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The concept of 'Stateless Ethereum' was conceived with the primary aim of mitigating Ethereum's unbounded state growth. The key facilitator of Stateless Ethereum is through the introduction of 'witnesses' into the ecosystem. The changes and potential consequences that these additional data packets pose on the network need to be identified and analysed to ensure that the Ethereum ecosystem can continue operating securely and efficiently. In this paper we propose a Bayesian Network model, a probabilistic graphical modelling approach, to capture the key factors and their interactions in Ethereum mainnet, the public Ethereum blockchain, focussing on the changes being introduced by Stateless Ethereum to estimate the health of the resulting Ethereum ecosystem. We use a mixture of empirical data and expert knowledge, where data are unavailable, to quantify the model. Based on the data and expert knowledge available to use at the time of modelling, the Ethereum ecosystem is expected to remain healthy following the introduction of Stateless Ethereum., In Proceedings MARS 2022, arXiv:2203.09299

Supplemental material, sj-pptx-4-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

Supplemental material, sj-pptx-8-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

Supplemental material, sj-pptx-7-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

Supplemental material, sj-docx-9-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

Hadwiger's Conjecture asserts that every $K_h$-minor-free graph is properly $(h-1)$-colourable. We prove the following improper analogue of Hadwiger's Conjecture: for fixed $h$, every $K_h$-minor-free graph is $(h-1)$-colourable with monochromatic components of bounded size. The number of colours is best possible regardless of the size of monochromatic components. It solves an open problem of Edwards, Kang, Kim, Oum and Seymour [\emph{SIAM J. Disc. Math.} 2015], and concludes a line of research initiated in 2007. Similarly, for fixed $t\geq s$, we show that every $K_{s,t}$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is best possible, solving an open problem of van de Heuvel and Wood [\emph{J.~London Math.\ Soc.} 2018]. We actually prove a single theorem from which both of the above results are immediate corollaries. For an excluded apex minor, we strengthen the result as follows: for fixed $t\geq s\geq 3$, and for any fixed apex graph $X$, every $K_{s,t}$-subgraph-free $X$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is again best possible., Comment: 81 pages!

Supplemental material, sj-pptx-3-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

We analyse the dynamics of networks in which a central pattern generator (CPG) transmits signals along one or more feedforward chains in a synchronous or phase-synchronous manner. Such propagating signals are common in biology, especially in locomotion and peristalsis, and are of interest for continuum robots. We construct such networks as feedforward lifts of the CPG. If the CPG dynamics is periodic, so is the lifted dynamics. Synchrony with the CPG manifests as a standing wave, and a regular phase pattern creates a travelling wave. We discuss Liapunov, asymptotic, and Floquet stability of the lifted periodic orbit and introduce transverse versions of these conditions that imply stability for signals propagating along arbitrarily long chains. We compare these notions to a simpler condition, transverse stability of the synchrony subspace, which is equivalent to Floquet stability when nodes are 1-dimensional., Comment: 38 pages, 9 figures

Supplemental material, sj-pptx-5-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

Supplemental material, sj-pptx-6-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

Supplemental material, sj-pptx-1-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

