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The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

In this paper, the state controllability of networked higher-dimensional linear time-invariant dynamical systems is considered, where communications are performed through one-dimensional connections. The influences on the controllability of such a networked system are investigated, which come from a combination of network topology, node-system dynamics, external control inputs and inner interactions. Particularly, necessary and sufficient conditions are presented for the controllability of the network with a general topology, as well as for some special settings such as cycles and chains, which show that the observability of the node system is necessary in general and the controllability of the node system is necessary for chains but not necessary for cycles. Moreover, two examples are constructed to illustrate that uncontrollable node systems can be assembled to a controllable networked system, while controllable node systems may lead to uncontrollable systems even for the cycle topology. This article is part of the themed issue ‘Horizons of cybernetical physics’. [ABSTRACT FROM AUTHOR]

Background: The dichotic digits test is one of the most widely used assessment tools for central auditory processing disorder. However, questions remain concerning the impact of cognitive factors on test results. Purpose: To develop the Dichotic Digits difference Test (DDdT), an assessment tool that could differentiate children with cognitive deficits from children with genuine dichotic deficits based on differential test results. The DDdT consists of four subtests: dichotic free recall (FR), dichotic directed left ear (DLE), dichotic directed right ear (DRE), and diotic. Scores for six conditions are calculated (FR left ear [LE], FR right ear [RE], and FR total, as well as DLE, DRE, and diotic). Scores for four difference measures are also calculated: dichotic advantage, right-ear advantage (REA) FR, REA directed, and attention advantage. Research Design: Experiment 1 involved development of the DDdT, including error rate analysis. Experiment 2 involved collection of normative and test-retest reliability data. Study Sample: Twenty adults (aged 25 yr 10 mo to 50 yr 7 mo, mean 36 yr 4 mo) took part in the development study; 62 normal-hearing, typically developing, primary-school children (aged 7 yr 1 mo to 11 yr 11 mo, mean 9 yr 4 mo) and 10 adults (aged 25 yr 0 mo to 51 yr 6 mo, mean 34 yr 10 mo) took part in the normative and test-retest reliability study. Data Collection and Analysis: In Experiment 1, error rate analysis was conducted on the 36 digit-pair combinations of the DDdT. Normative data collected in Experiment 2 were arcsine transformed to achieve a distribution that was closer to a normal distribution and z-scores calculated. Pearson product-moment correlations were used to determine the strength of relationships between DDdT conditions. Results: The development study revealed no significant differences in the adult population between test and retestonany DDdT condition. Error rates on 36 digit pairs ranged from 1.5% to 16.7%. The most and the least error-prone digits were removed before commencement of the normative data study, leaving 25 unique digit pairs. Average z-scores calculated from the arcsine-transformed data collected from the 62 children who took part in the normative data study revealed that FR dichotic processing (LE, RE, and total) was highly correlated with diotic processing (/"ranging from 0.5 to 0.6; p < 0.0001). Significant improvements in performance on retest occurred for the FR LE, RE, total, and diotic conditions (p ranging from 0.05 to 0.0004), the conditions that would be expected to improve with practice if the participant's response strategies are better the second time around. Conclusions: The addition of a diotic control task--that shares many response demands with the usual dichotic tasks--opens up the possibility of differentiating children who perform below expectations because of poor dichotic processing skills from those who perform poorly because of impaired attention, memory, or other cognitive abilities. The high correlation between dichotic and diotic performance suggests that factors other than dichotic performance play a substantial role in a child's ability to perform a dichotic listening task. This hypothesis is investigated further in the cognitive correlation study that follows in the companion paper (DDdT Study Part 2; Cameron et al, 2016). [ABSTRACT FROM AUTHOR]

