The Lattice of integer partitions and its infinite extension

In this paper, we use a simple discrete dynamical system to study the integers partitions and their lattice. The set of the reachable configurations equiped with the order induced by the transitions of the system is exactly the lattice of integer partitions equiped with the dominance ordering. We first explain how this lattice can be constructed, by showing its strong self-similarity property. Then, we define a natural extension of the system to infinity. Using a self-similar tree, we obtain an efficient coding of the obtained lattice. This approach gives an interesting recursive formula for the number of partitions of an integer, where no closed formula have ever been found. It also gives informations on special sets of partitions, such as length bounded partitions.Comment: To appear in LNCS special issue, proceedings of ORDAL'99. See http://www.liafa.jussieu.fr/~latap

Anyon Basis of c=1 Conformal Field Theory

We study the $c=1$ conformal field theory of a free compactified boson with radius $r=\sqrt{\beta}$ ($\beta$ is an integer). The Fock space of this boson is constructed in terms of anyon vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave function of multi anyon state is described by an eigenfunction of the Calogero-Sutherland (CS) model. The $c=1$ conformal field theory at $r=\sqrt{\beta}$ gives a field theory of CS model. This is a natural generalization of the boson-fermion correspondence in one dimension to boson-anyon correspondence. There is also an interesting duality between anyon with statistics $\theta=\pi/\beta$ and particle with statistics $\theta=\beta \pi$.Comment: 17 page

Excited States of Calogero-Sutherland Model and Singular Vectors of the WNW_N Algebra

Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the $W_N$ algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.Comment: LaTeX, 29 pages, 2 figures, New sections for skew-Jack polynomial and example of singular vectors adde

Single particle Green's function in the Calogero-Sutherland model for rational couplings β=p/q\beta=p/q

We derive an exact expression for the single particle Green function in the Calogero-Sutherland model for all rational values of the coupling $\beta$. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two type of intermediate states contribute. The firts one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.Comment: 9 pages, RevTeX, epsf.tex, 4 figures, files uuencode

Correspondence between conformal field theory and Calogero-Sutherland model

We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators $L_n$. We calculate explicitly the matrix elements of $L_n$ with respect to the Jack-basis. A combinatorial procedure which produces these matrix elements is conjectured. As a limiting case of the formula, we obtain a Pieri-type formula which represents a product of a power sum and a Jack symmetric function as a sum of Jack symmetric functions. Also, a similar expansion was found for the case when we differentiate the Jack symmetric functions with respect to power sums. As an application of our Jack-basis representation, a new diagrammatic interpretation is presented, why the singular vectors of the Virasoro algebra are proportional to the Jack symmetric functions with rectangular diagrams. We also propose a natural normalization of the singular vectors in the Verma module, and determine the coefficients which appear after bosonization in front of the Jack symmetric functions.Comment: 23 pages, references adde

Can religion kill? The association between membership of the Apostolic faith and child mortality in Zimbabwe

Existing literature has been equivocal about the effect of religion on utilization of health service and health outcomes. While followers of particularized theology hypothesis believe that doctrinal teachings, beliefs and values of religious groups directly influence health access and outcomes, the advocates of the selectivity hypothesis claim that the observed disparities between religious groups mainly reflect differential access to social and human capital which in turn determines health access and outcome rather than religion per se. Using household data from the Zimbabwe Multiple Indicator Monitoring Survey 2009, we find that household heads’ affiliation with apostolic faith put children under five years old at greater risk of death compared to other religious groups. This effect remains strong even after controlling for a wide range of socio-economic and demographics characteristics of the households in multivariate logit regressions

Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate

The Web of Human Sexual Contacts

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.Comment: 7 pages with 2 eps figures. Latex file. For more details or for downloading the PDF file of the published article see http://polymer.bu.edu/~amaral/WebofContacts.html . For more results on teh structure of complex networks see http://polymer.bu.edu/~amaral/Networks.htm