The analysis of invariant differential operators on certain multiplicity free spaces led recently to the introduction of a family of symmetric polynomials that is more general than Jack polynomials (see [KS], but also [OO1], [OO2]). They are called interpolation Jack polynomials, shifted Jack polynomials, or Capelli polynomials. Apart from being inhomogeneous, they are distinguished from classi...

The studies of multiplicity fluctuations in restricted domains of the phase space reveal the nature of particle correlations and are sensitive to the dynamics of the underlying process. The hadronic final state in DIS is a result of a hard partonic scattering at a large momentum transfersQ ≫ Λ. A subsequent parton cascade development down to some QCD cut-off Q0 and fragmentation occuring at sma...

This article interprets Jakob von Uexküll’s understanding of different beings’ Innenwelt, Gegenwelt, and umwelt through Deleuzian insights of multiplicity, context, and particularity. This Deleuzian interpolation into Uexküll’s insights acknowledges the absence of a unitary ‘human’ view of nature, recognizing instead that plural viewpoints of cultures, subgroups and individuals understand and i...

We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this paper, we show that multiplicity codes also admit powerful list-decoding and local list-decoding algorithms correcting a large fraction of errors. Sta...

The notion of scaling is hardly new. One of the earliest scaling arguments dates back to 1638 when Galileo Galilei published his infamous masterpiece entitled “Dialogues Concerning Two New Sciences”. Among other fundamental observations he examined the principle of similitude, the elementary properties of similar physical/biological structures. Galileo realized that the strength S of a bone inc...

These four years proved to be a very interesting and enjoyable period of my life. I was introduced to the international research community and visited many scientific events in different parts of the world. First of all, I want to heartily thank my supervisors, Antoon Kolen, Yves Crama, and Joris van de Klundert, for haven given me the opportunity to join the scientific world and academic commu...

This paper proves that, in a general financial model with incomplete markets, the multiplicity of certainty equilibria is not necessary for the existence of sunspot effects. These effects are present, by definition, when real economic variables differ across realizations of extrinsic uncertainty. In a financial model of incomplete markets with identical payouts across realizations of extrinsic ...