Multivariate Topology Simplification

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph

Interactive Visualization for Singular Fibers of Functions f : R3 → R2

Scalar topology in the form of Morse theory has provided computational tools that analyze and visualize data from scientific and engineering tasks. Contracting isocontours to single points encapsulates variations in isocontour connectivity in the Reeb graph. For multivariate data, isocontours generalize to fibers—inverse images of points in the range, and this area is therefore known as fiber topology. However, fiber topology is less fully developed than Morse theory, and current efforts rely on manual visualizations. This paper presents how to accelerate and semi-automate this task through an interface for visualizing fiber singularities of multivariate functions R3 → R2. This interface exploits existing conventions of fiber topology, but also introduces a 3D view based on the extension of Reeb graphs to Reeb spaces. Using the Joint Contour Net, a quantized approximation of the Reeb space, this accelerates topological visualization and permits online perturbation to reduce or remove degeneracies in functions under study. Validation of the interface is performed by assessing whether the interface supports the mathematical workflow both of experts and of less experienced mathematicians

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

Regional CO2 flux estimates for 2009-2010 based on GOSAT and ground-based CO2 observations

We present the application of a global carbon cycle modeling system to the estimation of monthly regional CO2 fluxes from the column-averaged mole fractions of CO2 (XCO2) retrieved from spectral observations made by the Greenhouse gases Observing SATellite (GOSAT). The regional flux estimates are to be publicly disseminated as the GOSAT Level 4 data product. The forward modeling components of the system include an atmospheric tracer transport model, an anthropogenic emissions inventory, a terrestrial biosphere exchange model, and an oceanic flux model. The atmospheric tracer transport was simulated using isentropic coordinates in the stratosphere and was tuned to reproduce the age of air. We used a fossil fuel emission inventory based on large point source data and observations of nighttime lights. The terrestrial biospheric model was optimized by fitting model parameters to observed atmospheric CO2 seasonal cycle, net primary production data, and a biomass distribution map. The oceanic surface pCO2 distribution was estimated with a 4-D variational data assimilation system based on reanalyzed ocean currents. Monthly CO2 fluxes of 64 sub-continental regions, between June 2009 and May 2010, were estimated from GOSAT FTS SWIR Level 2 XCO2 retrievals (ver. 02.00) gridded to 5° � 5° cells and averaged on a monthly basis and monthly-mean GLOBALVIEW-CO2 data. Our result indicated that adding the GOSAT XCO2 retrievals to the GLOBALVIEW data in the flux estimation brings changes to fluxes of tropics and other remote regions where the surface-based data are sparse. The uncertainties of these remote fluxes were reduced by as much as 60 through such addition. Optimized fluxes estimated for many of these regions, were brought closer to the prior fluxes by the addition of the GOSAT retrievals. In most of the regions and seasons considered here, the estimated fluxes fell within the range of natural flux variabilities estimated with the component models

Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in \O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.Comment: 25 pages. Updated with minor change

Self-consistent non-Markovian theory of a quantum state evolution for quantum information processing

It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of decoherence processes self-consistently. Our formulation is the first principle theory based on projection-operator formalism to obtain an exact reduced density operator in time-convolutionless form starting from the quantum Liouville equation for a noisy quantum computer. The advantage of our approach is that it is general enough to describe a realistic quantum computer in the presence of decoherence provided details of the Hamiltonians are known.Comment: 5page

Using satellites to monitor Severn Bridge structure, UK

The Severn Bridge is a large UK suspension bridge. In 2010, a series of field surveys was commissioned to monitor the magnitude and frequencies of the bridge’s movements, through attaching nine dual-frequency survey grade global navigation satellite system receivers on the bridge and two reference satellite receivers adjacent to the structure. The satellite antenna locations and configuration allow the movements of the north cable to be analysed at four locations, as well as the differential movements of the two suspension cables to each other. In addition, this configuration allows the movements of the tops of the towers to be compared to the cables’ movements, as well as with each other. All in all, this allowed the relative movements of the various locations on the bridge’s suspension cables and tower tops to be compared to each other, at a rate of up to 20 Hz. Overall, some 3 days of raw code and carrier phase satellite data were gathered. During these sessions, normal traffic loading was experienced. This paper describes the survey, presents a selection of the key results and draws conclusions about the effective use of satellite positioning systems to enhance structural health monitoring.The Highways Agency, Severn River Crossing plc and Mott MacDonal

The Orbiting Carbon Observatory (OCO-2) Tracks 2-3 Peta-Gram Increase in Carbon Release to the Atmosphere During the 2014-2016 El Nino

The powerful El Nio event of 2015-2016 - the third most intense since the 1950s - has exerted a large impact on the Earth's natural climate system. The column-averaged CO2 dry-air mole fraction (XCO2) observations from satellites and ground based networks are analyzed together with in situ observations for the period of September 2014 to October 2016. From the differences between satellite (OCO-2) observations and simulations using an atmospheric chemistry-transport model, we estimate that, relative to the mean annual fluxes for 2014, the most recent El Nio has contributed to an excess CO2 emission from the Earth's surface (land+ocean) to the atmosphere in the range of 2.4+/-0.2 PgC (1 Pg = 10(exp 15) g) over the period of July 2015 to June 2016. The excess CO2 flux is resulted primarily from reduction in vegetation uptake due to drought, and to a lesser degree from increased biomass burning. It is about the half of the CO2 flux anomaly (range: 4.4-6.7 PgC) estimated for the 1997/1998 El Nio. The annual total sink is estimated to be 3.9+/-0.2 PgC for the assumed fossil fuel emission of 10.1 PgC. The major uncertainty in attribution arise from error in anthropogenic emission trends, satellite data and atmospheric transport