The effect of host heterogeneity and parasite intragenomic interactions on parasite population structure

Understanding the processes that shape the genetic structure of parasite populations and the functional consequences of different parasite genotypes is critical for our ability to predict how an infection can spread through a host population and for the design of effective vaccines to combat infection and disease. Here, we examine how the genetic structure of parasite populations responds to host genetic heterogeneity. We consider the well-characterized molecular specificity of major histocompatibility complex binding of antigenic peptides to derive deterministic and stochastic models. We use these models to ask, firstly, what conditions favour the evolution of generalist parasite genotypes versus specialist parasite genotypes? Secondly, can parasite genotypes coexist in a population? We find that intragenomic interactions between parasite loci encoding antigenic peptides are pivotal in determining the outcome of evolution. Where parasite loci interact synergistically (i.e. the recognition of additional antigenic peptides has a disproportionately large effect on parasite fitness), generalist parasite genotypes are favoured. Where parasite loci act multiplicatively (have independent effects on fitness) or antagonistically (have diminishing effects on parasite fitness), specialist parasite genotypes are favoured. A key finding is that polymorphism is not stable and that, with respect to functionally important antigenic peptides, parasite populations are dominated by a single genotype

Competing density-wave orders in a one-dimensional hard-boson model

We describe the zero-temperature phase diagram of a model of bosons, occupying sites of a linear chain, which obey a hard-exclusion constraint: any two nearest-neighbor sites may have at most one boson. A special case of our model was recently proposed as a description of a ``tilted'' Mott insulator of atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to generate the transfer matrix of Baxter's hard-square model. Aided by exact solutions of a number of special cases, and by numerical studies, we obtain a phase diagram containing states with long-range density-wave order with period 2 and period 3, and also a floating incommensurate phase. Critical theories for the various quantum phase transitions are presented. As a byproduct, we show how to compute the Luttinger parameter in integrable theories with hard-exclusion constraints.Comment: 16 page

Universality relations in non-solvable quantum spin chains

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models

Divergent selection on locally adapted major histocompatibility complex immune genes experimentally proven in the field

Although crucial for the understanding of adaptive evolution, genetically resolved examples of local adaptation are rare. To maximize survival and reproduction in their local environment, hosts should resist their local parasites and pathogens. The major histocompatibility complex (MHC) with its key function in parasite resistance represents an ideal candidate to investigate parasite-mediated local adaptation. Using replicated field mesocosms, stocked with second-generation lab-bred three-spined stickleback hybrids of a lake and a river population, we show local adaptation of MHC genotypes to population-specific parasites, independently of the genetic background. Increased allele divergence of lake MHC genotypes allows lake fish to fight the broad range of lake parasites, whereas more specific river genotypes confer selective advantages against the less diverse river parasites. Hybrids with local MHC genotype gained more body weight and thus higher fitness than those with foreign MHC in either habitat, suggesting the evolutionary significance of locally adapted MHC genotypes

Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical Hamiltonians is a realization of an integrable Haldane system. The finite-size spectra of the critical Hamiltonians deviate in their structure from standard predictions by conformal invariance.Comment: 16 pages, to appear in Z. Phys. B, preprint Cologne-94-474

Quantized Skyrmion Fields in 2+1 Dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.Comment: Accepted for Physical Review

A class of ansatz wave functions for 1D spin systems and their relation to DMRG

We investigate the density matrix renormalization group (DMRG) discovered by White and show that in the case where the renormalization eventually converges to a fixed point the DMRG ground state can be simply written as a ``matrix product'' form. This ground state can also be rederived through a simple variational ansatz making no reference to the DMRG construction. We also show how to construct the ``matrix product'' states and how to calculate their properties, including the excitation spectrum. This paper provides details of many results announced in an earlier letter.Comment: RevTeX, 49 pages including 4 figures (macro included). Uuencoded with uufiles. A complete postscript file is available at http://fy.chalmers.se/~tfksr/prb.dmrg.p

Spectral Decomposition of Path Space in Solvable Lattice Model

We give the {\it spectral decomposition} of the path space of the U_q(\hatsl) vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the \hatsl level $l$ integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the \hatsl level $l$ integrable representations in consequence.Comment: 27 pages, Plain Tex, epsf.tex, 7 figures; minor revision. identical with the version to be published in Commun.Math.Phy

Extended scaling relations for planar lattice models

It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theory obtained as formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones by Kadanoff, [K], and by Luther and Peschel, [LP].Comment: 32 pages, 7 fi

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.Comment: to appear in Physical Review