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ALMA surveys have suggested that protoplanetary disks are not massive enough to form the known exoplanet population, under the assumption that the millimeter continuum emission is optically thin. In this work, we investigate how the mass determination is influenced when the porosity of dust grains is considered in radiative transfer models. The results show that disks with porous dust opacities yield similar dust temperature, but systematically lower millimeter fluxes compared to disks incorporating compact dust grains. Moreover, we recalibrate the relation between dust temperature and stellar luminosity for a wide range of stellar parameters, and calculate the dust masses of a large sample of disks using the traditionally analytic approach. The median dust mass from our calculation is about 6 times higher than the literature result, and this is mostly driven by the different opacities of porous and compact grains. A comparison of the cumulative distribution function between disk dust masses and exoplanet masses show that the median exoplanet mass is about 2 times lower than the median dust mass, if grains are porous, and there are no exoplanetary systems with masses higher than the most massive disks. Our analysis suggests that adopting porous dust opacities may alleviate the mass budget problem for planet formation. As an example illustrating the combined effects of optical depth and porous dust opacities on the mass estimation, we conduct new IRAM/NIKA-2 observations toward the IRAS 04370+2559 disk and perform a detailed radiative transfer modeling of the spectral energy distribution. The best-fit dust mass is roughly 100 times higher than the value from the traditionally analytic calculation. Future spatially resolved observations at various wavelengths are required to better constrain the dust mass., Comment: 11 pages, 7 figures, Accepted for publication in A&A

The composition of protoplanetary disks, and hence the initial conditions of planet formation, may be strongly influenced by the infall and thermal processing of material during the protostellar phase. Composition of dust and ice in protostellar envelopes, shaped by energetic processes driven by the protostar, serves as the fundamental building material for planets and complex organic molecules. As part of the JWST GO program, "Investigating Protostellar Accretion" (IPA), we observed an intermediate-mass protostar HOPS 370 (OMC2-FIR3) using NIRSpec/IFU and MIRI/MRS. This study presents the gas and ice phase chemical inventory revealed with the JWST in the spectral range of $\sim$2.9 to 28 $\mu$m and explores the spatial variation of volatile ice species in the protostellar envelope. We find evidence for thermal processing of ice species throughout the inner envelope. We present the first high-spatial resolution ($\sim 80$ au) maps of key volatile ice species H$_{2}$O, CO$_{2}$, $^{13}$CO$_2$, CO, and OCN$^-$, which reveal a highly structured and inhomogeneous density distribution of the protostellar envelope, with a deficiency of ice column density that coincides with the jet/outflow shocked knots. Further, we observe high relative crystallinity of H$_{2}$O ice around the shocked knot seen in the H$_2$ and OH wind/outflow, which can be explained by a lack of outer colder material in the envelope along the line of sight due to the irregular structure of the envelope. These observations show clear evidence of thermal processing of the ices in the inner envelope, close to the outflow cavity walls, heated by the luminous protostar., Comment: Submitted to ApJ. Main text:16 pages with 11 figures

Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted phylogenetic networks that has been extensively investigated in recent years. In this paper, we give a novel characterisation of a tree-child network $\mathcal{R}$ in terms of cherry-picking sequences that are sequences on the leaves of $\mathcal{R}$ and reduce it to a single vertex by repeatedly applying one of two reductions to its leaves. We show that our characterisation extends to unrooted tree-child networks which are mostly unexplored in the literature and, in turn, also offers a new approach to settling the computational complexity of deciding if an unrooted phylogenetic network can be oriented as a rooted tree-child network.

The spread of a graph $G$ is the difference $\lambda_1 - \lambda_n$ between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determined the graph on $n$ vertices with maximum spread for sufficiently large $n$. In this paper, we study a related question of maximizing the difference $\lambda_{i+1} - \lambda_{n-j}$ for a given pair $(i, j)$ over all graphs on $n$ vertices. We give upper bounds for all pairs $(i, j)$, exhibit an infinite family of pairs where the bound is tight, and show that for the pair $(1, 0)$ the extremal example is unique. These results contribute to a line of inquiry pioneered by Nikiforov aiming to maximize different linear combinations of eigenvalues over all graphs on $n$ vertices., Comment: 9 pages, 2 figures

A normal network is uniquely determined by the set of phylogenetic trees that it displays. Given a set $\mathcal{P}$ of rooted binary phylogenetic trees, this paper presents a polynomial-time algorithm that reconstructs the unique binary normal network whose set of displayed binary trees is $\mathcal{P}$, if such a network exists. Additionally, we show that any two rooted phylogenetic trees can be displayed by a normal network and show that this result does not extend to more than two trees. This is in contrast to tree-child networks where it has been previously shown that any collection of rooted phylogenetic trees can be displayed by a tree-child network. Lastly, we introduce a type of cherry-picking sequence that characterises when a collection $\mathcal{P}$ of rooted phylogenetic trees can be displayed by a normal network and, further, characterise the minimum number of reticulations needed over all normal networks that display $\mathcal{P}$. We then exploit these sequences to show that, for all $n\ge 3$, there exist two rooted binary phylogenetic trees on $n$ leaves that can be displayed by a tree-child network with a single reticulation, but cannot be displayed by a normal network with less than $n-2$ reticulations.

In comparison to phylogenetic trees, phylogenetic networks are more suitable to represent complex evolutionary histories of species whose past includes reticulation such as hybridisation or lateral gene transfer. However, the reconstruction of phylogenetic networks remains challenging and computationally expensive due to their intricate structural properties. For example, the small parsimony problem that is solvable in polynomial time for phylogenetic trees, becomes NP-hard on phylogenetic networks under softwired and parental parsimony, even for a single binary character and structurally constrained networks. To calculate the parsimony score of a phylogenetic network $N$, these two parsimony notions consider different exponential-size sets of phylogenetic trees that can be extracted from $N$ and infer the minimum parsimony score over all trees in the set. In this paper, we ask: What is the maximum difference between the parsimony score of any phylogenetic tree that is contained in the set of considered trees and a phylogenetic tree whose parsimony score equates to the parsimony score of $N$? Given a gap-free sequence alignment of multi-state characters and a rooted binary level-$k$ phylogenetic network, we use the novel concept of an informative blob to show that this difference is bounded by $k+1$ times the softwired parsimony score of $N$. In particular, the difference is independent of the alignment length and the number of character states. We show that an analogous bound can be obtained for the softwired parsimony score of semi-directed networks, while under parental parsimony on the other hand, such a bound does not hold.

