A randomized polynomial kernel for Subset Feedback Vertex Set

The Subset Feedback Vertex Set problem generalizes the classical Feedback Vertex Set problem and asks, for a given undirected graph $G=(V,E)$, a set $S \subseteq V$, and an integer $k$, whether there exists a set $X$ of at most $k$ vertices such that no cycle in $G-X$ contains a vertex of $S$. It was independently shown by Cygan et al. (ICALP '11, SIDMA '13) and Kawarabayashi and Kobayashi (JCTB '12) that Subset Feedback Vertex Set is fixed-parameter tractable for parameter $k$. Cygan et al. asked whether the problem also admits a polynomial kernelization. We answer the question of Cygan et al. positively by giving a randomized polynomial kernelization for the equivalent version where $S$ is a set of edges. In a first step we show that Edge Subset Feedback Vertex Set has a randomized polynomial kernel parameterized by $|S|+k$ with $O(|S|^2k)$ vertices. For this we use the matroid-based tools of Kratsch and Wahlstr\"om (FOCS '12) that for example were used to obtain a polynomial kernel for $s$-Multiway Cut. Next we present a preprocessing that reduces the given instance $(G,S,k)$ to an equivalent instance $(G',S',k')$ where the size of $S'$ is bounded by $O(k^4)$. These two results lead to a polynomial kernel for Subset Feedback Vertex Set with $O(k^9)$ vertices

Smaller Parameters for Vertex Cover Kernelization

We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this result by using modulators to $d$-quasi-forests, i.e., graphs where each connected component has a feedback vertex set of size at most $d$, and obtain kernels with $\mathcal{O}(|X|^{3d+9})$ vertices. Our result relies on proving that minimal blocking sets in a $d$-quasi-forest have size at most $d+2$. This bound is tight and there is a related lower bound of $\mathcal{O}(|X|^{d+2-\epsilon})$ on the bit size of kernels. In fact, we also get bounds for minimal blocking sets of more general graph classes: For $d$-quasi-bipartite graphs, where each connected component can be made bipartite by deleting at most $d$ vertices, we get the same tight bound of $d+2$ vertices. For graphs whose connected components each have a vertex cover of cost at most $d$ more than the best fractional vertex cover, which we call $d$-quasi-integral, we show that minimal blocking sets have size at most $2d+2$, which is also tight. Combined with existing randomized polynomial kernelizations this leads to randomized polynomial kernelizations for modulators to $d$-quasi-bipartite and $d$-quasi-integral graphs. There are lower bounds of $\mathcal{O}(|X|^{d+2-\epsilon})$ and $\mathcal{O}(|X|^{2d+2-\epsilon})$ for the bit size of such kernels

Loan characteristics, firm preferences and investment: Evidence from a unique experiment

This paper uses a unique experiment conducted as part of the Investment Survey of the European Investment Bank (EIB) to provide novel evidence on firms' preferences over loan characteristics and the relation between terms of credit and investment decisions. The design of the experiment allows revealing firm's financing preferences and willingness-to-pay in a clean and straightforward manner. The results show that firms are especially sensitive to the loan amount, the collateral requirement and the interest rate. Results are heterogeneous between sectors, size classes and types of projects.Die vorliegende Studie basiert auf einem Experiment im Rahmen der EIB-Umfrage zur Investitionstätigkeit (EIBIS). Es sollte neue Erkenntnisse über von Unternehmen bevorzugte Darlehensmerkmale und über die Beziehung zwischen Kreditbedingungen und Investitionsentscheidungen liefern. Aus dem Experiment lässt sich ablesen, welche Präferenzen Unternehmen bei Finanzierungen haben und unter welchen Bedingungen sie bereit sind, den geforderten Zinssatz zu zahlen. Wie sich gezeigt hat, sind vor allem die Höhe des Darlehens, die Besicherungsanforderungen und der Zinssatz für die Entscheidung maßgeblich. Die Ergebnisse fallen je nach Sektor, Unternehmensgröße und Projektart jedoch unterschiedlich aus

Preprocessing Under Uncertainty: Matroid Intersection

We continue the study of preprocessing under uncertainty that was initiated independently by Assadi et al. (FSTTCS 2015) and Fafianie et al. (STACS 2016). Here, we are given an instance of a tractable problem with a large static/known part and a small part that is dynamic/uncertain, and ask if there is an efficient algorithm that computes an instance of size polynomial in the uncertain part of the input, from which we can extract an optimal solution to the original instance for all (usually exponentially many) instantiations of the uncertain part. In the present work, we focus on the Matroid Intersection problem. Amongst others we present a positive preprocessing result for the important case of finding a largest common independent set in two linear matroids. Motivated by an application for intersecting two gammoids we also revisit Maximum Flow. There we tighten a lower bound of Assadi et al. and give an alternative positive result for the case of low uncertain capacity that yields a Maximum Flow instance as output rather than a matrix

