 Award ID(s):
 1659815
 NSFPAR ID:
 10220712
 Date Published:
 Journal Name:
 Journal of Combinatorial Mathematics and Combinatorial Computing (ISSN: 08353026)
 Volume:
 114
 Page Range / eLocation ID:
 293306
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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ter Beek, Maurice ; Koutny, Maciej ; Rozenberg, Grzegorz (Ed.)For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a oneout subgraph, called the 0context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all oneout graphs obtained from an essential motion represent 0context graphs of reactions systems with isomorphic transition graphs. All such 0context graphs are obtained from one another by swapping the outgoing edges of companion vertices.more » « less

null (Ed.)A longstanding conjecture by Kotzig, Ringel, and Rosa states that every tree admits a graceful labeling. That is, for any tree $T$ with $n$~edges, it is conjectured that there exists a labeling $f\colon V(T) \to \{0,1,\ldots,n\}$ such that the set of induced edge labels $\bigl\{ f(u)f(v) : \{u,v\}\in E(T) \bigr\}$ is exactly $\{1,2,\ldots,n\}$. We extend this concept to allow for multigraphs with edge multiplicity at most~$2$. A \emph{2fold graceful labeling} of a graph (or multigraph) $G$ with $n$~edges is a onetoone function $f\colon V(G) \to \{0,1,\ldots,n\}$ such that the multiset of induced edge labels is comprised of two copies of each element in $\bigl\{ 1,2,\ldots, \lfloor n/2 \rfloor \bigr\}$ and, if $n$ is odd, one copy of $\bigl\{ \lceil n/2 \rceil \bigr\}$. When $n$ is even, this concept is similar to that of 2equitable labelings which were introduced by Bloom and have been studied for several classes of graphs. We show that caterpillars, cycles of length $n \not\equiv 1 \pmod{4}$, and complete bipartite graphs admit 2fold graceful labelings. We also show that under certain conditions, the join of a tree and an empty graph (i.e., a graph with vertices but no edges) is $2$fold graceful.more » « less

Braverman, Mark (Ed.)For an abelian group H acting on the set [𝓁], an (H,𝓁)lift of a graph G₀ is a graph obtained by replacing each vertex by 𝓁 copies, and each edge by a matching corresponding to the action of an element of H. Expanding graphs obtained via abelian lifts, form a key ingredient in the recent breakthrough constructions of quantum LDPC codes, (implicitly) in the fiber bundle codes by Hastings, Haah and O'Donnell [STOC 2021] achieving distance Ω̃(N^{3/5}), and in those by Panteleev and Kalachev [IEEE Trans. Inf. Theory 2021] of distance Ω(N/log(N)). However, both these constructions are nonexplicit. In particular, the latter relies on a randomized construction of expander graphs via abelian lifts by Agarwal et al. [SIAM J. Discrete Math 2019]. In this work, we show the following explicit constructions of expanders obtained via abelian lifts. For every (transitive) abelian group H ⩽ Sym(𝓁), constant degree d ≥ 3 and ε > 0, we construct explicit dregular expander graphs G obtained from an (H,𝓁)lift of a (suitable) base nvertex expander G₀ with the following parameters: ii) λ(G) ≤ 2√{d1} + ε, for any lift size 𝓁 ≤ 2^{n^{δ}} where δ = δ(d,ε), iii) λ(G) ≤ ε ⋅ d, for any lift size 𝓁 ≤ 2^{n^{δ₀}} for a fixed δ₀ > 0, when d ≥ d₀(ε), or iv) λ(G) ≤ Õ(√d), for lift size "exactly" 𝓁 = 2^{Θ(n)}. As corollaries, we obtain explicit quantum lifted product codes of Panteleev and Kalachev of almost linear distance (and also in a wide range of parameters) and explicit classical quasicyclic LDPC codes with wide range of circulant sizes. Items (i) and (ii) above are obtained by extending the techniques of Mohanty, O'Donnell and Paredes [STOC 2020] for 2lifts to much larger abelian lift sizes (as a byproduct simplifying their construction). This is done by providing a new encoding of special walks arising in the trace power method, carefully "compressing" depthfirst search traversals. Result (iii) is via a simpler proof of Agarwal et al. [SIAM J. Discrete Math 2019] at the expense of polylog factors in the expansion.more » « less

