Gérard Kubryk

1. My research in computer science has focused on automatic customization of websites and time analysis. Time between two consultations and time to read the page itself, which involves determining the meaning to be given to this last time. 

 Two algorithms have been developed: 

1. •  one is based on an analogy with gravity that gives us a function of the age of previous consultations while not allowing us to reconstruct a history of these consultations. This age allows to determine an "altitude" which is proportional to the interest of the user for this page. The altitude increases with each consultation and decreases according to the time elapsed since the last consultation. The reverse calculation is impossible and preserves the user’s privacy.

1. •  the other is based on an analogy with ants and their pheromone deposition. The analogy is based on the successive deposits of pheromone at each passage of an ant and evaporation between two passages. This analogy gives us a function of the age of previous consultations without possibility of inverse calculation allowing to reconstruct the navigation of the user. 

2.  My research in Education has focused on the difficulties of accessing mathematics. Three themes were discussed:

   •  subitization, which in the end, seems to be an error in the analysis of psychologists at the beginning of the 20th century. My work seems to show that this is an alteration of the quantity evaluation function for small quantities. This alteration is caused by the combination of Bayesian analyses of our brain in front of what it perceives (assessment of a probability of possible responses and choice of the best probability) and the Fechner effect which determines a threshold of perception of variations according to the intensity of a stimulus: 

 k = delta(i) / i 

In this formula:

 k is the perception threshold of the stimulus variation

 i is the initial stimulus value                                                                                                                            delta(i) is the variation of the stimulus value

For example if there are 3 sweets, the brain has the following possible evaluations:

2 is too little (delta is equal to -1, above Fechner threshold)

3 delta equals 0 is included in the Fechner threshold possibilities

4 is too much (delta is equal to 1, above the Fechner threshold)

fractional values that are impossible

Conclusion: the probability of response 3 close to 1 (at the threshold of the response error) is the only one possible. This gives a fast answer and few errors.

2. •  the influence of the quality of the brain function of evaluating quantities on the learning of arithmetic and on the progress of the child in mathematics. This also degrades the subitization and thus the response times and the quality of the child’s responses in games in kindergarten with small amounts of pieces of wood for example. This complicated situation for the child is the beginning of his difficulties in mathematics which can be aggravated by the behavior of his environment.

   •  the child’s home, school environment (other children and teachers) and its negative and/or positive influence on the child’s learning ability.