Search

Lov\'{a}sz et al. proved that every $6$-edge-connected graph has a nowhere-zero $3$-flow. In fact, they proved a more technical statement which says that there exists a nowhere zero $3$-flow that extends the flow prescribed on the incident edges of a single vertex $z$ with bounded degree. We extend this theorem of Lov\'{a}sz et al. to allow $z$ to have arbitrary degree, but with the additional assumption that there is another vertex $x$ with large degree and no small cut separating $x$ and $z$. Using this theorem, we prove two results regarding the generation of minimal graphs with the property that prescribing the edges incident to a vertex with specific flow does not extend to a nowhere-zero $3$-flow. We use this to further strengthen the theorem of Lov\'{a}sz et al., as well as make progress on a conjecture of Li et al., Comment: 51 pages

A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi and Mohar proved that locally planar graphs are acyclically 7-colourable. In 2002, Borodin, Fon-Der-Flaass, Kostochka, Raspaud, and Sopena proved that planar graphs are acyclically 7-list-colourable. We prove that locally planar graphs are acyclically 9-list-colourable\textemdash no bound for acyclic list colouring locally planar graphs for any fixed number of colours was previously known., Comment: 19 pages, 4 figures

We present 5-1x10^7 Angstrom spectral energy distributions (SEDs) for twelve M dwarf stars covering spectral types M0-M8. Our SEDs are provided for community use as a sequel to the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) survey. The twelve stars include eight known exoplanet hosts and four stars chosen to fill out key parameter space in spectral type and rotation period. The SEDs are constructed from Hubble Space Telescope ultraviolet spectroscopy and XMM Newton, Chandra and/or Swift X-ray observations and completed with various model data, including Lyman alpha reconstructions, PHOENIX optical models, APEC coronal models and Differential Emission Measure models in the currently-unobservable Extreme Ultraviolet. We provide a complete overview of the Mega-MUSCLES program, including a description of the observations, models, and SED construction. The SEDs are available as MAST High-Level Science Products and we describe the various data products here. We also present ensemble measurements from our sample that are of particular relevance to exoplanet science, including the high-energy fluxes in the habitable zone and the FUV/NUV ratio. Combined with MUSCLES, Mega-MUSCLES provides SEDs covering a wide range of M\,dwarf spectral types and ages such that suitable proxies for any M dwarf planet host of interest may be found in our sample. However, we find that ultraviolet and X-ray fluxes can vary even between stars with similar parameters, such that observations of each exoplanet host star will remain the gold standard for interpreting exoplanet atmosphere observations., Comment: Updated Mega-MUSCLES SEDs available at https://doi.org/10.5281/zenodo.4556130

We show that for any positive integer $r$, the Weighted Maximum $k$-colourable Induced Subgraph problem can be solved in polynomial time for input graphs that do not contain $(P_5+ rK_1)$ as an induced subgraph, and give an explicit algorithm demonstrating this. This answers a question of Agrawal et al. (2024).

We evaluate the performance of various configurations of the Canadian Regional Climate Model (CRCM6-GEM5) in simulating 10-meter wind speeds using data from 27 AmeriFlux stations across North America. The assessment employs a hierarchy of error metrics, ranging from simple mean bias to advanced metrics that account for the dependence of wind speeds on variables such as friction velocity and stability. The results reveal that (i) the value of roughness length (z0) has a large effect on the simulation of wind speeds, (ii) using a lower limit for the Obhukov length instead of a lower limit for the lowest level wind speed seems to deteriorate the simulation of wind speeds under very stable conditions, (iii) the choice of stability function has a small but noticeable impact on the wind speeds, (iv) the turbulent orographic form drag scheme shows improvement over effective roughness length approach.

The weak degeneracy of a graph $G$ is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every $d$-degenerate graph is weakly $d$-degenerate, but the converse is not true in general (for example, all connected $d$-regular graphs except cycles and cliques are weakly $(d-1)$-degenerate). If $G$ is weakly $d$-degenerate, then the list-chromatic number of $G$ is at most $d+1$, and the same upper bound holds for various other parameters such as the DP-chromatic number and the paint number. Here we rectify a mistake in a paper of the first two authors and give a correct proof that planar graphs are weakly $4$-degenerate, strengthening the famous result of Thomassen that planar graphs are $5$-list-colorable., Comment: 13 pages, 3 figures

