arXiv subjects

Nils Haug

Publications and source records attributed to Nils Haug.

6 recordsLinked to original sources

arXiv2019

Identification of gatekeeper diseases on the way to cardiovascular mortality

Multimorbidity, the co-occurrence of two or more chronic diseases such as diabetes, obesity or cardiovascular diseases in one patient, is a frequent phenomenon. To make care more efficient, it is of relevance to understand how different diseases condition each other over the life time of a patient. However, most of our current knowledge on such patient careers is either confined to narrow time spans or specific (sets of) diseases. Here, we present a population-wide analysis of long-term patient trajectories by clustering them according to their disease history observed over 17 years. When patients acquire new diseases, their cluster assignment might change. A health trajectory can then be described by a temporal sequence of disease clusters. From the transitions between clusters we construct an age-dependent multilayer network of disease clusters. Random walks on this multilayer network provide a more precise model for the time evolution of multimorbid health states when compared to models that cluster patients based on single diseases. Our results can be used to identify decisive events that potentially determine the future disease trajectory of a patient. We find that for elderly patients the cluster network consists of regions of low, medium and high in-hospital mortality. Diagnoses of diabetes and hypertension are found to strongly increase the likelihood for patients to subsequently move into the high-mortality region later in life.

physics.med-ph↗

arXiv2018

Multicritical Scaling in a Lattice Model of Vesicles

Vesicles, or closed fluctuating membranes, have been modeled in two dimensions by self-avoiding polygons, weighted with respect to their perimeter and enclosed area, with the simplest model given by area-weighted excursions. These models generically show a tricritical phase transition between an inflated and a crumpled phase, with a scaling function given by the logarithmic derivative of the Airy function. Extending such a model, we find realizations of multicritical points of arbitrary order, with the associated multivariate scaling functions expressible in terms of generalized Airy integrals, as previously conjectured by John Cardy. This work therefore adds to the small list of models with a critical phase transition, for which exponents and the associated scaling functions are explicitly known.

cond-mat.stat-mech↗

arXiv2017

Area-width scaling in generalised Motzkin paths

We consider a generalised version of Motzkin paths, where horizontal steps have length $\ell$, with $\ell$ being a fixed positive integer. We first give the general functional equation for the area-length generating function of this model. Using a heuristic ansatz, we derive the area-length scaling behaviour in terms of a scaling function in one variable for the special cases of Dyck, (standard) Motzkin and Schröder paths, before generalising our approach to arbitrary $\ell$. We then derive an expression for the generating function of Schröder paths and analyse the scaling behaviour of this function rigorously in the vicinity of the tri-critical point of the model by applying the method of steepest descents for the case of two coalescing saddle points. Our results show that for Dyck and Schröder paths, the heuristic scaling ansatz reproduces the rigorous results.

cond-mat.stat-mech↗

arXiv2016

Higher-order Airy scaling in deformed Dyck paths

We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, 'jumps' orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their half-length, area and number of jumps. This represents the first example of an exactly solvable lattice path model showing a higher-order multicritical point. Applying the generalized method of steepest descents, we see that the associated two-variable scaling function is given by the logarithmic derivative of a generalized (higher-order) Airy integral.

math-ph↗

arXiv2014

Uniform asymptotics of area-weighted Dyck paths

Using the generalized method of steepest descents for the case of two coalescing saddle points, we derive an asymptotic expression for the bivariate generating function of Dyck paths, weighted according to their length and their area in the limit of the area generating variable tending towards 1. The result is valid uniformly for a range of the length generating variable, including the tricritical point of the model.

math-ph↗

arXiv2014

From generalized directed animals to the asymmetric simple exclusion process

Using the generalized normally ordered form of words in a locally-free group of $n$ generators, we show that in the limit $n\to\infty$, the partition function of weighted directed lattice animals on a semi-infinite strip coincides with the partition function of stationary configurations of the asymmetric simple exclusion process (ASEP) with arbitrary entry/escape rates through open boundaries. We relate the features of the ASEP in the different regimes of the phase diagram to the geometric features of the associated generalized directed animals by showing the results of numerical simulations. In particular, we show how the presence of shocks at the first order transition line translates into the directed animal picture. Using the evolution equation for generalized, weighted Lukasiewicz paths, we also provide a straightforward calculation of the known ASEP generating function.

cond-mat.stat-mech↗