Subtle selectivity in a pheromone sensor triumvirate desynchronizes competence and predation in a human gut commensal

Constantly surrounded by kin or alien organisms in nature, eukaryotes and prokaryotes developed various communication systems to coordinate adaptive multi-entity behavior. In complex and overcrowded environments, they require to discriminate relevant signals in a myriad of pheromones to execute appropriate responses. In the human gut commensal Streptococcus salivarius, the cytoplasmic Rgg/RNPP regulator ComR couples competence to bacteriocin-mediated predation. Here, we describe a paralogous sensor duo, ScuR and SarF, which circumvents ComR in order to disconnect these two physiological processes. We highlighted the recurring role of Rgg/RNPP in the production of antimicrobials and designed a robust genetic screen to unveil potent/optimized peptide pheromones. Further mutational and biochemical analyses dissected the modifiable selectivity toward their pheromone and operating sequences at the subtle molecular level. Additionally, our results highlight how we might mobilize antimicrobial molecules while silencing competence in endogenous populations of human microflora and temper gut disorders provoked by bacterial pathogens

Circuitry rewiring directly couples competence to predation in the gut dweller Streptococcus salivarius

Small distortions in transcriptional networks might lead to drastic phenotypical changes, especially in cellular developmental programs such as competence for natural transformation. Here, we report a pervasive circuitry rewiring for competence and predation interplay in commensal streptococci. Canonically, in streptococci paradigms such as Streptococcus pneumoniae and Streptococcus mutans, the pheromone-based two-component system BlpRH is a central node that orchestrates the production of antimicrobial compounds (bacteriocins) and incorporates signal from the competence activation cascade. However, the human commensal Streptococcus salivarius does not contain a functional BlpRH pair, while the competence signaling system ComRS directly couples bacteriocin production and competence commitment. This network shortcut might underlie an optimal adaptation against microbial competitors and explain the high prevalence of S. salivarius in the human digestive tract. Moreover, the broad spectrum of bacteriocin activity against pathogenic bacteria showcases the commensal and genetically tractable S. salivarius species as a user-friendly model for competence and bacterial predation

Roots and Consequences of Financial Distortions

This thesis links the roots and the consequences excess debt can have for an economy. Chapter 2 studies the impact financial frictions, caused by high debt levels, have on the business cycle. This helps understanding what the consequences of high debt levels are and how they translate to the real economy through business cycle fluctuations. The third chapter stands out as it does not study financial distortions directly but financial intermediation. Nevertheless, it is an important component in the debt and distortions nexus as an enormous share of external finance used by companies is provided by banks. Furthermore, the study sheds light on the question how the banking system is affected by measures introduced in the aftermath of the recent financial crisis, which was caused by financial distortions in the first place. The fourth and last chapter tries to uncover the roots of indebtedness of firms and studies the external finance preferences of European companies. They rely less, in comparison to their American counterparts, on external equity financing and the goal of this chapter is to analyze whether this is rooted in their preferences

Developing procedures for irrigation management of potatoes (Solanum tuberosum. L) using remote sensing-based crop coefficients, evapotranspiration and weather data

