123,488 research outputs found
On the Restricted Isometry of the Columnwise Khatri-Rao Product
No full textThe columnwise Khatri-Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often contingent on proving the restricted isometry property (RIP) of a certain system matrix expressible as a Khatri-Rao product of two matrices. In this paper, we analyze the RIP of a generic columnwise Khatri-Rao product matrix by deriving two upper bounds for its kth order restricted isometry constant (k-RIC) for different values of k. The first RIC bound is computed in terms of the individual RICs of the real-valued input matrices participating in the Khatri-Rao product. The second RIC bound is probabilistic and is specified in terms of the input matrix dimensions. We show that the Khatri-Rao product of a pair of m x n sized random matrices comprising independent and identically distributed sub-Gaussian entries satisfies k-RIP with arbitrarily high probability, provided m exceeds O(root k log(3/2) n). This is a substantially milder condition compared to O(k log n) rows needed to guarantee k-RIP of the input sub-Gaussian random matrices participating in the Khatri-Rao product. Our RIC bounds confirm that the Khatri-Rao product exhibits stronger restricted isometry compared to its constituent matrices for the same RIP order. The proposed RIC bounds are potentially useful in obtaining improved performance guarantees in several sparse signal recovery and tensor decomposition problems
Figure 2 from: Khatri I, Rustamani M (2011) Key to the Tribes and Genera of Deltocephaline Leafhoppers (Auchenorrhyncha, Hemiptera, Cicadellidae) of Pakistan. ZooKeys 104: 67-76. https://doi.org/10.3897/zookeys.104.906
No full textFigure 2 - a–o male genitalia. a, c, d, f (genital capsule); b (pygofer, caudal view); e (genital capsule, internal view); g (connective and style); h, i, n, o (valve, style and connective, dorsal view). j (style); k (connective); l (valve, styles, subgenital plates, connective and base of aedeagus); m (fused subgenital plates and valve (setae omitted), styles and base of connective). A Cicadulina bipunctata Ghauri B Macrosteles indrina (Pruthi) C Maiestas pruthii (Metcalf) D Hecalus sindhensis (Ahmed & Aziz) E Pseudosubhimalus bicolor Pruthi F Stirellus lahorensis (Distant) G Scaphoideus harlani Kitbamroong & Freytag H Neolimnus quadricornis Khatri & Webb I, J Psammotettix emarginata Singh K Bampurius pakistanicus Khatri & Webb L Jilinga gopii (Pruthi) M Goniagnathus (T.) quadripinnatus Dash & Viraktamath N Aconurella prolixa (Lethierry) O Stirellus lahorensis (Distant)
Matrix inequalities involving the Khatri-Rao product
No full textsummary:We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product
A Khatri-Rao product tensor network for efficient symmetric MIMO Volterra identification
No full textThe identification of symmetric tensor network MIMO Volterra models has been studied earlier via the computation of a Moore-Penrose pseudoinverse in tensor network form. The current state of the art requires the construction of a tensor network of a repeated Khatri-Rao product of a matrix with itself. This construction has a computational complexity that is dominated by one singular value decomposition (SVD) of an RI × IN matrix, where N is the number of measurements, I depends linearly on the number of inputs and input lags and R is the maximal tensor network rank. In this article, we prove an alternative method for constructing this tensor network without any computation whatsoever. The pseudoinverse can then be computed through an orthogonalization of the newly proposed tensor network. Furthermore, the proposed algorithm allows for the recursive identification of symmetric Volterra models of increasing degree D, which reduces the computation to one SVD of a RI × N matrix per step. Through numerical experiments we demonstrate how the proposed algorithm enables up to ten times faster identification of symmetric tensor network MIMO Volterra systems.Team Kim Batselie
A note on idempotent matrices
No full textAbstractLet H be an n × n matrix, and let the trace, the rank, the conjugate transpose, the Moore-Penrose inverse, and a g-inverse (or an inner inverse) of H be respectively denoted by trH, ρ(H), H∗, H†, and H−. This note develops two results: (i) the class of idempotent g-inverse of an idempotent matrix, and (ii) if H is an n × n matrix and ρ(H) = trH, then tr(H2H†H∗) ⩾ ρ(H), and the equality holds iff H is idempotent. This result is compared with the previous result of Khatri (1983), and some consequences of (i) and (ii) are given
Mapping the structure and development of Science using co-citation analysis
No full textCo-citation analysis is a unique method used for studying the cognitive structure of science andassessing the research productivity. It is a research tool for examining the intellectual development and structure of the scientific discipline. This paper illustrates principles, techniques and applications of co-citation analysis. It also introduces the newly emerging co-citation analysis softwares,especially SciVal Spotlight and CiteSpace. Co-citation analysis is based on grouping together the papers that are frequently cited in pairs. Combined with single-link clustering and multidimensional scaling techniques, co-citation analysis can literally map the structure of specialized research areas as well as science as a whole
Chiasmus alatus Pruthi
No full textChiasmus alatus Pruthi Material examined. No material examined. Remarks. Described from several syntypes (including 2 referred to as ‘holotypes’) from: Kuldana, near Murree, N. W. Himalayas; Oct., 1928 (Pruthi), and from numerous other specimens from throughout India.Published as part of Khatri, Imran & Webb, Michael D., 2010, The Deltocephalinae leafhoppers of Pakistan (Hemiptera, Cicadellidae), pp. 1-47 in Zootaxa 2365 on page 10, DOI: 10.5281/zenodo.19365
A Multi-Language Comparison of Influences on Author Verification using Character N-Grams
No full textWe create a new multi-language corpus for author verification based on Wikipedia talkpages, and evaluate the influence that differences in topic and time have on character n-gram author profiles. Topic alignment between two texts is found to increase author verification precision, and an authors writing style is found to change over time, but not more significantly after 3 years than after 1 year.Information ArchitectureWISElectrical Engineering, Mathematics and Computer Scienc
Neolimnus Linnavuori
No full textNeolimnus Linnavuori Remarks. In addition to the new species described here (see below), this genus contains three species, N. egyptiacus (Matsumura) from North Africa to India (see below), N. ageratus (Melichar) from central Africa and N. eberti Dlabola (1964) known only from a female from Afghanistan. The genus is distinctive in having an inner dorsal process of the subgenital plate (Figs 6 d, 7g), the first valvifer with a posterior lobe and the first valvulae twisted apically with dorsal teeth with the more apical situated more laterally (Fig. 5 g). The teeth of the first valvulae are reminiscent of those found in the unrelated Cicadulina (see Knight & Webb, 1993, fig. 142). Neolimnus egyptiacus (Matsumura) (Plate 1, c; Fig. 7). Scaphoideus karachiensis Ahmed, Murtaza & Malik. Syn. nov. Material examined. Pakistan: 1 Ƥ, Hub, 17.iv. 87; 13, 1 Ƥ, Tharparkar, 12.xi.07, I. Khatri. Remarks. This species is identified based on the figures of Linnavuori (1953). See also N. quadricornis sp. nov. described below. The change of spelling to aegyptiacus by other authors subsequent to its description would seem to be unnecessary. Scaphoideus karachiensis was described from a holotype male and several paratypes from: Karachi, grass, 20.vii. 1985, Babar (ZMUK); no type material could be found.Published as part of Khatri, Imran & Webb, Michael D., 2010, The Deltocephalinae leafhoppers of Pakistan (Hemiptera, Cicadellidae), pp. 1-47 in Zootaxa 2365 on page 7, DOI: 10.5281/zenodo.19365
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
