Singular vector structure of quantum curves

A series of algorithms for satellite retrievals of sun-induced chlorophyll fluorescence (SIF) have been developed and applied to different sensors. However, research on SIF retrieval using hyperspectral data is performed in narrow spectral windows, assuming that SIF remains constant. In this paper, based on the singular vector decomposition (SVD) technique, we present an approach for retrieving SIF, which can be applied to remotely sensed data with ultra-high spectral resolution and in a broad spectral window without assuming that the SIF remains constant. The idea is to combine the first singular vector, the pivotal information of the non-fluorescence spectrum, with the low-frequency contribution of the atmosphere, plus a linear combination of the remaining singular vectors to express the non-fluorescence spectrum. Subject to instrument settings, the retrieval was performed within a spectral window of approximately 7 nm that contained only Fraunhofer lines. In our retrieval, hyperspectral data of the O2-A band from the first Chinese carbon dioxide observation satellite (TanSat) was used. The Bayesian Information Criterion (BIC) was introduced to self-adaptively determine the number of free parameters and reduce retrieval noise. SIF retrievals were compared with TanSat SIF and OCO-2 SIF. The results showed good consistency and rationality. A sensitivity analysis was also conducted to verify the performance of this approach. To summarize, the approach would provide more possibilities for retrieving SIF from hyperspectral data.

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Ensemble Construction and Verification of the Probabilistic ENSO Prediction in the LDEO5 Model

Journal of Climate ◽

10.1175/2010jcli3453.1 ◽

2010 ◽

Vol 23 (20) ◽

pp. 5476-5497 ◽

Cited By ~ 16

Author(s):

Yanjie Cheng ◽

Youmin Tang ◽

Peter Jackson ◽

Dake Chen ◽

Ziwang Deng

Keyword(s):

High Frequency ◽

Singular Vector ◽

Southern Oscillation ◽

Initial Perturbation ◽

Probabilistic Prediction ◽

Construction Methods ◽

Sea Surface Temperature Anomaly ◽

Probabilistic Forecasts ◽

Construction Strategy ◽

Construction Strategies

Abstract El Niño–Southern Oscillation (ENSO) retrospective ensemble-based probabilistic predictions were performed for the period of 1856–2003 using the Lamont-Doherty Earth Observatory, version 5 (LDEO5), model. To obtain more reliable and skillful ENSO probabilistic predictions, first, four ensemble construction strategies were investigated: (i) the optimal initial perturbation with singular vector of sea surface temperature anomaly (SSTA), (ii) the realistic high-frequency anomalous winds, (iii) the stochastic optimal pattern of anomalous winds, and (iv) a combination of the first and the third strategy. Second, verifications were conducted to examine the reliability and resolution of the probabilistic forecasts provided by the four methods. Results suggest that reliability of ENSO probabilistic forecast is more sensitive to the choice of ensemble construction strategy than the resolution, and a reliable and skillful ENSO probabilistic prediction system may not necessarily have the best deterministic prediction skills. Among these ensemble construction methods, the fourth strategy produces the most reliable and skillful ENSO probabilistic prediction, benefiting from the joint contributions of the stochastic optimal winds and the singular vector of SSTA. In particular, the stochastic optimal winds play an important role in improving the ENSO probabilistic predictability for the LDEO5 model.

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Comments on orientifolds without vector structure

Journal of High Energy Physics ◽

10.1088/1126-6708/2008/08/016 ◽

2008 ◽

Vol 2008 (08) ◽

pp. 016-016 ◽

Cited By ~ 12

Author(s):

Constantin Bachas ◽

Massimo Bianchi ◽

Ralph Blumenhagen ◽

Dieter Lüst ◽

Timo Weigand

Keyword(s):

Vector Structure

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COMBED 3-MANIFOLDS WITH CONCAVE BOUNDARY, FRAMED LINKS, AND PSEUDO-LEGENDRIAN LINKS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216501000706 ◽

2001 ◽

Vol 10 (01) ◽

pp. 1-35 ◽

Cited By ~ 7

Author(s):

RICCARDO BENEDETTI ◽

CARLO PETRONIO

Keyword(s):

Vector Field ◽

Finite Order ◽

Singular Vector ◽

Contact Structures ◽

Winding Number ◽

Legendrian Links ◽

Concave Boundary

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M, v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly ∂M≠∅, and v may be tangent to ∂M, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M, v, L), with (M, v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transverality-preserving simultaneous homotopy of v and isotopy of L). All realizations are based on the notion of branched standard spine, and build on results previously obtained, Links are encoded by means of diagrams on branched spines, where the diagram is C 1 with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.

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