The numerical syllogistic is the extension of the traditional syllogistic with numerical quantifiers of the forms at least C and at most C. It is known that, for the traditional syllogistic, a finite collection of rules, similar in spirit to the classical syllogisms, constitutes a sound and complete proof-system. The question arises as to whether such a proof system exists for the numerical syl...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...

This article deals with basic concepts of leadership based on the research of the French sinologist François Jullien. It addresses particularly the concept of efficacy in Greek thought in comparison with Daoist thought (Zhuangzi). This comparison is particularly relevant because classical Chinese philosophy developed over thousands of years with hardly any influence from the West. The spirit of...

This chapter illustrates two aspects of automata theory related to lineartime temporal logic LTL used for the verification of computer systems. First, we present a translation from LTL formulae to Büchi automata. The aim is to design an elementary translation which is reasonably efficient and produces small automata so that it can be easily taught and used by hand on real examples. Our translat...

We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization in the classical spirit by superposing two harmonic oscillators of the same angular frequency along two orthogonal axes. By describing each oscillator by a s-parametrized quasidistribution, we de...

We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point o...

This chapter illustrates two aspects of automata theory related to lineartime temporal logic LTL used for the verification of computer systems. First, we present a translation from LTL formulae to Büchi automata. The aim is to design an elementary translation which is reasonably efficient and produces small automata so that it can be easily taught and used by hand on real examples. Our translat...