"March 2011".Project Number: 2009-10 Condition Monitoring at Lindsay-Mulcra-Wallpolla Islands - M/BUS/87-2,3,4 BW283.MDFRC item.This report details the condition monitoring undertaken at Lindsay, Mulcra and Wallpolla (LMW) Islands as part of the 2009/10 Living Murray Condition Monitoring Program. Icon Site condition monitoring has been developed to: Determine the change in environmental condition of individual assets resulting from water application and the implementation of works programs under The Living Murray (TLM). Assess whether sustainable native fish, bird and vegetation communities are being maintained across the Icon Sites. The Outcomes Evaluation Framework stipulates that measurable targets be created to unambiguously assess whether a pre-determined level of condition has been achieved. At the time of writing, such targets had not been developed for LMW. In the absence of defined targets, this report focuses upon Icon Site specific objectives. Icon Site specific objectives presented in the Outcomes Evaluation Framework have been further refined as part of the Lindsay-Mulcra-Wallpolla Environmental Management Plan. Together these objectives form the basis for condition monitoring at Lindsay-Mulcra-Wallpolla of which there are six vegetation components and one fish component. River Red Gum The ecological objectives for River Red Gum (RRG) at Lindsay, Mulcra and Wallpolla are: Current area maintained. Maintain current condition and extent of River Red Gum communities to sustain species assemblages and processes typical of such woodland. Large scale mapping at regular intervals is required to quantify changes in the distribution and areal extent of River Red Gum at LMW. Currently there is no such mapping program underway, so it is not possible to know if current area of RRG is being maintained. Significant increases in Crown Condition scores between the sampling events of 2008/09 and 2009/10 suggest changes in the conditions favourable for tree growth on the LMW floodplain. This is attributed to environmental watering at Mulcra Horseshoe Lagoon and a break in drought conditions. However, with the notable exception of the relatively small area of extant Red Gum with Flood Tolerant Understorey (RGFTU) at Mulcra Island, the recent improvement observed for RRG trees at LMW represents a change in the previous downward trend in condition rather than a return to acceptable condition. Stand condition modelling conducted by Cunningham et al.(2009) reports that the extent of severely degraded stands was higher in the Mallee (Hattah, Chowilla and LMW) than at other TLM Icon Sites, that the majority of stands were in a stressed condition in 2003 and that this had increased by 4% by 2009. Recruitment must keep pace with mortality for a population to remain sustainable and this must occur within the current spatial context if the present distribution is to be maintained (i.e. ecological objectives are to be met). Size-class frequency distributions for Fringing Red Gum Woodland (FRGW) indicate a relative abundance of trees within the smaller size classes suggesting sustainable recruitment. However, despite indications of recent improvement in the condition of trees on average, population viability assessments suggest there are long-term sustainability concerns for Red Gum Forest (RGF) communities at LMW. Black Box The ecological objectives for Black Box (BB) at LMW are: At least 20% of the original area of Black Box vegetation maintained. Improve condition to sustain species assemblages and processes typical of Black Box woodland. Ecological Vegetataion Class (EVC) mapping conducted in 2005 provides the most accurate and up to date information about the areal extent of Black Box at LMW and is therefore the logical choice for a BB areal standard. However, in the absence of an ongoing program mapping the distribution of Black Box at the Icon Site scale, it is not possible to know what proportion of the original area of Black Box is being maintained. Size-class distributions for Black Box communities do not approximate inverse J-shaped curves indicative of sustainable populations. Further, between 2008/09 and 2009/10 there was a reduction in the relative proportion of Diameter at Breast Hight (DBH) 16 ds/m, DPI 2008) and an increase in abundance could be indicative of an increase in site salinity. It is recommended that soil salinity testing be undertaken at the LMW Icon Site. Of concern are the appearances and/or incr

We prove that for every planar graph $X$ of treedepth $h$, there exists a positive integer $c$ such that for every $X$-minor-free graph $G$, there exists a graph $H$ of treewidth at most $f(h)$ such that $G$ is isomorphic to a subgraph of $H\boxtimes K_c$. This is a qualitative strengthening of the Grid-Minor Theorem of Robertson and Seymour (JCTB 1986), and treedepth is the optimal parameter in such a result. As an example application, we use this result to improve the upper bound for weak coloring numbers of graphs excluding a fixed graph as a minor.

MDFRC item.First published online 2012.1. Floodplain wetlands are areas of high biodiversity and conservation value, including those in semi-arid regions. River regulation has resulted in disconnection from the main river channel of several ephemeral wetland systems, with profound modifications to their natural wetting/drying cycles that have contributed to the decline in diversity, distribution and abundance of native fish. 2. From 2005 to 2011, a series of managed inundation events through pumping followed by natural inundation allowed assessment and comparison of the fish assemblage developing in Hattah Lakes, a semi-arid wetland system of the regulated Murray River (Victoria, Australia). 3. As a result of one-way pumping from the main channel to Hattah Lakes, a ‘filtered’ fish assemblage consisting mainly of small-bodied native species and very low numbers of non-native species fully developed within 2 years. After disconnection from the main river channel in the absence of pumping, within-system recruitment also occurred, but later drying of all water bodies caused the entire fish assemblage to perish. Conversely, following two-way flooding by natural inundation a more diverse fish assemblage developed, including large-bodied native species but also non-native species, some of which were previously unrecorded. 4. Managed inundation through pumping in Hattah Lakes represents a viable option for the creation of fish habitat, for promoting recruitment, and as a measure of rehabilitation. However, the absence of connectivity back to the main river channel means that future measures should be implemented to maintain a refuge water pool until the next inundation event. Long-term monitoring is a key component of the integrated wetland conservation framework adopted by the Ramsar Wetland Convention, and this is especially relevant to the conservation of semi-arid wetlands world-wide including Hattah Lakes.