Accretion bursts from low-mass young stellar objects (YSOs) are known for many decades. In recent years, the first accretion bursts of massive YSOs (MYSOs) have been observed. These phases of intense protostellar growth are of particular importance for studying massive star formation. Bursts of MYSOs are accompanied by flares of Class II methanol masers (hereafter masers), caused by an increase in exciting mid-infrared (MIR) emission. The G323.46$-$0.08 (hereafter G323) event extends the small sample of known MYSO bursts. Maser observations of the MYSO G323 show evidence of a flare, which was presumed to be caused by an accretion burst. This should be verified with IR data. We used time-dependent radiative transfer (TDRT) to characterize the heating and cooling timescales for eruptive MYSOs and to infer the main burst parameters. The G323 accretion burst is confirmed. It reached its peak in late 2013/early 2014 with a Ks-band increase of 2.5mag. TDRT indicates that the duration of the thermal afterglow in the far-infrared (FIR) can exceed the burst duration by years. The latter was proved by SOFIA observations, which indicate a flux increase of $(14.2\pm4.6)$% at $70\, \rm \mu m$ and $(8.5\pm6.1)$% at $160\, \mu$m in 2022 (2 years after the burst end). A one-sided light echo emerged that was propagating into the interstellar medium. The G323 burst is probably the most energetic MYSO burst observed so far. Within $8.4 \rm \, yrs$, an energy of $(0.9\pm_{0.8}^{2.5}) \times 10^{47}\,\rm erg$ was released. The short timescale points to the accretion of a compact body, while the burst energy corresponds to an accumulated mass of at least $(7\pm_{6}^{20})\,M_{Jup}$ and possibly even more if the protostar is bloated. In this case, the accretion event might have triggered protostellar pulsations, which give rise to the observed maser periodicity.

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{s,t}$-minor. We show that for any $t\geq s \geq 2$ and sufficiently large $n$, there is an integer $\xi_{t}$ such that the extremal $n$-vertex $K_{s,t}$-minor-free graph attaining the maximum spread is the graph obtained by joining a graph $L$ on $(s-1)$ vertices to the disjoint union of $\lfloor \frac{2n+\xi_{t}}{3t}\rfloor$ copies of $K_t$ and $n-s+1 - t\lfloor \frac{2n+\xi_t}{3t}\rfloor$ isolated vertices. Furthermore, we give an explicit formula for $\xi_{t}$ and an explicit description for the graph $L$ for $t \geq \frac32(s-3) +\frac{4}{s-1}$., Comment: Minor revisions. arXiv admin note: text overlap with arXiv:2212.05540

This work aims to utilize the increased sensitivity and resolution of the JWST to quantify the HDO/H$_{2}$O ratio in ices toward young stellar objects (YSOs) and to determine if the HDO/H$_{2}$O ratios measured in the gas phase toward massive YSOs (MYSOs) are representative of the ratios in their ice envelopes. Two protostars observed in the Investigating Protostellar Accretion (IPA) program using JWST NIRSpec were analyzed: HOPS 370, an intermediate-mass YSO (IMYSO), and IRAS 20126+4104, a MYSO. The HDO ice toward these sources was detected above the 3$\sigma$ level and quantified via its 4.1 $\mu$m band. The contributions from the CH$_{3}$OH combination modes to the observed optical depth in this spectral region were constrained via the CH$_{3}$OH 3.53 $\mu$m band to ensure that the integrated optical depth of the HDO feature was not overestimated. H$_{2}$O ice was quantified via its 3 $\mu$m band. From these fits, ice HDO/H$_{2}$O abundance ratios of 4.6$\pm$1.8$\times$10$^{-3}$ and 2.6$\pm$1.2$\times$10$^{-3}$ are obtained for HOPS 370 and IRAS 20126+4104, respectively. The simultaneous detections of both crystalline HDO and crystalline H$_{2}$O corroborate the assignment of the observed feature at 4.1 $\mu$m to HDO ice. The ice HDO/H$_{2}$O ratios are similar to the highest reported gas HDO/H$_{2}$O ratios measured toward MYSOs as well as the hot inner regions of isolated low-mass protostars, suggesting that at least some of the gas HDO/H$_{2}$O ratios measured toward massive hot cores are representative of the HDO/H$_{2}$O ratios in ices. The need for an H$_{2}$O-rich CH$_{3}$OH component in the CH$_{3}$OH ice analysis supports recent experimental and observational results that indicate that some CH$_{3}$OH ice may form prior to the CO freeze-out stage in H$_{2}$O-rich ice layers., Comment: Accepted for publication in A&A. 23 pages, 17 figures, 10 tables

Mid-infrared emission features probe the properties of ionized gas, and hot or warm molecular gas. The Orion Bar is a frequently studied photodissociation region (PDR) containing large amounts of gas under these conditions, and was observed with the MIRI IFU aboard JWST as part of the "PDRs4All" program. The resulting IR spectroscopic images of high angular resolution (0.2") reveal a rich observational inventory of mid-IR emission lines, and spatially resolve the substructure of the PDR, with a mosaic cutting perpendicularly across the ionization front and three dissociation fronts. We extracted five spectra that represent the ionized, atomic, and molecular gas layers, and measured the most prominent gas emission lines. An initial analysis summarizes the physical conditions of the gas and the potential of these data. We identified around 100 lines, report an additional 18 lines that remain unidentified, and measured the line intensities and central wavelengths. The H I recombination lines originating from the ionized gas layer bordering the PDR, have intensity ratios that are well matched by emissivity coefficients from H recombination theory, but deviate up to 10% due contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni, and show how certain line ratios vary between the five regions. We observe the pure-rotational H$_2$ lines in the vibrational ground state from 0-0 S(1) to 0-0 S(8), and in the first vibrationally excited state from 1-1 S(5) to 1-1 S(9). We derive H$_2$ excitation diagrams, and approximate the excitation with one thermal (~700 K) component representative of an average gas temperature, and one non-thermal component (~2700 K) probing the effect of UV pumping. We compare these results to an existing model for the Orion Bar PDR and highlight the differences with the observations., Comment: 26 pages, 12 figures, 3 tables. Submitted to A&A, under review (1st revision)

In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the existence of solutions to Ricci flow on short time intervals, and prove that Ricci flow preserves graphs with nonnegative (resp. positive) curvature., Comment: 14 pages, 8 figures, comments welcome!

Devriendt and Lambiotte recently introduced the \emph{node resistance curvature}, a notion of graph curvature based on the effective resistance matrix. In this paper, we begin the study of the behavior of the node resistance curvature under the operation of the Cartesian graph product. We study the natural question of global positivity of node resistance curvature of the Cartesian product of positively-curved graphs, and prove that, whenever $m,n\ge3$, the node resistance curvature of the interior vertices of a $m\times n$ grid is always nonpositive, while it is always nonnegative on the boundary of such grids. For completeness, we also prove a number of results on node resistance curvature in $2\times n$ grids and exhibit a counterexample to a generalization. We also give generic bounds and suggest several further questions for future study.

Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photo-dissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, impacting planet formation within the disks. We report JWST and Atacama Large Millimetere Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modelling their kinematics and excitation allows us to constrain the physical conditions within the gas. We quantify the mass-loss rate induced by the FUV irradiation, finding it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk.

