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One of the major problems in combinatorics is to determine the number of $r$-uniform hypergraphs ($r$-graphs) on $n$ vertices which are free of certain forbidden structures. This problem dates back to the work of Erd\H{o}s, Kleitman and Rothschild, who showed that the number of $K_r$-free graphs on $n$ vertices is $2^{\text{ex}(n,K_r)+o(n^2)}$. Their work was later extended to forbidding graphs as induced subgraphs by Pr\"omel and Steger. Here, we consider one of the most basic counting problems for $3$-graphs. Let $E_1$ be the $3$-graph with $4$ vertices and $1$ edge. What is the number of induced $\{K_4^3,E_1\}$-free $3$-graphs on $n$ vertices? We show that the number of such $3$-graphs is of order $n^{\Theta(n^2)}$. More generally, we determine asymptotically the number of induced $\mathcal{F}$-free $3$-graphs on $n$ vertices for all families $\mathcal{F}$ of $3$-graphs on $4$ vertices. We also provide upper bounds on the number of $r$-graphs on $n$ vertices which do not induce $i \in L$ edges on any set of $k$ vertices, where $L \subseteq \big \{0,1,\ldots,\binom{k}{r} \big\}$ is a list which does not contain $3$ consecutive integers in its complement. Our bounds are best possible up to a constant multiplicative factor in the exponent when $k = r+1$. The main tool behind our proof is counting the solutions of a constraint satisfaction problem., Comment: 18 pages

In this paper, we present the design, development, and characteristics of the novel aerosol mass spectrometer ERICA (ERC Instrument for Chemical composition of Aerosols; ERC – European Research Council) and selected results from the first airborne field deployment. The instrument combines two well-established methods of real-time in situ measurements of fine particle chemical composition. The first method is the laser desorption and ionization technique, or laser ablation technique, for single-particle mass spectrometry (here with a frequency-quadrupled Nd:YAG laser at λ = 266 nm). The second method is a combination of thermal particle desorption, also called flash vaporization, and electron impact ionization (like the Aerodyne aerosol mass spectrometer). The same aerosol sample flow is analyzed using both methods simultaneously, each using time-of-flight mass spectrometry. By means of the laser ablation, single particles are qualitatively analyzed (including the refractory components), while the flash vaporization and electron impact ionization technique provides quantitative information on the non-refractory components (i.e., particulate sulfate, nitrate, ammonia, organics, and chloride) of small particle ensembles. These techniques are implemented in two consecutive instrument stages within a common sample inlet and a common vacuum chamber. At its front end, the sample air containing the aerosol particles is continuously injected via an aerodynamic lens. All particles which are not ablated by the Nd:YAG laser in the first instrument stage continue their flight until they reach the second instrument stage and impact on the vaporizer surface (operated at 600 ∘C). The ERICA is capable of detecting single particles with vacuum aerodynamic diameters (dva) between ∼ 180 and 3170 nm (d50 cutoff). The chemical characterization of single particles is achieved by recording cations and anions with a bipolar time-of-flight mass spectrometer. For the measurement of non-refractory components, the particle size range extends from approximately 120 to 3500 nm (d50 cutoff; dva), and the cations are detected with a time-of-flight mass spectrometer. The compact dimensions of the instrument are such that the ERICA can be deployed on aircraft, at ground stations, or in mobile laboratories. To characterize the focused detection lasers, the ablation laser, and the particle beam, comprehensive laboratory experiments were conducted. During its first deployments the instrument was fully automated and operated during 11 research flights on the Russian high-altitude research aircraft M-55 Geophysica from ground pressure and temperature to 20 km altitude at 55 hPa and ambient temperatures as low as −86 ∘C. In this paper, we show that the ERICA is capable of measuring reliably under such conditions.