Supplemental material, sj-docx-9-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

"June 2010".Project Number: Post-watering vegetation condition assessment for Lake Yando - M/BUS/347.MDFRC item.This document reports on the results of a vegetation survey which was carried out at Lake Yando in March 2010. Lake Yando is an 83 Ha wetland, located approximately nine kilometres north-east of Boort, Victoria. The wetland filled historically from Venables Creek and in years of larger floods, would have received water from Kinypanial Creek via Lake Boort, as well as Lake Lyndger (NCCMA 2010). Development of irrigation infrastructure in the region led to changes in the wetland flooding regime with connection to the irrigation system causing Lake Yando to become flooded with irrigation outfall water for prolonged periods of time (NCCMA 2010). This increased water permanence contributed to substantial changes in vegetation structure and composition at Lake Yando, including the death of established River Red Gum (Eucalyptus camaldulensis) trees across the wetland base and an increase in the extent of Cumbungi (Typha spp.) stands (NCCMA 2010). Modifications to the water delivery system around 1999 have allowed Lake Yando to dry completely in recent years. Management of the site is currently focused on the reinstatement of a more natural flooding regime, including alternating wet and dry phases. This is designed to support the environmental values of the wetland. A specific environmental watering plan (EWP) is being developed for Lake Yando, as well as a number of other wetland and waterway sites, as part of the Northern Victorian Irrigation Renewal Project (NVIRP). As part of the EWP development process, the vegetation at Lake Yando was surveyed by The Murray-Darling Freshwater Research Centre (MDFRC) staff in October 2009. This survey was conducted to obtain baseline data on vegetation composition, condition and distribution that could be used to identify vegetation water requirements and set watering targets. To maintain and/or improve the integrity of the vegetation community at Lake Yando the recommended goal proposed by NCCMA (2010) was: ‘To provide a watering regime typical of a deep freshwater marsh that supports the maintenance and recruitment of River Red Gum and promotes the growth of a diverse range of aquatic and amphibious plant species offering a variety of habitats to waterbirds, reptiles and amphibians.’ In October 2009 water was delivered to Lake Yando to meet a number of ecological objectives, including those specific to vegetation, as summarised in the goal statement above. The survey reported on here was used to assess how the recent watering event has affected the vegetation community at Lake Yando and to determine whether progress is being made toward achieving the objectives proposed by NCCMA (2010).

Supplemental material, sj-pptx-2-cix-10.1177_11769351231161478 for RNA-seq and Single-Cell Transcriptome Analyses of TRAIL Receptors Gene Expression in Human Osteosarcoma Cells and Tissues by Wenyu Feng, Haiyingjie Lin, Emel Rothzerg, Dezhi Song, Wenxiang Zhao, Tingting Ning, Qingjun Wei, Jinmin Zhao, David Wood, Yun Liu and Jiake Xu in Cancer Informatics

This study analyzes actuator disc (AD) models of horizontal-axis turbines to determine optimal performance, defined as the maximum power extracted at any tip speed ratio. We use the calculus of variations to maximize rotor torque relative to the thrust without making any assumptions about the rotor loading. The torque was obtained from the angular momentum equation and the thrust from the Kutta-Joukowsky equation which depends on the circumferential velocity and tip speed ratio. The optimality requirement is that the pitch of the vorticity exiting the rotor must be constant across the wake and equal to the ratio of torque to thrust. This result generalizes the classical finding of Betz and Goldstein that optimal lightly-loaded ADs have constant pitch. Optimizing the torque in the far-wake, well downstream of the rotor, leads to the same requirement of constant pitch. This implies that the pitch of an optimal rotor is constant everywhere in the wake at all tip speed ratios. We show that it is not possible for the pitch to reach its optimal value because of the vorticity distribution in the wake, and propose modifications to the pitch at the rotor and in the far-wake. The axial and circumferential velocities in the far-wake, which are easily determined, were used to find those at the rotor from the “disc loading equation” for the angular momentum which is also the normalized bound circulation at the rotor. For the simplest case of a lightly-loaded rotor at zero tip speed ratio, the induced circumferential velocity is linear in radius and the axial component is quadratic, As the tip speed ratio increases, the optimal power and thrust asymptote to the familiar Betz-Joukowsky values, and the induced axial velocity and rotor bound circulation become constant. At low tip speed ratios, the optimal wakes are constrained by the need to avoid breakdown of the flow at high swirl, and the conventional thrust equation, involving the axial velocity only, is inaccurate. As found in previous studies, the power coefficient increases monotonically with tip speed ratio, but the thrust coefficient reaches a maximum value slightly above the Betz-Joukowsky limit at a tip speed ratio of two, before decreasing towards the limit.

Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve this result by replacing "4" by "3" and with $H$ planar. We in fact prove a more general result in terms of so-called framed graphs. This implies that every $(g,d)$-map graph is contained in $ H \boxtimes P\boxtimes K_\ell$, for some planar graph $H$ with treewidth $3$, where $\ell=\max\{2g\lfloor \frac{d}{2} \rfloor,d+3\lfloor\frac{d}{2}\rfloor-3\}$. It also implies that every $(g,1)$-planar graph (that is, graphs that can be drawn in a surface of Euler genus $g$ with at most one crossing per edge) is contained in $H\boxtimes P\boxtimes K_{\max\{4g,7\}}$, for some planar graph $H$ with treewidth $3$.

Ecological processes are complex, often exhibiting non-linear, interactive, or hierarchical relationships. Furthermore, models identifying drivers of phenology are constrained by uncertainty regarding predictors, interactions across scales, and legacy impacts of prior climate conditions. Nonetheless, measuring and modeling ecosystem processes such as phenology remains critical for management of ecological systems and the social systems they support. We used random forest models to assess which combination of climate, location, edaphic, vegetation composition, and disturbance variables best predict several phenological responses in three dominant land cover types in the U.S. Northwestern Great Plains (NWP). We derived phenological measures from the 25-year series of AVHRR satellite data and characterized climatic predictors (i.e., multiple moisture and/or temperature based variables) over seasonal and annual timeframes within the current year and up to 4 years prior. We found that antecedent conditions, from seasons to years before the current, were strongly associated with phenological measures, apparently mediating the responses of communities to current-year conditions. For example, at least one measure of antecedent-moisture availability [precipitation or vapor pressure deficit (VPD)] over multiple years was a key predictor of all productivity measures. Variables including longer-term lags or prior year sums, such as multi-year-cumulative moisture conditions of maximum VPD, were top predictors for start of season. Productivity measures were also associated with contextual variables such as soil characteristics and vegetation composition. Phenology is a key process that profoundly affects organism-environment relationships, spatio-temporal patterns in ecosystem structure and function, and other ecosystem dynamics. Phenology, however, is complex, and is mediated by lagged effects, interactions, and a diversity of potential drivers; nonetheless, the incorporation of antecedent conditions and contextual variables can improve models of phenology.

This is a preliminary study as part of a larger series of studies examining the effect of motivational interviewing on problematic pornography use. One element of Motivational Interviewing involves providing normative data to clients as a benchmark for their own patterns of behavior. The purpose of this study is to gather descriptive norms on pornography use in Utah to provide reliable information about what can be considered typical pornography use.

Isoniazid toxicity from self-poisoning or dosing errors remains common in regions of the world where tuberculosis is prevalent. Although the treatment of isoniazid poisoning is centered on supportive care and pyridoxine administration, extracorporeal treatments (ECTRs), such as hemodialysis, have been advocated to enhance elimination of isoniazid. No systematic reviews or evidence-based recommendations currently exist on the benefit of ECTRs for isoniazid poisoning. The Extracorporeal Treatments in Poisoning (EXTRIP) workgroup systematically collected and rated the available evidence on the effect of and indications for ECTRs in cases of isoniazid poisoning. We conducted a systematic review of the literature, screened studies, extracted data on study characteristics, outcomes, and measurement characteristics, summarized findings, and formulated recommendations following published EXTRIP methods. Forty-three studies (two animal studies, 34 patient reports or patient series, and seven pharmacokinetic studies) met inclusion criteria. Toxicokinetic or pharmacokinetic analysis was available for 60 patients, most treated with hemodialysis (n = 38). The workgroup assessed isoniazid as "Moderately Dialyzable" by hemodialysis for patients with normal kidney function (quality of evidence = C) and "Dialyzable" by hemodialysis for patients with impaired kidney function (quality of evidence = A). Clinical data for ECTR in isoniazid poisoning were available for 40 patients. Mortality of the cohort was 12.5%. Historical controls who received modern standard care including appropriately dosed pyridoxine generally had excellent outcomes. No benefit could be extrapolated from ECTR, although there was evidence of added costs and harms related to the double lumen catheter insertion, the extracorporeal procedure itself, and the extracorporeal removal of pyridoxine. The EXTRIP workgroup suggests against performing ECTR in addition to standard care (weak recommendation, very low quality of evidence) in patients with isoniazid poisoning. If standard dose pyridoxine cannot be administered, we suggest performing ECTR only in patients with seizures refractory to GABAA receptor agonists (weak recommendation, very low quality of evidence).

