Variability is an inherent feature of motor output both between and within subjects in all categories of tasks. Yet traditionally this feature of motor behavior has been dismissed as insignificant in many theories of motor control and operationally treated as a standard deviation in distributional statistics. In theories about the variability of motor output, the most common position has been that variability reflects noise. Recently some optimal control theories have been proposed stating that motor system minimizes variability both in sensory information and in motor output. This principle of optimality suggests that variability is a nuisance and should be controlled in order to minimize 'costs' functions. In other words, variability is regarded as a dysfunctional aspect of a sensorimotor system, resulting from some random fluctuations that compromise the deterministic relation between a 'sensori- input and a 'motor- output. This view has been challenged by other theoretical approaches that regard variability as a central factor for adapting behaviors. On the one hand the dynamic systems theory places greater emphasis on the space-time characteristics of coordination patterns in tasks requiring multiple degrees of freedom. Within this framework variability reflects the capacity for flexible and adaptive sensorimotor systems to adapt to specific environmental and tasks demands. On the other hand, the selectionist approach of operant conditioning postulates that new behaviors are shaped based on variations of other responses: variability is necessary to adapt to changes in reinforcement contingencies. Thus variations of behavior leading to the final response are selectively reinforced driving gradual changes in the topography of the response. It follows that variability is useful ' if not necessary ' for learning new behaviors. This hypothesis have rarely been tested, except for one study in which experimental manipulations of the level of variability revealed that only rats trained to produce variable responses were able to acquire a difficult-to-learn sequence. To our knowledge, the possibility to control behavioral variability has never been tested for sensorimotor control in humans, except for one of our recent study. In this set of experiments we showed that one could increase or decrease variability of latencies distributions in saccades and manual responses, independently from the medians, by manipulating reinforcement contingencies. Our interpretation is that some of the observed variability reflects environmental constraints controlling the response instead of depending solely on internal noise. In other words, we propose that variability in behavior also results from loose environmental constraints. A fundamental question involving variability has been the understanding of the emergence of new responses using the concept of shaping. In shaping a response-reinforcer contingency is gradually changed to select environment-behavior relations that progressively approach some criterion response topography. In contrast, the classical engineer-like approach of sensorimotor control usually regards a change in the system as a re-calibration of some parameter. For instance in adaptation phenomenon in which the outcome of the system is modified by applying some constant perturbation, the system progressively adapt in order to compensate for this change in its dynamics. Within the oculomotor system, this has been extensively studied by shifting a target during a saccade so that the latter becomes dysmetric. The conventional view has been to view saccade adaptation as a servo-mechanism, in which the presence of an 'error signal' changes the parameters of the saccadic system, thereby reducing the error over many trials. According to this conceptualization, saccade adaptation is learning only in the most restricted sense of the word, in that a change in behavior occurs as a consequence of an adjustment of some unspecified internal gain. We propose to test whether variations of motor behaviors are under the control of reinforcement contingencies. Moreover we intend to test for a relationship between variability and the ability to adapt to changes in the environment. These hypothesis will be addressed in the saccadic system and the arm movement system and involve behavioral studies. We anticipate that this project will provide a solid framework for studying other forms of sensorimotor plasticity. If the results corroborate our hypothesis this will constitute a breakthrough in the study of motor learning, with fundamental implications for the understanding of plasticity in other systems.

