scholarly journals A Note on Inclusion Intervals of Matrix Singular Values

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Shu-Yu Cui ◽  
Gui-Xian Tian
Keyword(s):  
Singular Values ◽  
Inclusion Relation ◽  
Inclusion Interval ◽  
Special Case

We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.

The New qd Algorithms

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 459-491 ◽  
Author(s):  
Beresford N. Parlett
Keyword(s):  
Singular Values ◽  
Eigenvalues And Eigenvectors ◽  
Triangular Factorization ◽  
Matrix Computation ◽  
Important Special Case ◽  
Singular Vectors ◽  
Tridiagonal Matrices ◽  
Recent Origin ◽  
Special Case

Let us think about ways to find both eigenvalues and eigenvectors of tridiagonal matrices. An important special case is the computation of singular values and singular vectors of bidiagonal matrices. The discussion is addressed both to specialists in matrix computation and to other scientists whose main interests lie elsewhere. The reason for hoping to communicate with two such diverse sets of readers at the same time is that the content of the survey, though of recent origin, is quite elementary and does not demand familiarity with much beyond triangular factorization and the Gram-Schmidt process for orthogonalizing a set of vectors. For some readers the survey will cover familiar territory but from a novel perspective. The justification for presenting these ideas is that they lead to new variations of current methods that run a lot faster while achieving greater accuracy.

scholarly journals Semantic diversity is best measured with unscaled vectors: Reply to Cevoli, Watkins and Rastle (2020)

2021 ◽  
Author(s):  
Paul Hoffman ◽  
Matthew A. Lambon Ralph ◽  
Timothy T. Rogers
Keyword(s):  
Word Recognition ◽  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Word Meaning ◽  
Singular Values ◽  
Semantic Representations ◽  
Diversity Measure ◽  
Contextual Variability ◽  
Original Measure ◽  
Special Case

AbstractSemantic diversity refers to the degree of semantic variability in the contexts in which a particular word is used. We have previously proposed a method for measuring semantic diversity based on latent semantic analysis (LSA). In a recent paper, Cevoli et al. (2020) attempted to replicate our method and obtained different semantic diversity values. They suggested that this discrepancy occurred because they scaled their LSA vectors by their singular values, while we did not. Using their new results, they argued that semantic diversity is not related to ambiguity in word meaning, as we originally proposed. In this reply, we demonstrate that the use of unscaled vectors provides better fits to human semantic judgements than scaled ones. Thus we argue that our original semantic diversity measure should be preferred over the Cevoli et al. version. We replicate Cevoli et al.’s analysis using the original semantic diversity measure and find (a) our original measure is a better predictor of word recognition latencies than the Cevoli et al. equivalent and (b) that, unlike Cevoli et al.’s measure, our semantic diversity is reliably associated with a measure of polysemy based on dictionary definitions. We conclude that the Hoffman et al. semantic diversity measure is better-suited to capturing the contextual variability among words and that words appearing in a more diverse set of contexts have more variable semantic representations. However, we found that homonyms did not have higher semantic diversity values than non-homonyms, suggesting that the measure does not capture this special case of ambiguity.

scholarly journals Semantic diversity is best measured with unscaled vectors: Reply to Cevoli, Watkins and Rastle (2020)

2021 ◽  
Author(s):  
Paul Hoffman ◽  
Matt Lambon Ralph ◽  
Timothy Thomas Rogers
Keyword(s):  
Word Recognition ◽  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Singular Values ◽  
Semantic Representations ◽  
Critical Stage ◽  
Diversity Measure ◽  
Contextual Variability ◽  
Original Measure ◽  
Special Case

Semantic diversity refers to the degree of semantic variability in the contexts in which a particular word is used. In 2013, we proposed a method for measuring semantic diversity based on latent semantic analysis (LSA) (Hoffman, Lambon Ralph, & Rogers, 2013). In a recent paper, Cevoli, Watkins and Rastle (2020) criticised our method, noting that we had failed to scale our LSA vectors by their singular values, which they considered to be a critical stage in the analysis. They presented new analyses using their own semantic diversity measure that included this step. In this reply, we demonstrate that the use of unscaled vectors provides better fits to human semantic judgements than scaled ones. Thus we argue that our original semantic diversity measure should be preferred over the Cevoli et al. version. We replicate Cevoli et al.’s analysis using the original semantic diversity measure and find (a) our original measure is a better predictor of word recognition latencies than the Cevoli et al. equivalent and (b) that, unlike Cevoli et al.’s measure, our semantic diversity is reliably associated with a measure of polysemy based on dictionary definitions. We conclude that the original Hoffman et al. semantic diversity measure is better-suited to capturing the contextual variability among words and that words appearing in a more diverse set of contexts have more variable semantic representations. However, we found that homonyms did not have higher semantic diversity values than non-homonyms, suggesting that the measure does not capture this special case of ambiguity.

scholarly journals Multiplicative convolution of real asymmetric and real anti-symmetric matrices

2019 ◽  
Vol 10 (4) ◽  
pp. 467-492 ◽  
Author(s):  
Mario Kieburg ◽  
Peter J. Forrester ◽  
Jesper R. Ipsen
Keyword(s):  
Probability Distribution ◽  
Random Matrices ◽  
Singular Values ◽  
Symmetric Matrices ◽  
Orthogonal Matrices ◽  
Unitary Matrices ◽  
Correlation Kernel ◽  
Multiplicative Convolution ◽  
Special Case ◽  
Double Contour

AbstractThe singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a polynomial ensemble. It is furthermore the case that the corresponding bi-orthogonal system can be determined in terms of Meijer G-functions, and the correlation kernel given as an explicit double contour integral. It has recently been shown that the Hermitised product {X_{M}\cdots X_{2}X_{1}AX_{1}^{T}X_{2}^{T}\cdots X_{M}^{T}}, where each {X_{i}} is a standard real Gaussian matrix and A is real anti-symmetric, exhibits analogous properties. Here we use the theory of spherical functions and transforms to present a theory which, for even dimensions, includes these properties of the latter product as a special case. As an example we show that the theory also allows for a treatment of this class of Hermitised product when the {X_{i}} are chosen as sub-blocks of Haar distributed real orthogonal matrices.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

Impact of Digitalization on Service Work in Knowledge-Intensive Business Services: An Empirical Study in Tax Consultancies

2019 ◽  
Vol 3 (4) ◽  
pp. 209-222
Author(s):  
Philipp K. Görs ◽  
Henning Hummert ◽  
Anne Traum ◽  
Friedemann W. Nerdinger
Keyword(s):  
Work Engagement ◽  
Service Work ◽  
Psychological Consequences ◽  
Business Services ◽  
Knowledge Intensive Business Services ◽  
Positive Effects ◽  
Knowledge Intensive ◽  
The Impact ◽  
Positive Effect ◽  
Special Case

Digitalization is a megatrend, but there is relatively little knowledge about its consequences for service work in general and specifically in knowledge-intensive business services (KIBS). We studied the impact of digitalization on psychological consequences for employees in tax consultancies as a special case of KIBS. We compare two tax consulting jobs with very different job demands, those of tax consultants (TCs) and assistant tax consultants (ATCs). The results show that the extent of digitalization at the workplace level for ATCs correlates significantly positively with their job satisfaction. For TCs, the same variable correlates positively with their work engagement. These positive effects of digitalization are mediated in the case of ATCs by the impact on important job characteristics. In the case of TCs, which already have very good working conditions, the impact is mediated by the positive effect on self-efficacy. Theoretical and practical consequences of these results are discussed.

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