The clustering of a graph coloring is the maximum size of monochromatic components. This paper studies colorings with bounded clustering in graph classes with bounded layered treewidth, which include planar graphs, graphs of bounded Euler genus, graphs embeddable on a fixed surface with a bounded number of crossings per edge, map graphs, amongst other examples. Our main theorem says that every graph with layered treewidth at most $k$ and with maximum degree at most $\Delta$ is $3$-colorable with clustering $O(k^{19}\Delta^{37})$. This is the first known polynomial bound on the clustering. This greatly improves upon a corresponding result of Esperet and Joret for graphs of bounded genus., Comment: This paper is extracted from arXiv:1905.08969. The corresponding part in arXiv:1905.08969 will be deleted

Layered treewidth and row treewidth are recently introduced graph parameters that have been key ingredients in the solution of several well-known open problems. It follows from the definitions that the layered treewidth of a graph is at most its row treewidth plus 1. Moreover, a minor-closed class has bounded layered treewidth if and only if it has bounded row treewidth. However, it has been open whether row treewidth is bounded by a function of layered treewidth. This paper answers this question in the negative. In particular, for every integer $k$ we describe a graph with layered treewidth 1 and row treewidth $k$. We also prove an analogous result for layered pathwidth and row pathwidth.

A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the `usual suspects'. Our results imply that treewidth and Hadwiger number are linearly tied on the class of circle graphs, and that the unavoidable induced subgraphs of a vertex-minor-closed class with large treewidth are the usual suspects if and only if the class has bounded rank-width. Using the same tools, we also study the treewidth of graphs $G$ that have a circular drawing whose crossing graph is well-behaved in some way. In this setting, we show that if the crossing graph is $K_t$-minor-free, then $G$ has treewidth at most $12t-23$ and has no $K_{2,4t}$-topological minor. On the other hand, we show that there are graphs with arbitrarily large Hadwiger number that have circular drawings whose crossing graphs are $2$-degenerate.

We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end, define the "underlying treewidth" of a graph class $\mathcal{G}$ to be the minimum non-negative integer $c$ such that, for some function $f$, for every graph ${G \in \mathcal{G}}$ there is a graph $H$ with ${\text{tw}(H) \leq c}$ such that $G$ is isomorphic to a subgraph of ${H \boxtimes K_{f(\text{tw}(G))}}$. We introduce disjointed coverings of graphs and show they determine the underlying treewidth of any graph class. Using this result, we prove that the class of planar graphs has underlying treewidth 3; the class of $K_{s,t}$-minor-free graphs has underlying treewidth $s$ (for ${t \geq \max\{s,3\}}$); and the class of $K_t$-minor-free graphs has underlying treewidth ${t-2}$. In general, we prove that a monotone class has bounded underlying treewidth if and only if it excludes some fixed topological minor. We also study the underlying treewidth of graph classes defined by an excluded subgraph or excluded induced subgraph. We show that the class of graphs with no $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a subdivided star, and that the class of graphs with no induced $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a star.

Additional file 6: Fig. S4. Genotyping with Ca_06500 allele specific primers. Cropped gel pictures showing PCR results using Ca_06500Rwt primer (left) and Ca_6500Rm reverse primer (right) of WT (ICC 640), PM405, and F2 plants 1, 2, 3, 4, 10, and 11. Plants 2, 3, and 4 had nodules and were phenotyped as WT. Samples 1, 10, and 11 did not have nodules and were phenotyped as mutants. For original, uncropped gel images see Additional file 12: Fig. S6 and Additional file 13: Fig. S7. Ca_06416, annotated as Heat Shock Protein 4, was ~ 900 kb away from Ca_06500 on pseudochromosomes Ca2 in the ICC 4958 v3.0 reference assembly. The mutation was a single base G > T transversion and resulted in loss of an AvaI restriction site. For purposes of genotyping, we designed a primer pair targeting this site and ran PCR using DNA from the PM405 segregating population. We subjected the PCR products to restriction enzyme digestion, with the expectation that only the WT allele should be digested, while the PM405 allele would not be digested due to the mutational loss of the AvaI site. Recombination was evident between the Ca_06416 candidate gene and both the Ca_06500 gene and the nodulation phenotype. With respect to the two candidate genes, recombination was evident in individuals 3, 7, and 19, each of which was heterozygous for one marker and not the other. With respect to nodulation phenotype, individual 19 was non-nodulating (inferred genotype rn4/rn4) and was heterozygous at the Ca_06416 locus. Five of the nodulating chickpea plants showed complete digestion as would be expected of homozygosity for the wild type allele, and these five plants were also homozygous for the wild type (CAA) allele of the Ca_06500 gene. However, of the ten plants that showed partial digestion, as would be expected for heterozygosity, only seven were also heterozygous at the Ca_06500 locus, while three (plants 3, 7, and 19) were homozygous and therefore counted as recombinants between the Ca_06500 and Ca_06416 loci (Additional file 5: Table S3). Four of the non-nodulating chickpea plants showed no digestion, but one plant (number 19) showed partial digestion, indicative of heterozygosity and therefore of recombination between the Ca_06416 mutation site and the rn4 mutation site. On this basis, three instances of recombination between the Ca_06500 and Ca_06416 loci are evident in 19 F2 individuals (Additional file 7: Table S3), representing 2 �� 19 = 38 gametes, thus establishing a recombination frequency of 3/38 = 0.079 or about 8%. One instance of recombination is evident between the rn4 locus and Ca_06416, establishing a recombination frequency of 1/38 = 0.026 or about 3%, while no recombination was detected between the rn4 and Ca06500 loci.

