The entanglement of a pure bipartite state is uniquely measured by the von-Neumann entropy of its reduced density matrices. Though it cannot specify all the non-local characteristics of pure entangled states. It was proven that for every possible value of entanglement of a bipartite system, there exists an infinite number of equally entangled pure states, not comparable (satisfies Nielsen’s criteria) to each other. In this work, we investigate other **correlation** **measures** of pure bipartite states that are able to differentiate the quantum correlations of the states with entropy of entanglement. In Schmidt rank 3, we consider the whole set of states having same entanglement and compare how minutely such states can be distinguished by other **correlation** **measures**. Then for different values of entanglement we compare the sets of states belonging to the same entanglement and also investigate the graphs of different **correlation** **measures**. We extend our search to Schmidt rank 4 and 5 also.

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In Fig.1 the **correlation** spectra for two pairs of stocks is shown computed with each of the three **correlation** **measures**. In both cases the Fourier correla- tion method provides a much smoother spectrum than the other two methods (Pearson and Covolatility Adjusted) which use interpolation. The ”Epps ef- fect“ 1 can also be observed in the two plots and displays one of the properties

The estimation of intra-day correlations over short periods of time (eg. a month) is of high practical value for day trading and hedging purposes. In fact, such estimates are more sensitive to short timescale economic changes than **correlation** **measures** obtained from averaging over several months. Thus, we choose to investigate a month of tick-by-tick data aiming to compare the quality of the information that can be derived by applying each of the two methods on lim- ited statistics. The Fourier estimates reproduce the structural changes on ﬁltered **correlation** matrices observed in previous studies [8, 9, 10, 11, 12, 13, 14, 15, 16] with much larger data sets. Moreover, we show that the Fourier estimates are suﬃciently accurate to reveal further structural changes in the full, unﬁltered, **correlation** matrices.

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The plots in Figure 5 exemplify four diﬀerent types of **correlation** evolution with time scale. Plots a) and b) show the **correlation** structure of two intra-sector pairs of stocks. The corre- lation between Intel and Cisco (highly liquid, β intc =1, β csco =1.2) reaches a stable level after approximately 15 minutes whilst for Heinz and Campbell (lower liquidity, β hnz =14, β cpb =23) it takes about 2 hours to stabilize. Plots c) and d) are inter-sector examples. In Figure 5.c, on a time scale smaller than an hour Lucent (high liquidity, β lu =3.7) and Halliburton (average liquidity, β hal =11.3) have little **correlation** and this turns into anti-**correlation** when the time scale increases. Boeing (β ba =8.4) and Xerox (β xrx =15.9) in Figure 5.d start as poorly corre- lated on a 3 minutes time scale, the **correlation** coeﬃcient then rises steadily to 0.55 on a 2 hour time scale and falls back to a less signiﬁcant level (0.2) at 4 hours.

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Permanent repository link: http://openaccess.city.ac.uk/14601/ Link to published version: http://dx.doi.org/10.1016/j.physa.2004.06.127 Copyright and reuse: City Research Online aims to [r]

The paper proposes two (2) **measures** for correlating fractal random variables. The **correlation** **measures** depict the extent to which roughness in one variable induces roughness to the other. The first measure, fractal **correlation**, directly uses the usual moment-based product moment **correlation** of the fractal **measures** λ x and λ y at each point (x i ,y i ). Each of the fractal

Pearson **correlation** **measures** the relationship between the performance which is return on asset (ROA) and the internal and external factors such as current ratio, quick ratio, average -collection period, debt to income, operational ratio, operating margin, index, gross domestic product (GDP), inflation and exchange rate. The positive value of the result will representative the positive relationship and reversely.

