Publications at the Department of Mathematics and Natural Sciences from 2019

Results: 586
Created on: Wed, 06 Jul 2022 23:07:51 +0200 in 0.0912 sec

Aigner-Horev, Elad; Person, Yury;
On sparse random combinatorial matrices. - In: Discrete mathematics, Bd. 345 (2022), 11, 113017

Let Qn,d denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at random from the subset of vectors in {0,1}n having precisely d entries equal to 1. We present a short proof of the fact that P[det⁡(Qn,d)=0]=O(n1/2log3/2⁡nd)=o(1), whenever ω(n1/2log3/2⁡n)=d≤n/2. In particular, our proof accommodates sparse random combinatorial matrices in the sense that d=o(n) is allowed. We also consider the singularity of deterministic integer matrices A randomly perturbed by a sparse combinatorial matrix. In particular, we prove that P[det⁡(A+Qn,d)=0]=O(n1/2log3/2⁡nd), again, whenever ω(n1/2log3/2⁡n)=d≤n/2 and A has the property that (1,-d) is not an eigenpair of A.
Hörsch, Florian; Szigeti, Zoltán;
Reachability in arborescence packings. - In: Discrete applied mathematics, Bd. 320 (2022), S. 170-183

Fortier et al. proposed several research problems on packing arborescences and settled some of them. Others were later solved by Matsuoka and Tanigawa and by Gao and Yang. The last open problem is settled in this article. We show how to turn an inductive idea used in the latter two articles into a simple proof technique that allows to relate previous results on arborescence packings. We prove that a strong version of Edmonds’ theorem on packing spanning arborescences implies Kamiyama, Katoh and Takizawa’s result on packing reachability arborescences and that Durand de Gevigney, Nguyen and Szigeti’s theorem on matroid-based packing of arborescences implies Király’s result on matroid-reachability-based packing of arborescences. Further, we deduce a new result on matroid-reachability-based packing of mixed hyperarborescences from a theorem on matroid-based packing of mixed hyperarborescences due to Fortier et al.. Finally, we deal with the algorithmic aspects of the problems considered. We first obtain algorithms to find the desired packings of arborescences in all settings and then apply Edmonds’ weighted matroid intersection algorithm to also find solutions minimizing a given weight function.
Henkel, Thomas; Mayer, Günter; Hampl, Jörg; Cao-Riehmer, Jialan; Ehrhardt, Linda; Schober, Andreas; Groß, Gregor Alexander;
From microtiter plates to droplets - there and back again. - In: Micromachines, ISSN 2072-666X, Bd. 13 (2022), 7, 1022, S. 1-13

Droplet-based microfluidic screening techniques can benefit from interfacing established microtiter plate-based screening and sample management workflows. Interfacing tools are required both for loading preconfigured microtiter-plate (MTP)-based sample collections into droplets and for dispensing the used droplets samples back into MTPs for subsequent storage or further processing. Here, we present a collection of Digital Microfluidic Pipetting Tips (DMPTs) with integrated facilities for droplet generation and manipulation together with a robotic system for its operation. This combination serves as a bidirectional sampling interface for sample transfer from wells into droplets (w2d) and vice versa droplets into wells (d2w). The DMPT were designed to fit into 96-deep-well MTPs and prepared from glass by means of microsystems technology. The aspirated samples are converted into the channel-confined droplets’ sequences separated by an immiscible carrier medium. To comply with the demands of dose-response assays, up to three additional assay compound solutions can be added to the sample droplets. To enable different procedural assay protocols, four different DMPT variants were made. In this way, droplet series with gradually changing composition can be generated for, e.g., 2D screening purposes. The developed DMPT and their common fluidic connector are described here. To handle the opposite transfer d2w, a robotic transfer system was set up and is described briefly.
Bang-Jensen, Jørgen; Kriesell, Matthias;
Good acyclic orientations of 4-regular 4-connected graphs. - In: Journal of graph theory, ISSN 1097-0118, Bd. 100 (2022), 4, S. 698-720

