Searcharxiv⌕ Search

arXiv subjects

Fabian Lehmann

Publications and source records attributed to Fabian Lehmann.

22 records · Page 2Linked to original sources

Lotaru: Locally Estimating Runtimes of Scientific Workflow Tasks in Heterogeneous Clusters

Many scientific workflow scheduling algorithms need to be informed about task runtimes a-priori to conduct efficient scheduling. In heterogeneous cluster infrastructures, this problem becomes aggravated because these runtimes are required for each task-node pair. Using historical data is often not feasible as logs are typically not retained indefinitely and workloads as well as infrastructure changes. In contrast, online methods, which predict task runtimes on specific nodes while the workflow is running, have to cope with the lack of example runs, especially during the start-up. In this paper, we present Lotaru, a novel online method for locally estimating task runtimes in scientific workflows on heterogeneous clusters. Lotaru first profiles all nodes of a cluster with a set of short-running and uniform microbenchmarks. Next, it runs the workflow to be scheduled on the user's local machine with drastically reduced data to determine important task characteristics. Based on these measurements, Lotaru learns a Bayesian linear regression model to predict a task's runtime given the input size and finally adjusts the predicted runtime specifically for each task-node pair in the cluster based on the micro-benchmark results. Due to its Bayesian approach, Lotaru can also compute robust uncertainty estimates and provides them as an input for advanced scheduling methods. Our evaluation with five real-world scientific workflows and different datasets shows that Lotaru significantly outperforms the baselines in terms of prediction errors for homogeneous and heterogeneous clusters.

cs.DC↗

Deformations of asymptotically conical Spin(7)-manifolds

We consider the moduli space $\mathcal{M}_ν$ of torsion-free, asymptotically conical (AC) Spin(7)-structures which are defined on the same manifold and asymptotic to the same Spin(7)-cone with decay rate $ν<0$. We show that $\mathcal{M}_ν$ is an orbifold if $ν$ is a generic rate in the non-$L^2$ regime $(-4,0)$. Infinitesimal deformations are given by topological data and solutions to a non-elliptic first-order PDE system on the compact link of the asymptotic cone. As an application, we show that the classical Bryant-Salamon metric on the bundle of positive spinors on $S^4$ has no continuous deformations as an AC Spin(7)-metric.

math.DG↗

Geometric transitions with Spin(7) holonomy via a dynamical system

We clarify the global geometry of two 1-parameter families of cohomogeneity one Spin(7) holonomy metrics with generic orbit the Aloff--Wallach space $N(1,-1) \cong \mathrm{SU}(3)/\mathrm{U}(1)$ and singular orbits $S^5$ and $\mathbb{C}P^2$, which at short distance were shown to exist by Reidegeld. The two families fit into the geography of previously known families of cohomogeneity one metrics with exceptional holonomy and provide a Spin(7) analogue of the well-known conifold transition in the setting of Calabi--Yau 3-folds. Furthermore, we discover that there is another transition to families of Spin(7) holonomy metrics which have a similar asymptotic behaviour on one end, but are singular on the other end. We obtain our results by relating the Spin(7)-equations to a simple dynamical system on a 3-dimensional cube.

math.DG↗

Probing the Interface of a Phase-Separated State in a Repulsive Bose-Fermi Mixture

We probe the interface between a phase-separated Bose-Fermi mixture consisting of a small BEC of $^{41}$K residing in a large Fermi sea of $^6$Li. We quantify the residual spatial overlap between the two components by measuring three-body recombination losses for variable strength of the interspecies repulsion. A comparison with a numerical mean-field model highlights the importance of the kinetic energy term for the condensed bosons in maintaining the thin interface far into the phase-separated regime. Our results demonstrate a corresponding smoothing of the phase transition in a system of finite size.

quant-ph↗