On the classification of easy quantum groups

In 2009, Banica and Speicher began to study the compact quantum subgroups of the free orthogonal quantum group containing the symmetric group S_n. They focused on those whose intertwiner spaces are induced by some partitions. These so-called easy quantum groups have a deep connection to combinatorics. We continue their work on classifying these objects introducing some new examples of easy quantum groups. In particular, we show that the six easy groups O_n, S_n, H_n, B_n, S_n' and B_n' split into seven cases on the side of free easy quantum groups. Also, we give a complete classification in the half-liberated case.Comment: 39 pages; appeared in Advances in Mathematics, Vol. 245, pages 500-533, 201

Decompositions of complete uniform hypergraphs into Hamilton Berge cycles

In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if $n$ divides $\binom{n}{k}$, then the complete $k$-uniform hypergraph on $n$ vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence $v_1,e_1,v_2,\dots,v_n,e_n$ of distinct vertices $v_i$ and distinct edges $e_i$ so that each $e_i$ contains $v_i$ and $v_{i+1}$. So the divisibility condition is clearly necessary. In this note, we prove that the conjecture holds whenever $k \ge 4$ and $n \ge 30$. Our argument is based on the Kruskal-Katona theorem. The case when $k=3$ was already solved by Verrall, building on results of Bermond

Gauss decomposition for Chevalley groups, revisited

In the 1960's Noboru Iwahori and Hideya Matsumoto, Eiichi Abe and Kazuo Suzuki, and Michael Stein discovered that Chevalley groups $G=G(\Phi,R)$ over a semilocal ring admit remarkable Gauss decomposition $G=TUU^-U$, where $T=T(\Phi,R)$ is a split maximal torus, whereas $U=U(\Phi,R)$ and $U^-=U^-(\Phi,R)$ are unipotent radicals of two opposite Borel subgroups $B=B(\Phi,R)$ and $B^-=B^-(\Phi,R)$ containing $T$. It follows from the classical work of Hyman Bass and Michael Stein that for classical groups Gauss decomposition holds under weaker assumptions such as \sr(R)=1 or \asr(R)=1. Later the second author noticed that condition \sr(R)=1 is necessary for Gauss decomposition. Here, we show that a slight variation of Tavgen's rank reduction theorem implies that for the elementary group $E(\Phi,R)$ condition \sr(R)=1 is also sufficient for Gauss decomposition. In other words, $E=HUU^-U$, where $H=H(\Phi,R)=T\cap E$. This surprising result shows that stronger conditions on the ground ring, such as being semi-local, \asr(R)=1, \sr(R,\Lambda)=1, etc., were only needed to guarantee that for simply connected groups $G=E$, rather than to verify the Gauss decomposition itself

Muscular compartment syndrome and in vivo optical spectroscopy monitoring: a new model

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WASSTONEHENGEANOBSERVATORY?

pointedexactlytothedirectionofsunriseatsolstice.Severalsimilarcoincidenceswerediscovered,whichleadmanypeopletobelievethatStonehengewasanancientobservatory.Inthispaper,weanalyzethisproblemfromageometricviewpointandshowthatsimilar coincidencescanhappen(withaprobability)forrandomlyplaced stones.Thus,Stonehenge'scoincidencescannotbeviewedasproof thatthisplacewasanobservatory. In1965,G.S.HawkinsandJ.B.Whitepublishedabook(Hawkins etal1965)inwhichtheyarguedthatStonehenge,amysterious 1.HAWKINS:ITWAS ancientthree-circlestonestructureinEngland,wasactuallyan ancientobservatory.Forexample,theydiscoveredthatadirection formedbytwoof60stonesoftheoutercirclepoints(withahigh accuracy,lessthan1)wasthedirectioninwhichthesunrises duringthesolarsolstice(actually,tothedirectioninwhichsun rose placetwostonesatrandom,thentheprobabilitythatthesetwo stonespointinthisdirectionisminuscule. 4;000yearsago,whenStonehengewasbuilt).Ifwesimply tweenthestonescouldbeinterpretedinreasonableastronomicaltheauthorsusedacomputertocheckifanyotherdirectionsbe-terms,andtheyindeedfoundmanysuchdirections. Toconvincethosewhowerenotconvincedbythiscoincidence, arethankfultoMariaBeltranforvaluablecomments

Automated Cluster-Based Web Service Performance Tuning

system to improve the performance of a cluster-based web service system. The performance improvement cannot easily be achieved by tuning individual components for such a system. The experimental results show that there is no single configuration for the system that performs well for all kinds of workloads. By tuning the parameters, the Active Harmony helps the system adapt to different workloads and improve the performance up to 16%. For scalability, we demonstrate how to reduce the time when tuning a large system with many tunable parameters. Finally an algorithm is proposed to automatically adjust the structure of cluster-based web systems, and the system throughput is improved up to 70 % using this technology. I