Simplified broken Lefschetz fibrations and trisections of 4-manifolds

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only allow us to produce various interesting families of examples, but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.Comment: 17 pages, 7 figure

Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the systemreservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the n-th order approximation are given. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.Comment: 34pages, no figur

Mass-conserving tracer transport modelling on a reduced latitude-longitude grid with NIES-TM

The need to perform long-term simulations with reasonable accuracy has led to the development of mass-conservative and efficient numerical methods for solving the transport equation in forward and inverse models. We designed and implemented a flux-form (Eulerian) tracer transport algorithm in the National Institute for Environmental Studies Transport Model (NIES TM), which is used for simulating diurnal and synoptic-scale variations of tropospheric long-lived constituents, as well as their seasonal and inter-annual variability. Implementation of the flux-form method requires the mass conservative wind fields. However, the model is off-line and is driven by datasets from a global atmospheric model or data assimilation system, in which vertically integrated mass changes are not in balance with the surface pressure tendency and mass conservation is not achieved. To rectify the mass-imbalance, a flux-correction method is employed. To avoid a singularity near the poles, caused by the small grid size arising from the meridional convergence problem, the proposed model uses a reduced latitude–longitude grid scheme, in which the grid size is doubled several times approaching the poles. This approach overcomes the Courant condition in the Polar Regions, maintains a reasonably high integration time-step, and ensures adequate model performance during simulations. To assess the model performance, we performed global transport simulations for SF<sub>6</sub>, <sup>222</sup>Rn, and CO<sub>2</sub>. The results were compared with observations available from the World Data Centre for Greenhouse Gases, GLOBALVIEW, and the Hateruma monitoring station, Japan. Overall, the results show that the proposed flux-form version of NIES TM can produce tropospheric tracer transport more realistically than previously possible. The reasons for this improvement are discussed

Time-convolutionless reduced-density-operator theory of a noisy quantum channel: a two-bit quantum gate for quantum information processing

An exact reduced-density-operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then, we apply the formulation to model a two-bit quantum gate composed of coupled spin systems in which the Heisenberg coupling is controlled by the tunneling barrier between neighboring quantum dots. Gate Characteristics including the entropy, fidelity, and purity are calculated numerically for both mixed and entangled initial states

A Conditional Yeast E1 Mutant Blocks the Ubiquitin–Proteasome Pathway and Reveals a Role for Ubiquitin Conjugates in Targeting Rad23 to the Proteasome

E1 ubiquitin activating enzyme catalyzes the initial step in all ubiquitin-dependent processes. We report the isolation of uba1-204, a temperature-sensitive allele of the essential Saccharomyces cerevisiae E1 gene, UBA1. Uba1-204 cells exhibit dramatic inhibition of the ubiquitin–proteasome system, resulting in rapid depletion of cellular ubiquitin conjugates and stabilization of multiple substrates. We have employed the tight phenotype of this mutant to investigate the role ubiquitin conjugates play in the dynamic interaction of the UbL/UBA adaptor proteins Rad23 and Dsk2 with the proteasome. Although proteasomes purified from mutant cells are intact and proteolytically active, they are depleted of ubiquitin conjugates, Rad23, and Dsk2. Binding of Rad23 to these proteasomes in vitro is enhanced by addition of either free or substrate-linked ubiquitin chains. Moreover, association of Rad23 with proteasomes in mutant and wild-type cells is improved upon stabilizing ubiquitin conjugates with proteasome inhibitor. We propose that recognition of polyubiquitin chains by Rad23 promotes its shuttling to the proteasome in vivo

Spectroscopic evidence of the formation of (V,Ti)O₂ solid solution in VO₂ thinner films grown on TiO₂(001) substrates

We have prepared VO2 thin films epitaxially grown on TiO2(001) substrates with thickness systematically varied from 2.5 to 13 nm using a pulsed laser deposition method, and studied the transport property and electronic states of the films by means of resistivity and in situ synchrotron photoemission spectroscopy (SRPES). In resistivity measurements, the 13-nm-thick film exhibits a metal-insulator transition at around 290 K on cooling with change of three orders of magnitudes in resistivity. As the film thickness decreases, the metal-insulator transition broadens and the transition temperature increases. Below 4 nm, the films do not show the transition and become insulators. In situ SRPES measurements of near the Fermi level valence band find that the electronic state of the 2.5-nm-thick film is different than that of the temperature-induced insulator phase of VO2 itself although these two states are insulating. Ti 2p core-level photoemission measurements reveal that Ti ions exist near the interface between the films and TiO2 substrates, with a chemical state similar to that in (V,Ti)O-2 solid solution. These results indicate that insulating (V,Ti)O-2 solid solution is formed in the thinner films. We propose a simple growth model of a VO2 thin film on a TiO2(001) substrate. Near the interface, insulating (V,Ti) O-2 solid solution is formed due to the diffusion of Ti ions from the TiO2 substrate into the VO2 film. The concentration of Ti in (V,Ti) O-2 is relatively high near the interface and decreases toward the surface of the film. Beyond a certain film thickness (about 7 nm in the case of the present 13-nm-thick film), the VO2 thin film without any Ti ions starts to grow. Our work suggests that developing a technique for preparing the sharp interface between the VO2 thin films and TiO2 substrates is a key issue to study the physical property of an ultrathin film of "pure" VO2, especially to examine the presence of the novel electronic state called a semi-Dirac point phase predicted by calculations

Enabling Personalized Composition and Adaptive Provisioning of Web Services

The proliferation of interconnected computing devices is fostering the emergence of environments where Web services made available to mobile users are a commodity. Unfortunately, inherent limitations of mobile devices still hinder the seamless access to Web services, and their use in supporting complex user activities. In this paper, we describe the design and implementation of a distributed, adaptive, and context-aware framework for personalized service composition and provisioning adapted to mobile users. Users specify their preferences by annotating existing process templates, leading to personalized service-based processes. To cater for the possibility of low bandwidth communication channels and frequent disconnections, an execution model is proposed whereby the responsibility of orchestrating personalized processes is spread across the participating services and user agents. In addition, the execution model is adaptive in the sense that the runtime environment is able to detect exceptions and react to them according to a set of rules