Site description. This data package consists of data obtained from sampling surface soil (the 07.6 cm depth profile) in black mangrove (Avicennia germinans) dominated forest and black needlerush (Juncus roemerianus) saltmarsh along the Gulf of Mexico coastline in peninsular westcentral Florida, USA. This location has a subtropical climate with mean daily temperatures ranging from 15.4 °C in January to 27.8 °C in August, and annual precipitation of 1336 mm. Precipitation falls as rain primarily between June and September. Tides are semidiurnal, with 0.57 m median amplitudes during the year preceding sampling (U.S. NOAA National Ocean Service, Clearwater Beach, Florida, station 8726724). Sealevel rise is 4.0 ± 0.6 mm per year (19732020 trend, mean ± 95 % confidence interval, NOAA NOS Clearwater Beach station). The A. germinans mangrove zone is either adjacent to water or fringed on the seaward side by a narrow band of red mangrove (Rhizophora mangle). A nearmonoculture of J. roemerianus is often adjacent to and immediately landward of the A. germinans zone. The transition from the mangrove to the J. roemerianus zone is variable in our study area. An abrupt edge between closedcanopy mangrove and J. roemerianus monoculture may extend for up to several hundred meters in some locations, while other stretches of ecotone present a gradual transition where smaller, widely spaced trees are interspersed into the herbaceous marsh. Juncus roemerianus then extends landward to a high marsh patchwork of succulent halophytes (including Salicornia bigellovi, Sesuvium sp., and Batis maritima), scattered dwarf mangrove, and salt pans, followed in turn by upland vegetation that includes Pinus sp. and Serenoa repens. Field design and sample collection. We established three study sites spaced at approximately 5 km intervals along the western coastline of the central Florida peninsula. The sites consisted of the Salt Springs (28.3298°, 82.7274°), Energy Marine Center (28.2903°, 82.7278°), and Green Key (28.2530°, 82.7496°) sites on the Gulf of Mexico coastline in Pasco County, Florida, USA. At each site, we established three plot pairs, each consisting of one saltmarsh plot and one mangrove plot. Plots were 50 m^2 in size. Plots pairs within a site were separated by 2301070 m, and the mangrove and saltmarsh plots composing a pair were 70170 m apart. All plot pairs consisted of directly adjacent patches of mangrove forest and J. roemerianus saltmarsh, with the mangrove forests exhibiting a closed canopy and a tree architecture (height 46 m, crown width 1.53 m). Mangrove plots were located at approximately the midpoint between the seaward edge (watermangrove interface) and landward edge (mangrovemarsh interface) of the mangrove zone. Saltmarsh plots were located 2025 m away from any mangrove trees and into the J. roemerianus zone (i.e., landward from the mangrovemarsh interface). Plot pairs were coarsely similar in geomorphic setting, as all were located on the Gulf of Mexico coastline, rather than within major sheltering formations like Tampa Bay, and all plot pairs fit the tidedominated domain of the Woodroffe classification (Woodroffe, 2002, "Coasts: Form, Process and Evolution", Cambridge University Press), given their conspicuous semidiurnal tides. There was nevertheless some geomorphic variation, as some plot pairs were directly open to the Gulf of Mexico while others sat behind keys and spits or along small tidal creeks. Our use of a plotpair approach is intended to control for this geomorphic variation. Plot center elevations (cm above mean sea level, NAVD 88) were estimated by overlaying the plot locations determined with a global positioning system (Garmin GPS 60, Olathe, KS, USA) on a LiDARderived bareearth digital elevation model (Dewberry, Inc., 2019). The digital elevation model had a vertical accuracy of ± 10 cm (95 % CI) and a horizontal accuracy of ± 116 cm (95 % CI). Soil samples were collected via coring at low tide in June 2011. From each plot, we collected a composite soil sample consisting of three discrete 5.1 cm diameter soil cores taken at equidistant points to 7.6 cm depth. Cores were taken by tapping a sleeve