Additional file 8: Table S4. Coding sequence variants identified in chickpea mutant PM233. Table S4 legend. Top tBLASTn hits were taken from the NCBI nucleotide collection database. The position coordinates are those of the ICC 4958 v3.0 genome reference assembly. The Ref (reference) allele is the allele in the ICC 4958 v3.0 genome reference assembly. The Alt (alternate) allele is the allele seen in the PM233 Illumina reads.

Assume $\lambda=\{k_1,k_2, \ldots, k_q\}$ is a partition of $k_{\lambda} = \sum_{i=1}^q k_i$. A $\lambda$-list assignment of $G$ is a $k_\lambda$-list assignment $L$ of $G$ such that the colour set $\bigcup_{v \in V(G)}L(v)$ can be partitioned into $|\lambda|= q$ sets $C_1,C_2,\ldots,C_q$ such that for each $i$ and each vertex $v$ of $G$, $|L(v) \cap C_i| \ge k_i$. We say $G$ is \emph{$\lambda$-choosable} if $G$ is $L$-colourable for any $\lambda$-list assignment $L$ of $G$. The concept of $\lambda$-choosability is a refinement of choosability that puts $k$-choosability and $k$-colourability in the same framework. If $|\lambda|$ is close to $k_\lambda$, then $\lambda$-choosability is close to $k_\lambda$-colourability; if $|\lambda|$ is close to $1$, then $\lambda$-choosability is close to $k_\lambda$-choosability. This paper studies Hadwiger's Conjecture in the context of $\lambda$-choosability. Hadwiger's Conjecture is equivalent to saying that every $K_t$-minor-free graph is $\{1 \star (t-1)\}$-choosable for any positive integer $t$. We prove that for $t \ge 5$, for any partition $\lambda$ of $t-1$ other than $\{1 \star (t-1)\}$, there is a $K_t$-minor-free graph $G$ that is not $\lambda$-choosable. We then construct several types of $K_t$-minor-free graphs that are not $\lambda$-choosable, where $k_\lambda - (t-1)$ gets larger as $k_\lambda-|\lambda|$ gets larger. In partcular, for any $q$ and any $\epsilon > 0$, there exists $t_0$ such that for any $t \ge t_0$, for any partition $\lambda$ of $\lfloor (2-\epsilon)t \rfloor$ with $|\lambda| =q$, there is a $K_t$-minor-free graph that is not $\lambda$-choosable. The $q=1$ case of this result was recently proved by Steiner, and our proof uses a similar argument. We also generalize this result to $(a,b)$-list colouring.

Additional file 7: Table S3. Results of PCR genotyping analysis of candidate genes Ca_06500 andCa_06416. Three plants (shown in bold) displayed recombination between the two candidate genes, of which one plant (number 19) also displayed recombination between Ca_06416 and the rn4 locus.

We investigate the product structure of hereditary graph classes admitting strongly sublinear separators. We characterise such classes as subgraphs of the strong product of a star and a complete graph of strongly sublinear size. In a more precise result, we show that if any hereditary graph class $\mathcal{G}$ admits $O(n^{1-\epsilon})$ separators, then for any fixed $\delta\in(0,\epsilon)$ every $n$-vertex graph in $\mathcal{G}$ is a subgraph of the strong product of a graph $H$ with bounded tree-depth and a complete graph of size $O(n^{1-\epsilon+\delta})$. This result holds with $\delta=0$ if we allow $H$ to have tree-depth $O(\log\log n)$. We prove a product strengthening of the result of Dvo\v{r}\'ak and Norin [SIAM J. Discrete Math., 2016] for graphs of polynomial expansion. Finally, we prove that $n$-vertex graphs of bounded treewidth are subgraphs of the product of a graph with tree-depth $d$ and a complete graph of size $O(n^{1/d})$, which is best possible., Comment: v2: added bad news subsection

A squaregraph is a plane graph in which each internal face is a $4$-cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semi-strong product of an outerplanar graph and a path. We generalise this result for infinite squaregraphs, and show that this is best possible in the sense that "outerplanar graph" cannot be replaced by "forest".

