Counting single-qubit Clifford equivalent graph states is #P-Complete

Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer codes. We here consider the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>. We show that this problem is #P-Complete. To prove our main result we make use of the notion of isotropic systems in graph theory. We review the definition of isotropic systems and point out their strong relation to graph states. We believe that these isotropic systems can be useful beyond the results presented in this paper.Comment: 10 pages, no figure

Do Polls Influence Opinions? Investigating Poll Feedback Loops Using the Novel Dynamic Response Feedback Experimental Procedure

Opinion polls may inadvertently affect public opinion, as people may change their attitudes after learning what others think. A disconcerting possibility is that opinion polls have the ability to create information cascades, wherein the majority opinion becomes increasingly larger over time. Testing poll influence on attitudes toward Syrian refugees and mandatory measles vaccination, we field survey experiments on a probability-based online survey panel. Through a novel automated procedure labeled the dynamic response feedback, we measure whether the answers from early poll respondents can influence the opinions of subsequent respondents who learn the answers of the previous respondents. Using this procedure, no feedback loops are identified.publishedVersio

Verdsettelse av Renewable Energy Corporation ASA

Studentarbeid i økonomi og ledelse (bachelorgrad) - Universitetet i Nordland, 2011I denne bacheloroppgaven har vi hatt verdsettelse som tema, der vi har sett nærmere på Renewable Energy Corporation ASA(REC). Problemstillingen vår har vært: “Hva er verdien av Renewable Energy Corporation ASA 1.1.2011?” REC er en vertikalt integrert bedrift som produserer solenergi. De er et konsern som driver i alle deler av verdikjeden, fra produksjon av silisium – wafere – solceller – solcellepanel – solcellemoduler. Selskapet ble notert på Oslo Børs i 2006 til en aksjekurs på 107,50 NOK. Etter noteringen har aksjen vært svært volatil, med toppnotering på 301 NOK i slutten av 2007. Som med de fleste andre ble også REC hardt rammet av finanskrisen, og aksjekursen har etter den tiden falt til 17,79 NOK den 1.1.2011. Oppgaven er en casestudie der vi har brukt relevant litteratur samt offentlig tilgjengelig selskaps- og bransjeinformasjon. Videre har vi gjennomgått ulike modeller som kan benyttes ved verdsettelse, og vi konkluderte med at den kontantstrømbaserte modellen var den mest egnede for oppgaven vår, nærmere bestemt; fri kontantstrøm til totalkapitalen. For å kunne gjennomføre verdsettelsen ved bruk av denne modellen beregnet vi et avkastningskrav til totalkapitalen(WACC) på 8,9 %. Dette ble brukt til å diskontere fremtidige kontantstrømmer. Før vi beregnet fremtidige frie kontantstrømmer gjorde vi analyser av makroforhold, bransjen og selskapet selv. Vi startet med en strategisk analyse der vi tok i bruk VRIO, Porters 5’Forces og en SWOT-analyse. Etter dette gjorde vi en regnskapsanalyse av REC der vi beregnet ulike nøkkeltall fra 2006 og til i dag. På bakgrunn av disse analysene ble de fremtidige kontantstrømmene beregnet. Vi beregnet disse kontantstrømmene frem til 2016, en tidsperiode på seks år. Dette ble så brukt i “Gordons-formel” sammen med avkastningskravet på 8,9 % og en forventet vekst på 2,5 %. Vi fant da ut at aksjekursen 1.1.2011 var 20,93 NOK, noe som representerte et avvik på ca. 17 % fra markedets verdi på 17,79 NOK. Avslutningsvis gjennomførte vi en sensitivitetsanalyse der vi testet ut hvordan endringer på vesentlige forutsetninger og faktorer spilte inn på vår estimering av aksjekursen. De forutsetningene vi testet i sensitivitetsanalysen var inntektsvekst, endring i kostnader, endring i vekst(g) og endring i avkastningskrav. Våre funn i denne analysen indikerte at REC er følsom for endringer i disse viktige faktorene, og verdien av RECs aksje svingte mye ved små endringer i innsatsfaktorene

Endophytes dominate fungal communities in six-year-old veteranisation wounds in living oak trunks

Old trees are rare in the landscape, as are many of their associated species. Veteranisation is a method by which attempts are made to create microhabitats, otherwise found only in old trees, in younger trees at an earlier stage than would occur naturally. Here, we analysed the early fungal succession in 6 y-old veteranisation wounds in ca. 100 y old living oak trunks by DNA-barcoding of the wood at eight sites in Sweden and Norway. We hypothesised basidiomycetes would be most abundant, and exposed sapwood and heartwood would select for different communities. We identified 686 fungal taxa, mainly ascomycetes, with a large overlap in species composition and surprisingly similar species richness, i.e. 325 vs. 308–360, between intact and different types of damaged wood, respectively. Endophytes continued to be present and common in damaged wood. The results demonstrate that damage to sapwood and heartwood partly select for different fungi and that 6 y is too early to evaluate if veteranisation can positively favour fungi of conservation interest

Current and future impact of osteoarthritis on health care: a population-based study with projections to year 2032.