The project aims to carry an in-depth investigation on the algorithmic features of some deductive patterns in pre-modern mathematics. The project will be mainly focused on Greek mathematics, but perspectives will be opened on such mathematical cultures as Arabo-Latin, Babylonian. Chinese, Egyptian and Indian, where algorithms played a major role in shaping deductive patterns. Task 1) Chinese mathematical texts (Andrea Bréard) Research will focus on the treatment of finite arithmetical series in Zhu Shijie's The Jade Mirror of Four Primordials and Qing-dynasty commentaries written after its rediscovery at the beginning of the 19th century. Systematically deductive aspects by which Zhu Shijie constructs a system of finite arithmetical series will be studied. Task 2) Greek mathematical texts (Fabio Acerbi, Nathalie Gasiglia, Myriam Hecquet, Bernard Vitrac) Task 2.1) Deductive structures in Greek mathematics. A wide ranging study of the interactions between deductive patterns in mathematical proofs, the ancient method of analysis and synthesis, and ancient Greek logic, in particular Stoic logic. A software will be produced to analyze the 'deductive density' of a Greek mathematical text. Task 2.2) Edition of Greek mathematical texts. i) The Metrica by Hero of Alexandria. Their edition in the Heronian Opera omnia is unsatisfactory. ii) The so-called Geometrica and Stereometrica. These 'treatises' have been edited in the Heronian Opera omnia, but they are in fact philological patchworks made up of disparate treatises attested in manuscripts of the metrological corpus. iii) The De polygonis numeris by Diophantus of Alexandria. It has been edited in the Diophantine Opera omnia, but the edition is not satisfactory. iv) The anonymous Prolegomena to the Almagest. The entire text still lies unedited. Task 3) Arabic and Latin mathematical texts (Marc Moyon, Mohamed Aballagh) The possible filiations between the Arab tradition of al-Andalus and the Latin texts written from the 12th century are studied: the pre-algebraic practices will be privileged with the Arab texts of misâha [measurement] and the Latin Practica Geometria. Latin texts of interest: 1) The Liber mensurationum by Abû Bakr. This treatise has been edited, but still lies not translated. 2) The Liber Saydi Abuothmi and the Liber Aderameti. Only a (non critical) edition and a light commentary do exist. 3) The Liber embadorum by Abraham Bar Hiyya. On the Arabic side, the seminal role of the work of the Maghreb mathematician Ibn al-Banna al-Murrakushi (1256-1321) in the development of logistic and algebra in 14th century Maghreb mathematics will be studied, through edition and translation of Ibn Zakariya al-Gharnati's Commentary on Ibn al-Banna's Talkhis Task 4) Babylonian and Egyptian Mathematical texts (James Ritter) Research is proposed in the following two directions: 1) The mathematical corpus in the case of Egypt has been systematically explored from the algorithmic point of view. A similar near exhaustive analysis needs to be carried out for the Mesopotamian mathematical texts. In both cases the structural role of subalgorithms, branchings and so forth need to be made explicit and their logical and pedagogical roles understood. 2) The similarity between the algorithmic structure of the mathematical texts and those from other disciplines has only been touched upon up to now. New examples have recently been uncovered in unexpected areas: glass-making, harp-tuning. Task 5) Egyptian Demotic mathematical texts (Annette Imhausen) As Egyptian mathematics has traditionally been seen as having reached the height of its development in the early Middle Kingdom, it is planned to extend the scope of the studies of Egyptian mathematics by taking up the Demotic mathematical problem texts, which are written in an algorithmic style. In 1972 R. Parker claimed to discern a Mesopotamian influence in some of the problems. Examining their procedures for solving problems in terms of an algorithmic analysis makes it possible to achieve a detailed comparison of the respective mathematical methods they used. Task 6) Sanskrit mathematical texts of the Indian subcontinent (Agathe Keller, Catherine Singh) A comparative study of mathematical texts from the 5th to the 12th century will be undertaken, examining what characterizes the way they express algorithms. The goals are: 1) editing and translating portions of the commentaries to the Âryabhatîya, a 5th century astronomical text with a mathematical chapter. 2) editing and translating portions of a commentary (ca. 864) to the Brâhmasphutasiddhânta, an astronomical treatise critical of the Âryabhatîya, with a mathematical chapter. 3) editing and translating portions of the commentaries to two practical mathematical treatises during this period, the Patiganita and the Ganitasârasangraha. 4) Setting up a close comparison of the modes of expressing and explaining algorithms in these different set of texts.

The Time-Us project aims to reconstruct the remuneration and time budgets of women and men working in the textile trades in four French industrial regions (Lille, Paris, Lyon, Marseille) in an European and long-term perspective, by bringing together a multidisciplinary team of technology, economic and labour historians, natural language processing (NLP) experts and sociologists specializing in Le Play’s families’ budgets. The role of women in industrial development is now largely recognized in both sociological and economic studies on developing countries and the historiography of the first industrial revolution in Europe. Yet data on their remuneration, schedules and domestic work and that of men working in the same sectors remain deficient for many regions, especially for France. A full understanding of economic development cannot be achieved without assessing the quantity of women’s paid and unpaid work, and the male/female distribution of time spent on domestic work. The Time-Us project aims to collect missing data for France in a key sector of the first industrial revolution: textiles. The goal is to create comparable series on the remuneration and time allocation of employed men and women through, first, classical sources and company and trade association archives, and second, the piecing together of a series of qualitative sources identifying words and actions associated with work in both domestic and non-domestic activities. By proposing an exercise that has never been tackled for France to date, it aims to provide keys to understanding the gender gap by analyzing changes in work and time uses during the first industrialization process, and goes to the core of issues raised in the DEFI 8’s Axe 3. “Transformations in work and employment, organizational change” – and in the sub-areas “Family life/professional life balance and work time /social times” and “Women and men at work: the challenge of professional equality and the role of work”.