A graph where each vertex $v$ has a list $L(v)$ of available colors is $L$-colorable if there is a proper coloring such that the color of $v$ is in $L(v)$ for each $v$. A graph is $k$-choosable if every assignment $L$ of at least $k$ colors to each vertex guarantees an $L$-coloring. Given a list assignment $L$, an $L$-request for a vertex $v$ is a color $c\in L(v)$. In this paper, we look at a variant of the widely studied class of precoloring extension problems from [Z. Dvo\v{r}\'ak, S. Norin, and L. Postle: List coloring with requests. J. Graph Theory 2019], wherein one must satisfy "enough", as opposed to all, of the requested set of precolors. A graph $G$ is $\varepsilon$-flexible for list size $k$ if for any $k$-list assignment $L$, and any set $S$ of $L$-requests, there is an $L$-coloring of $G$ satisfying an $\varepsilon$-fraction of the requests in $S$. It is conjectured that planar graphs are $\varepsilon$-flexible for list size $5$, yet it is proved only for list size $6$ and for certain subclasses of planar graphs. We give a stronger version of the main tool used in the proofs of the aforementioned results. By doing so, we improve upon a result by Masa\v{r}\'ik and show that planar graphs without $K_4^-$ are $\varepsilon$-flexible for list size $5$. We also prove that planar graphs without $4$-cycles and $3$-cycle distance at least 2 are $\varepsilon$-flexible for list size $4$. Finally, we introduce a new (slightly weaker) form of $\varepsilon$-flexibility where each vertex has exactly one request. In that setting, we provide a stronger tool and we demonstrate its usefulness to further extend the class of graphs that are $\varepsilon$-flexible for list size $5$., Comment: 18 pages, 4 figures

The Erd\H{o}s-Simonovits stability theorem states that for all \epsilon >0 there exists \alpha >0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - \alpha n^2, then one can remove \epsilon n^2 edges from G to obtain an r-partite graph. F\"uredi gave a short proof that one can choose \alpha=\epsilon. We give a bound for the relationship of \alpha and \varepsilon which is asymptotically sharp as \epsilon \to 0., Comment: 12 pages, 1 figure

We present a novel and compact design of a constant-pressure inlet (CPI) developed for use in airborne aerosol mass spectrometry. In particular, the inlet system is optimized for aerodynamic lenses commonly used in aerosol mass spectrometers, in which efficient focusing of aerosol particles into a vacuum chamber requires a precisely controlled lens pressure, typically of a few hectopascals. The CPI device can also be used in condensation particle counters (CPCs), cloud condensation nucleus counters (CCNCs), and gas-phase sampling instruments across a wide range of altitudes and inlet pressures. The constant pressure is achieved by changing the inner diameter of a properly scaled O-ring that acts as a critical orifice. The CPI control keeps air pressure and thereby mass flow rate (≈0.1 L min−1) upstream of an aerodynamic lens constant, deviating at most by only ±2 % from a preset value. In our setup, a pressure sensor downstream of the O-ring maintains control of the pinch mechanism via a feedback loop and setpoint conditions are reached within seconds. The device was implemented in a few instruments, which were successfully operated on different research aircraft covering a wide range of ambient pressures, from sea level up to about 55 hPa. Details of operation and the quality of aerosol particle transmission were evaluated by laboratory experiments and in-flight data with a single-particle mass spectrometer.

An ordered graph is a simple graph with an ordering on its vertices. Define the ordered path P n to be the monotone increasing path with n edges. The ordered size Ramsey number r ( P r , P s ) is the minimum number m for which there exists an ordered graph H with m edges such that every two-coloring of the edges of H contains a red copy of P r or a blue copy of P s . For 2 ≤ r ≤ s , we show 1 8 r 2 s ≤ r ( P r , P s ) ≤ C r 2 s ( log s ) 3 , where C > 0 is an absolute constant. This problem is motivated by the recent results of Bucic et al. (2019) and Letzter and Sudakov (2019) for oriented graphs.