Thesis (MScAgric)--Stellenbosch University, 2025.Hols, R. W. B. 2025. Developing procedures for irrigation management of potatoes (Solanum tuberosum. L) using remote sensing-based crop coefficients, evapotranspiration and weather data. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/8f16ac4d-7e28-4829-a208-6e4c6a2a52a5Efficient irrigation management is essential for sustainable agriculture, especially in water scarce regions like the Sandveld in the Western Cape. Accurate estimation of crop coefficients (Kc) and evapotranspiration (ET) is fundamental for optimizing irrigation. Normalised difference vegetation indices (NDVI), leaf area index (LAI) and green canopy cover (GCC%) have previously been used in different crop types and were demonstrated to be successful in estimating basal crop coefficients (Kcb) and ET. However, the potential of using these remote sensing techniques to improve water management in irrigated potatoes (Solanum tuberosum L.) has yet to be investigated. The aim of this study was to develop remote sensing -based Kc’s for potatoes to facilitate irrigation water management. The study was conducted during the 2023 summer growing season. Five trial sites were identified in the Sandveld region and planted with potato cultivars Mondial, FL2108, Sifra, and Lanorma. The study assessed the use of remote sensing techniques, canopy cover and Kcb in combination with weather data and infield measurements as a viable method to estimate Kc’s and ET, which were then compared with the FAO-56 approach. Drainage was measured using G3 Drain Gauges and soil water content (SWC) was monitored usings capacitance sensors. Rain gauges recorded rainfall and pressure transducers monitored irrigation amounts. Two Eddy-Covariance (ECV) systems were installed in Fields 2 and 5 monitoring H₂0 and CO₂ fluxes. Infield measurements were taken around four sampling points in each field. The measurements included fractional interception of photosynthetically active radiation (FIPAR) using a AccuPAR LP-80 Ceptometer and canopy cover (GCC%) measurements using the Canopeo® mobile application. Plant sampling was conducted through the growing season and destructive growth analysis was performed. Satellite images at 5-day intervals were derived from the Sentinel-2 satellite. Substantial rainfall, ranging between 72 and 118 mm, was recorded during the early stages of the growing season for Fields 1-3, as the Western Cape province experienced a very wet winter and spring in 2023. This led to early drainage and variations in the total seasonal water inputs across the different fields, which was also reflected in differences in irrigation amounts applied (18 -120 mm, respectively). Good linear correlations between NDVI and GCC% and NDVI and FIPAR were obtained with average R² values of 0.98 and 0.93 respectively. On average Kc_FAO- 56 values were 0.15 lower than the Kc_NDVI values during the initial stage of the growing season, while being 0.11, 0.17 and 0.12 higher during the development-, mid-, and end-season stages. Average Kc_NDVI and Kc_ECV values aligned closely with each other, estimating similar mid-season Kc values of 0.98. Average ET_NDVI and ET_ECV values were closely related (146 and 414.3 mm), while the ET_FAO-56 approach overestimated seasonal ET. Furthermore, the comparison between ET_NDVI and ET_ECV produced RMSE and MAE values of 0.8 mm day⁻¹ and 0.57 mm day⁻¹ which outperformed other estimation methods. The results of this study indicate that remotely sensed phenology information offers a more dynamic and accurate approach in the real-time development of Kc values and ET estimation, compared to the FAO-56 approach for potato production in the Sandveld.Master

On Kernelization for Edge Dominating Set under Structural Parameters

In the NP-hard Edge Dominating Set problem (EDS) we are given a graph G=(V,E) and an integer k, and need to determine whether there is a set F subseteq E of at most k edges that are incident with all (other) edges of G. It is known that this problem is fixed-parameter tractable and admits a polynomial kernelization when parameterized by k. A caveat for this parameter is that it needs to be large, i.e., at least equal to half the size of a maximum matching of G, for instances not to be trivially negative. Motivated by this, we study the existence of polynomial kernelizations for EDS when parameterized by structural parameters that may be much smaller than k. Unfortunately, at first glance this looks rather hopeless: Even when parameterized by the deletion distance to a disjoint union of paths P_3 of length two there is no polynomial kernelization (under standard assumptions), ruling out polynomial kernelizations for many smaller parameters like the feedback vertex set size. In contrast, somewhat surprisingly, there is a polynomial kernelization for deletion distance to a disjoint union of paths P_5 of length four. As our main result, we fully classify for all finite sets H of graphs, whether a kernel size polynomial in |X| is possible when given X such that each connected component of G-X is isomorphic to a graph in H

Approximate Turing Kernelization for Problems Parameterized by Treewidth

We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $\alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm that, when given access to an oracle that outputs $c$-approximate solutions in $O(1)$ time, obtains an $(\alpha \cdot c)$-approximate solution to the considered problem, using calls to the oracle of size at most $f(k)$ for some function $f$ that only depends on the parameter. Using this definition, we show that Independent Set parameterized by treewidth $\ell$ has a $(1+\varepsilon)$-approximate Turing kernel with $O(\frac{\ell^2}{\varepsilon})$ vertices, answering an open question posed by Lokshtanov et al. [STOC 2017]. Furthermore, we give $(1+\varepsilon)$-approximate Turing kernels for the following graph problems parameterized by treewidth: Vertex Cover, Edge Clique Cover, Edge-Disjoint Triangle Packing and Connected Vertex Cover. We generalize the result for Independent Set and Vertex Cover, by showing that all graph problems that we will call "friendly" admit $(1+\varepsilon)$-approximate Turing kernels of polynomial size when parameterized by treewidth. We use this to obtain approximate Turing kernels for Vertex-Disjoint $H$-packing for connected graphs $H$, Clique Cover, Feedback Vertex Set and Edge Dominating Set