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The driving forces of change in environmental indicators : an analysis based on divisia index decomposition techniques
This book addresses several index decomposition analysis methods to assess progress made by EU countries in the last decade in relation to energy and climate change concerns. Several applications of these techniques are carried out in order to decompose changes in both energy and environmental aggregates. In addition to this, a new methodology based on classical spline approximations is introduced, which provides useful mathematical and statistical properties. Once a suitable set of determinant factors has been identified, these decomposition methods allow the researcher to quantify the respective contributions of these factors. A proper interpretation of findings enables the design of strategies and a number of energy and environmental policies to control the variables of interest. This book also analyses the impact of several factors that allow control of these variables; among them, assessment of the specific contribution of improved energy efficiency is particularly relevant. A number of divisia-index-based techniques for decomposing changes in a generic indicator are now available, and these range from classical techniques based on Laspeyres and Paasche weights to more refined approaches relying on logarithmic mean weighting schemes. This book is intended for undergraduates and graduates of energy economics and environmental sciences, environmental policy advisors, and industrial engineers.
Book
The categorical DT/PT correspondence and quasi-BPS categories for local surfaces
We construct semiorthogonal decompositions of Donaldson–Thomas (DT) categories for reduced curve classes on local surfaces into products of quasi-BPS categories and Pandharipande–Thomas (PT) categories, giving a categorical analogue of the numerical DT/PT correspondence for Calabi–Yau 3-folds. The main ingredient is a categorical wall-crossing formula for DT/PT quivers (which appear as Ext quivers in the DT/PT wall-crossing) proved in our previous paper. We also study quasi-BPS categories of points on local surfaces and propose conjectural computations of their K-theory analogous to formulas already known for the three-dimensional affine space.
Journal Article
On nonemptiness of Newton strata in the BdR+-Grassmannian for GLn
We study the Newton stratification in the BdR+-Grassmannian for GLn associated to an arbitrary (possibly nonbasic) element of B(GLn). Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in B(GLn), our classification is given by some explicit conditions in terms of Newton polygons. For the proof, we proceed by induction on n using a previous result of the author that classifies all extensions of two given vector bundles on the Fargues–Fontaine curve.
Journal Article
Lower Semicontinuity in L1 of a Class of Functionals Defined on BV with Carathéodory Integrands
We prove lower semicontinuity in L1Ω for a class of functionals G:BVΩ⟶ℝ of the form Gu=∫Ωgx,∇udx+∫ΩψxdDsu where g:Ω×ℝN⟶ℝ, Ω⊂ℝN is open and bounded, g·,p∈L1Ω for each p, satisfies the linear growth condition limp⟶∞gx,p/p=ψx∈CΩ∩L∞Ω, and is convex in p depending only on p for a.e. x. Here, we recall for u∈BVΩ; the gradient measure Du=∇u dx+dDsux is decomposed into mutually singular measures ∇u dx and dDsux. As an example, we use this to prove that ∫Ωψxα2x+∇u2 dx+∫ΩψxdDsu is lower semicontinuous in L1Ω for any bounded continuous ψ and any α∈L1Ω. Under minor addtional assumptions on g, we then have the existence of minimizers of functionals to variational problems of the form Gu+u−u0L1 for the given u0∈L1Ω, due to the compactness of BVΩ in L1Ω.
Journal Article
Correction: Intrinsic Image Decomposition via Structure-Preserving Image Smoothing and Material Recognition
[This corrects the article DOI: 10.1371/journal.pone.0166772.].
Journal Article
Applying the Geometric Mean Decomposition in Joint Transceiver Design for Multi-Input Multi-Output (MIMO) Communications
In recent years, considerable attention has been paid to the joint optimal transceiver design for multi-input multioutput (MIMO) communication systems. In this paper, we propose a joint transceiver design that combines the geo- metric mean decomposition (GMD) with either the conventional zero-forcing VBLAST decoder or the more recent zero-forcing dirty paper precoder (ZFDP). Our scheme decomposes a MIMO channel into multiple identical parallel subchannels, which can make it rather convenient to design modulation/demodulation and coding/decoding schemes. Moreover, we prove that our scheme is asymptotically optimal for (moderately) high SNR in terms of both channel throughput and bit error rate (BER) performance. This desirable property is not shared by any other conventional schemes. We also consider the subchannel selection issues when some of the subchannels are too poor to be useful. Our scheme can also be combined with orthogonal frequency division multi- plexing (OFDM) for intersymbol interference (ISI) suppression. The effectiveness of our approaches has been validated by both theoretical analyses and numerical simulations.
Journal Article
A note on various decompositions of nano continuity
The Primary intend of this article is to present a unique decomposition from which some of the decompositions using various continuities follow as special cases. Our goal is to show why these decompositions hold and what they have in common. Likewise, we shall show that the two decompositions in our present work are actually equivalent and acquired a new decomposition in nts.
Journal Article
A Comparative Analysis of Signal Decomposition Techniques for Structural Health Monitoring on an Experimental Benchmark
Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals.
Journal Article
Data decomposition: from independent component analysis to sparse representations
This paper provides a unifying review of some recent approaches of decomposing data, images, and signals into sets of components. We start from the classical algebraic method of singular value decomposition and then introduce principal and independent component analysis. The text continues with the main subject of this paper, sparse representation and decomposition, emphasizing their biological plausibility. In this paper emphasis will be given to the geometric perspective, with the mathematics kept to a minimum.
Journal Article