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## The formal language of propositional logic

After briefly introducing Aristotle's syllogistics in the last blog post, I should now actually explain how it were received and elaborated in antiquity, the Middle Ages and into modern times. In particular, the work of Gottfried Wilhelm Leibniz (1646 to 1716), in which important approaches to moder...

## Trouche, L. (2003). It and mathematics environments, what uses do you use for what learning?

mathematics, seen as a parangon of pure sciences, often give the image of science built in poor technological environments; however, they have developed by forging powerful material and symbolic tools for themselves (or by exploiting them). Mathematics teaching is generally more in line with the ima...

## Matheron Yves. Memory and study of mathematics. An anthropological didactic approach

From the foreword, Yves Matheron — a teacher researcher in the teaching of mathematics — presents his book and discusses its title. It is not a volume organising the presentation of research from different disciplines on memory and mathematics study. Memory is not regarded in his book as neuroscienc...

## Memoryless Control Design for Persistent Surveillance under Safety Constraints

This paper deals with the design of time-invariant memoryless control policies for robots that move in a finite two- dimensional lattice and are tasked with persistent surveillance of an area in which there are forbidden regions. We model each robot as a controlled Markov chain whose state comprises...

## Strategic Learning and the Topology of Social Networks

We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals, and by observing the actions of their neighbors in a social network. We show that the question of whether or not the agen...

## Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures

International audience The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention, or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene...

## Evaluating Education Systems

This paper proposes two dominance criteria for evaluating education systems described as joint distributions of the pupils' cognitive skill achievements and family backgrounds. The first criterion is shown to be the smallest transitive ranking of education systems compatible with three elementary pr...

## Kinetic models for optimal control of wealth inequalities

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the cor...

## The Least Spanning Area of a Knot and the Optimal Bounding Chain Problem

Two fundamental objects in knot theory are the minimal genus surface and the least area surface bounded by a knot in a 3-dimensional manifold. When the knot is embedded in a general 3-manifold, the problems of finding these surfaces were shown to be NP-complete and NP-hard respectively. However, the...

## Symmetry invariance for adapting biological systems

We study in this paper certain properties of the responses of dynamical systems to external inputs. The motivation arises from molecular systems biology. and, in particular, the recent discovery of an important transient property, related to Weber's law in psychophysics: "fold-change detection" in a...

## Speeding up SAT solver by exploring CNF symmetries : Revisited

Boolean Satisfiability solvers have gone through dramatic improvements in their performances and scalability over the last few years by considering symmetries. It has been shown that by using graph symmetries and generating symmetry breaking predicates (SBPs) it is possible to break symmetries in Co...

## A Random Matrix--Theoretic Approach to Handling Singular Covariance Estimates

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$ dimensional random vector the maximum likelihood estimate is...

## Autonomous workshops: students’ activity and experience

Independence at school, both the ability to develop among students and the ability to mobilise at home, is widely developed in classes, in various forms and with very different degrees of freedom. Students’ activity and experience of autonomous work situations are studied here to better understand w...

## Living in a research situation: the tiling of the kitchen

In this workshop, we will propose that the participants test, in groups, a research situation for the Class (SIRC) on a paving. This situation, resulting from research into discrete mathematics, offers first simple results and others which are less accessible, with some prolongations even being open...

## Asymptotic behaviour of gossip processes and small world networks

Both small world models of random networks with occasional long range connections and gossip processes with occasional long range transmission of information have similar characteristic behaviour. The long range elements appreciably reduce the effective distances, measured in space or in time, betwe...

## An overview of mathematical issues arising in the Geometric complexity theory approach to VP v.s. VNP

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the Geometric Complexity Theory program to prove a variant of Valiant's algebraic analog of the P not equal to NP conjecture. We also describe the precise separation of complexity classe...

## Adaptive Control Design under Structured Model Information Limitation: A Cost-Biased Maximum-Likelihood Approach

Networked control strategies based on limited information about the plant model usually results in worse closed-loop performance than optimal centralized control with full plant model information. Recently, this fact has been established by utilizing the concept of competitive ratio, which is define...

## Mathematically modelling Bayes’ theorem to investigate the origin of a forest fire

[ES] Mathematic modelling (MMT) is a basic element for teaching mathematics in engineering. The MMT phases would be to translate the actual problem into a mathematical problem, to solve the problem, to interpret the result in real key and finally to validate it. Bayesian probability is one of the to...