A consortium of polar scientists combined observational forces in a field campaign of unprecedented complexity to uncover the secrets of clouds and their role in Arctic amplification. Two research aircraft, an icebreaker research vessel, an ice-floe camp including an instrumented tethered balloon, and a permanent ground-based measurement station were employed in this endeavour. Clouds play an important role in Arctic amplification. This term represents the recently observed enhanced warming of the Arctic relative to the global increase of near-surface air temperature. However, there are still important knowledge gaps regarding the interplay between Arctic clouds and aerosol particles, surface properties, as well as turbulent and radiative fluxes that inhibit accurate model simulations of clouds in the Arctic climate system. In an attempt to resolve this so-called Arctic cloud puzzle, two comprehensive and closely coordinated field studies were conducted: the ”Arctic CLoud Observations Using airborne measurements during polar Day (ACLOUD)” aircraft campaign, and the ”Physical feedbacks of Arctic boundary layer, Sea ice, Cloud and AerosoL (PASCAL)” ice breaker expedition. Both observational studies were performed in the framework of the German ”ArctiC Amplification:Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)3” project. They took place in the vicinity of Svalbard (Norway) in May and June 2017. ACLOUD and PASCAL explored four pieces of the Arctic cloud puzzle: Cloud properties, aerosol impact on clouds, atmospheric radiation, and turbulent-dynamical processes. The two instrumented Polar 5 and Polar 6 aircraft, the icebreaker research vessel (RV) Polarstern, an ice-floe camp including an instrumented tethered balloon, and the permanent, ground-based measurement station at Ny-Ålesund (Svalbard) were employed to observe Arctic low and mid-level, mixed-phase clouds, and to investigate related atmospheric and surface processes. The Polar 5 aircraft served as a remote sensing observatory examining the clouds from above by downward-looking sensors; the Polar 6 aircraft operated as a flying in-situ measurement laboratory sampling inside and below the clouds. Most of the collocated Polar 5/6 flights were conducted either above RV Polarstern or over the Ny-Ålesund station, both of which monitored the clouds from below using similar but upward-looking remote sensing techniques as the Polar 5 aircraft. Several of the flights were carried out underneath collocated satellite tracks. The paper motivates the scientific objectives of the ACLOUD/PASCAL observations and describes the measured quantities, retrieved parameters, and the applied complementary instrumentation. Furthermore, it discusses selected measurement results, and poses critical research questions to be answered in future papers analyzing the data from the two field campaigns.

A triangle $T'$ is $\varepsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\varepsilon$. Given a triangle $T$, $\varepsilon>0$ and $n\in\mathbb{N}$, B\'ar\'any and F\"uredi asked to determine the maximum number of triangles $h(n,T,\varepsilon)$ being $\varepsilon$-similar to $T$ in a planar point set of size $n$. We show that for almost all triangles $T$ there exists $\varepsilon=\varepsilon(T)>0$ such that $h(n,T,\varepsilon)=n^3/24 (1+o(1))$. Exploring connections to hypergraph Tur\'an problems, we use flag algebras and stability techniques for the proof., Comment: 20 pages

A well-known conjecture by Erdős states that every triangle-free graph on n vertices can be made bipartite by removing at most \(n^2/25\) edges. This conjecture was known for graphs with edge density at least 0.4 and edge density at most 0.172. Here, we will extend the edge density for which this conjecture is true; we prove the conjecture for graphs with edge density at most 0.2486 and for graphs with edge density at least 0.3197. Further, we prove that every triangle-free graph can be made bipartite by removing at most \(n^2/23.5\) edges improving the previously best bound of \(n^2/18\).

In this paper we analyze aerosol particle composition measurements from five research missions conducted between 2014 and 2018 sampling the upper troposphere and lower stratosphere (UTLS), to assess the meridional extent of particles containing meteoric material. Additional data sets from a ground based study and from a low altitude aircraft mission are used to confirm the existence of meteoric material in lower tropospheric particles. Single particle laser ablation techniques with bipolar ion detection were used to measure the chemical composition of particles in a size range of approximately 150 nm to 3 μm. The five UTLS aircraft missions cover a latitude range from 15 to 68° N, altitudes up to 21 km, and a potential temperature range from 280 to 480 K. In total, 338 363 single particles were analyzed, of which 147 338 particles were measured in the stratosphere. Of these particles, 50 688 were characterized by high abundances of magnesium, iron, and rare iron oxide compounds, together with sulfuric acid. This particle type was found almost exclusively in the stratosphere (48 610 particles) and is interpreted as meteoric material immersed or dissolved within stratospheric sulfuric acid particles. Below the tropopause, the observed fraction of this particle type decreases sharply. However, small fractional abundances were observed below 3000 m a.s.l. in the Canadian Arctic and also at the Jungfraujoch high altitude station (3600 m a.s.l.). Thus, the removal pathway by sedimentation and/or mixing into the troposphere is confirmed. In the tropical lower stratosphere, only a small fraction (

We present a novel and compact design of a constant pressure inlet (CPI) developed for use in airborne aerosol mass spectrometry. In particular the inlet system is optimized for aerodynamic lenses commonly used in aerosol mass spectrometers, where efficient focusing of aerosol particles into a vacuum chamber requires a precisely controlled lens pressure, typically of a few hPa. The CPI device can also be used in gas phase sampling instruments in a large range of altitude and inlet pressure. The constant pressure is achieved by changing the inner diameter of a properly scaled O-ring that acts as a critical orifice. The CPI control keeps air pressure and thereby mass flow rate (≈ 0.1 l/min) upstream of an aerodynamic lens constant, deviating at most by only ± 2 % from a pre-set value. In our setup a pressure sensor downstream of the O-ring controls the pinch mechanism via a feedback loop and setpoint conditions are reached within seconds. The device was implemented in a few instruments, which were successfully operated on different research aircraft covering a wide range of ambient pressures, from sea level up to about 55 hPa. Details of operation and quality of aerosol particle transmission are evaluated by laboratory experiments and in-flight data with a single particle mass spectrometer.