The origin and evolution of CO gas in debris disks has been debated since its initial detection. The gas could have a primordial origin, as a remnant of the protoplanetary disk or a secondary exocometary origin. This paper investigates the origin of gas in two debris disks, HD110058 and HD131488, using HST observations of CI and CO, which play critical roles in the gas evolution. We fitted several electronic transitions of CI and CO rovibronic bands to derive column densities and temperatures for each system, revealing high CO column densities ($\sim$3-4 orders of magnitude higher than $\beta$ Pictoris), and low CI/CO ratios in both. Using the exogas model, we simulated the radial evolution of the gas in the debris disk assuming a secondary gas origin. We explored a wide range of CO exocometary release rates and $\alpha$ viscosities, which are the key parameters of the model. Additionally, we incorporated photodissociation due to stellar UV to the exogas model and found that it is negligible for typical CO-rich disks and host stars, even at a few au due to the high radial optical depths in the EUV. We find that the current steady-state secondary release model cannot simultaneously reproduce the CO and CI HST-derived column densities, as it predicts larger CI/CO ratios than observed. Our direct UV measurement of low CI/CO ratios agrees with results derived from recent ALMA findings and may point to vertical layering of CI, additional CI removal, CO shielding processes, or different gas origin scenarios., Comment: 21 pages, 16 figures, accepted to MNRAS

For a graph $G$ and a list assignment $L$ with $|L(v)|=k$ for all $v$, an $L$-packing consists of $L$-colorings $\varphi_1,\cdots,\varphi_k$ such that $\varphi_i(v)\ne\varphi_j(v)$ for all $v$ and all distinct $i,j\in\{1,\ldots,k\}$. Let $\chi^{\star}_{\ell}(G)$ denote the smallest $k$ such that $G$ has an $L$-packing for every $L$ with $|L(v)|=k$ for all $v$. Let $\mathcal{P}_k$ denote the set of all planar graphs with girth at least $k$. We show that (i) $\chi^{\star}_{\ell}(G)\le 8$ for all $G\in \mathcal{P}_3$ and (ii) $\chi^{\star}_{\ell}(G)\le 5$ for all $G\in \mathcal{P}_4$ and (iii) $\chi^{\star}_{\ell}(G)\le 4$ for all $G\in \mathcal{P}_5$. Part (i) makes progress on a problem of Cambie, Cames van Batenburg, Davies, and Kang. We also construct outerplanar graphs $G$ such that $\chi^{\star}_{\ell}(G)=4$, which matches the known upper bound $\chi^{\star}_{\ell}(G)\le 4$ for all outerplanar graphs. Finally, we consider the analogue of $\chi^{\star}_{\ell}$ for correspondence coloring, $\chi^{\star}_c$. In fact, all bounds stated above for $\chi^{\star}_{\ell}$ also hold for $\chi^{\star}_c$., Comment: 20 pages, 15 figures, 2nd version incorporates reviewer feedback, to appear in J. of Graph Theory; 3rd version updates title to match the final journal version

We present high-spectral resolution M-band spectra from iSHELL on NASA's Infrared Telescope Facility (IRTF) along the line of sight to the debris disk host star HD 32297. We also present a Gemini Planet Imager (GPI) H-band polarimetric image of the HD 131488 debris disk. We search for fundamental CO absorption lines in the iSHELL spectra of HD 32297 but do not detect any. We place an upper limit on the CO column density of $\sim$6$\times10^{15}$ cm$^{-2}$. By combining the column density upper limit, the CO mass measured with ALMA, and the geometrical properties of the disk, we estimate the scale height of the CO to be $\lesssim$ 2 au across the radial extent of the disk ($\sim$80-120 au). We use the same method to estimate the CO scale height of three other edge-on, CO-rich debris disks that all have CO observed in absorption with HST as well as in emission with ALMA: $\beta$ Pictoris, HD 110058, and HD 131488. We compare our estimated CO scale heights of these four systems to the millimeter dust scale heights and find that, under the assumption of hydrostatic equilibrium, there is a potential correlation between the CO and millimeter dust scale heights. There are multiple factors that affect the gas vertical structure such as turbulence, photodissociation with weak vertical mixing, as well as where the gas originates. One possible explanation for the potential correlation could be that the gas and dust are of a similar secondary origin in these four systems., Comment: Accepted for publication in The Astrophysical Journal. 11 figures, 19 pages