Additional file 2: Table S1. Primer pairs and their outcomes in the analysis of mutant PM233. The amplicon labels A1-A4 correspond to the expected amplicons depicted in Fig. 1. The primer sequences were designed based on the ICC 4958 v3.0 desi reference genome [36].

Product structure theorems are a collection of recent results that have been used to resolve a number of longstanding open problems on planar graphs and related graph classes. One particularly useful version states that every planar graph $G$ is contained in the strong product of a $3$-tree $H$, a path $P$, and a $3$-cycle $K_3$; written as $G\subsetcong H\boxtimes P\boxtimes K_3$. A number of researchers have asked if this theorem can be strengthened so that the maximum degree in $H$ can be bounded by a function of the maximum degree in $G$. We show that no such strengthening is possible. Specifically, we describe an infinite family $\mathcal{G}$ of planar graphs of maximum degree $5$ such that, if an $n$-vertex member $G$ of $\mathcal{G}$ is isomorphic to a subgraph of $H\boxtimes P\boxtimes K_c$ where $P$ is a path and $H$ is a graph of maximum degree $\Delta$ and treewidth $t$, then $t\Delta c \ge 2^{\Omega(\sqrt{\log\log n})}$., Comment: 14 pages, 4 figures

PurposeOur goal was to evaluate the comparative effectiveness of robot-assisted laparoscopic prostatectomy (RALP) and open radical prostatectomy (ORP) in a multicenter study.Materials and methodsWe evaluated men with localized prostate cancer at 11 high-volume academic medical centers in the United States from the PROST-QA (2003-2006) and the PROST-QA/RP2 cohorts (2010-2013) with a pre-specified goal of comparing RALP (549) and ORP (545). We measured longitudinal patient-reported health-related quality of life (HRQOL) at pre-treatment and at 2, 6, 12, and 24 months, and pathological and perioperative outcomes/complications.ResultsDemographics, cancer characteristics, and margin status were similar between surgical approaches. ORP subjects were more likely to undergo lymphadenectomy (89% vs 47%; p

Additional file 12 Cropped Gel 1. Fig. S7. Uncropped image of gel from Fig. S4.

We determine which properties of 2-layer drawings characterise bipartite graphs of bounded pathwidth.

Recent results show that several important graph classes can be embedded as subgraphs of strong products of simpler graphs classes (paths, small cliques, or graphs of bounded treewidth). This paper develops general techniques to bound the chromatic number (and its popular variants, such as fractional, clustered, or defective chromatic number) of the strong product of general graphs with simpler graphs classes, such as paths, and more generally graphs of bounded treewidth. We also highlight important links between the study of (fractional) clustered colouring of strong products and other topics, such as asymptotic dimension in metric theory and topology, site percolation in probability theory, and the Shannon capacity in information theory., Comment: 26 pages, 2 figures: v2. the proofs of Theorem 16 and Lemma 31 have been corrected

Additional file 13 Cropped Gel 2. Fig. S8. Uncropped image of gel from Fig. S4.

Supplemental material, sj-pdf-1-prs-10.1177_20414196211052062 for Blast mitigation using polymeric 3D printed auxetic re-entrant honeycomb structures: A preliminary study by Richard Critchley, Rachael Hazael, Kamran Bhatti, David Wood, Alan Peare, Stephen Johnson and Tracey Temple in International Journal of Protective Structures

