Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods

Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically solved iteratively by a Krylov subspace method. We propose a preconditioner which takes an advantage of the recursive hierarchy in the structure of the global matrices. In particular, the matrices posses a recursive hierarchical two-by-two structure, with one of the submatrices block diagonal. Each one of the diagonal blocks in this submatrix is closely related to the deterministic mean-value problem, and the action of its inverse is in the implementation approximated by inner loops of Krylov iterations. Thus our hierarchical Schur complement preconditioner combines, on each level in the approximation of the hierarchical structure of the global matrix, the idea of Schur complement with loops for a number of mutually independent inner Krylov iterations, and several matrix-vector multiplications for the off-diagonal blocks. Neither the global matrix, nor the matrix of the preconditioner need to be formed explicitly. The ingredients include only the number of stiffness matrices from the truncated Karhunen-Lo\`{e}ve expansion and a good preconditioned for the mean-value deterministic problem. We provide a condition number bound for a model elliptic problem and the performance of the method is illustrated by numerical experiments.Comment: 15 pages, 2 figures, 9 tables, (updated numerical experiments

Balancing heat saving and supply in local energy planning: Insights from 1970-1989 buildings in three European countries

This study investigates the cost balance between heat energy savings through building envelope retrofits and supply from low-carbon decentralised and centralised technologies in a generic urban district, composed of residential and non-residential buildings from the 1970–1989 construction period. For generalisability, the district is analysed in three European countries (Bulgaria, Germany, Finland), each with distinct weather conditions and price levels. Using bottom-up energy modelling and adopting a societal perspective that includes external costs, the study finds the cost-effectiveness of retrofits to be context-specific. In Bulgaria, retrofits prove largely cost-effective, whereas in Germany and Finland, high labour and material costs pose challenges. Heat pumps, whether decentralised in buildings or centralised in district heating systems, emerge as key options for heat supply, even in cold climates. The study underscores the importance of integrated energy planning in line with the ‘energy efficiency first’ principle and corresponding incentive structures to promote sustainable urban energy systems

Decoherence and Programmable Quantum Computation

An examination of the concept of using classical degrees of freedom to drive the evolution of quantum computers is given. Specifically, when externally generated, coherent states of the electromagnetic field are used to drive transitions within the qubit system, a decoherence results due to the back reaction from the qubits onto the quantum field. We derive an expression for the decoherence rate for two cases, that of the single-qubit Walsh-Hadamard transform, and for an implementation of the controlled-NOT gate. We examine the impact of this decoherence mechanism on Grover's search algorithm, and on the proposals for use of error-correcting codes in quantum computation.Comment: submitted to Phys. Rev. A 35 double-spaced pages, 2 figures, in LaTe

Role of electromagnetically induced transparency in resonant four-wave-mixing schemes.

Published versio

Generic model of an atom laser

We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in steady-state. We study the transient regime of this atom laser and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semi-classical theory of the laser.Comment: 15 pages, including 5 figures, submitted to Phys. Rev. A, revised manuscript, file also available at http://www.physik.uni-ulm.de/quan/users/kne

Experimentally based contact energies decode interactions responsible for protein–DNA affinity and the role of molecular waters at the binding interface

A major obstacle towards understanding the molecular basis of transcriptional regulation is the lack of a recognition code for protein–DNA interactions. Using high-quality crystal structures and binding data on the promiscuous family of C2H2 zinc fingers (ZF), we decode 10 fundamental specific interactions responsible for protein–DNA recognition. The interactions include five hydrogen bond types, three atomic desolvation penalties, a favorable non-polar energy, and a novel water accessibility factor. We apply this code to three large datasets containing a total of 89 C2H2 transcription factor (TF) mutants on the three ZFs of EGR. Guided by molecular dynamics simulations of individual ZFs, we map the interactions into homology models that embody all feasible intra- and intermolecular bonds, selecting for each sequence the structure with the lowest free energy. These interactions reproduce the change in affinity of 35 mutants of finger I (R2 = 0.998), 23 mutants of finger II (R2 = 0.96) and 31 finger III human domains (R2 = 0.94). Our findings reveal recognition rules that depend on DNA sequence/structure, molecular water at the interface and induced fit of the C2H2 TFs. Collectively, our method provides the first robust framework to decode the molecular basis of TFs binding to DNA