The pseudoforest version of the Strong Nine Dragon Tree Conjecture states that if a graph $G$ has maximum average degree $\text{mad}(G) = 2 \max_{H \subseteq G} \frac{e(G)}{v(G)}$ at most $2(k + \frac{d}{k+d+1})$, then it has a decomposition into $k+1$ pseudoforests where in one pseudoforest $F$ the components of $F$ have at most $d$ edges. This was proven in 2020. We strengthen this theorem by showing that we can find such a decomposition where additionally $F$ is acyclic, the diameter of the components of $F$ is at most $2\ell + 2$, where $\ell = \lfloor\frac{d-1}{k+1} \rfloor$, and at most $2\ell + 1$ if $d \equiv 1 \bmod k+1$. Furthermore, for any component $K$ of $F$ and any $z \in \mathbb N$, we have $diam(K) \leq 2z$ if $e(K) \geq d - z(k-1) + 1$. We also show that both diameter bounds are best possible as an extension for both the Strong Nine Dragon Tree Conjecture for pseudoforests and its original conjecture for forests. In fact, they are still optimal even if we only enforce $F$ to have any constant maximum degree, instead of enforcing every component of $F$ to have at most $d$ edges., Comment: 28 pages, 3 figures

Combining 3D vision with tactile sensing could unlock a greater level of dexterity for robots and improve several manipulation tasks. However, obtaining a close-up 3D view of the location where manipulation contacts occur can be challenging, particularly in confined spaces, cluttered environments, or without installing more sensors on the end effector. In this context, this paper presents StereoTac, a novel vision-based sensor that combines tactile sensing with 3D vision. The proposed sensor relies on stereoscopic vision to capture a 3D representation of the environment before contact and uses photometric stereo to reconstruct the tactile imprint generated by an object during contact. To this end, two cameras were integrated in a single sensor, whose interface is made of a transparent elastomer coated with a thin layer of paint with a level of transparency that can be adjusted by varying the sensor's internal lighting conditions. We describe the sensor's fabrication and evaluate its performance for both tactile perception and 3D vision. Our results show that the proposed sensor can reconstruct a 3D view of a scene just before grasping and perceive the tactile imprint after grasping, allowing for monitoring of the contact during manipulation., Comment: 8 pages, 11 figures, submitted to IEEE Robotics and Automation Letters (RA-L) on March 11 2023

We show that there exists a constant $c > 0$ such that if $G$ is a planar graph with 5-correspondence assignment $(L,M)$, then $G$ has at least $2^{c\cdot v(G)}$ distinct $(L,M)$-colourings. This confirms a conjecture of Langhede and Thomassen. More broadly, we introduce a general method showing how hyperbolicity theorems for certain families of critical graphs can be used to derive lower bounds on the number of colourings of the associated class of planar graphs. Hence our main result follows from this method plus a technical theorem (that we proved in a previous paper) involving the hyperbolicity of graphs critical for $5$-correspondence colouring. We further demonstrate our method in the case of counting 3-correspondence colourings of planar graphs of girth at least five. Finally, we use these theorems to show analogous results hold in the case of counting 5-correspondence colourings of locally planar graphs, and counting 3-correspondence colourings of locally planar graphs of girth at least five., Comment: 22 pages, 2 figures

The Nancy Grace Roman Space Telescope Coronagraph Instrument is a critical technology demonstrator for NASA's Habitable Worlds Observatory. With a predicted visible-light flux ratio detection limit of 1E-8 or better, it will be capable of reaching new areas of parameter space for both gas giant exoplanets and circumstellar disks. It is in the final stages of integration and test at the Jet Propulsion Laboratory, with an anticipated delivery to payload integration in the coming year. This paper will review the instrument systems, observing modes, potential observing applications, and overall progress toward instrument integration and test., Comment: Proceedings of SPIE: Techniques and Instrumentation for Detection of Exoplanets XI, vol. 12680 (2023)

The origin and evolution of gas in debris disks is still not well understood. Secondary gas production from cometary material or a primordial origin have been proposed. So far, observations have mostly concentrated on CO, with only few C observations available. We create an overview of the C and CO content of debris disk gas and use it test state-of-the-art models. We use new and archival ALMA observations of CO and CI emission, complemented by CII data from Herschel, for a sample of 14 debris disks. This expands the number of disks with ALMA measurements of both CO and CI by ten disks. We present new detections of CI emission towards three disks: HD 21997, HD 121191 and HD 121617. We use a simple disk model to derive gas masses and column densities. We find that current state-of-the-art models of secondary gas production overpredict the neutral carbon content of debris disk gas. This does not rule out a secondary origin, but might indicate that the models require an additional C removal process. Alternatively, the gas might be produced in transient events rather than a steady-state collisional cascade. We also test a primordial gas origin by comparing our results to a simplified thermo-chemical model. This yields promising results, but more detailed work is required before a conclusion can be reached. Our work demonstrates that the combination of C and CO data is a powerful tool to advance our understanding of debris disk gas., Comment: 90 pages, 60 figures. Accepted for publication in ApJ. version 2: additional acknowledgement. versions 3, 4: minor edits