Given integers $n > k > 0$, and a set of integers $L \subset [0, k-1]$, an \emph{$L$-system} is a family of sets $\mathcal{F} \subset \binom{[n]}{k}$ such that $|F \cap F'| \in L$ for distinct $F, F'\in \mathcal{F}$. $L$-systems correspond to independent sets in a certain generalized Johnson graph $G(n, k, L)$, so that the maximum size of an $L$-system is equivalent to finding the independence number of the graph $G(n, k, L)$. The \emph{Lov\'asz number} $\vartheta(G)$ is a semidefinite programming approximation of the independence number $\alpha$ of a graph $G$. In this paper, we determine the leading order term of $\vartheta(G(n, k, L))$ of any generalized Johnson graph with $k$ and $L$ fixed and $n\rightarrow \infty$. As an application of this theorem, we give an explicit construction of a graph $G$ on $n$ vertices with a large gap between the Lov\'asz number and the Shannon capacity $c(G)$. Specifically, we prove that for any $\epsilon > 0$, for infinitely many $n$ there is a generalized Johnson graph $G$ on $n$ vertices which has ratio $\vartheta(G)/c(G) = \Omega(n^{1-\epsilon})$, which improves on all known constructions. The graph $G$ \textit{a fortiori} also has ratio $\vartheta(G)/\alpha(G) = \Omega(n^{1-\epsilon})$, which greatly improves on the best known explicit construction., Comment: 21 pages; modified the statement of Theorem 1.6 and expanded the proof of Lemma 2.11; some minor revisions

The structure and composition of simple ices can be modified during stellar evolution by protostellar heating. Key to understanding the involved processes are thermal and chemical tracers that can diagnose the history and environment of the ice. The 15.2 $\mu$m bending mode of $^{12}$CO$_2$ has proven to be a valuable tracer of ice heating events but suffers from grain shape and size effects. A viable alternative tracer is the weaker $^{13}$CO$_2$ isotopologue band at 4.39 $\mu$m which has now become accessible at high S/N with the $\textit{James Webb}$ Space Telescope (JWST). We present JWST NIRSpec observations of $^{13}$CO$_2$ ice in five deeply embedded Class 0 sources spanning a wide range in luminosities (0.2 - 10$^4$ L$_{\odot}$ ) taken as part of the Investigating Protostellar Accretion Across the Mass Spectrum (IPA) program. The band profiles vary significantly, with the most luminous sources showing a distinct narrow peak at 4.38 $\mu$m. We first apply a phenomenological approach and show that a minimum of 3-4 Gaussian profiles are needed to fit the $^{13}$CO$_2$ absorption feature. We then combine these findings with laboratory data and show that a 15.2 $\mu$m $^{12}$CO$_2$ band inspired five-component decomposition can be applied for the isotopologue band where each component is representative of CO$_2$ ice in a specific molecular environment. The final solution consists of cold mixtures of CO$_2$ with CH$_3$OH, H$_2$O and CO as well as segregated heated pure CO$_2$ ice. Our results are in agreement with previous studies of the $^{12}$CO$_2$ ice band, further confirming that $^{13}$CO$_{2}$ is a useful alternative tracer of protostellar heating events. We also propose an alternative solution consisting only of heated CO$_2$:CH$_3$OH and CO$_2$:H$_2$O ices and warm pure CO$_2$ ice for decomposing the ice profiles of the two most luminous sources in our sample.

Recently, there has been a growing interest in the relationships between unrooted and rooted phylogenetic networks. In this context, a natural question to ask is if an unrooted phylogenetic network U can be oriented as a rooted phylogenetic network such that the latter satisfies certain structural properties. In a recent preprint, Bulteau et al. claim that it is computational hard to decide if U has a funneled (resp. funneled tree-child) orientation, for when the internal vertices of U have degree at most 5. Unfortunately, the proof of their funneled tree-child result appears to be incorrect. In this paper, we present a corrected proof and show that hardness remains for other popular classes of rooted phylogenetic networks such as funneled normal and funneled reticulation-visible. Additionally, our results hold regardless of whether U is rooted at an existing vertex or by subdividing an edge with the root.

We aim to investigate the origin of the HI Br$\gamma$ emission in young stars by using GRAVITY to image the innermost region of circumstellar disks, where important physical processes such as accretion and winds occur. With high spectral and angular resolution, we focus on studying the continuum and the HI Br$\gamma$-emitting area of the Herbig star HD58647. Using VLTI-GRAVITY, we conducted observations of HD58647 with both high spectral and high angular resolution. Thanks to the extensive $uv$ coverage, we were able to obtain detailed images of the circumstellar environment at a sub-au scale, specifically capturing the continuum and the Br$\gamma$-emitting region. Through the analysis of velocity-dispersed images and photocentre shifts, we were able to investigate the kinematics of the HI Br$\gamma$-emitting region. The recovered continuum images show extended emission where the disk major axis is oriented along a position angle of 14\degr. The size of the continuum emission at 5-sigma levels is $\sim$ 1.5 times more extended than the sizes reported from geometrical fitting (3.69 mas $\pm$ 0.02 mas). This result supports the existence of dust particles close to the stellar surface, screened from the stellar radiation by an optically thick gaseous disk. Moreover, for the first time with GRAVITY, the hot gas component of HD58647 traced by the Br$\gamma$ ,has been imaged. This allowed us to constrain the size of the Br$\gamma$-emitting region and study the kinematics of the hot gas; we find its velocity field to be roughly consistent with gas that obeys Keplerian motion. The velocity-dispersed images show that the size of the hot gas emission is from a more compact region than the continuum (2.3 mas $\pm$ 0.2 mas). Finally, the line phases show that the emission is not entirely consistent with Keplerian rotation, hinting at a more complex structure in the hot gaseous disk., Comment: accepted in A&A on 20/11/2023

We investigate the bright CO fundamental emission in the central regions of five protostars in their primary mass assembly phase using new observations from JWST's Near-Infrared Spectrograph (NIRSpec) and Mid-Infrared Instrument (MIRI). CO line emission images and fluxes are extracted for a forest of $\sim$150 ro-vibrational transitions from two vibrational bands, $v=1-0$ and $v=2-1$. However, ${}^{13}$CO is undetected, indicating that ${}^{12}$CO emission is optically thin. We use H$_2$ emission lines to correct fluxes for extinction and then construct rotation diagrams for the CO lines with the highest spectral resolution and sensitivity to estimate rotational temperatures and numbers of CO molecules. Two distinct rotational temperature components are required for $v=1$ ($\sim600$ to 1000 K and 2000 to $\sim 10^4$ K), while one hotter component is required for $v=2$ ($\gtrsim 3500$ K). ${}^{13}$CO is depleted compared to the abundances found in the ISM, indicating selective UV photodissociation of ${}^{13}$CO; therefore, UV radiative pumping may explain the higher rotational temperatures in $v=2$. The average vibrational temperature is $\sim 1000$ K for our sources and is similar to the lowest rotational temperature components. Using the measured rotational and vibrational temperatures to infer a total number of CO molecules, we find that the total gas masses range from lower limits of $\sim10^{22}$ g for the lowest mass protostars to $\sim 10^{26}$ g for the highest mass protostars. Our gas mass lower limits are compatible with those in more evolved systems, which suggest the lowest rotational temperature component comes from the inner disk, scattered into our line of sight, but we also cannot exclude the contribution to the CO emission from disk winds for higher mass targets., Comment: 31 pages, 7 figures, 4 tables, received to ApJ December 10 2023, accepted to ApJ August 4 2024

The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research., Comment: 17 pages; minor revisions