into the soil until its top was flush with the soil surface, sliding a hand under the core, and lifting it up. Cores were then capped and transferred on ice to our laboratory at the University of South Florida (Tampa, Florida, USA), where they were combined in plastic zipper bags, and homogenized by hand into plotlevel composite samples on the day they were collected. A damp soil subsample was immediately taken from each composite sample to initiate 1 y incubations for determination of active C and N (see below). The remainder of each composite sample was then placed in a drying oven (60 °C) for 1 week with frequent mixing of the soil to prevent aggregation and liberate water. Organic wetland soils are sometimes dried at 70 °C, however high drying temperatures can volatilize nonwater liquids and oxidize and decompose organic matter, so 50 °C is also a common drying temperature for organic soils (Gardner 1986, "Methods of Soil Analysis: Part 1", Soil Science Society of America); we accordingly chose 60 °C as a compromise between sufficient water removal and avoidance of nonwater mass loss. Bulk density was determined as soil dry mass per core volume (adding back the dry mass equivalent of the damp subsample removed prior to drying). Dried subsamples were obtained for determination of soil organic matter (SOM), mineral texture composition, and extractable and total carbon (C) and nitrogen (N) within the following week. Sample analyses. A dried subsample was apportioned from each composite sample to determine SOM as mass loss on ignition at 550 °C for 4 h. After organic matter was removed from soil via ignition, mineral particle size composition was determined using a combination of wet sieving and density separation in 49 mM (3 %) sodium hexametaphosphate ((NaPO_3)_6) following procedures in Kettler et al. (2001, Soil Science Society of America Journal 65, 849852). The percentage of dry soil mass composed of silt and clay particles (hereafter, fines) was calculated as the mass lost from dispersed mineral soil after sieving (0.053 mm mesh sieve). Fines could have been slightly underestimated if any clay particles were burned off during the preceding ignition of soil. An additional subsample was taken from each composite sample to determine extractable N and organic C concentrations via 0.5 M potassium sulfate (K_2SO_4) extractions. We combined soil and extractant (ratio of 1 g dry soil:5 mL extractant) in plastic bottles, reciprocally shook the slurry for 1 h at 120 rpm, and then gravity filtered it through Fisher G6 (1.6 μm pore size) glass fiber filters, followed by colorimetric detection of nitrite (NO_2^) + nitrate (NO_3^) and ammonium (NH_4^+) in the filtrate (Hood Nowotny et al., 2010,Soil Science Society of America Journal 74, 10181027) using a microplate spectrophotometer (Biotek Epoch, Winooski, VT, USA). Filtrate was also analyzed for dissolved organic C (referred to hereafter as extractable organic C) and total dissolved N via combustion and oxidation followed by detection of the evolved CO_2 and N oxide gases on a Formacs HT TOC/TN analyzer (Skalar, Breda, The Netherlands). Extractable organic N was then computed as total dissolved N in filtrate minus extractable mineral N (itself the sum of extractable NH_4N and NO_2N + NO_3N). We determined soil total C and N from dried, milled subsamples subjected to elemental analysis (ECS 4010, Costech, Inc., Valencia, CA, USA) at the University of South Florida Stable Isotope Laboratory. Median concentration of inorganic C in unvegetated surface soil at our sites is 0.5 % of soil mass (Anderson, 2019, Univ. of South Florida M.S. thesis via methods in Wang et al., 2011, Environmental Monitoring and Assessment 174, 241257). Inorganic C concentrations are likely even lower in our samples from under vegetation, where organic matter would dilute the contribution of inorganic C to soil mass. Nevertheless, the presence of a small inorganic C pool in our soils may be counted in the total C values we report. Extractable organic C is necessarily of organic C origin given the method (sparging with HCl) used in detection. Active