A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

What neuroimaging and perceptions of self-other similarity can tell us about the mechanism underlying mentalizing

Carruthers' "mindreading is prior" model postulates one unitary mindreading mechanism working identically for self and other. While we agree about shared mindreading mechanisms, there is also evidence from neuroimaging and mentalizing about dissimilar others that suggest factors that differentially affect self-versus-other mentalizing. Such dissociations suggest greater complexity than the mindreading is prior model allows.

Similarity not favourability : the role of donor prototypes in predicting willingness to donate organs while living

Using an extended Prototype/Willingness Model, we examined the predictors of willingness to donate an organ to a partner/family member and a stranger while living. A questionnaire assessed university students’ (N = 284) attitudes, subjective norm, prototype favourability, prototype similarity, moral norm, and willingness to donate organs in each recipient scenario. All variables, except prototype favourability, predicted willingness to donate organs in both situations. Future strategies should emphasise perceived approval from important others for living donation, the consistency of living donation with one’s own morals, and encourage perceptions of similarity between oneself and living donors to increase acceptance of living donation.

Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

XML Schema Element Similarity Measures: A Schema Matching Context

In this paper, we classify, review, and experimentally compare major methods that are exploited in the definition, adoption, and utilization of element similarity measures in the context of XML schema matching. We aim at presenting a unified view which is useful when developing a new element similarity measure, when implementing an XML schema matching component, when using an XML schema matching system, and when comparing XML schema matching systems.

Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet

Similarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527–529) using a stream function of the form ψ=αxf(η)+βx2g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of ψ

A survey on the relationship between trust and interest similarity in online social networks

A remarkable growth in quantity and popularity of online social networks has been observed in recent years. There is a good number of online social networks exists which have over 100 million registered users. Many of these popular social networks offer automated recommendations to their users. This automated recommendations are normally generated using collaborative filtering systems based on the past ratings or opinions of the similar users. Alternatively, trust among the users in the network also can be used to find the neighbors while making recommendations. To obtain the optimum result, there must be a positive correlation exists between trust and interest similarity. Though the positive relations between trust and interest similarity are assumed and adopted by many researchers; no survey work on real life people’s opinion to support this hypothesis is found. In this paper, we have reviewed the state-of-the-art research work on trust in online social networks and have presented the result of the survey on the relationship between trust and interest similarity. Our result supports the assumed hypothesis of positive relationship between the trust and interest similarity of the users.

Similarity metrics within a point of view

In vector space based approaches to natural language processing, similarity is commonly measured by taking the angle between two vectors representing words or documents in a semantic space. This is natural from a mathematical point of view, as the angle between unit vectors is, up to constant scaling, the only unitarily invariant metric on the unit sphere. However, similarity judgement tasks reveal that human subjects fail to produce data which satisfies the symmetry and triangle inequality requirements for a metric space. A possible conclusion, reached in particular by Tversky et al., is that some of the most basic assumptions of geometric models are unwarranted in the case of psychological similarity, a result which would impose strong limits on the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this fundamental criticism of of the applicability of vector space models of cognition. We argue that pairs of words imply a context which in turn induces a point of view, allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVV's. Different pairs of words will invoke different contexts and different POVV's. Hence the triangle inequality ceases to be a valid constraint on the angles. We test the proposal on a few triples of words and outline further research.