In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular sequences or morphological data. Interestingly, it has been known for some time that any binary phylogenetic tree can be (convexly) defined by a set of at most four characters, and that there are binary phylogenetic trees for which three characters are not enough. Thus, it is of interest to characterise those phylogenetic trees that are defined by a set of at most three characters. In this paper, we provide such a characterisation, in particular proving that a binary phylogenetic tree $T$ is defined by a set of at most three characters precisely if $T$ has no internal subtree isomorphic to a certain tree., Comment: 21 pages, 9 figures

Investigating Protostellar Accretion (IPA) is a JWST Cycle~1 GO program that uses NIRSpec IFU and MIRI MRS to obtain 2.9--28~$\mu$m spectral cubes of young, deeply embedded protostars with luminosities of 0.2 to 10,000~L$_{\odot}$ and central masses of 0.15 to 12~M$_{\odot}$. In this Letter, we report the discovery of a highly collimated atomic jet from the Class~0 protostar IRAS~16253$-$2429, the lowest luminosity source ($L_\mathrm{bol}$ = 0.2 $L_\odot$) in the IPA program. The collimated jet is detected in multiple [Fe~II] lines, [Ne~II], [Ni~II], and H~I lines, but not in molecular emission. The atomic jet has a velocity of about 169~$\pm$~15~km\,s$^{-1}$, after correcting for inclination. The width of the jet increases with distance from the central protostar from 23 to~60 au, corresponding to an opening angle of 2.6~$\pm$~0.5\arcdeg. By comparing the measured flux ratios of various fine structure lines to those predicted by simple shock models, we derive a shock {speed} of 54~km\,s$^{-1}$ and a preshock density of 2.0$\times10^{3}$~cm$^{-3}$ at the base of the jet. {From these quantities and using a suite of jet models and extinction laws we compute a mass loss rate between $0.4 -1.1\times10^{-10}~M_{\odot}$~yr~$^{-1}$.} The low mass loss rate is consistent with simultaneous measurements of low mass accretion rate ($2.4~\pm~0.8~\times~10^{-9}~M_{\odot}$~yr$^{-1}$) for IRAS~16253$-$2429 from JWST observations (Watson et al. in prep), indicating that the protostar is in a quiescent accretion phase. Our results demonstrate that very low-mass protostars can drive highly collimated, atomic jets, even during the quiescent phase., Comment: Accepted to ApJL. Comments and feedback welcome

For a $k$-uniform hypergraph $\mathcal{H}$, the \emph{codegree squared sum} $\text{co}_2(\mathcal{H})$ is the square of the $\ell_2$-norm of the codegree vector of $\mathcal{H}$, and for a family $\mathscr{F}$ of $k$-uniform hypergraphs, the codegree squared extremal number $\text{exco}_2(n, \mathscr{F})$ is the maximum codegree squared sum of a hypergraph on $n$ vertices which does not contain any hypergraph in $\mathscr{F}$. Balogh, Clemen and Lidick\'y recently introduced the codegree squared extremal number and determined it for a number of $3$-uniform hypergraphs, including the complete graphs $K_4^3$ and $K_5^3$. In this paper, we give a number of exact or asymptotic results for hypergraph Tur\'an problems in the $\ell_2$-norm, including the first exact results for arbitrary $k$. Namely, we prove a version of the classical Erd\H{o}s-Ko-Rado theorem for the codegree squared extremal number: if $\mathcal{F} \subset \binom{[n]}{k}$ is intersecting and $n\ge 2k$, then \[\text{co}_2(\mathcal{F}) \le \binom{n-1}{k-1}(1+(n-k+1)(k-1)),\] with equality only for the star for $n > 2k$. Our main tool is an inequality of Bey, which also gives a general upper bound on $\text{exco}_2(n, \mathscr{F})$. We also prove versions of the Erd\H{o}s Matching Conjecture and the $t$-intersecting Erd\H{o}s-Ko-Rado theorem for the codegree squared extremal number for large $n$, determine the exact codegree squared extremal number of minimal and linear $3$-paths and $3$-cycles, and determine asymptotically the codegree squared extremal number of minimal and linear $s$-paths and $s$-cycles for $s\ge 4$. Lastly, we derive a number of exact or asymptotic results for graph Tur\'an-type problems in the $\ell_2$-norm from spectral extremal results for certain fobridden subgraph problems and the well-known Hofmeister's inequality., Comment: 26 pages; added some results on graph Tur\'an problems in the $\ell_2$-norm

(Abridged) We investigate the impact of radiative feedback from massive stars on their natal cloud and focus on the transition from the HII region to the atomic PDR (crossing the ionisation front (IF)), and the subsequent transition to the molecular PDR (crossing the dissociation front (DF)). We use high-resolution near-IR integral field spectroscopic data from NIRSpec on JWST to observe the Orion Bar PDR as part of the PDRs4All JWST Early Release Science Program. The NIRSpec data reveal a forest of lines including, but not limited to, HeI, HI, and CI recombination lines, ionic lines, OI and NI fluorescence lines, Aromatic Infrared Bands (AIBs including aromatic CH, aliphatic CH, and their CD counterparts), CO2 ice, pure rotational and ro-vibrational lines from H2, and ro-vibrational lines HD, CO, and CH+, most of them detected for the first time towards a PDR. Their spatial distribution resolves the H and He ionisation structure in the Huygens region, gives insight into the geometry of the Bar, and confirms the large-scale stratification of PDRs. We observe numerous smaller scale structures whose typical size decreases with distance from Ori C and IR lines from CI, if solely arising from radiative recombination and cascade, reveal very high gas temperatures consistent with the hot irradiated surface of small-scale dense clumps deep inside the PDR. The H2 lines reveal multiple, prominent filaments which exhibit different characteristics. This leaves the impression of a "terraced" transition from the predominantly atomic surface region to the CO-rich molecular zone deeper in. This study showcases the discovery space created by JWST to further our understanding of the impact radiation from young stars has on their natal molecular cloud and proto-planetary disk, which touches on star- and planet formation as well as galaxy evolution., Comment: 52 pages, 30 figures, submitted to A&A

Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9--28 $\mu$m spectral cubes of five young protostars with luminosities of 0.2-10,000 L$_{\odot}$ in their primary accretion phase. This paper introduces the NIRSpec 2.9--5.3 $\mu$m data of the inner 840-9000 au with spatial resolutions from 28-300 au. The spectra show rising continuum emission; deep ice absorption; emission from H$_{2}$, H~I, and [Fe~II]; and the CO fundamental series in emission and absorption. Maps of the continuum emission show scattered light cavities for all five protostars. In the cavities, collimated jets are detected in [Fe~II] for the four $< 320$~L$_{\odot}$ protostars, two of which are additionally traced in Br-$\alpha$. Knots of [Fe~II] emission are detected toward the most luminous protostar, and knots of [FeII] emission with dynamical times of $< 30$~yrs are found in the jets of the others. While only one jet is traced in H$_2$, knots of H$_2$ and CO are detected in the jets of four protostars. H$_2$ is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H$_2$ emission is seen along the walls of a single cavity, while in three cavities narrow shells of H$_2$ emission are found, one of which has an [Fe~II] knot at its apex. These data show cavities containing collimated jets traced in atomic/ionic gas surrounded by warm molecular gas in a wide-angle wind and/or gas accelerated by bow shocks in the jets., Comment: 26 pages, 12 figures

