An abstract approach to polychromatic coloring

The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic colorings using hypergraphs on ordered vertex sets. We introduce an abstract version of a framework by Smorodinsky and Yuditsky, used for polychromatic coloring halfplanes, and apply it to so-called ABA-free hypergraphs, which are a generalization of interval graphs. Using our methods, we prove that (2k−1)-uniform ABA-free hypergraphs have a polychromatic k-coloring, a problem posed by the second author. We also prove the same for hypergraphs defined on a point set by pseudohalfplanes. These results are best possible. We also introduce several new notions that seem to be important for investigating polychromatic colorings and ϵ -nets, such as shallow hitting sets. We pose several open problems related to them. For example, is it true that given a finite point set S on a sphere and a set of halfspheres F, such that {S ∩ F | F ∈ F} is a Sperner family, we can select an R ⊂ S such that 1 ≤ |F ∩ R| ≤ 2 holds for every F ∈ F?. © Springer International Publishing Switzerland 2016

Induced and Non-Induced Poset Saturation Problems

A subfamily $\mathcal{G}\subseteq \mathcal{F}\subseteq 2^{[n]}$ of sets is a non-induced (weak) copy of a poset $P$ in $\mathcal{F}$ if there exists a bijection $i:P\rightarrow \mathcal{G}$ such that $p\le_P q$ implies $i(p)\subseteq i(q)$. In the case where in addition $p\le_P q$ holds if and only if $i(p)\subseteq i(q)$, then $\mathcal{G}$ is an induced (strong) copy of $P$ in $\mathcal{F}$. We consider the minimum number $sat(n,P)$ [resp.\ $sat^*(n,P)$] of sets that a family $\mathcal{F}\subseteq 2^{[n]}$ can have without containing a non-induced [induced] copy of $P$ and being maximal with respect to this property, i.e., the addition of any $G\in 2^{[n]}\setminus \mathcal{F}$ creates a non-induced [induced] copy of $P$. We prove for any finite poset $P$ that $sat(n,P)\le 2^{|P|-2}$, a bound independent of the size $n$ of the ground set. For induced copies of $P$, there is a dichotomy: for any poset $P$ either $sat^*(n,P)\le K_P$ for some constant depending only on $P$ or $sat^*(n,P)\ge \log_2 n$. We classify several posets according to this dichotomy, and also show better upper and lower bounds on $sat(n,P)$ and $sat^*(n,P)$ for specific classes of posets. Our main new tool is a special ordering of the sets based on the colexicographic order. It turns out that if $P$ is given, processing the sets in this order and adding the sets greedily into our family whenever this does not ruin non-induced [induced] $P$-freeness, we tend to get a small size non-induced [induced] $P$-saturating family

An ultralow-loss and lightweight cellulose-coated silica foam for planar Fresnel zone plate lens applications in future 6G devices

Abstract Several passive components of fifth-generation (5G) and future sixth-generation (6G) telecommunication devices require substrate materials of very low dielectric permittivity and losses to avoid wave absorption, reflection, and interference. Apart from their dielectric properties, these materials shall be also affordable and sufficiently robust to enable postprocessing and integration of functional electrical components. Herein, we demonstrate a Fresnel zone plate lens for operation at 300 GHz, whose structure is supported on substrate made of an ultraporous silica foam with a nanocellulose thin film coating. The effective dielectric permittivity and loss of the substrate ( ϵ r = 1.018 ± 0.003 and tan δ < 3 × 10 −4 at 300 GHz) is close to that of air. Experiments show that the fabricated Fresnel zone plate lens connected to a waveguide with total gain of 20 dB and angular beamwidth of 2.9° in good agreement with microwave simulations. The proposed lens structure has additional advantages such as small volume, ultralight weight, and simulations indicate 60 GHz bandwidth making it particularly appealing for radio front-ends of future 6G devices

Bio-based smart materials for food packaging and sensors:a review

Abstract Food industry must guarantee food safety and seek sustainable solutions for increasing shelf life and decreasing food waste. Bio-based smart packaging is a potential option, where sustainability and real-time monitoring of food quality are combined assuring health safety and providing economic and environmental benefits. In this context, bio-based refers not only to packaging materials that are from renewable sources and biodegradable, but also to the sensor elements. The scope of this review is to explore the state-of-the-art of bio-based polymers used as food contact materials and to highlight the potential of natural compounds for sensing chemical and physical changes of the environment to monitor the food quality. Finally, different sustainability aspects of the bio-based materials are discussed

Optimization of a hydrogen combustion mechanism using both direct and indirect measurements

Journal articleThe Keromnes et al. (2013) mechanism for hydrogen combustion has been optimized using a large set of indirect experimental data, consisting of ignition measurements in shock tubes (566 datapoints in 43 datasets) and rapid compression machines (219/19), and flame velocity measurements (364/59), covering wide ranges of temperature (800 K-2300 K), pressure (0.1 bar-65 bar) and equivalence ratio (phi = 0.2-5.0). According to the sensitivity analysis carried out at each experimental datapoint, 30 Arrhenius parameters and 3 third body collision efficiency parameters of 11 elementary reactions could be optimized using these experimental data. 1749 directly measured rate coefficient values in 56 datasets belonging to the 11 reaction steps were also utilized. Prior uncertainty ranges of the rate coefficients were determined from literature data. Mechanism optimization has led to a new hydrogen combustion mechanism, a set of newly recommended rate parameters with their covariance matrix, and temperature-dependent posterior uncertainty ranges of the rate coefficients. The optimized mechanism generated here was tested together with 13 recent hydrogen combustion mechanisms and proved to be the best one.OTKA (Hungarian Science Research Fund) grants #K84054 and #NN10052