arXiv subjects

Frank Hausser

Publications and source records attributed to Frank Hausser.

7 recordsLinked to original sources

arXiv2022

Towards ML Methods for Biodiversity: A Novel Wild Bee Dataset and Evaluations of XAI Methods for ML-Assisted Rare Species Annotations

Insects are a crucial part of our ecosystem. Sadly, in the past few decades, their numbers have worryingly decreased. In an attempt to gain a better understanding of this process and monitor the insects populations, Deep Learning may offer viable solutions. However, given the breadth of their taxonomy and the typical hurdles of fine grained analysis, such as high intraclass variability compared to low interclass variability, insect classification remains a challenging task. There are few benchmark datasets, which impedes rapid development of better AI models. The annotation of rare species training data, however, requires expert knowledge. Explainable Artificial Intelligence (XAI) could assist biologists in these annotation tasks, but choosing the optimal XAI method is difficult. Our contribution to these research challenges is threefold: 1) a dataset of thoroughly annotated images of wild bees sampled from the iNaturalist database, 2) a ResNet model trained on the wild bee dataset achieving classification scores comparable to similar state-of-the-art models trained on other fine-grained datasets and 3) an investigation of XAI methods to support biologists in annotation tasks.

cs.AI↗

arXiv2012

Return Radius and volume of recrystallized material in Ostwald Ripening

Within the framework of the LSW theory of Ostwald ripening the amount of volume of the second (solid) phase that is newly formed by recrystallization is investigated. It is shown, that in the late stage, the portion of the newly generated volume formed within an interval from time $t_0$ to $t$ is a certain function of $t/t_0$ and an explicit expression of this volume is given. To achieve this, we introduce the notion of the {\it return radius} $r(t,t_0)$, which is the unique radius of a particle at time $t_0$ such that this particle has -- after growing and shrinking -- the same radius at time $t$. We derive a formula for the return radius which later on is used to obtain the newly formed volume. Moreover, formulas for the growth rate of the return radius and the recrystallized material at time $t_0$ are derived.

math-ph↗

arXiv2007

Morphological stability of electromigration-driven vacancy islands

The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of the island. In the limit of fast attachment/detachment kinetics a circle translating at constant velocity is a stationary solution of the problem. In contrast to earlier work [O. Pierre-Louis and T.L. Einstein, Phys. Rev. B 62, 13697 (2000)] we show that the circular solution remains linearly stable for arbitrarily large driving forces. The numerical solution of the full nonlinear problem nevertheless reveals a fingering instability at the trailing end of the island, which develops from finite amplitude perturbations and eventually leads to pinch-off. Relaxing the condition of instantaneous attachment/detachment kinetics, we obtain non-circular elongated stationary shapes in an analytic approximation which compares favorably to the full numerical solution.

cond-mat.mtrl-sci↗

arXiv2005

Complex shape evolution of electromigration-driven single-layer islands

The shape evolution of two-dimensional islands through periphery diffusion biased by an electromigration force is studied numerically using a continuum approach. We show that the introduction of crystal anisotropy in the mobility of edge atoms induces a rich variety of migration modes, which include oscillatory and irregular behavior. A phase diagram in the plane of anisotropy strength and island size is constructed. The oscillatory motion can be understood in terms of stable facets which develop on one side of the island and which the island then slides past. The facet orientations are determined analytically.

cond-mat.mtrl-sci↗

arXiv1999

Integral Theory for Quasi-Hopf Algebras

We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and uniqueness (up to scalar multiples) of integrals in H. Among other applications we prove a Maschke type Theorem for diagonal crossed products as constructed by the authors.

math.QA↗

arXiv1997

Doubles of Quasi-Quantum Groups

Drinfeld showed that any finite dimensional Hopf algebra \G extends to a quasitriangular Hopf algebra \D(\G), the quantum double of \G. Based on the construction of a so--called diagonal crossed product developed by the authors, we generalize this result to the case of quasi--Hopf algebras \G. As for ordinary Hopf algebras, as a vector space the ``quasi--quantum double'' \D(\G) is isomorphic to the tensor product of \G and its dual \dG. We give explicit formulas for the product, the coproduct, the R--matrix and the antipode on \D(\G) and prove that they fulfill Drinfeld's axioms of a quasitriangular quasi--Hopf algebra. In particular \D(\G) becomes an associative algebra containing \G as a quasi--Hopf subalgebra. On the other hand, \dG \otimes 1 is not a subalgebra of \D(\G) unless the coproduct on \G is strictly coassociative. It is shown that the category of finite dimensional representations of \D(\G) coincides with what has been called the double category of \G--modules by S. Majid [M2]. Thus our construction gives a concrete realization of Majid's abstract definition of quasi--quantum doubles in terms of a Tannaka--Krein--like reconstruction procedure. The whole construction is shown to generalize to weak quasi--Hopf algebras with \D(\G) now being linearly isomorphic to a subspace of \dG \otimes \G.

q-alg↗

arXiv1997

Diagonal Crossed Products by Duals of Quasi-Quantum Groups

Let \G be a (weak) quasi-Hopf algebra. Using a two-sided \G-coaction on an algebra \M, we construct what we call the diagonal crossed product as a new associative algebra structure on \M\otimes \dG, where \dG is the dual of \G. This construction is largely motivated by the special case \M = \G, for which we obtain an explicit definition of the quantum double \D(\G) for quasi-Hopf algebras. Applications of our formalism include the field algebra construction of Mack and Schomerus as well as the formulation of Hopf Spin chains or lattice current algebras based on truncated quantum groups at roots of unity. A complete proof that \D(\G) is even a (weak) quasi-triangular quasi-Hopf algebra will be given in a separate paper.

q-alg↗