An st-ordering of a graph G=(V,E) is an ordering v1,v2,…,vn of its vertex set such that s=v1,t=vn and every vertex vi with i=2,3,…,n-1 has both a lower numbered and a higher numbered neighbor. Such orderings have played an important role in algorithms for planarity testing. It is well-known that every 2-connected graph has an st-ordering for every choice of distinct vertices s,t. An st-ordering of a graph G corresponds directly to a so-called bipolar orientation of G, that is, an acyclic orientation D of G in which s is the unique source and t is the unique sink. Clearly every bipolar orientation of a graph has an out-branching rooted at the source vertex and an in-branching rooted at the sink vertex. In this paper, we study graphs which admit a bipolar orientation that contains an out-branching and in-branching which are arc-disjoint (such an orientation is called good). A 2T-graph is a graph whose edge set can be decomposed into two edge-disjoint spanning trees. Clearly a graph has a good orientation if and only if it contains a spanning 2T-graph with a good orientation, implying that 2T-graphs play a central role. It is a well-known result due to Tutte and Nash-Williams, respectively, that every 4-edge-connected graph contains a spanning 2T-graph. Vertex-minimal 2T-graphs with at least two vertices, also known as generic circuits, play an important role in rigidity theory for graphs. Recently with Bessy and Huang we proved that every generic circuit has a good orientation. In fact, we may specify the roots of the two branchings arbitrarily as long as they are distinct. Using this, several results on good orientations of 2T-graphs were obtained. It is an open problem whether there exists a polynomial algorithm for deciding whether a given 2T-graph has a good orientation. Complex constructions of 2T-graphs with no good orientation were given in work by Bang-Jensen, Bessy, Huang and Kriesell (2021) indicating that the problem might be very difficult. In this paper, we focus on so-called quartics which are 2T-graphs where every vertex has degree 3 or 4. We identify a sufficient condition for a quartic to have a good orientation, give a polynomial algorithm to recognize quartics satisfying the condition and a polynomial algorithm to produce a good orientation when this condition is met. As a consequence of these results we prove that every 4-regular and 4-connected graph has a good orientation, where, as for generic circuits, we may specify the roots of the two branchings arbitrarily as long as they are distinct. We also provide evidence that even for quartics it may be difficult to find a characterization of those instances which have a good orientation. We also show that every graph on n≥8 vertices and of minimum degree at least has a good orientation. Finally we pose a number of open problems.
Cao-Riehmer, Jialan; Chande, Charmi; Köhler, Michael;
Microtoxicology by microfluidic instrumentation: a review. - In: Lab on a chip, ISSN 1473-0189, (2022), insges. 24 S.

Microtoxicology is concerned with the toxic effects of small amounts of substances. This review paper discusses the application of small amounts of noxious substances for toxicological investigation in small volumes. The vigorous development of miniaturized methods in microfluidics over the last two decades involves chip-based devices, micro droplet-based procedures, and the use of micro-segmented flow for microtoxicological studies. The studies have shown that the microfluidic approach is particularly valuable for highly parallelized and combinatorial dose-response screenings. Accurate dosing and mixing of effector substances in large numbers of microcompartments supplies detailed data of dose-response functions by highly concentration-resolved assays and allows evaluation of stochastic responses in case of small separated cell ensembles and single cell experiments. The investigations demonstrate that very different biological targets can be studied using miniaturized approaches, among them bacteria, eukaryotic microorganisms, cell cultures from tissues of multicellular organisms, stem cells, and early embryonic states. Cultivation and effector exposure tests can be performed in small volumes over weeks and months, confirming that the microfluicial strategy is also applicable for slow-growing organisms. Here, the state of the art of miniaturized toxicology, particularly for studying antibiotic susceptibility, drug toxicity testing in the miniaturized system like organ-on-chip, environmental toxicology, and the characterization of combinatorial effects by two and multi-dimensional screenings, is discussed. Additionally, this review points out the practical limitations of the microtoxicology platform and discusses perspectives on future opportunities and challenges.
Derkach, Volodymyr; Hassi, Seppo; Malamud, Mark;
Generalized boundary triples, II : some applications of generalized boundary triples and form domain invariant Nevanlinna functions. - In: Mathematische Nachrichten, ISSN 1522-2616, Bd. 295 (2022), 6, S. 1113-1162

