all directions. I will present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. I will describe new functions and tools in DDLab to generate iso-groups and manipulate iso-rule tables, for multi-value as well as binary, in one, two, and three dimensions. These methods include editing, filing, filtering, searching, mutating, analyzing dynamics by input-frequency and entropy, and identifying the critical iso-groups for glider-gun/eater dynamics. I will illustrate these ideas and methods for two dimensional CA on square and hexagonal lattices, focusing on mutant families of logical universal rules found in iso-rule-space, as well as among the narrower iso-subsets of totalistic and survival/birth rules.

A New Kind of Automata, That May Be Our Universe

Stephen Wolfram

Wolfram Research, USA

A class of models intended to be as minimal and structureless as possible is introduced.

Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of fundamental physics are seen, suggesting the possibility that the models may provide a new approach to finding a fundamental theory of physics. Quantum mechanics and general relativity-both introduced more than a century ago-have delivered many impressive successes in physics. But so far they have not allowed the formulation of a complete, fundamental theory of our universe, and at this point it seems worthwhile to try exploring other foundations from which space, time, general relativity, quantum mechanics, and all the other known features of physics could emerge.

The purpose here is to introduce a class of models that could be relevant. The models are set up to be as minimal and structureless as possible, but despite the simplicity of their construction, they can nevertheless exhibit great complexity and structure in their behavior. Even independent of their possible relevance to fundamental physics, the models appear to be of significant interest in their own right, not least as sources of examples amenable to rich analysis by modern methods in mathematics and mathematical physics.

But what is potentially significant for physics is that with exceptionally little input, the models already seem able to reproduce some important and sophisticated features of known fundamental physics-and give suggestive indications of being able to reproduce much more.

Our approach here is to carry out a fairly extensive empirical investigation of the models, then to use the results of this to make connections with known mathematical and other features of physics. We do not know a priori whether any model that we would recognize as simple can completely describe the operation of our universealthough the very existence of physical laws does seem to indicate some simplicity. But it is basically inevitable that if a simple model exists, then almost nothing about the universe as we normally perceive it-including notions like space and time-will fit recognizably into the model.

And given this, the approach we take is to consider models that are as minimal and structureless as possible, so that in effect there is the greatest opportunity for the phenomenon of emergence to operate. The models introduced here have their origins in network-based models studied in the 1990s, but the present models are more minimal and structureless. They can be thought of as abstracted versions of a surprisingly wide range of types of mathematical and computational systems, including combinatorial, functional, categorical, algebraic, and axiomatic ones.

Special Session: Algorithmic Information Dynamics

Algorithmic Information Dynamics (AID) [1] is an algorithmic probabilistic framework for causal discovery and causal analysis. It enables the solution of inverse problems on the basis of algorithmic probability, using computational tools drawn from algorithmic complexity theory. AID studies dynamical systems in software space where all possible computable models live and is able to explain discrete longitudinal data such as particle orbits in state and phase space, or to approximate continuous systems by discrete computable models. AID provides tools such as algorithmic perturbation analysis to guide the search and use of precomputed models to find relevant generative mechanisms representing causal first principles of a domain of interest, and is an alternative or complement to other approaches and methods of experimental inference, such as statistical machine learning and classical information theory. AID is related to other areas such as computational mechanics and program synthesis. However, unlike methods such as Bayesian networks, AID does not rely on graphical models or the (often inaccessible) empirical estimation of mass probability distributions. AID encompasses the foundations and methods that make the area of algorithmic information and algorithmic complexity more relevant to scientific discovery and causal analysis. AID also connects with and across other parallel fields of active research such as logical inference, causal reasoning, and neuro-symbolic computation. AID studies how candidate discrete computable equations such as how generating mechanisms are affected by changes in observed phenomena over time as a result of a system evolving (e.g., under the influence of noise) or being externally perturbed (the location in time and space of such perturbations being hypothesized using algorithmic perturbation analysis).

Presenters in this session included Dr. Narsis Kiani, Dr. Felipe S. Abrahão, Dr. Santiago Hernández-Orozco, Dr. Jürgen Riedel, Dr. Victor Iapascurta, Cameron Sajedi, Martin Lind, and Dr. Hector Zenil who presented a number of introductions to the foundations, methods, and applications of AID, ranging from complex networks [2] to machine learning [3], cryptocurrency (Automacoin), and an application to epileptic seizure prediction [4].

In the context of the cryptocurrency project, the conference served as a platform to introduce Automacoin [5]. Automacoin was conceived to be the first cryptocurrency designed to be Turing-universal and also the most eco-friendly of all coins, as its computations are not only the most general-purpose and fundamental, but are stored and never lost or wasted, so they remain available which increases its value.

The Automacoin network behind the cryptocurrency computation is not only meaningful but it may, in a fundamental way, be considered to be the ultimate meaningful task that intelligent beings can perform to use all the energy available to answer all possible questions by mechanistic (computable) means.

  1,2 1 Escuela Superior de Cómputo, Instituto Politécnico Nacional, Mexico 2 Unconventional Computing Lab, University of the West of England, Bristol, UK Unconventional and natural computing has the capacity to handle information at an atomic and molecular level. Examples of these developments can be found in collision-based computers, reaction-diffusion computers, Physarum computers, quantum computers, molecular computing, and DNA computers. In this way, the cellular automata theory conceived by John von Neumann as a tool of super computation which work with indivisible elements and they are inherently and massively parallel. The second essential element and problem on these abstract machines is controller and design reliable components from unreliable organisms. Indeed, this issue is the nature of any unconventional computing architecture.

  1,2 1 IMAGES ESPACE-DEV, University of Perpignan Via Domitia, France 2 ESPACE-DEV, University of Montpellier, IRD, Université des Antilles, Université de Guyane, Université de La Réunion, France {yacoubi,sara.dridi,theo.plenet}@univ-perp.fr

Complex cellular automata repository. http://www.comunidad.escom.ipn.mx/genaro/Complex_CA_ repository.html.

This year, AUTOMATA also included a special session on Algorithmic Information Dynamics, an exciting new area of research.

We are indebted to the Steering Committee, Program Committee, and additional reviewers for their valuable help during the last months. We acknowledge the generous support and funding provided by IFIP, Oxford Immune Algorithmics, and the FQXi by way of the Silicon Valley Community Foundation.