Research on in utero opioid exposure impacts has focused on Neonatal Opioid Withdrawal Syndrome (NOWS). However, possible impacts on fetal growth and newborn wellbeing have emerged, with inconsistencies likely driven by methodological issues. Our goal was to compare birth outcomes between newborns with prenatal opioid exposure and a matched control group. Participants were identified via manual review of electronic medical records of all deliveries over five years within a regional health system (6 delivery hospitals across 2 states). From over 18,000 births, 300 with prenatal opioid exposure and 300 control newborns matched on exposure, medical, and background factors were included. Additional factors were statistically controlled. Outcomes included pregnancy/delivery complications, newborn size, and newborn health complications. Compared to biochemically verified controls, exposed newborns had higher rates of fetal growth restriction, weighed less, had decreased length and head circumference, and had higher rates of respiratory distress, sepsis, and jaundice. No significant differences in gestational length, Apgar scores, or neonatal hypoglycemia were found. Adjusted regression analyses revealed that compared to controls, those exposed had an average 150 g decrease in birth weight, a two-fold increased risk for IUGR (OR = 2.09), a nearly three-fold (OR = 2.80) increased risk for jaundice, a more than seven-fold (OR = 7.40) increased risk for respiratory distress, and a thirty-fold (OR = 30.47) increased risk for sepsis. Results suggest significant pregnancy and newborn outcomes beyond NOWS following pregnancy opioid use, informing clinical screening and treatment decisions to enhance health and wellbeing in pregnancy, during the neonatal period, and beyond.

Additional file 9 Leonard Jar. Fig. S6. The Leonard Jar assembly used in this study. The upper and lower chambers are made from polycarbonate ���Magenta ��� GA7 vessels��� (Sigma-Aldrich). A) Fully assembled Leonard Jar with chickpea seedling. B) Fully assembled Leonard Jar without plant or planting substrate. C) Disassembled components of Leonard Jar. 1) Top magenta box with two holes cut in the bottom. 2) Tubing allowing adding nutrient solution to bottom magenta box. 3) Bottom magenta box with no holes in it. 4) Syringe with tip cut off and partially stuffed with cotton. Nutrient solution from the bottom magenta box wicks upward through the syringe into the top magenta box.

A graph class $\mathcal{G}$ has linear growth if, for each graph $G \in \mathcal{G}$ and every positive integer $r$, every subgraph of $G$ with radius at most $r$ contains $O(r)$ vertices. In this paper, we show that every graph class with linear growth has bounded treewidth.

Supplemental material, sj-docx-1-cix-10.1177_11769351221140101 for Single-Cell Transcriptome Analysis Reveals Paraspeckles Expression in Osteosarcoma Tissues by Emel Rothzerg, Wenyu Feng, Dezhi Song, Hengyuan Li, Qingjun Wei, Archa Fox, David Wood, Jiake Xu and Yun Liu in Cancer Informatics

Supplemental material, sj-pdf-1-prs-10.1177_20414196211052062 for Blast mitigation using polymeric 3D printed auxetic re-entrant honeycomb structures: A preliminary study by Richard Critchley, Rachael Hazael, Kamran Bhatti, David Wood, Alan Peare, Stephen Johnson and Tracey Temple in International Journal of Protective Structures

Additional file 10: Supplemental Methods. CTAB extraction methods used in this study.

In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly one of $u$ and $v$ is coloured red. Bonnet, Kim, Thomass\'e and Watrigant [J. ACM 2022] defined the twin-width of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has maximum degree at most $k$. For any graph parameter $f$, we define the reduced $f$ of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has $f$ at most $k$. Our focus is on graph classes with bounded reduced bandwidth, which implies and is stronger than bounded twin-width (reduced maximum degree). We show that every proper minor-closed class has bounded reduced bandwidth, which is qualitatively stronger than an analogous result of Bonnet et al.\ for bounded twin-width. In many instances, we also make quantitative improvements. For example, all previous upper bounds on the twin-width of planar graphs were at least $2^{1000}$. We show that planar graphs have reduced bandwidth at most $466$ and twin-width at most $583$. Our bounds for graphs of Euler genus $\gamma$ are $O(\gamma)$. Lastly, we show that fixed powers of graphs in a proper minor-closed class have bounded reduced bandwidth (irrespective of the degree of the vertices). In particular, we show that map graphs of Euler genus $\gamma$ have reduced bandwidth $O(\gamma^4)$. Lastly, we separate twin-width and reduced bandwidth by showing that any infinite class of expanders excluding a fixed complete bipartite subgraph has unbounded reduced bandwidth, while there are bounded-degree expanders with twin-width at most 6., Comment: 35 pages, 4 figures

Additional file 5: Table S2. Primer pairs and their outcomes in the analysis of chickpea mutant PM405. Note that the Rm primer has a 21 base 5��� extension relative to the Rwt primer, and also differs at the 3��� base, which is the mutation site. Homozygosity for the wild type (CAA) allele was indicated if the common forward primer produced a band only with the 06500wt reverse primer. Homozygosity for the mutant (CA) allele was indicated if the common forward primer produced a band only with the 06500Rm reverse primer. Heterozygosity was indicated if the predicted products were generated with both primer combinations.