Inclusive e$^+$e$^-$ production has been studied with HADES in $\pi^-$ + p, $\pi^-$ + C and $\pi^- + \mathrm{CH}_2$ reactions, using the GSI pion beam at $\sqrt{s_{\pi p}}$ = 1.49 GeV. Invariant mass and transverse momentum distributions have been measured and reveal contributions from Dalitz decays of $\pi^0$, $\eta$ mesons and baryon resonances. The transverse momentum distributions are very sensitive to the underlying kinematics of the various processes. The baryon contribution exhibits a deviation up to a factor seven from the QED reference expected for the dielectron decay of a hypothetical point-like baryon with the production cross section constrained from the inverse $\gamma$ n$\rightarrow \pi^-$ p reaction. The enhancement is attributed to a strong four-momentum squared dependence of the time-like electromagnetic transition form factors as suggested by Vector Meson Dominance (VMD). Two versions of the VMD, that differ in the photon-baryon coupling, have been applied in simulations and compared to data. VMD1 (or two-component VMD) assumes a coupling via the $\rho$ meson and a direct coupling of the photon, while in VMD2 (or strict VMD) the coupling is only mediated via the $\rho$ meson. The VMD2 model, frequently used in transport calculations for dilepton decays, is found to overestimate the measured dielectron yields, while a good description of the data can be obtained with the VMD1 model assuming no phase difference between the two amplitudes. Similar descriptions have also been obtained using a time-like baryon transition form factor model where the pion cloud plays the major role., Comment: (HADES collaboration)

For a fixed positive integer $k$ and a graph $G$, let $\lambda_k(G)$ denote the $k$-th largest eigenvalue of the adjacency matrix of $G$. In 2017, Tait and Tobin proved that the maximum $\lambda_1(G)$ among all outerplanar graphs on $n$ vertices is achieved by the fan graph $K_1\vee P_{n-1}$. In this paper, we consider a similar problem of determining the maximum $\lambda_2$ among all connected outerplanar graphs on $n$ vertices. For $n$ even and sufficiently large, we prove that the maximum $\lambda_2$ is uniquely achieved by the graph $(K_1\vee P_{n/2-1})\!\!-\!\!(K_1\vee P_{n/2-1})$, which is obtained by connecting two disjoint copies of $(K_1\vee P_{n/2-1})$ through a new edge joining their smallest degree vertices. When $n$ is odd and sufficiently large, the extremal graphs are not unique. The extremal graphs are those graphs $G$ that contain a cut vertex $u$ such that $G\setminus \{u\}$ is isomorphic to $2(K_1\vee P_{n/2-1})$. We also determine the maximum $\lambda_2$ among all 2-connected outerplanar graphs and asymptotically determine the maximum of $\lambda_k(G)$ among all connected outerplanar graphs for any fixed $k$., Comment: 32 pages; minor revisions

The JWST has captured the most detailed and sharpest infrared images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR). We investigate the fundamental interaction of far-ultraviolet photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of 0.1-1" (0.0002-0.002 pc or 40-400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. A complex, structured, and folded DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate.

(Abridged) Mid-infrared observations of photodissociation regions (PDRs) are dominated by strong emission features called aromatic infrared bands (AIBs). The most prominent AIBs are found at 3.3, 6.2, 7.7, 8.6, and 11.2 $\mu$m. The most sensitive, highest-resolution infrared spectral imaging data ever taken of the prototypical PDR, the Orion Bar, have been captured by JWST. We provide an inventory of the AIBs found in the Orion Bar, along with mid-IR template spectra from five distinct regions in the Bar: the molecular PDR, the atomic PDR, and the HII region. We use JWST NIRSpec IFU and MIRI MRS observations of the Orion Bar from the JWST Early Release Science Program, PDRs4All (ID: 1288). We extract five template spectra to represent the morphology and environment of the Orion Bar PDR. The superb sensitivity and the spectral and spatial resolution of these JWST observations reveal many details of the AIB emission and enable an improved characterization of their detailed profile shapes and sub-components. While the spectra are dominated by the well-known AIBs at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 $\mu$m, a wealth of weaker features and sub-components are present. We report trends in the widths and relative strengths of AIBs across the five template spectra. These trends yield valuable insight into the photochemical evolution of PAHs, such as the evolution responsible for the shift of 11.2 $\mu$m AIB emission from class B$_{11.2}$ in the molecular PDR to class A$_{11.2}$ in the PDR surface layers. This photochemical evolution is driven by the increased importance of FUV processing in the PDR surface layers, resulting in a "weeding out" of the weakest links of the PAH family in these layers. For now, these JWST observations are consistent with a model in which the underlying PAH family is composed of a few species: the so-called 'grandPAHs'., Comment: 25 pages, 10 figures, to appear in A&A

G34.26+0.15 is a region of high-mass star formation that contains a broad range of young stellar objects in different stages of evolution, including a hot molecular core, hyper-compact HII regions and a prototypical cometary ultra-compact HII region. Previous high-sensitivity single dish observations by our group resulted in the detection of broad 6035 MHz OH absorption in this region; the line showed a significant blue-shifted asymmetry indicative of molecular gas expansion. We present high-sensitivity Karl G. Jansky Very Large Array (VLA) observations of the 6035 MHz OH line conducted to image the absorption and investigate its origin with respect to the different star formation sites in the region. In addition, we report detection of 6030 MHz OH absorption with the VLA and further observations of 4.7 GHz and 6.0 GHz OH lines obtained with the Arecibo Telescope. The 6030 MHz OH line shows a very similar absorption profile as the 6035 MHz OH line. We found that the 6035 MHz OH line absorption region is spatially unresolved at $\sim 2$" scales, and it is coincident with one of the bright ionized cores of the cometary HII region that shows broad radio recombination line emission. We discuss a scenario where the OH absorption is tracing the remnants of a pole-on molecular outflow that is being ionized inside-out by the ultra-compact HII region., Comment: 19 pages, 6 figures. Accepted for publication in The Astrophysical Journal

The fragmentation mode of high-mass molecular clumps and the accretion processes that form the most massive stars ($M\gtrsim 8M_\odot$) are still not well understood. To this end, we have undertaken a large observational program (CORE) making use of interferometric observations from the Northern Extended Millimetre Array (NOEMA) for a sample of 20 luminous ($L>10^4L_\odot$) protostellar objects in the 1.37 mm wavelength regime in both continuum and line emission, reaching $\sim$0.4" resolution (800 au at 2 kpc). Using the dense gas tracer CH$_3$CN, we find velocity gradients across 13 cores perpendicular to the directions of bipolar molecular outflows, making them excellent disk candidates. Specific angular momentum ($j$) radial profiles are on average $\sim10^{-3}$ km /s pc and follow $j \propto r^{1.7}$, consistent with a poorly resolved rotating and infalling envelope/disk model. Fitting the velocity profiles with a Keplerian model, we find protostellar masses in the range of $\sim 10-25$ $M_\odot$. Modelling the level population of CH$_3$CN lines, we present temperature maps and find median gas temperatures in the range $70-210$ K. We create Toomre $Q$ maps to study the stability of the disks and find almost all (11 of 13) disk candidates to be prone to fragmentation due to gravitational instabilities at the scales probed by our observations. In particular, disks with masses greater than $\sim10-20\%$ of the mass of their host (proto)stars are Toomre unstable, and more luminous protostellar objects tend to have disks that are more massive and hence more prone to fragmentation. Our finings show that most disks around high-mass protostars are prone to disk fragmentation early in their formation due to their high disk to stellar mass ratio. This impacts the accretion evolution of high-mass protostars which will have significant implications for the formation of the most massive stars., Comment: 27 pages, 12 figures, 6 appendices - accepted for publication in Astronomy and Astrophysics

