Estimates of the topological degree of a class of piecewise linear maps with applications

We provide some new estimates for the topological degree of a class of continuous and piecewise linear maps based on a classical integral computation formula. We provide applications to some nonlinear problems that exhibit a local [Formula: see text] structure.

On the Recurrence Properties of Narayana’s Cows Sequence

In this paper, we consider the recurrence properties of two generalized forms of Narayana’s cows sequence. On the one hand, we study Narayana’s cows sequence at negative indices and express it as the linear combination of the sequence at positive indices. On the other hand, we study the convolved Narayana number and obtain a computation formula for it.

PTSD as a mediator of the relationship between trauma and psychotic experiences

Background Traumatic experiences are associated with a higher risk of psychotic illnesses, but little is known about potentially modifiable mechanisms underlying this relationship. This study aims to examine whether post-traumatic stress disorder (PTSD) symptoms mediate the relationship between trauma and psychotic experiences (PEs). Methods We used data from the Avon Longitudinal Study of Parents and Children to examine whether: PTSD symptoms mediate the relationships between (a) childhood trauma and adolescent PEs (study of adolescent PEs; n = 2952), and (b) childhood/adolescent trauma and PEs in early adulthood (study of adult PEs; n = 2492). We examined associations between variables using logistic regression, and mediation using the parametric g-computation formula. Results Exposure to trauma was associated with increased odds of PEs (adolescent PEs: ORadjusted 1.48, 95% CI 1.23–1.78; adult PEs: ORadjusted 1.57, 95% CI 1.25–1.98) and PTSD symptoms (adolescent PTSD: ORadjusted 1.59, 95% CI 1.31–1.93; adult PTSD: ORadjusted 1.50, 95% CI 1.36–1.65). The association between PTSD symptoms and PE was stronger in adolescence (ORadjusted 4.63, 95% CI 2.34–9.17) than in adulthood (ORadjusted 1.62, 95% CI 0.80–3.25). There was some evidence that PTSD symptoms mediated the relationship between childhood trauma and adolescent PEs (proportion mediated 14%), though evidence of mediation was weaker for adult PEs (proportion mediated 8%). Conclusions These findings are consistent with the hypothesis that PTSD symptoms partly mediate the association between trauma exposure and PEs. Targeting PTSD symptoms might help prevent the onset of psychotic outcomes.

A simple index of prediction accuracy in multiple regression analysis

Objectives Within the context of multiple regression the coefficient of determination can be converted to a probability of agreement between the actual and predicted outcomes, suitably dichotomized. Methods This probability of agreement can be used as a simple index of prediction accuracy to help capture the probability of a correct prediction in multiple regression. Results The simple index of prediction accuracy makes the multiple correlation comprehensible to statisticians and laypeople alike. Two examples are provided to demonstrate the application of the simple index. Conclusions In short, the paper introduces the simple index, its computation formula, and its theoretical affinity to the confusion matrix, binomial effect size, probit model, and tetrachoric correlation.

Privacy-Preserved Approximate Classification Based on Homomorphic Encryption

Privacy is a crucial issue for outsourcing computation, which means that clients utilize cloud infrastructure to perform online prediction without disclosing sensitive information. Homomorphic encryption (HE) is one of the promising cryptographic tools resolving privacy issue in this scenario. However, a bottleneck in application of HE is relatively high computational overhead. In this paper, we study the privacy-preserving classification problem. To this end, we propose a novel privacy-preserved approximate classification algorithm. It exploits a set of decision trees to reduce computational complexity during homomorphic evaluation computation formula, the time complexity of evaluating a polynomial is degraded from O n to O log n . As a result, for an MNIST dataset, the Micro- f 1 score of the proposed algorithm is 0 . 882 , compared with 0 . 912 of the standard method. For the Credit dataset, the algorithm achieves 0 . 601 compared with 0 . 613 of the method. These results show that our algorithm is feasible and practical in real world problems.

Fidelity-based unitary operation-induced quantum correlation for continuous-variable systems

We propose a measure of nonclassical correlation [Formula: see text] in terms of local Gaussian unitary operations based on square of the fidelity [Formula: see text] for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of [Formula: see text] for any [Formula: see text]-mode Gaussian states is presented and an estimation of [Formula: see text] for any [Formula: see text]-mode Gaussian states is given. For any [Formula: see text]-mode Gaussian states, [Formula: see text] does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing [Formula: see text] in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that [Formula: see text] is much better in detecting quantum correlations of Gaussian states.

UNIVERSITY IS ARCHITECTURE FOR THE RESEARCH EVALUATION SUPPORT

The measuring of research results can be used in different ways e.g. for assignment of research grants and afterwards for evaluation of project’s results. It can be used also for recruiting or promoting research institutions’ staff. Because of a wide usage of such measurement, the selection of appropriate measures is important. At the same time there does not exist a common view which metrics should be used in this field, moreover many existing metrics that are widely used are often misleading due to different reasons, e.g. computed from incomplete or faulty data, the metric’s computation formula may be invalid or the computation results can be interpreted wrongly. To produce a good framework for research evaluation, the mentioned problems must be solved in the best possible way by integrating data from different sources to get comprehensive view of academic institutions’ research activities and to solve data quality problems. We will present a data integration system that integrates university information system with library information system and with data that are gathered through API from Scopus and Web of Science databases. Data integration problems and data quality problems that we have faced are described and possible solutions are presented. Metrics that are defined and computed over these integrated data and their analysis possibilities are also discussed.

Flexibility Calculation of Like-U Type Flexure Hinge

A new like-U type flexure hinge structure is proposed, based on Castigliano’s second theorem and calculus theory. Taking the centrifugal angle parameters as the integration variable, and defining the intermediate parameters, it deduces the analytic computational formula for the like-U type flexure hinge flexibility. By changing the structural parameter of the flexure hinge, it is able to transform four different structure flexure hinges, and the deduced analytic computation formula can be applied to all of these four structures flexure hinges. After the twelve flexure hinges of different structures have been analyzed by applying finite-element method, it is found that the results are in good agreement with the results of analytic computation formula. Thus, the validity of the analytic computation formula is verified, realize accurate design and computation for such flexure hinges is realized, and the theoretical base for technical application of like-U type flexure hinge is provided.