C and N represent the fractions of organic C and N that are mineralizable by soil microorganisms under aerobic conditions in longterm soil incubations. To quantify active C and N, 60 g of fieldmoist soil were apportioned from each composite sample, placed in a filtration apparatus, and incubated in the dark at 25 °C and field capacity moisture for 365 d (as in Lewis et al., 2014, Ecosphere 5, art59). Moisture levels were maintained by frequently weighing incubated soil and wetting them up to target mass. Daily CO_2 flux was quantified on 29 occasions at 0.53 week intervals during the incubation period (with shorter intervals earlier in the incubation), and these per day flux rates were integrated over the 365 d period to compute an estimate of active C. Observations of per day flux were made by sealing samples overnight in airtight chambers fitted with septa and quantifying headspace CO_2 accumulation by injecting headspace samples (obtained through the septa via needle and syringe) into an infrared gas analyzer (PP Systems EGM 4, Amesbury, MA, USA). To estimate active N, each incubated sample was leached with a C and N free, 35 psu solution containing micronutrients (Nadelhoffer, 1990, Soil Science Society of America Journal 54, 411415) on 19 occasions at increasing 16 week intervals during the 365 d incubation, and then extracted in 0.5 M K_2SO_4 at the end of the incubation in order to remove any residual mineral N. Active N was then quantified as the total mass of mineral N leached and extracted. Mineral N in leached and extracted solutions was detected as NH_4N and NO_2N + NO_3N via colorimetry as above. This incubation technique precludes new C and N inputs and persistently leaches mineral N, forcing microorganisms to meet demand by mineralizing existing pools, and thereby directly assays the potential activity of soil organic C and N pools present at the time of soil sampling. Because this analysis commences with disrupting soil physical structure, it is biased toward higher estimates of active fractions. Calculations. Nonmobile C and N fractions were computed as total C and N concentrations minus the extractable and active fractions of each element. This data package reports surfacesoil constituents (moisture, fines, SOM, and C and N pools and fractions) in both gravimetric units (mass constituent / mass soil) and areal units (mass constituent / soil surface area integrated through 7.6 cm soil depth, the depth of sampling). Areal concentrations were computed as X × D × 7.6, where X is the gravimetric concentration of a soil constituent, D is soil bulk density (g dry soil / cm^3), and 7.6 is the sampling depth in cm.more » « less

This dataset includes multiple fields: (i) files for monthly and annual fields for the max curl line and the zero curl line at 0.1 degree longitudinal resolutions; (ii) files for monthly and annual GS path obtained from Altimetry and originally processed by Andres (2016) at 0.1 degree longitudinal resolution. The maximum curl line (MCL) and the zero curl line (ZCL) calculations are briefly described here and are based on the original wind data (at 1.25 x 1.25 degree) provided by the Japanese reanalysis (JRA55; Kobayashi et al., 2015) and available at https://zenodo.org/record/8200832 (Gifford et al. 2023). For details see Gifford, 2023.
The wind stress curl (WSC) fields used for the MCL and ZCL calculations extend from 80W to 45W and 30N to 45N at the 1.25 by 1.25degree resolution. The MCL is defined as the maximum WSC values greater than zero within the domain per 1.25 degree longitude. As such, it is a function of longitude and is not a constant WSC value unlike the zero contour. High wind stress curl values that occurred near the coast were not included within this calculation. After MCL at the 1.25 resolution was obtained the line was smoothed with a gaussian smoothing and interpolated on to a 0.1 longitudinal resolution. The smoothed MCL lines at 0.1 degree resolution are provided in separate files for monthly and annual averages (2 files). Similarly, 2 other files (monthly and annual) are provided for the ZCL.