The Erdős–Szekeres Theorem stated in terms of graphs says that any red–blue coloring of the edges of the ordered complete graph K r s + 1 contains a red copy of the monotone increasing path with r edges or a blue copy of the monotone increasing path with s edges. Although r s + 1 is the minimum number of vertices needed for this result, not all edges of K r s + 1 are necessary. We characterize the subgraphs of K r s + 1 with this coloring property as follows: they are exactly the subgraphs that contain all the edges of a graph we call the circus tent graph C T ( r , s ) . Additionally, we use similar proof techniques to improve upon the bounds on the online ordered size Ramsey number of a path given by Perez-Gimenez, Pralat, and West.

The Electronic Journal of Combinatorics, 27 (1), ISSN:1097-1440, ISSN:1077-8926

The custom-built Portable Fine Particle Concentrator (PFPC) is evaluated for the measurement of ice nucleating particles (INPs) in the atmosphere. The concentrations of INPs in remote regions of the atmosphere are very low, often close to instrumental detection limits. The PFPC is a dual slit-nozzle virtual impactor where particles are concentrated from an input flow of 250 LPM (litres per minute) into an output flow of 10 LPM. The enrichment factors (EFs) for ambient particles with diameters between 0.4 and 2.5 µm were found to be 21 ± 5 at sea level and 18 ± 2 at a field station 3580 meters above sea level for the PFPC operated in horizontal configuration. Similar enhancement factors (16 ± 5) in the concentrations of INPs measured by the Horizontal Ice Nucleation Chamber at the high-altitude station were observed when the air mass was characterized by high numbers of particles larger than 0.5 µm. When the number size distribution was dominated by particles smaller than 0.5 µm, the INP EF was considerably lower. Corroborating short-term measurements were provided by additional INP-measuring instruments, the Fast Ice Nucleus CHamber and the Frankfurt Ice Deposition Freezing Experiment. Results from two aerosol mass spectrometers also indicate significant particle enhancement using the PFPC. These results indicate that the PFPC can be usefully deployed to improve the detection efficiency of ambient INP measurements. Copyright © 2019 American Association for Aerosol Research

To date, only a few studies have investigated the potential of coal fly ash particles to trigger heterogeneous ice nucleation in cloud droplets. The presented measurements aim at expanding the sparse dataset and improving process understanding of how physico-chemical particle properties influence the freezing behavior of coal fly ash particles immersed in water. Firstly, immersion freezing measurements were performed with two single particle techniques, i.e., the Leipzig Aerosol Cloud Interaction Simulator and the Spectrometer for Ice Nuclei. The effect of suspension time on the efficiency of the coal fly ash particles when immersed in a cloud droplet is analyzed based on the different residence times of the two instruments and employing both dry and wet particle generation. Secondly, two cold stage setups, one using microliter sized droplets (Leipzig Ice Nucleation Array) and one using nanoliter sized droplets (Weizman Supercooled Droplets Observation on Microarray setup) were applied. We found that coal fly ash particles are comparable to mineral dust in their immersion freezing behavior when being dry-generated. However, a significant decrease in immersion freezing efficiency was observed during experiments with wet-generated particles in LACIS and SPIN. The efficiency of wet-generated particles is in agreement with the cold stage measurements. In order to understand the reason behind the deactivation, a series of chemical composition, morphology, and crystallography analyses (single particle mass spectrometry, scanning electron microscopy coupled with energy dispersive X-ray microanalysis, X-ray diffraction analysis) was performed with dry- and wet-generated particles. From these investigations, we conclude that anhydrous CaSO4 and CaO, which, if investigated in pure form, show the same qualitative immersion freezing behavior as observed for dry-generated coal fly ash particles, contribute to triggering heterogeneous ice nucleation at the particle-water interface. The observed deactivation in contact with water is related to changes of the particle surface propertieswhich are potentially caused by hydration of CaSO4 and CaO. The contribution of coal fly ash to the ambient population of ice nucleating particles therefore depends on whether and for how long particles are immersed in cloud droplets.