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Background: Impaired insulin sensitivity is a key abnormality underlying the development of type 2 diabetes. Measuring insulin sensitivity is therefore of importance in identifying individuals at risk of developing diabetes and for the evaluation of diabetes-focused interventions. A number of **measures** have been proposed for this purpose. Among these the hyperinsulinemic euglycemic clamp (HEC) is considered the gold standard. However, as the HEC is a costly, time consuming and invasive method requiring trained staff, there is a need for simpler so called surrogate **measures**. Main message: A frequently used approach to evaluate surrogate **measures** is through **correlation** with the HEC. We discuss limitations with this method. We suggest other aspects to take into consideration, such as repeatability, reproducibility, systematic biases and discrimination ability. In addition, we focus on three frequently used surrogate **measures**. We argue that they are one-to-one transformations of each other, and therefore question the benefits of further comparison between them. They give the same results in all rank-based methods, for instance Spearman correlations, Mann-Whitney tests and receiver operating characteristic (ROC) analysis.

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The results obtained from the BIO-ENV analysis showed that, unlike similar types of habitat, the type of sediment was not found to exert an important role on the meiofaunal community (Castel et al. 1990; Castel 1992; Gourbault and Renaud-Mornant 1990). Spear- man’s tests showed a negative **correlation** between the silt-clay percentage and the density of all meiobenthic organisms (ρ=–0.51, P<<0.01) and between the same variable and the percentage of nematodes ( ρ =–0.71, P<<0.01). Additionally, the percentage of copepods was positively correlated with the silt-clay percentage ( ρ =0.56, P<<0.01). The above indicate that although the type of sediment may be correlated with the density values, other environmental variables produce strong gradients across the lagoon, limiting the distribution of the individuals and determining the pattern of the meio- benthic community. However, the biogenic processes and microturbating factors may be underestimated by analysing purely geological sedimentary differences (Watling 1991); thus it is likely that detritus, bacteria and water-sediment chemistry reflect more accurately the sedimentary habitat of Gialova meiofauna. In par- ticular, the stable, flocculent organic sediments of la- goons will be of more importance to the animals dwell- ing in them than the gross mineral particles commonly tested by sediment analysis.

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More generally, existing standalone (or tradi- tional) text similarity **measures** rely on the inter- sections between token sets and/or text sizes and frequency, including **measures** such as the Co- sine similarity, Euclidean distance, Levenshtein (Sankoff and Kruskal, 1983), Jaccard (Jain and Dubes, 1988) and Jaro (Jaro, 1989). The se- quential nature of natural language is taken into account mostly through word n-grams and skip- grams which capture distinct slices of the analysed texts but do not preserve the order in which they appear.

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Spearman's Correlation between Assessment of Capacity of Everyday Decision Making ACED – Money Management and Measures of CR LEQ for All Participants N=29.. Spearman's Correlation betwee[r]

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Although CSF volume and percentage of brain parenchymal volume both showed a strong correla- tion with T2 lesion volume (positive and negative, respectively), they showed a stronger **correlation** with peak height of the histogram. Loss of parenchymal volume in MS most likely reflects a combination of pathologic processes, including demyelination, gliosis, and neuronal loss. The net effect of these pathologic processes results in loss of brain parenchyma. FSE T2-weighted MR imaging is sensitive only to the areas of macroscopic disease. There is evidence to suggest that magnetization transfer imaging can detect mac- roscopic and microscopic disease as well as neuronal loss (12–15, 46). The increased sensitivity of magne- tization transfer imaging as compared with FSE T2- weighted imaging results in superior **correlation** of the peak height of the MTR histogram with global volume loss. This finding supports the hypothesis that the MTR histogram may offer a better quantification of total disease burden in patients with MS than provided by volume measurements on FSE T2- weighted images.

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Positive outcomes from infant cardiac arrest depend on, in part, the effective delivery of resuscitation techniques, including quality infant cardiopulmonary resuscitation (iCPR), which is crucial for perfusion of vital organs [11, 12]. Quality iCPR is dependent on achieving four inter- nationally recommended quality **measures**: chest com- pression depth; chest compression rate; complete chest recoil; and appropriate compression duty cycle, (the por- tion of time spent in compression) [13–15]. However, it has been demonstrated that the quality of chest compres- sions during paediatric CPR (including infant) delivered by lay persons, basic life support (BLS) and highly-trained- rescuers in both simulated and real paediatric cardiac ar- rest events is often performed inadequately, incorrectly, inconsistently or with excessive interruption [15–18].