Like the MCL, the ZCL is a line derived from 1.25 degree longitude throughout the domain under the condition that it's the line of zero WSC. The ZCL is constant at 0 and does not vary spatially like the MCL. If there are more than one location of zero curl for a given longitude the first location south of the MCL is selected. Similar to the MCL, the ZCL was smoothed with a gaussian smoothing and interpolated on to a 0.1 longitudinal resolution.
The above files span the years from 1980 through 2019. So, the monthly files have 480 months starting January 1980, and the annual files have 40 years of data. The files are organized with each row being a new time step and each column being a different longitude. Therefore, the monthly MCL and ZCL files are each 480 x 351 for the 0.1 resolution data. Similarly, the annual files are 40 x 351 for the 0.1 degree resolution data.
Note that the monthly MCLs and ZCLs are obtained from the monthly windstress curl fields. The annual MCLs and ZCLs are obtained from the annual windstress curl fields.
Since the monthly curl fields preserves more atmospheric mesoscales than the annual curl fields, the 12month average of the monthly MCLs and ZCLs will not match with the annual MCLs and ZCLs derived from the annual curl field. The annual MCLs and ZCLs provided here are obtained from the annual curl fields and representative metrics of the wind forcing on an annual timescale.
Furthermore, the monthly Gulf Stream axis path (25 cm isoheight from Altimeter, reprocessed by Andres (2016) technique) from 1993 through 2019 have been made available here. A total of 324 monthly paths of the Gulf Stream are tabulated. In addition, the annual GS paths for these 27 years (19932019) of altimetry era have been put together for ease of use. The monthly Gulf Stream paths have been resampled and reprocessed for uniqueness at every 0.1 degree longitude from 75W to 50W and smoothed with a 100 km (10 point) running average via matlab. The uniqueness has been achieved by using Consolidator algorithm (D’Errico, 2023).
Each monthly or annual GS path has 251 points between 75W to 50W at 0.1 degree resolution.
Please contact igifford@earth.miami.edu for any queries. {"references": ["Andres, M., 2016. On the recent destabilization of the Gulf Stream path downstream of Cape Hatteras. Geophysical Research Letters, 43(18), 98369842.", "D'Errico, J., 2023. Consolidator (https://www.mathworks.com/matlabcentral/fileexchange/ 8354consolidator), MATLAB Central File Exchange. Retrieved June 17, 2023.", "Gifford, Ian. H., 2023. The Synchronicity of the Gulf Stream Free Jet and the Wind Induced Cyclonic Vorticity Pool. MS Thesis, University of Massachusetts Dartmouth. 75pp.", "Gifford, Ian, H., Avijit Gangopadhyay, Magdalena Andres, Glen Gawarkiewicz, Hilde Oliver, Adrienne Silver, 2023. Wind Stress, Wind Stress Curl, and Upwelling Velocities in the Northwest Atlantic (8045W, 3045N) during 19802019, https://zenodo.org/record/8200832.", "Kobayashi, S., Ota, Y., Harada, Y., Ebita, A., Moriya, M., Onoda, H., Onogi, K., Kamahori, H., Kobayashi, C., Endo, H. and Miyaoka, K., 2015. The JRA55 reanalysis: General specifications and basic characteristics.\u202fJournal of the Meteorological Society of Japan. Ser. II,\u202f93(1), pp.548. Kobayashi, S., Ota, Y., Harada, Y., Ebita, A., Moriya, M., Onoda, H., Onogi, K., Kamahori, H., Kobayashi, C., Endo, H. and Miyaoka, K., 2015. The JRA55 reanalysis: General specifications and basic characteristics.\u202fJournal of the Meteorological Society of Japan. Ser. II,\u202f93(1), pp.548."]}