NMR and MD studies of the temperature-dependent dynamics of RNA YNMG-tetraloops

In a combined NMR/MD study, the temperature-dependent changes in the conformation of two members of the RNA YNMG-tetraloop motif (cUUCGg and uCACGg) have been investigated at temperatures of 298, 317 and 325 K. The two members have considerable different thermal stability and biological functions. In order to address these differences, the combined NMR/MD study was performed. The large temperature range represents a challenge for both, NMR relaxation analysis (consistent choice of effective bond length and CSA parameter) and all-atom MD simulation with explicit solvent (necessity to rescale the temperature). A convincing agreement of experiment and theory is found. Employing a principle component analysis of the MD trajectories, the conformational distribution of both hairpins at various temperatures is investigated. The ground state conformation and dynamics of the two tetraloops are indeed found to be very similar. Furthermore, both systems are initially destabilized by a loss of the stacking interactions between the first and the third nucleobase in the loop region. While the global fold is still preserved, this initiation of unfolding is already observed at 317 K for the uCACGg hairpin but at a significantly higher temperature for the cUUCGg hairpin

Sudden switching in qubits

Analytic solutions are developed for two-state systems (e.g. qubits) strongly perturbed by a series of rapidly changing pulses, called `kicks'. The evolution matrix may be expressed as a time ordered product of evolution matrices for single kicks. Single, double, and triple kicks are explicitly considered, and the onset of observability of time ordering is examined. The effects of different order of kicks on the dynamics of the system are studied and compared with effects of time ordering in general. To determine the range of validity of this approach, the effect of using pulses of finite widths for 2s-2p transitions in atomic hydrogen is examined numerically.Comment: 22 pages, 7 figure

European Code against Cancer, 4th Edition: Cancer screening

In order to update the previous version of the European Code against Cancer and formulate evidence-based recommendations, a systematic search of the literature was performed according to the methodology agreed by the Code Working Groups. Based on the review, the 4th edition of the European Code against Cancer recommends: “Take part in organized cancer screening programmes for: • Bowel cancer (men and women)• Breast cancer (women)• Cervical cancer (women).”Organized screening programs are preferable because they provide better conditions to ensure that the Guidelines for Quality Assurance in Screening are followed in order to achieve the greatest benefit with the least harm. Screening is recommended only for those cancers where a demonstrated life-saving effect substantially outweighs the potential harm of examining very large numbers of people who may otherwise never have, or suffer from, these cancers, and when an adequate quality of the screening is achieved. EU citizens are recommended to participate in cancer screening each time an invitation from the national or regional screening program is received and after having read the information materials provided and carefully considered the potential benefits and harms of screening. Screening programs in the European Union vary with respect to the age groups invited and to the interval between invitations, depending on each country's cancer burden, local resources, and the type of screening test used For colorectal cancer, most programs in the EU invite men and women starting at the age of 50–60 years, and from then on every 2 years if the screening test is the guaiac-based fecal occult blood test or fecal immunochemical test, or every 10 years or more if the screening test is flexible sigmoidoscopy or total colonoscopy. Most programs continue sending invitations to screening up to the age of 70–75 years. For breast cancer, most programs in the EU invite women starting at the age of 50 years, and not before the age of 40 years, and from then on every 2 years until the age of 70–75 years. For cervical cancer, if cytology (Pap) testing is used for screening, most programs in the EU invite women starting at the age of 25–30 years and from then on every 3 or 5 years. If human papillomavirus testing is used for screening, most women are invited starting at the age of 35 years (usually not before age 30 years) and from then on every 5 years or more. Irrespective of the test used, women continue participating in screening until the age of 60 or 65 years, and continue beyond this age unless the most recent test results are normal

Adherence to colorectal cancer screening: Four rounds of faecal immunochemical test-based screening

Background:The effectiveness of faecal immunochemical test (FIT)-based screening programs is highly dependent on consistent participation over multiple rounds. We evaluated adherence to FIT screening over four rounds and aimed to identify determinants of participation behaviour.Methods:A total of 23 339 randomly selected asymptomatic persons aged 50-74 years were invited for biennial FIT-based colorectal cancer screening between 2006 and 2014. All were invited for every consecutive round, except for those who had moved out of the area, passed the upper age limit, or had tested positive in a previous screening round. A reminder letter was sent to non-responders. We calculated participation rates per round, response rates to a reminder letter, and differences in participation between subgroups defined by age, sex, and socioeconomic status (SES).Results:Over the four rounds, participation rates increased significantly, from 60% (95% CI 60-61), 60% (95% CI 59-60), 62% (95% CI 61-63) to 63% (95% CI 62-64; P for trend<0.001) with significantly higher participation rates in women in all rounds (P<0.001). Of the 17 312 invitees eligible for at least two rounds of FIT screening, 12 455 (72%) participated at least once, whereas 4857 (28%) never participated; 8271 (48%) attended all rounds when eligible. Consistent participation was associated with older age, female sex, and higher SES. Offering a reminder letter after the initial invite in the first round increased uptake with 12%; in subsequent screening rounds this resulted in an additional uptake of up to 10%.Conclusions:In four rounds of a pilot biennial FIT-screening program, we observed a consistently high and increasing participation rate, whereas sending reminders remain effective. The substantial proportion of inconsistent participants suggests the existence of incidental barriers to participation, which, if possible, should be identified and removed