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Adrenoleukodystrophy (ALD) is a cerebral degenerative disease that affects predominantly the white matter (1–5). Boys with childhood- onset cerebral ALD (COCALD) have a mean age of onset of 7 years, with demyelination and deterioration progressing rapidly to death over an average of 3 to 4 years. No biochemical test distinguishes between these forms or reflects the degree of deterioration (1, 6). Abnormalities on magnetic resonance (MR) images correlate well with neuropsychological **measures** (7). However, detection of objective changes on MR

[ill attempted to correlate a physical image quality measure (i.e. the noise of the screen-film radiographs) with a subjective measure (i.e. the visual detectability of simulated lung no[r]

Different **measures** have been developed to measure the similarity between Wikipedia articles in different languages (see Section 2) which can be used to filter out non-similar documents. However, little past work has analysed whether or not these methods correlate with human assessments across multiple languages. In this work we have collected manual judgments on Wikipedia articles in various language pairs, which include 7 under-resourced languages. We analyse the judgments gathered for inter-assessor agreement and compare the judgments with two **measures** of document-level similarity based on using language dependent and language-independent features. Being able to reliably measure the similarity of Wikipedia articles across languages would assist in using Wikipedia as a source of comparable data.

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Putnam’s analysis remains ultimately at the level of the quantifying individual behaviour. From his perspective he is unable to provide meaningful **measures** of cohesion in society at large, let alone to provide meaningful explanations of changes over time. Where there should be analysis of cultural and ideological shifts, of changes in economic and social structures, and of new institutional arrangements, there are simply extrapolations made from individual associations. True to his liberal, individualist tradition, he overlooks the importance of role of the state and institutions in providing the structural basis for social cohesion (Skocpol, 1996), remaining largely silent on the effects on social relations of two decades neo-liberal government, with rising consumerism and individualism and the gradual dismantling of the welfare apparatus. Despite his own empirical demonstrations of the clear cross-regional correlations between social capital and income equality, he fails to explore the connections in America between declining social capital and rising inequality and social conflict. In Putnam’s hands, social capital provides a distinctly romantic view of society devoid of power, politics and conflict (Edward and Foley, 1998; Skocpol, 1996).

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In this section, we investigate constrained optimization problems based on finding a maxi- mally informative **correlation** matrix close to a target matrix. We cover two types of cases; those optimizations parameterized in terms of a **correlation** matrix, and those in terms of a Euclidean embedding. In the latter case, we derive the analytic forms of cost functions for some **measures** of informativeness that can be applied directly to an embedding without requiring the explicit calculation of a **correlation** matrix. In particular, we show that when applied to an embedding, the Bures-based cost function is convex and corresponds to a novel matrix norm, which is a combination of trace seminorms on orthogonal subspaces. As this norm is non-differentiable, we describe its proximal operator, which requires the definition of the proximal operator for the squared trace norm. Using the Bures-based measure of informativeness as a cost function, we detail the optimization problem of finding a maxi- mally informative **correlation** matrix nearby a target matrix, where nearness is assessed via the Euclidean distance between the embeddings. Although constraining the embedding to ensure it corresponds to a **correlation** matrix is non-convex, we relax this constraint to yield a completely convex optimization problem, the solutions of which can satisfy the original constraint. We propose an alternating direction method of multiplier (ADMM) algorithm that uses the proximal operator for the Bures-based cost function to solve this problem. 4.1 Maximally Informative **Correlation** Matrices

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Measures of correlation and computer algebra Halkos, George and Tsilika, Kyriaki Department of Economics, University of Thessaly.[r]

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Co-citation forms a relational document network. Co-citation-based **measures** are found to be effective in retrieving relevant documents. However, they are far from ideal and need further enhancements. Co-opinion concept was proposed and tested in previous research and found to be effective in retrieving relevant documents. The present study endeavors to explore the **correlation** between opinion (dis)similarity **measures** and the traditional co-citation-based ones including Citation Proximity Index (CPI), co-citedness and co-citation context similarity. The results show significant, though weak to medium, correlations between the variables. The correlations are direct for co-opinion measure, while being inverse for the opinion distance. Accordingly, the two groups of **measures** are revealed to represent some similar aspects of the document relation. Moreover, the weakness of the correlations implies that there are different dimensions represented by the two groups.

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