High-mass protostars (M$_{\star} >$ 8 M$_{\odot}$) are thought to gain the majority of their mass via short, intense bursts of growth. This episodic accretion is thought to be facilitated by gravitationally unstable and subsequently inhomogeneous accretion disks. Limitations of observational capabilities, paired with a lack of observed accretion burst events has withheld affirmative confirmation of the association between disk accretion, instability and the accretion burst phenomenon in high-mass protostars. Following its 2019 accretion burst, a heat-wave driven by a burst of radiation propagated outward from the high-mass protostar G358.93-0.03-MM1. Six VLBI (very long baseline interferometry) observations of the raditively pumped 6.7 GHz methanol maser were conducted during this period, tracing ever increasing disk radii as the heat-wave propagated outward. Concatenating the VLBI maps provided a sparsely sampled, milliarcsecond view of the spatio-kinematics of the accretion disk covering a physical range of $\sim$ 50 - 900 AU. We term this observational approach `heat-wave mapping'. We report the discovery of a Keplerian accretion disk with a spatially resolved four-arm spiral pattern around G358.93-0.03-MM1. This result positively implicates disk accretion and spiral arm instabilities into the episodic accretion high-mass star formation paradigm., Comment: Published in Nature Astronomy in 2023

High-mass stars are thought to accumulate much of their mass via short, infrequent bursts of disk-aided accretion. Such accretion events are rare and difficult to observe directly but are known to drive enhanced maser emission. In this Letter we report high-resolution, multi-epoch methanol maser observations toward G358.93-0.03 which reveal an interesting phenomenon; the sub-luminal propagation of a thermal radiation "heat-wave" emanating from an accreting high-mass proto-star. The extreme transformation of the maser emission implies a sudden intensification of thermal infrared radiation from within the inner (40 mas, 270 au) region. Subsequently, methanol masers trace the radial passage of thermal radiation through the environment at $\geq$ 4-8\% the speed of light. Such a high translocation rate contrasts with the $\leq$ 10 km s$^{-1}$ physical gas motions of methanol masers typically observed using very long baseline interferometry (VLBI). The observed scenario can readily be attributed to an accretion event in the high-mass proto-star G358.93-0.03-MM1. While being the third case in its class, G358.93-0.03-MM1 exhibits unique attributes hinting at a possible `zoo' of accretion burst types. These results promote the advantages of maser observations in understanding high-mass star formation, both through single-dish maser monitoring campaigns and via their international cooperation as VLBI arrays., Comment: Published in Nature Astronomy in 2020

In this note, we improve the lower bounds for the maximum size of the $k$th largest eigenvalue of the adjacency matrix of a graph for several values of $k$. In particular, we show that closed blowups of the icosahedral graph improve the lower bound for the maximum size of the fourth largest eigenvalue of a graph, answering a question of Nikiforov., Comment: Minor revisions

The production of $\Sigma^0$ hyperons in proton proton collisions at a beam kinetic energy of 3.5 GeV impinging on a liquid hydrogen target was investigated using data collected with the HADES setup. The total production cross section is found to be $\mathrm{\sigma (pK^{+}\Sigma^{0}) [\mu b] = 17.7 \pm 1.7 (stat) \pm 1.6 (syst)}$. Differential cross section distributions of the exclusive channel $\mathrm{pp \rightarrow pK^{+}\Sigma^{0}}$ were analyzed in the center-of-mass, Gottfried-Jackson and helicity reference frames for the first time at the excess energy of 556 MeV. The data support the interplay between pion and kaon exchange mechanisms and clearly demonstrate the contribution of interfering nucleon resonances decaying to $\mathrm{K^{+}\Sigma^{0}}$. The Bonn-Gatchina partial wave analysis was employed to analyse the data. Due to the limited statistics, it was not possible to obtain an unambiguous determination of the relative contribution of intermediate nucleon resonances to the final state. However nucleon resonances with masses around 1.710 $\mathrm{GeV/c^{2}}$ ($\mathrm{N^{*}(1710)}$) and 1.900 $\mathrm{GeV/c^{2}}$ ($\mathrm{N^{*}(1900)}$ or $\mathrm{\Delta^{*}(1900)}$) are preferred by the fit.

Semi-directed phylogenetic networks have recently emerged as a class of phylogenetic networks sitting between rooted (directed) and unrooted (undirected) phylogenetic networks as they contain both directed as well as undirected edges. While the spaces of rooted phylogenetic networks and unrooted phylogenetic networks have been analyzed in recent years and various rearrangement moves to traverse these spaces have been introduced, the results do not immediately carry over to semi-directed phylogenetic networks. Here, we propose a simple rearrangement move for semi-directed phylogenetic networks, called cut edge transfer (CET), and show that the space of semi-directed level-$1$ networks with precisely $k$ reticulations is connected under CET. This level-$1$ space is currently the predominantly used search space for most algorithms that reconstruct semi-directed phylogenetic networks. Hence, every semi-directed level-$1$ network with a fixed number of reticulations and leaf set can be reached from any other such network by a sequence of CETs. By introducing two additional moves, CET$^+$ and CET$^-$, that allow for the addition or deletion of reticulations, we then establish connectedness for the space of all semi-directed phylogenetic networks on a fixed leaf set. As a byproduct of our results for semi-directed phylogenetic networks, we also show that the space of rooted level-$1$ networks with a fixed number of reticulations and leaf set is connected under CET, when translated into the rooted setting.

Hadron production ($\pi^\pm$, proton, $\Lambda$, $K_S^0$, $K^\pm$) in $\pi^- + \mathrm{C}$ and $\pi^- + \mathrm{W}$ collisions is investigated at an incident pion beam momentum of $1.7~\mathrm{GeV}/c$. This comprehensive set of data measured with HADES at SIS18/GSI significantly extends the existing world data on hadron production in pion induced reactions and provides a new reference for models that are commonly used for the interpretation of heavy-ion collisions. The measured inclusive differential production cross-sections are compared with state-of-the-art transport model (GiBUU, SMASH) calculations. The (semi-) exclusive channel $\pi^- + A \rightarrow \Lambda + K_S^0 +X$, in which the kinematics of the strange hadrons are correlated, is also investigated and compared to a model calculation. Agreement and remaining tensions between data and the current version of the considered transport models are discussed.