Robotic manipulators navigating cluttered shelves or cabinets may find it challenging to avoid contact with obstacles. Indeed, rearranging obstacles may be necessary to access a target. Rather than planning explicit motions that place obstacles into a desired pose, we suggest allowing incidental contacts to rearrange obstacles while monitoring contacts for safety. Bypassing object identification, we present a method for categorizing object motions from tactile data collected from incidental contacts with a capacitive tactile skin on an Allegro Hand. We formalize tactile cues associated with categories of object motion, demonstrating that they can determine with $>90$% accuracy whether an object is movable and whether a contact is causing the object to slide stably (safe contact) or tip (unsafe)., Comment: This paper has been accepted to be presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2022

We generalize a framework of list colouring results to correspondence colouring. Correspondence colouring is a generalization of list colouring wherein we localize the meaning of the colours available to each vertex. As pointed out by Dvo\v{r}\'ak and Postle, both of Thomassen's theorems on the 5-choosability of planar graphs and 3-choosability of planar graphs of girth at least five carry over to the correspondence colouring setting. In this paper, we show that the family of graphs that are critical for 5-correspondence colouring as well as the family of graphs of girth at least five that are critical for 3-correspondence colouring form hyperbolic families. Analogous results for list colouring were shown by Postle and Thomas and by Dvo\v{r}\'ak and Kawarabayashi, respectively. Using results on hyperbolic families due to Postle and Thomas, we show further that this implies that locally planar graphs are 5-correspondence colourable; and, using results of Dvo\v{r}\'ak and Kawarabayashi, that there exist linear-time algorithms for the decidability of 5-correspondence colouring for embedded graphs. We show analogous results for 3-correspondence colouring graphs of girth at least five., Comment: 28 pages, 4 figures

Multi-wavelength scattered light imaging of debris disks may inform dust properties including typical size and mineral composition. Existing studies have investigated a small set of individual systems across a variety of imaging instruments and filters, calling for uniform comparison studies to systematically investigate dust properties. We obtain the surface brightness of dust particles in debris disks by post-processing coronagraphic imaging observations, and compare the multi-wavelength reflectance of dust. For a sample of resolved debris disks, we perform a systematic analysis on the reflectance properties of their birth rings. We reduced the visible and near-infrared images of 23 debris disk systems hosted by A through M stars using two coronagraphs onboard the Hubble Space Telescope: the STIS instrument observations centering at 0.58 $\mu$m, and the NICMOS instrument at 1.12 $\mu$m or 1.60 $\mu$m. For proper recovery of debris disks, we used classical reference differential imaging for STIS, and adopted non-negative matrix factorization with forward modeling for NICMOS. By dividing disk signals by stellar signals to take into account of intrinsic stellar color effects, we systematically obtained and compared the reflectance of debris birth rings at ~90 deg scattering angle. Debris birth rings typically exhibit a blue color at ~90 deg scattering angle. As the stellar luminosity increases, the color tends to be more neutral. A likely L-shaped color-albedo distribution indicates a clustering of scatterer properties. The observed color trend correlates with the expected blow-out size of dust particles. The color-albedo clustering likely suggests different populations of dust in these systems. More detailed radiative transfer models with realistic dust morphology will contribute to explaining the observed color and color-albedo distribution of debris systems., Comment: 17 pages, 8 figures, 3 tables. A&A accepted

The United Nations (UN) Sustainable Development Goals (SDGs) challenge the global community to build a world where no one is left behind. Recognizing that research plays a fundamental part in supporting these goals, attempts have been made to classify research publications according to their relevance in supporting each of the UN's SDGs. In this paper, we outline the methodology that we followed when mapping research articles to SDGs and which is adopted by Times Higher Education in their Social Impact rankings. We compare our solution with other existing queries and models mapping research papers to SDGs. We also discuss various aspects in which the methodology can be improved and generalized to other types of content apart from research articles. The results presented in this paper are the outcome of the SDG Research Mapping Initiative that was established as a partnership between the University of Southern Denmark, the Aurora European Universities Alliance (represented by Vrije Universiteit Amsterdam), the University of Auckland, and Elsevier to bring together broad expertise and share best practices on identifying research contributions to UN's Sustainable Development Goals., Comment: 16 pages, 2 figures, 12 tables, 24 references