The paper is a continuation of Part I and contains several further results on generalized boundary triples, the corresponding Weyl functions, and applications of this technique to ordinary and partial differential operators. We establish a connection between Post's theory of boundary pairs of closed nonnegative forms on the one hand and the theory of generalized boundary triples of nonnegative symmetric operators on the other hand. Applications to the Laplacian operator on bounded domains with smooth, Lipschitz, and even rough boundary, as well as to mixed boundary value problem for the Laplacian are given. Other applications concern with the momentum, Schrödinger, and Dirac operators with local point interactions. These operators demonstrate natural occurrence of ES$ES$-generalized boundary triples with domain invariant Weyl functions and essentially selfadjoint reference operators A0.
Kirchhoff, Jonas;
Linear port-Hamiltonian systems are generically controllable. - In: IEEE transactions on automatic control, ISSN 1558-2523, Bd. 67 (2022), 6, S. 3220-3222

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian systems. This implies that a random, continuously distributed port-Hamiltonian system is almost surely controllable.
Mathew, Sobin; Lebedev, Sergey P.; Lebedev, A. A.; Hähnlein, Bernd; Stauffenberg, Jaqueline; Manske, Eberhard; Pezoldt, Jörg;
Silicon carbide - graphene nano-gratings on 4H and 6H semi-insulating SiC. - In: Materials science forum, ISSN 1662-9752, Bd. 1062 (2022), S. 170-174

A technical methodology of fabrication of hierarchically scaled multitude graphene nanogratings with varying pitches ranging from the micrometer down to sub 40 nm scale combined with sub 10 nm step heights on 4H and 6H semi-insulating SiC for length scale measurements is proposed. The nanogratings were fabricated using electron-beam lithography combined with dry etching of graphene, incorporating a standard semiconductor processing technology. A scientific evaluation of critical dimension, etching step heights, and surface characterization of graphene nanograting on both polytypes were compared and evaluated.
Berger, Thomas; Dennstädt, Dario;
Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2804-2809

We study tracking control for nonlinear systems with known relative degree and stable internal dynamics by the recently introduced technique of Funnel MPC. The objective is to achieve the evolution of the tracking error within a prescribed performance funnel. We propose a novel stage cost for Funnel MPC, extending earlier designs to the case of arbitrary relative degree, and show that the control objective as well as initial and recursive feasibility are always achieved - without requiring any terminal conditions or a sufficiently long prediction horizon. We only impose an additional feasibility constraint in the optimal control problem.
Strutynska, Nataliia Yu.; Grynyuk, Iryna I.; Vasyliuk, Olga M.; Prylutska, Svitlana V.; Vovchenko, Ludmila L.; Kraievska, I. A.; Slobodyanik, Nikolai S.; Ritter, Uwe; Prylutskyy, Yury I.;
Novel whitlockite/alginate/C60 fullerene composites: synthesis, characterization and properties for medical application. - In: The Arabian journal for science and engineering, ISSN 2191-4281, Bd. 47 (2022), 6, S. 7093-7104

The hybrid composite materials in form of spheres based on whitlockite-related calcium phosphate, Alginate (20, 30 or 50 wt.%) and C60 Fullerene (C60; 2 or 5 wt.%) were fabricated. According to XRD, elemental analysis and SEM data, the whitlockite-related (hexagonal system, space group R3c) calcium phosphate containing 0.42 wt.% of sodium was obtained in the form of particles with size 50-80 nm. It has been found that the addition of Alginate (20 wt.%) to prepared calcium phosphate leads to an increase in the compressive strength of composite by two times (from 137 to 358 MPa), and value of Young's modulus on 20% (from 460 to 558 MPa), while the presence of C60 in composition did not significant influence on this characteristic. The antibacterial activity of prepared composites with different composition and amounts (2.5, 5 or 10 mM) against Lactobacillus rhamnosus, Lactobacillus salivarius, Staphylococcus aureus and Pseudomonas aeruginosa was studied. All prepared samples did not effect on Lactobacillus. The addition of 5 wt.% C60 to phosphate-Alginate (30 wt.%) composite resulted in a tenfold decrease in the survival rate of the S. aureus strain at 5 and 10 mM of samples while P. aeruginosa was less sensitive to action of this sample and inhibition of bacteria growth was occurred only at its amount 10 mM. Thus, the results of mechanical properties and impact of created nanostructured hybrid composites on normal human microbiota (Lactobacillus) as well as pathogenic strain (S. aureus and P. aeruginosa) indicate the suitability of these promising materials for further biological test for bone therapy.