Background: The Dichotic Digits difference Test (DDdT) was developed to investigate the relationship between dichotic processing and cognitive abilities and, through the use of differential test scores, to provide professionals with a clinical tool that could aid in differentiation of clients with genuine dichotic deficits from those where cognitive disorders affect test performance. The DDdT consists of four subtests: dichotic free recall (FR), dichotic directed left ear, dichotic directed right ear, and diotic. Scores are calculated for six conditions: FR left ear (LE), right ear (RE), and total, as well as the directed left ear, directed right ear, and diotic, and four difference measures: dichotic advantage, RE advantage FR, RE advantage directed, and attention advantage. Purpose: To investigate the role of cognitive abilities on DDdT test performance. Research Design: Correlational analysis between the various DDdT conditions and difference measures, as well as between dichotic, diotic, and cognitive factors (memory, intelligence, and attention). Study Sample: Fifty typically developing children (aged 7 yr 0 mo to 12yr 1 mo, mean = 9yr2mo) and ten children recruited from the Australian Flearing CAPD Service who were diagnosed with a memory or dichotic deficit (aged 7 yr 0 mo to 15 yr 0 mo, mean = 9 yr 5 mo) took part in the study. Data Collection and Analysis: The Pearson product moment correlations were used to determine the strength of relationships between DDdT conditions as well as relationships between scores on these conditions and performance on the various cognitive assessment tools, which included the number memory forward and reversed subtests of the Test of Auditory Processing Skills-Third Edition, IVA + Plus Continuous Performance Test, and the Test of Non-Verbal Intelligence-4 (TONI-4). A parent questionnaire (Fisher's Auditory Checklist) and a participant questionnaire (Listening Inventory for Education) were also administered. Results: Diotic performance was significantly correlated with performance on all the DDdT dichotic FR conditions (r = 0.6-0.8; p < 0.00001). Further, significant correlations were found between the FR LE, total, and diotic conditions, and the cognitive measures of attention and memory, with r ranging from 0.4 to 0.5 (p < 0.01-0.001). Right-ear performance was not significantly correlated to any cognitive measure, except for FR RE and number memory forward (r = 0.35; p = 0.006). The DDdT dichotic advantage measure was investigated in a subset of clinical children and found to aid in differentiating true dichotic from spurious results. Conclusions: As found in the DDdT normative data study that precedes in the companion paper (DDdT Study Part 1; Cameron et al, 2016), the high correlation between dichotic and diotic performances by the clinical and typically developing participants suggests that factors other than dichotic performance play a substantial role in a child's ability to perform a dichotic listening task. Indeed, 61% of the variance in FR total scores for the children in this study was accounted for by factors that do not involve the perception of dichotic stimuli. This view is supported by the correlations between measures of attention and memory and dichotic scores. This result has wide-spread implications in respect to interpretation of central auditory processing disorder test results and further investigation of the use of the DDdT in a clinical population is warranted. [ABSTRACT FROM AUTHOR]

Information is often described as a reduction of uncertainty associated with a restriction of possible choices. Despite appearing in Hartley's foundational work on information theory, there is a surprising lack of a formal treatment of this interpretation in terms of exclusions. This paper addresses the gap by providing an explicit characterisation of information in terms of probability mass exclusions. It then demonstrates that different exclusions can yield the same amount of information and discusses the insight this provides about how information is shared amongst random variables—lack of progress in this area is a key barrier preventing us from understanding how information is distributed in complex systems. The paper closes by deriving a decomposition of the mutual information which can distinguish between differing exclusions; this provides surprising insight into the nature of directed information. [ABSTRACT FROM AUTHOR]

• Directed C H functionalization is emergent as a powerful tool in organic synthesis. • Amides and thioamides are versatile directing groups for C(sp3) H activation. • Cyclometalation and amidyl radical based C(sp3) H functionalizations are reviewed. • Success stories in amide directed remote C(sp3) H functionalizations are highlighted. C H activation is gaining substantial attention from synthetic and process chemists in recent years. Regio- and stereo-selective C H functionalization particularly facilitated by carboxylic acids and derivatives as directing groups has been progressing to an extent that this transformation could be conceived as one of the steps to assemble molecules in modern retrosynthetic analysis. This digest paper covers the most recent developments in C(sp3) H functionalization using carboxylic acid derivatives such as amides or thioamides as a directing group and highlights new reaction discoveries and applications. The content of this review is organized based on the types of directing groups and the mechanism by which the C(sp3) H bond is believed to be activated. [ABSTRACT FROM AUTHOR]