1,720,980 research outputs found
Approximating real stability radii
No full textThe stability radius of an matrix (or distance to instability)
is a well-known measure of robustness of stability of the linear stable dynamical system
. Such a distance is commonly measured either in the -norm or in the
Frobenius norm.
Even if the matrix is real, the distance to instability is most often considered
with respect to complex valued matrices (in such case the two norms turn out to be
equivalent) and restricting the distance to real matrices makes the problem more complicated,
and in the case of Frobenius norm - to our knowledge - unresolved.
Here we present a novel approach to approximate real stability radii, particularly well-suited
for large sparse matrices.
The method consists of a two level iteration, the inner one aiming to compute the \eps-
pseudospectral abscissa of a low-rank ( or ) dynamical system, and the outer one
consisting of an exact Newton iteration.
Due to its local convergence property it generally provides upper bounds for the stability radii but in practice usually computes the correct values.
The method requires the computation of the rightmost eigenvalue of a sequence of matrices, each of them given by the sum of the original matrix and a low-rank one.
This makes it particularly suitable for large sparse problems, for which several existing methods become inefficient, due to the fact that they require to solve full Hamiltonian eigenvalue problems and/or compute multiple SVDs
Differential equations for real-structured defectivity measures.
No full textLet be a real matrix with all distinct eigenvalues. We propose a new method for the computation of the distance of the matrix from the set of real defective matrices, i.e., the set of those real matrices with at least one multiple eigenvalue with algebraic multiplicity larger than its geometric multiplicity.
For 0 < \eps \le w_\R(A), this problem is closely related to the computation of the most ill-conditioned \eps-pseudoeigenvalues of , that is points in the \eps-pseudospectrum of characterized by the highest condition number.
The method we propose couples a system of differential equations on a low rank manifold which determines the \eps-pseudoeigenvalue closest to coalesce, with a fast Newton-like iteration aiming to determine the minimal value \eps such that an \eps-pseudoeigenvalue becomes defective.
The method has a local behaviour; this means that in general we find upper bounds for . However, they usually provide good approximations, in those (simple) cases where we can check this.
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The methodology can be extended to a structured matrix, where it is required that the distance is computed within some manifold defining the structure of the matrix. In this paper we extensively examine the case of real matrices. As far as we know, there do not exist methods in the literature able to compute such distance
Updating the water budget of the Gran Sasso carbonate fractured/karstified aquifer (Central Italy) for a sustainable management of groundwater resources
No full textKarst aquifers are fundamental in the water supply of European countries, where outcrops of carbonate rocks are very common, providing abundant groundwater resources. The Gran Sasso karst aquifer, selected as representative study area for Italy in the EU-funded KARMA project, is characterized by both high percentage of withdrawals for drinking purposes and significant interaction between groundwater and underground works. The recharge evaluation of the aquifer has been carried out considering the 2001–2020 monitoring period, comparing three different methods: the Turc and APLIS methods, on annual scale, and the Thornthwaite method, on monthly scale, territorially distributed by 100 x 100 m cells on GIS basis. The total recharge considers not only rainfall but also the contribution of snow melting on infiltration. The results show similar mean recharge values in 2001–2020 for all methods, corresponding to 19.9, 18.5, and 19.4 m3/s, respectively, from Turc, Thornthwaite, and APLIS methods. A significant contribution to recharge from snowmelt has been confirmed (3.2 m3/s included in the above-mentioned values). These values can be considered reliable with respect to real discharge of the regional aquifer. The obtained results can be used to provide updated information to the drinking water companies for a suitable management of the available resource
Differential equations for real-structured defectivity measures
Full text linkLet A be a real matrix with all distinct eigenvalues. We propose a new method for the computation of the distance w_R(A) of the matrix A from the set of real defective matrices, i.e., the set of those real matrices with at least one multiple eigenvalue with algebraic multiplicity larger than its geometric multiplicity. For 0 < ε ≤ w_R(A), this problem is closely related to the computation of the most ill-conditioned ε-pseudoeigenvalues of A, that is, points in the ε-pseudospectrum of A characterized by the highest condition number. The method we propose couples a system of differential equations on a low-rank manifold which determines the ε-pseudoeigenvalue closest to coalescence, with a fast Newton-like iteration aiming to determine the minimal value ε such that an ε- pseudoeigenvalue becomes defective. The method has a local behavior; this means that, in general, we find upper bounds for w_R(A). However, these bounds usually provide good approximations, in those (simple) cases where we can check this. The methodology can be extended to a structured matrix, where it is required that the distance be computed within some manifold defining the structure of the matrix. In this paper we extensively examine the case of real matrices. As far as we know, there do not exist methods in the literature able to compute such distance
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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