To estimate the current and future (to year 2032) impact of osteoarthritis (OA) health care seeking

Counting single-qubit Clifford equivalent graph states is #ℙ-complete

Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer codes. We here consider the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>. We show that this problem is #P-Complete. To prove our main result we make use of the notion of isotropic systems in graph theory. We review the definition of isotropic systems and point out their strong relation to graph states. We believe that these isotropic systems can be useful beyond the results presented in this paper

How to transform graph states using single-qubit operations: computational complexity and algorithms

Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed into another graph (target)state,using a specific set of quantum operations (LC+LPM+CC): single-qubit Clifford operations(LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. This question is of interest for effective routing or state preparation decisions in a quantum network or distributed quantum processor and also in the design of quantum repeater schemes and quantum error-correction codes. We first show that deciding whether a graph state|G〉can be transformed into another graph state|G′〉using LC+LPM+CC is NP-complete, which was previously not known. We also show that the problem remains NP-complete even if|G′〉is restricted to be the GHZ-state. However, we also provide efficient algorithms for two situations of practical interest. Our results make use of the insight that deciding whether a graph state|G〉can be transformed to another graph state|G′〉is equivalent to a known decision problem in graph theory, namely the problem of deciding whether a graph G′ is a vertex-minor of a graph G. The computational complexity of the vertex-minor problem was prior to this paper an open question in graph theory. We prove that the vertex-minor problem is NP-complete by relating it to a new decision problem on 4-regular graphs which we call the semi-ordered Eulerian tour problem

Transforming graph states to Bell-pairs is NP-Complete

Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of Bell pairs between distant nodes in the network. Here we focus on the problem of transforming multipartite entangled states into the tensor product of bipartite Bell pairs between specific nodes using only a certain class of local operations and classical communication. In particular we study the problem of deciding whether a given graph state, and in general a stabilizer state, can be transformed into a set of Bell pairs on specific vertices using only single-qubit Clifford operations, single-qubit Pauli measurements and classical communication. We prove that this problem is NP-Complete

DNA methylation-based subtype prediction for pediatric acute lymphoblastic leukemia.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.We present a method that utilizes DNA methylation profiling for prediction of the cytogenetic subtypes of acute lymphoblastic leukemia (ALL) cells from pediatric ALL patients. The primary aim of our study was to improve risk stratification of ALL patients into treatment groups using DNA methylation as a complement to current diagnostic methods. A secondary aim was to gain insight into the functional role of DNA methylation in ALL.We used the methylation status of ~450,000 CpG sites in 546 well-characterized patients with T-ALL or seven recurrent B-cell precursor ALL subtypes to design and validate sensitive and accurate DNA methylation classifiers. After repeated cross-validation, a final classifier was derived that consisted of only 246 CpG sites. The mean sensitivity and specificity of the classifier across the known subtypes was 0.90 and 0.99, respectively. We then used DNA methylation classification to screen for subtype membership of 210 patients with undefined karyotype (normal or no result) or non-recurrent cytogenetic aberrations ('other' subtype). Nearly half (n = 106) of the patients lacking cytogenetic subgrouping displayed highly similar methylation profiles as the patients in the known recurrent groups. We verified the subtype of 20% of the newly classified patients by examination of diagnostic karyotypes, array-based copy number analysis, and detection of fusion genes by quantitative polymerase chain reaction (PCR) and RNA-sequencing (RNA-seq). Using RNA-seq data from ALL patients where cytogenetic subtype and DNA methylation classification did not agree, we discovered several novel fusion genes involving ETV6, RUNX1, and PAX5.Our findings indicate that DNA methylation profiling contributes to the clarification of the heterogeneity in cytogenetically undefined ALL patient groups and could be implemented as a complementary method for diagnosis of ALL. The results of our study provide clues to the origin and development of leukemic transformation. The methylation status of the CpG sites constituting the classifiers also highlight relevant biological characteristics in otherwise unclassified ALL patients.Swedish Foundation for Strategic Research RBc08-008 Swedish Cancer Society CAN2010/592 Swedish Childhood Cancer Foundation 11098 Swedish Research Council for Science and Technology 90559401 Swedish Research Council FORTE Swedish Research Council FORMAS Swedish Research Council VINNOVA Swedish Research Council VR 259-2012-2