8,885 research outputs found
Size reconstructibility of graphs
The deck of a graph is given by the multiset of (unlabelled) subgraphs
. The subgraphs are referred to as the cards of .
Brown and Fenner recently showed that, for , the number of edges of a
graph can be computed from any deck missing 2 cards. We show that, for
sufficiently large , the number of edges can be computed from any deck
missing at most cards.Comment: 15 page
Labeling Schemes for Bounded Degree Graphs
We investigate adjacency labeling schemes for graphs of bounded degree
. In particular, we present an optimal (up to an additive
constant) adjacency labeling scheme for bounded degree trees.
The latter scheme is derived from a labeling scheme for bounded degree
outerplanar graphs. Our results complement a similar bound recently obtained
for bounded depth trees [Fraigniaud and Korman, SODA 10], and may provide new
insights for closing the long standing gap for adjacency in trees [Alstrup and
Rauhe, FOCS 02]. We also provide improved labeling schemes for bounded degree
planar graphs. Finally, we use combinatorial number systems and present an
improved adjacency labeling schemes for graphs of bounded degree with
Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries
Longest common extension queries (LCE queries) and runs are ubiquitous in
algorithmic stringology. Linear-time algorithms computing runs and
preprocessing for constant-time LCE queries have been known for over a decade.
However, these algorithms assume a linearly-sortable integer alphabet. A recent
breakthrough paper by Bannai et.\ al.\ (SODA 2015) showed a link between the
two notions: all the runs in a string can be computed via a linear number of
LCE queries. The first to consider these problems over a general ordered
alphabet was Kosolobov (\emph{Inf.\ Process.\ Lett.}, 2016), who presented an
-time algorithm for answering LCE queries. This
result was improved by Gawrychowski et.\ al.\ (accepted to CPM 2016) to time. In this work we note a special \emph{non-crossing} property
of LCE queries asked in the runs computation. We show that any such
non-crossing queries can be answered on-line in time, which
yields an -time algorithm for computing runs
Aram Dorsum: an extensive mid-Noachian age fluvial depositional system in Arabia Terra, Mars
A major debate in Mars science is the nature of the early Mars climate, and the availability of precipitation and runoff. Observations of relict erosional valley networks have been proposed as evidence for extensive surface run‐off around the Noachian‐Hesperian boundary. However, these valley networks only provide a time‐integrated record of landscape evolution and thus the timing, relative timescales and intensity of aqueous activity required to erode the valleys remain unknown. Here, we investigate an ancient fluvial sedimentary system in western Arabia Terra, now preserved in positive relief. This ridge, ‘Aram Dorsum’, is flat‐topped, branching, ~ 85 km long, and particularly well‐preserved. We show that Aram Dorsum was an aggradational alluvial system and that the existing ridge was once a large river channel‐belt set in extensive flood plains, many of which are still preserved. Smaller, palaeochannel‐belts feed the main system; their setting and network pattern suggest a distributed source of water. The alluvial succession is up to 60 m thick, suggesting a formation time of 105 to 107 years by analogy to Earth. Our observations are consistent with Aram Dorsum having formed by long‐lived flows of water, sourced both locally, and regionally as part of a wider alluvial system in Arabia Terra. This suggests frequent or seasonal precipitation as the source of water. Correlating our observations with previous regional‐scale mapping shows that Aram Dorsum formed in the mid‐Noachian, making it one of the oldest fluvial systems described on Mars and indicating climatic conditions that sustained surface river flows on early Mars
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BENCH-SCALE STEAM REFORMING OF ACTUAL TANK 48H WASTE
Fluidized Bed Steam Reforming (FBSR) has been demonstrated to be a viable technology to remove >99% of the organics from Tank 48H simulant, to remove >99% of the nitrate/nitrite from Tank 48H simulant, and to form a solid product that is primarily carbonate based. The technology was demonstrated in October of 2006 in the Engineering Scale Test Demonstration Fluidized Bed Steam Reformer1 (ESTD FBSR) at the Hazen Research Inc. (HRI) facility in Golden, CO. The purpose of the Bench-scale Steam Reformer (BSR) testing was to demonstrate that the same reactions occur and the same product is formed when steam reforming actual radioactive Tank 48H waste. The approach used in the current study was to test the BSR with the same Tank 48H simulant and same Erwin coal as was used at the ESTD FBSR under the same operating conditions. This comparison would allow verification that the same chemical reactions occur in both the BSR and ESTD FBSR. Then, actual radioactive Tank 48H material would be steam reformed in the BSR to verify that the actual tank 48H sample reacts the same way chemically as the simulant Tank 48H material. The conclusions from the BSR study and comparison to the ESTD FBSR are the following: (1) A Bench-scale Steam Reforming (BSR) unit was successfully designed and built that: (a) Emulated the chemistry of the ESTD FBSR Denitration Mineralization Reformer (DMR) and Carbon Reduction Reformer (CRR) known collectively as the dual reformer flowsheet. (b) Measured and controlled the off-gas stream. (c) Processed real (radioactive) Tank 48H waste. (d) Met the standards and specifications for radiological testing in the Savannah River National Laboratory (SRNL) Shielded Cells Facility (SCF). (2) Three runs with radioactive Tank 48H material were performed. (3) The Tetraphenylborate (TPB) was destroyed to > 99% for all radioactive Bench-scale tests. (4) The feed nitrate/nitrite was destroyed to >99% for all radioactive BSR tests the same as the ESTD FBSR. (5) The radioactive Tank 48H DMR product was primarily made up of soluble carbonates. The three most abundant species were thermonatrite, [Na{sub 2}CO{sub 3} {center_dot} H{sub 2}O], sodium carbonate, [Na{sub 2}CO{sub 3}], and trona, [Na{sub 3}H(CO{sub 3}){sub 2} {center_dot} 2H{sub 2}O] the same as the ESTD FBSR. (6) Insoluble solids analyzed by X-Ray Diffraction (XRD) did not detect insoluble carbonate species. However, they still may be present at levels below 2 wt%, the sensitivity of the XRD methodology. Insoluble solids XRD characterization indicated that various Fe/Ni/Cr/Mn phases are present. These crystalline phases are associated with the insoluble sludge components of Tank 48H slurry and impurities in the Erwin coal ash. The percent insoluble solids, which mainly consist of un-burnt coal and coal ash, in the products were 4 to 11 wt% for the radioactive runs. (7) The Fe{sup +2}/Fe{sub total} REDOX measurements ranged from 0.58 to 1 for the three radioactive Bench-scale tests. REDOX measurements > 0.5 showed a reducing atmosphere was maintained in the DMR indicating that pyrolysis was occurring. (8) Greater than 90% of the radioactivity was captured in the product for all three runs. (9) The collective results from the FBSR simulant tests and the BSR simulant tests indicate that the same chemistry occurs in the two reactors. (10) The collective results from the BSR simulant runs and the BSR radioactive waste runs indicates that the same chemistry occurs in the simulant as in the real waste. The FBSR technology has been proven to destroy the organics and nitrates in the Tank 48H waste and form the anticipated solid carbonate phases as expected
Computed tomography attenuation of periaortic adipose tissue in abdominal aortic aneurysms
Purpose: To assess periaortic adipose tissue attenuation on CT angiography indifferent abdominal aortic aneurysm disease states.Materials and Methods: In a retrospective observational study from January 2018 to December 2022, periaortic adipose tissue attenuation was assessed on CT angiography in patients with asymptomatic or symptomatic (including rupture) abdominal aortic aneurysms, and control individuals without aneurysms. Adipose tissue attenuation was measured using semi-automated software in periaortic aneurysmal and non-aneurysmal segments of the abdominal aorta, and in subcutaneous and visceral adipose tissue. Periaortic adipose tissue attenuation values between the three groups was assessed using Students t-test and Wilcoxon rank sum test followed by a multi-regression model.Results: Eighty-eight individuals (median age, 70 [IQR, 65-78] years; 78 male and 10 female) were included: 70 patients with abdominal aortic aneurysms (40 asymptomatic and 30 symptomatic including 24 with rupture), and 18 controls. There was no evidence of differences in the periaortic adipose tissue attenuation in the aneurysmal segment in asymptomatic patients versus controls ((-81.44±7 versus -83.27±9 HU, Hounsfield units, P=0.43) and attenuation in non-aneurysmal segments between asymptomatic patients versus controls (-75.43±8 versus -78.81±6 HU, P=0.08). However, symptomatic patients demonstrated higher periaortic adipose tissue attenuation in both aneurysmal (-57.85±7 HU, P<0.0001) and non-aneurysmal segments (-58.16±8 HU, P<0.0001) when compared with the other two groups.Conclusions: Periaortic adipose tissue CT attenuation was not increased in stableabdominal aortic aneurysm disease. There was a generalised increase in attenuation in patients with symptomatic disease, likely reflecting the systemic consequences of acute rupture
The generalized 3-edge-connectivity of lexicographic product graphs
The generalized -edge-connectivity of a graph is a
generalization of the concept of edge-connectivity. The lexicographic product
of two graphs and , denoted by , is an important graph
product. In this paper, we mainly study the generalized 3-edge-connectivity of
, and get upper and lower bounds of .
Moreover, all bounds are sharp.Comment: 14 page
Radioactive Demonstration Of Mineralized Waste Forms Made From Hanford Low Activity Waste (Tank SX-105, Tank AN-103, And AZ-101/102) By Fluidized Bed Steam Reformation (FBSR)
Fluidized Bed Steam Reforming (FBSR) is a robust technology for the immobilization of a wide variety of radioactive wastes. Applications have been tested at the pilot scale for the high sodium, sulfate, halide, organic and nitrate wastes at the Hanford site, the Idaho National Laboratory (INL), and the Savannah River Site (SRS). Due to the moderate processing temperatures, halides, sulfates, and technetium are retained in mineral phases of the feldspathoid family (nepheline, sodalite, nosean, carnegieite, etc). The feldspathoid minerals bind the contaminants such as Tc-99 in cage (sodalite, nosean) or ring (nepheline) structures to surrounding aluminosilicate tetrahedra in the feldspathoid structures. The granular FBSR mineral waste form that is produced has a comparable durability to LAW glass based on the short term PCT testing in this study, the INL studies, SPFT and PUF testing from previous studies as given in the columns in Table 1-3 that represent the various durability tests. Monolithing of the granular product was shown to be feasible in a separate study. Macro-encapsulating the granular product provides a decrease in leaching compared to the FBSR granular product when the geopolymer is correctly formulated
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