Fractional isomorphism of graphs

AbstractLet the adjacency matrices of graphs G and H be A and B. These graphs are isomorphic provided there is a permutation matrix P with AP=PB, or equivalently, A=PBPT. If we relax the requirement that P be a permutation matrix, and, instead, require P only to be doubly stochastic, we arrive at two new equivalence relations on graphs: linear fractional isomorphism (when we relax AP=PB) and quadratic fractional isomorphism (when we relax A=PBPT). Further, if we allow the two instances of P in A=PBPT to be different doubly stochastic matrices, we arrive at the concept of semi-isomorphism.We present necessary and sufficient conditions for graphs to be linearly fractionally isomorphic, we prove that quadratic fractional isomorphism is the same as isomorphism and we relate semi-isomorphism to isomorphism of bipartite graphs

Experimental Investigation of a 16-inch Impulse-type Supersonic-compressor Rotor

Performance data and characteristics of a 16-inch impulse-type supersonic-compressor rotor are presented. The experimental portion of this investigation was conducted in Freon-12. A peak pressure ratio of 3.6 was obtained with an adiabatic efficiency of 0.80 at design conditions. Performance was continuous from impulse operation, at open throttle, to shock-in-rotor operation at the stall condition

A NATUREZA DAS CIDADES

A NATUREZA DAS CIDADE

Earliest Holocene south Greenland ice sheet retreat within its late Holocene extent

Early Holocene summer warmth drove dramatic Greenland ice sheet (GIS) retreat. Subsequent insolation-driven cooling caused GIS margin readvance to late Holocene maxima, from which ice margins are now retreating. We use ¹⁰Be surface exposure ages from four locations between 69.4°N and 61.2°N to date when in the early Holocene south to west GIS margins retreated to within these late Holocene maximum extents. We find that this occurred at 11.1 ± 0.2 ka to 10.6 ± 0.5 ka in south Greenland, significantly earlier than previous estimates, and 6.8 ± 0.1 ka to 7.9 ± 0.1 ka in southwest to west Greenland, consistent with existing ¹⁰Be ages. At least in south Greenland, these ¹⁰Be ages likely provide a minimum constraint for when on a multicentury timescale summer temperatures after the last deglaciation warmed above late Holocene temperatures in the early Holocene. Current south Greenland ice margin retreat suggests that south Greenland may have now warmed to or above earliest Holocene summer temperatures.Keywords: Early Holocene climate, Greenland ice sheet, Cosmogenic datin

A Genome-Wide Scan of Ashkenazi Jewish Crohn's Disease Suggests Novel Susceptibility Loci

Crohn's disease (CD) is a complex disorder resulting from the interaction of intestinal microbiota with the host immune system in genetically susceptible individuals. The largest meta-analysis of genome-wide association to date identified 71 CD–susceptibility loci in individuals of European ancestry. An important epidemiological feature of CD is that it is 2–4 times more prevalent among individuals of Ashkenazi Jewish (AJ) descent compared to non-Jewish Europeans (NJ). To explore genetic variation associated with CD in AJs, we conducted a genome-wide association study (GWAS) by combining raw genotype data across 10 AJ cohorts consisting of 907 cases and 2,345 controls in the discovery stage, followed up by a replication study in 971 cases and 2,124 controls. We confirmed genome-wide significant associations of 9 known CD loci in AJs and replicated 3 additional loci with strong signal (p<5×10−6). Novel signals detected among AJs were mapped to chromosomes 5q21.1 (rs7705924, combined p = 2×10−8; combined odds ratio OR = 1.48), 2p15 (rs6545946, p = 7×10−9; OR = 1.16), 8q21.11 (rs12677663, p = 2×10−8; OR = 1.15), 10q26.3 (rs10734105, p = 3×10−8; OR = 1.27), and 11q12.1 (rs11229030, p = 8×10−9; OR = 1.15), implicating biologically plausible candidate genes, including RPL7, CPAMD8, PRG2, and PRG3. In all, the 16 replicated and newly discovered loci, in addition to the three coding NOD2 variants, accounted for 11.2% of the total genetic variance for CD risk in the AJ population. This study demonstrates the complementary value of genetic studies in the Ashkenazim

The equivariant stable homotopy theory around isometric linear maps

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