Phylogenetic networks are a special type of graph which generalize phylogenetic trees and that are used to model non-treelike evolutionary processes such as recombination and hybridization. In this paper, we consider {\em unrooted} phylogenetic networks, i.e. simple, connected graphs $\mathcal{N}=(V,E)$ with leaf set $X$, for $X$ some set of species, in which every internal vertex in $\mathcal{N}$ has degree three. One approach used to construct such phylogenetic networks is to take as input a collection $\mathcal{P}$ of phylogenetic trees and to look for a network $\mathcal{N}$ that contains each tree in $\mathcal{P}$ and that minimizes the quantity $r(\mathcal{N}) = |E|-(|V|-1)$ over all such networks. Such a network always exists, and the quantity $r(\mathcal{N})$ for an optimal network $\mathcal{N}$ is called the hybrid number of $\mathcal{P}$. In this paper, we give a new characterization for the hybrid number in case $\mathcal{P}$ consists of two trees. This characterization is given in terms of a cherry picking sequence for the two trees, although to prove that our characterization holds we need to define the sequence more generally for two forests. Cherry picking sequences have been intensively studied for collections of rooted phylogenetic trees, but our new sequences are the first variant of this concept that can be applied in the unrooted setting. Since the hybrid number of two trees is equal to the well-known tree bisection and reconnection distance between the two trees, our new characterization also provides an alternative way to understand this important tree distance.

The spread of a graph $G$ is the difference between the largest and smallest eigenvalues of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{2,t}$-minor. We show that for any $t\geq 2$, there is an integer $\xi_t$ such that the maximum spread of an $n$-vertex $K_{2,t}$-minor-free graph is achieved by the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+\xi_t}{3t}\rfloor$ copies of $K_t$ and $n-1 - t\lfloor \frac{2n+\xi_t}{3t}\rfloor$ isolated vertices. The extremal graph is unique, except when $t\equiv 4 \mod 12$ and $\frac{2n+ \xi_t} {3t}$ is an integer, in which case the other extremal graph is the graph obtained by joining a vertex to the disjoint union of $\lfloor \frac{2n+\xi_t}{3t}\rfloor-1$ copies of $K_t$ and $n-1-t(\lfloor \frac{2n+\xi_t}{3t}\rfloor-1)$ isolated vertices. Furthermore, we give an explicit formula for $\xi_t$., Comment: Minor revisions. arXiv admin note: text overlap with arXiv:2209.13776

In the context of reconstructing phylogenetic networks from a collection of phylogenetic trees, several characterisations and subsequently algorithms have been established to reconstruct a phylogenetic network that collectively embeds all trees in the input in some minimum way. For many instances however, the resulting network also embeds additional phylogenetic trees that are not part of the input. However, little is known about these inferred trees. In this paper, we explore the relationships among all phylogenetic trees that are embedded in a given phylogenetic network. First, we investigate some combinatorial properties of the collection P of all rooted binary phylogenetic trees that are embedded in a rooted binary phylogenetic network N. To this end, we associated a particular graph G, which we call rSPR graph, with the elements in P and show that, if |P|=2^k, where k is the number of vertices with in-degree two in N, then G has a Hamiltonian cycle. Second, by exploiting rSPR graphs and properties of hypercubes, we turn to the well-studied class of rooted binary level-1 networks and give necessary and sufficient conditions for when a set of rooted binary phylogenetic trees can be embedded in a level-1 network without inferring any additional trees. Lastly, we show how these conditions translate into a polynomial-time algorithm to reconstruct such a network if it exists., Comment: final version of accepted manuscript

The total amount of dust grains in protoplanetary disks is one of the key properties that characterize the potential for planet formation. With (sub-)millimeter flux measurements, literature studies usually derive the dust mass using an analytic form under the assumption of optically thin emission, which may lead to substantial underestimation. In this work, we conduct a parameter study with the goal of investigating the effects of disk structure and dust properties on the underestimation through self-consistent radiative transfer models. Different dust models, scattering modes and approaches for dust settling are considered and compared. The influences of disk substructures, such as rings and crescents, on the mass derivation are investigated as well. The results indicate that the traditional analytic method can underestimate the mass by a factor of a few to hundreds, depending on the optical depth along the line of sight set mainly by the true dust mass, disk size and inclination. As an application, we perform a detailed radiative transfer modeling of the spectral energy distribution of DoAr 33, one of the observed DSHARP disks. When the DSHARP dust opacities are adopted, the most probable dust mass returned from the Bayesian analysis is roughly 7 times higher than the value given by the analytic calculation. Our study demonstrates that estimating disk dust masses from radiative transfer modeling is one solution for alleviating the problem of insufficient mass for planet formation raised in the ALMA era., Comment: 16 pages, 9 figures, accepted for publication in A&A

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on $n-1$ vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on $\lceil (2n-1)/3\rceil$ vertices and $\lfloor(n-2)/3\rfloor$ isolated vertices. For planar graphs, we show that the extremal $n$-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on $\lceil(2n-2)/3\rceil$ vertices and $\lfloor(n-4)/3\rfloor$ isolated vertices.

A set system $\mathcal{F}$ is $t$-\textit{intersecting}, if the size of the intersection of every pair of its elements has size at least $t$. A set system $\mathcal{F}$ is $k$-\textit{Sperner}, if it does not contain a chain of length $k+1$. Our main result is the following: Suppose that $k$ and $t$ are fixed positive integers, where $n+t$ is even with $t\le n$ and $n$ is large enough. If $\mathcal{F}\subseteq 2^{[n]}$ is a $t$-intersecting $k$-Sperner family, then $|\mathcal{F}|$ has size at most the size of the sum of $k$ layers, of sizes $(n+t)/2,\ldots, (n+t)/2+k-1$. This bound is best possible. The case when $n+t$ is odd remains open.

The global polarization of {\Lambda} hyperons along the total orbital angular momentum of a relativistic heavy-ion collision is presented based on the high statistics data samples collected in Au+Au collisions at \sqrt{s_{NN}} = 2.4 GeV and Ag+Ag at 2.55 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at GSI, Darmstadt. This is the first measurement below the strangeness production threshold in nucleon-nucleon collisions. Results are reported as a function of the collision centrality as well as a function of the hyperon transverse momentum (p_T) and rapidity (y_{CM}) for the range of centrality 0--40%. We observe a strong centrality dependence of the polarization with an increasing signal towards peripheral collisions. For mid-central (20--40%) collisions the polarization magnitudes are (%) = 6.8 \pm 1.3 (stat.) \pm 2.1 (syst.) for Au+Au and (%) = 6.2 \pm 0.4 (stat.) \pm 0.6 (syst.) for Ag+Ag, which are the largest values observed so far. This observation thus provides a continuation of the increasing trend previously observed by STAR and contrasts expectations from recent theoretical calculations predicting a maximum in the region of collision energies about 3 GeV. The observed polarization is of a similar magnitude as predicted by 3D fluid dynamics and the UrQMD plus thermal vorticity model and significantly above results from the AMPT model., Comment: 8 pages, 4 figures

We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules with three novel new reduction rules. Two of the rules are based on the idea of topologically transforming the trees in a distance-preserving way in order to guarantee execution of earlier reduction rules. The third rule extends the local neighbourhood approach introduced in (Kelk and Linz, Annals of Combinatorics 24(3), 2020) to more global structures, allowing new situations to be identified when deletion of a leaf definitely reduces the TBR distance by one. The bound on the kernel size is tight up to an additive term. Our results also apply to the equivalent problem of computing a Maximum Agreement Forest (MAF) between two unrooted binary phylogenetic trees. We anticipate that our results will be more widely applicable for computing agreement-forest based dissimilarity measures., Comment: 38 pages. In this version a figure has been added, some references have been added, some small typo's have been fixed and the introduction and conclusion have been slightly extended. Submitted for journal review

