Search results for "vector space"
showing 10 items of 287 documents
Asymptotic and bootstrap tests for subspace dimension
2022
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li (2016). The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test…
Semantic Computing of Moods Based on Tags in Social Media of Music
2014
Social tags inherent in online music services such as Last.fm provide a rich source of information on musical moods. The abundance of social tags makes this data highly beneficial for developing techniques to manage and retrieve mood information, and enables study of the relationships between music content and mood representations with data substantially larger than that available for conventional emotion research. However, no systematic assessment has been done on the accuracy of social tags and derived semantic models at capturing mood information in music. We propose a novel technique called Affective Circumplex Transformation (ACT) for representing the moods of music tracks in an interp…
High-resolution transmission electron microscopic investigations of molybdenum thin films on faceted α-Al2O3
2005
Epitaxially grown Mo films on a faceted corundum (α-Al2O3)mplane were investigated by transmission electron microscopy. Low- and high-resolution images were taken from a cross-section specimen cut perpendicular to the facets. It was possible to identify unambiguously the crystallographic orientation of these facets and explain the considerable deviation (∼10°) of the experimental interfacet angle, as measured with atomic force microscopy (AFM), from the expected value. For the first time, proof is given for a smooth \{10\bar{1}1\} facet and a curvy facet with orientation near to \{10\bar{1}\bar{2}\}. Moreover, the three-dimensional epitaxial relationship of an Mo film on a faceted corundumm…
Gradient estimates for the perfect conductivity problem in anisotropic media
2018
Abstract We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension which characterize the singular behavior of the electric field as the distance between the inclusions goes to zero.
Mind the depth: The vertical dimension of a small-scale coastal fishery shapes selection on species, size, and sex in wrasses
2020
Small‐scale fisheries (SSFs) tend to target shallow waters, but the depth distributions of coastal fish can vary depending on species, size, and sex. This creates a scope for a form of fishing selectivity that has received limited attention but can have considerable implications for monitoring and management of these fisheries. We conducted a case study on the Norwegian wrasse fishery, a developing SSF in which multiple species are caught in shallow waters (mean depth = 4.5 m) to be used as cleaner fish in aquaculture. Several of these wrasses have life histories and behaviors that are sensitive to selective fishing mortality, such as sexual size dimorphism, paternal care, and sex change. A…
Applying Hypothesis of Self-Similarity for Flow-Resistance Law in Calabrian Gravel-Bed Rivers
2018
In this paper, the results of an investigation carried out to test the applicability of a flow-resistance law on gravel-bed rivers in southern Italy (fiumare) are reported. First, dimensional analysis and self-similarity theory are applied for deducing the flow-resistance law (i.e., relationship among friction factor, mean velocity, shear stress, and physical properties) for gravel-bed rivers with a high boulder concentration. The proposed approach is calibrated and tested using two independent data sets (104 reaches of some Calabrian fiumare). Then, the incomplete self-similarity hypothesis is also applied to theoretically deduce the flow-velocity profile, which was integrated for obtainin…
Time-resolved buildup of twisted indirect exchange interaction in two-dimensional systems
2019
We study theoretically the time-domain dynamics of the spin-dependent Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between driven magnetic impurities localized in a spin-orbit-coupled two-dimensional system. Particular attention is given to the influence of the spin-orbit coupling (SOC) on the system's dynamical response to a time-dependent precessional motion of the localized magnetic moment. We show that, via the RKKY mechanism, a flip of the spin $z$ component of one localized moment affects all $x,\phantom{\rule{4pt}{0ex}}y$, and $z$ spin components of the other localized moment. The Friedel oscillations and the transient spin current triggered by the time-varying localized spin dep…
Partitions of finite vector spaces: An application of the frobenius number in geometry
1978
Gamma-convergence of Gaussian fractional perimeter
2021
Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 - {s\to 1^{-}} . Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.
Weak separation condition, Assouad dimension, and Furstenberg homogeneity
2015
We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.