Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

Some Instructive Mathematical Errors

We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad categories of errors. First, we consider some significant errors made by highly-regarded mathematicians. In some cases these errors were not detected until many years after their publication. Second, we consider in some detail an error that was recently detected by the author. This error in a refereed journal led to further errors by at least one author who relied on the (incorrect) result. Finally, we mention some instructiveerrors that have been detected in the author's own published papers.

Hypercorrection in English: an intervarietal corpus-based study

This article aims to provide a fresh approach to the study of hypercorrection, the misguided application of a real or imagined rule – typically in response to prescriptive pressure – in which the speaker's attempt to be ‘correct’ leads to an ‘incorrect’ result. Instead of more familiar sources of information on hypercorrection such as attitude elicitation studies and prescriptive commentary, insights are sought from quantitative and qualitative data extracted from the 2-billion-word Global Web-based English corpus (GloWbE; Davies 2013). Five categories are investigated: case-marked pronouns, -ly and non-ly adverbs, agreement with number-transparent nouns, (extended uses of) irrealis were, and ‘hyperforeign’ noun suffixation. The nature and extent of hypercorrection in these categories, across the twenty English varieties represented in GloWbE, are investigated and discussed. Findings include a tendency for hypercorrection to be more common in American than in British English, and more prevalent in the ‘Inner Circle’ (IC) than in the ‘Outer Circle’ (OC) varieties (particularly with established constructions which have been the target of institutionalised prescriptive commentary over a long period of time).

The Southern Annular Mode in CMIP6 simulations

<p>Stratospheric ozone depletion, along with increases in long-lived greenhouse gases, is well known to cause a strengthening of the Southern Annular Mode (SAM), the leading mode of variability in the Southern Hemisphere.  I here analyze simulations contributed to CMIP6 for signatures of these two leading drivers of climate change. For the period 1957-2014, seasonally large disagreements are found between four observational references; CMIP6-derived trends are in agreement with two out of four commonly used references. Using a regression analysis applied to model simulations with and without interactive ozone chemistry, a strengthening of the SAM in summer is attributed nearly completely to ozone depletion because a further strengthening influence due to long-lived greenhouse gases is almost fully counterbalanced by a weakening influence due to stratospheric ozone increases associated with these greenhouse gas increases. Ignoring such ozone feedbacks (an approach commonly used with no-chemistry climate models) would yield comparable contributions from these two influences, an incorrect result. In winter, trends are smaller but an influence of greenhouse gas-mediated ozone feedbacks is also identified. The regression analysis furthermore yields significant differences in the attribution of SAM changes to the two influences between models with and without interactive ozone chemistry, with ozone depletion and GHG increases playing seasonally a stronger and weaker, respectively, role in the chemistry models versus the no-chemistry ones. The results suggest that adequately representing stratospheric ozone feedbacks in climate models is critical for a correct attribution of trends in the SAM.</p>

Modularity based Community Detection in Social Networks

The community detection is an interesting and highly focused area in the analysis of complex networks (CNA). It identifies closely connected clusters of nodes. In recent years, several approaches have been proposed for community detection and validation of the result. Community detection approaches that use modularity as a measure have given much weight-age by the research community. Various modularity based community detection approaches are given for different domains. The network in the real-world may be weighted, heterogeneous or dynamic. So, it is inappropriate to apply the same algorithm for all types of networks because it may generate incorrect result. Here, literature in the area of community detection and the result evaluation has been extended with an aim to identify various shortcomings. We think that the contribution of facts given in this paper can be very useful for further research.

Новый способ обработки изображений, полученных шлирен-методом с фоновым экраном

Testing of the Background Oriented Schlieren technique was performed. Нot air flow with known temperature was used as an object. It was found that the technique may give an incorrect result on objects of millimeter size. It was found that the error occurs when using standard software. Another processing method and its software implementation are proposed.

Properties of perturbations in beyond Horndeski theories

We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyze the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.

A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems

The aim of this note is to present some second-order Karush–Kuhn–Tucker necessary optimality conditions for vector optimization problems, which modify the incorrect result in ((10), Thm. 3.2).

Efficient and Secure Top-k Query Processing on Hybrid Sensed Data

The ubiquity of mobile devices equipped with various sensors has promoted the advent of a novel data sensing paradigm. Based on the traditional static sensing mode, the mobile sensing (sensor) nodes collaboratively collect data with the static sensor nodes. This large volume of hybrid sensed data is then sent to the storage nodes for flexible management and top-k query services. One crucial security issue is that the compromised storage node may falsify or drop some data during the query processing, which returns fake or incorrect result to the query users. In this paper, we propose an efficient and verifiable scheme (EVTopk) for secure top-k query processing on hybrid sensed data, which is suitable for the tiered hybrid sensing network where mobile nodes exist. The basic idea is to bind each data record, generated by static or mobile sensing nodes, with the corresponding location where it is sensed. Then some verification information is created sequentially, which is submitted along with the encrypted locations and hybrid sensed data for user’s verification. The security and efficiency of EVTopk are thoroughly analyzed in theory and evaluated in our experiments, respectively.

Empirical evaluation of directional-dependence tests

Testing of directional dependence is a method to infer causal direction that recently has attracted some attention. Previous examples by e.g. von Eye and DeShon (2012a) and extensive simulation studies by Pornprasertmanit and Little (2012) have demonstrated that under specific assumptions, directional-dependence tests can recover the true causal direction between two variables. Simulation results are important in the evaluation of any statistical method, but they are necessarily less complex than real data that come with potential irregularities (e.g. departures from linearity, presence of confounders, etc.). In this article, we evaluate the performance of directional-dependence tests using benchmark data consisting of 65 variable pairs with known causal order. We find that between 21% and 43% of all cases are correctly classified using different directional-dependence tests that rely on differences in skew, kurtosis, or a combined measure. We then examine some of the assumptions of the directional-dependence test and find that for virtually all variable pairs, some assumptions are violated. When only pairs in which assumptions are fulfilled are selected, performance of all directional-dependence tests improves. We probe whether particular features of the variable pairs impact whether a test yields a correct or incorrect result, but find no strong predictors. Our findings provide a complimentary picture to previously conducted simulation studies, and highlight the fact that directional-dependence tests are prone to causal classification errors when key assumptions are violated. Such violations are potentially common in real data.