First information on the time-like electromagnetic structure of baryons in the second resonance region has been obtained from measurements of dielectron (e+ e-) invariant-mass and angular distributions in the quasi-free reaction $\pi-$ p $\rightarrow$ n e+ e- at $\sqrt{s_{\pi p}}$ = 1.49 GeV with the High Acceptance Di-Electron Spectrometer (HADES) at GSI using the pion beam impinging on a CH$_2$ target. We find a total cross section $\sigma$ = 2.97 $\pm$ 0.07data $\pm$ 0.21acc $\pm$ 0.31Zeff $\mu$b. In complement to the analysis of the inclusive e+ e- channel, this data set provides a crucial test of the description of baryon time-like transitions. Approaches based on a Vector Meson Dominance amplitude containing direct photon and vector meson ($\rho$) couplings to the baryon provide a satisfactory agreement with the data. A good description is also obtained by electromagnetic time-like baryon transition form factors in a covariant spectator-quark model, pointing to the dominance of meson-cloud effects. The dielectron angular distributions exhibit the contributions of virtual photons ($\gamma^*$) with longitudinal polarization, in contrast to real photons. The virtual photon angular dependence supports the dominance of J=3/2, I=1/2 contributions observed in both the $\gamma^*$n and the $\pi \pi$n channels., Comment: revised version, 7 pages, 3 figures

Ultra-high angular resolution in astronomy has always been an important vehicle for making fundamental discoveries. Recent results in direct imaging of the vicinity of the supermassive black hole in the nucleus of the radio galaxy M87 by the millimeter VLBI system Event Horizon Telescope and various pioneering results of the Space VLBI mission RadioAstron provided new momentum in high angular resolution astrophysics. In both mentioned cases, the angular resolution reached the values of about 10-20 microrcseconds. Further developments toward at least an order of magnitude "sharper" values are dictated by the needs of astrophysical studies and can only be achieved by placing millimeter and submillimeter wavelength interferometric systems in space. A concept of such the system, called Terahertz Exploration and Zooming-in for Astrophysics (THEZA), has been proposed in the framework of the ESA Call for White Papers for the Voayage 2050 long term plan in 2019. In the current paper we discuss several approaches for addressing technological challenges of the THEZA concept. In particular, we consider a novel configuration of a space-borne millimeter/sub-millimeter antenna which might resolve several bottlenecks in creating large precise mechanical structures. The paper also presents an overview of prospective space-qualified technologies of low-noise analogue front-end instrumentation for millimeter/sub-millimeter telescopes, data handling and processing. The paper briefly discusses approaches to the interferometric baseline state vector determination and synchronisation and heterodyning system. In combination with the original ESA Voyage 2050 White Paper, the current work sharpens the case for the next generation microarcsceond-level imaging instruments and provides starting points for further in-depth technology trade-off studies., Comment: The paper on 29 pages contains 12 figures, accepted for publication in Acta Astronautica, based on the presentation at the 72nd IAC, Dubai, UAE, October 2021

We describe an impedance-based method for cell barrier integrity testing. A four-electrode electrical impedance spectroscopy (EIS) setup can be realized by simply connecting a commercial chopstick-like electrode (STX-1) to a potentiostat allowing monitoring cell barriers cultivated in transwell inserts. Subsequent electric circuit modeling of the electrical impedance results the capacitive properties of the barrier next to the well-known transepithelial electrical resistance (TEER). The versatility of the new method was analyzed by the EIS analysis of a Caco-2 monolayer in response to (a) different membrane coating materials, (b) two different permeability enhancers ethylene glycol-bis(2-aminoethylether)-N,N,N',N'-tetraacetic acid (EGTA) and saponin, and (c) sonoporation. For the different membrane coating materials, the TEERs of the standard and new protocol coincide and increase during cultivation, while the capacitance shows a distinct maximum for three different surface materials (no coating, Matrigel, and collagen I). The permeability enhancers cause a decline in the TEER value, but only saponin alters the capacitance of the cell layer by two orders of magnitude. Hence, cell layer capacitance and TEER represent two independent properties characterizing the monolayer. The use of commercial chopstick-like electrodes to access the impedance of a barrier cultivated in transwell inserts enables remarkable insight into the behavior of the cellular barrier with no extra work for the researcher. This simple method could evolve into a standard protocol used in cell barrier research.

Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that the objective function can be observed directly. We consider the case where the objective function must be estimated, often using a noisy function, as in simulation. We present a finite-time analysis of algorithm performance that combines estimation with a sampling distribution. We present a framework called Hesitant Adaptive Search with Estimation, and derive an upper bound on function evaluations that is cubic in dimension, under certain conditions. We extend the framework to Quantile Adaptive Search with Estimation, which focuses sampling points from a series of nested quantile level sets. The analyses suggest that computational effort is better expended on sampling improving points than refining estimates of objective function values during the progress of an adaptive search algorithm.

The Large Interferometer For Exoplanets (LIFE) initiative is developing the science and a technology roadmap for an ambitious space mission featuring a space-based mid-infrared (MIR) nulling interferometer in order to detect the thermal emission of hundreds of exoplanets and characterize their atmospheres. In order to quantify the science potential of such a mission, in particular in the context of technical trade-offs, an instrument simulator is required. In addition, signal extraction algorithms are needed to verify that exoplanet properties (e.g., angular separation, spectral flux) contained in simulated exoplanet datasets can be accurately retrieved. We present LIFEsim, a software tool developed for simulating observations of exoplanetary systems with an MIR space-based nulling interferometer. It includes astrophysical noise sources (i.e., stellar leakage and thermal emission from local zodiacal and exo-zodiacal dust) and offers the flexibility to include instrumental noise terms in the future. LIFEsim provides an accessible way for predicting the expected SNR of future observations as a function of various key instrument and target parameters. The SNRs of the extracted spectra are photon-noise dominated, as expected from our current simulations. From single epoch observations in our mock survey of small ($R < 1.5 R_\mathrm{Earth}$) planets orbiting within the habitable zones of their stars, we find that typical uncertainties in the estimated effective temperature of the exoplanets are $\lesssim$10%, for the exoplanet radius $\lesssim$20%, and for the separation from the host star $\lesssim$2%. SNR values obtained in the signal extraction process deviate less than 10% from purely photon-counting statistics based SNRs. (abridged), Comment: Accepted for publication in A&A; 15 pages (main text incl. 13 figures and 1 table) + appendix; comments are welcome

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given rooted phylogenetic tree is of recurring interest. This problem, formally know as Tree Containment, is NP-complete in general and polynomial-time solvable for certain classes of phylogenetic networks. In this paper, we connect ideas from quantum computing and phylogenetics to present an efficient Quadratic Unconstrained Binary Optimization formulation for Tree Containment in the general setting. For an instance (N,T) of Tree Containment, where N is a phylogenetic network with n_N vertices and T is a phylogenetic tree with n_T vertices, the number of logical qubits that are required for our formulation is O(n_N n_T)., Comment: final version accepted for publication in Theoretical Computer Science