46 research outputs found
On 4-point correlation functions in simple polymer models
We derive an exact formula for the covariance of cartesian distances in two
simple polymer models, the freely-jointed chain and a discrete flexible model
with nearest-neighbor interaction. We show that even in the interaction-free
case correlations exist as long as the two distances at least partially share
the same segments. For the interacting case, we demonstrate that the naive
expectation of increasing correlations with increasing interaction strength
only holds in a finite range of values. Some suggestions for future
single-molecule experiments are made
Large-N Asymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
We derive the large-, all order asymptotic expansion for a system of particles with mean field interactions on top of a Coulomb repulsion at temperature , under the assumptions that the interactions are analytic, off-critical, and satisfy a local strict convexity assumptio
Riemann-Hilbert approach to a generalized sine kernel and applications
We investigate the asymptotic behavior of a generalized sine kernel acting on
a finite size interval [-q,q]. We determine its asymptotic resolvent as well as
the first terms in the asymptotic expansion of its Fredholm determinant.
Further, we apply our results to build the resolvent of truncated Wiener--Hopf
operators generated by holomorphic symbols. Finally, the leading asymptotics of
the Fredholm determinant allows us to establish the asymptotic estimates of
certain oscillatory multidimensional coupled integrals that appear in the study
of correlation functions of quantum integrable models.Comment: 74 page
Combinatorics of generalized Bethe equations
A generalization of the Bethe ansatz equations is studied, where a scalar
two-particle S-matrix has several zeroes and poles in the complex plane, as
opposed to the ordinary single pole/zero case. For the repulsive case (no
complex roots), the main result is the enumeration of all distinct solutions to
the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial
interpretations of the Fuss-Catalan and related numbers are obtained. On the
one hand, they count regular orbits of the permutation group in certain factor
modules over Z^M, and on the other hand, they count integer points in certain
M-dimensional polytopes
Stable population structure in Europe since the Iron Age, despite high mobility
Ancient DNA research in the past decade has revealed that European population structure changed dramatically in the prehistoric period (14,000–3000 years before present, YBP), reflecting the widespread introduction of Neolithic farmer and Bronze Age Steppe ancestries. However, little is known about how population structure changed from the historical period onward (3000 YBP - present). To address this, we collected whole genomes from 204 individuals from Europe and the Mediterranean, many of which are the first historical period genomes from their region (e.g. Armenia and France). We found that most regions show remarkable inter-individual heterogeneity. At least 7% of historical individuals carry ancestry uncommon in the region where they were sampled, some indicating cross-Mediterranean contacts. Despite this high level of mobility, overall population structure across western Eurasia is relatively stable through the historical period up to the present, mirroring geography. We show that, under standard population genetics models with local panmixia, the observed level of dispersal would lead to a collapse of population structure. Persistent population structure thus suggests a lower effective migration rate than indicated by the observed dispersal. We hypothesize that this phenomenon can be explained by extensive transient dispersal arising from drastically improved transportation networks and the Roman Empire’s mobilization of people for trade, labor, and military. This work highlights the utility of ancient DNA in elucidating finer scale human population dynamics in recent history