A New Approach to Fuzzy Arithmetic

This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Examining Cognitive Processing in Children with an Arithmetic Disability

Currently there is no consensus as to the specific cognitive impairments that characterize mathematical disabilities (MD) or specific subtypes such as an arithmetic disability (AD). The present study sought to address this concern by examining cognitive processes that might undergird AD in children. The present study utilized archival data to conduct two investigations. The first investigation examined the executive functioning and working memory of children with AD. An age-matched achievement-matched design was employed to explore whether children with AD exhibit developmental lags or deficits in these cognitive domains. While children with AD did not exhibit impairments in verbal working memory or colour word inhibition, they did demonstrate impairments in shifting attention, visual-spatial working memory, and quantity inhibition. As children with AD did not perform more poorly than their younger achievement-matched peers on any of these tasks, impairments in specific areas of executive functioning and working memory appeared to reflect a developmental lag rather than a cognitive deficit. The second study examined the phonological processing performance of children with AD compared to children with comorbid disabilities in arithmetic and word recognition (AD/WRD) and to typically achieving (TA) children. Results indicated that, while children with AD did demonstrate impairments on all isolated naming speed tasks, trail making digits, and memory for digits, they did not demonstrate impairments on measures of phonological awareness, nonword repetition, serial processing speed, or serial naming speed. In contrast, children with AD/WRD demonstrated impairments on measures of phonological awareness, phonological short-term memory, isolated naming speed, serial processing speed, and the alphabet a-z task. Overall, results suggested that phonological processing impairments are more prominent in children with a WRD than children with an AD. Together, these studies further our understanding of the nature of the cognitive processes that underlie AD by focusing upon rarely used methods (i.e., age-matched achievement-matched design) and under-examined cognitive domains (i.e., phonological processing).

Differential ability and attainment in language and arithmetic of Dutch primary school pupils.

Background. In pre-school and primary education pupils differ in many abilities and competences (‘giftedness’). Yet mainstream educational practice seems rather homogeneous in providing age-based or grade-class subject matter approaches. Aims. To clarify whether pupils scoring initially at high ability level do develop and attain differently at school with respect to language and arithmetic compared with pupils displaying other initial ability levels. To investigate whether specific individual, family or educational variables co-vary with the attainment of these different types of pupils in school. Samples. Data from the large-scale PRIMA cohort study including a total of 8258 grade 2 and 4 pupils from 438 primary schools in The Netherlands. Methods. Secondary analyses were carried out to construct gain scores for both language and arithmetic proficiency and a number of behavioural, attitudinal, family and educational characteristics. The pupils were grouped into different ability categories (highly able; able; above average; average and below). Further analyses used Pearson correlations and analyses of variance both between and within ability categories. Cross-validation was done by introducing a cohort of younger pupils in pre-school and grouping both cohorts into decile groups based on initial ability in language and arithmetic. Results. Highly able pupils generally decreased in attainment in both language and arithmetic, whereas pupils in average and below average groups improved their language and arithmetic scores. Only with highly able pupils were some educational characteristics correlated with the pupils’ development in achievement, behaviour and attitudes. Conclusions. Pre-school and primary education should better match pupils’ differences in abilities and competences from their start in pre-school to improve their functioning, learning processes and outcomes. Recommendations for educational improvement strategies are presented in closing.

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity.

Recent evidence has highlighted the important role that number ordering skills play in arithmetic abilities (e.g., Lyons & Beilock, 2011). In fact, Lyons et al. (2014) demonstrated that although at the start of formal mathematics education number comparison skills are the best predictors of arithmetic performance, from around the age of 10, number ordering skills become the strongest numerical predictors of arithmetic abilities. In the current study we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was partially mediated by number ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor which included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain

This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in lambda-clam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.

Bounded Arithmetic and Randomized Computation

In this work, we develop a randomized bounded arithmetic for probabilistic computation, following the approach adopted by Buss for non-randomized computation. This work relies on a notion of representability inspired by of Buss' one, but depending on a non-standard quantitative and measurable semantic. Then, we establish that the representable functions are exactly the ones in PPT. Finally, we extend the language of our arithmetic with a measure quantifier, which is true if and only if the quantified formula's semantic has measure greater than a given threshold. This allows us to define purely logical characterizations of standard probabilistic complexity classes such as BPP, RP, co-RP and ZPP.

Rolandic Epilepsy And Dyslexia.

Although benign epilepsy with centrotemporal spikes (BECTS) is an idiopathic, age-related epilepsy syndrome with favorable outcome, recent studies have shown impairment in specific neuropsychological tests. The objective of this study was to analyze the comorbidity between dyslexia and BECTS. Thirty-one patients with clinical and electroencephalographic diagnosis of BECTS (group A) and 31 paired children (group B) underwent a language and neuropsychological assessment performed with several standardized protocols. Our findings were categorized as: a) dyslexia; b) other difficulties; c) without difficulties. Our results were compared and statistically analyzed. Our data showed that dyslexia occurred in 19.4% and other difficulties in 74.2% of our patients. This was highly significant when compared with the control group (p<0.001). Phonological awareness, writing, reading, arithmetic, and memory tests showed a statistically significant difference when comparing both groups. Our findings show significant evidence of the occurrence of dyslexia in patients with BECTS.

Audiogram Comparison Of Workers From Five Professional Categories.

Introduction. Noise is a major cause of health disorders in workers and has unique importance in the auditory analysis of people exposed to it. The purpose of this study is to evaluate the arithmetic mean of the auditory thresholds at frequencies of 3, 4, and 6 kHz of workers from five professional categories exposed to occupational noise. Methods. We propose a retrospective cross-sectional cohort study to analyze 2.140 audiograms from seven companies having five sectors of activity: one footwear company, one beverage company, two ceramics companies, two metallurgical companies, and two transport companies. Results. When we compared two categories, we noticed a significant difference only for cargo carriers in comparison to the remaining categories. In all activity sectors, the left ear presented the worst values, except for the footwear professionals (P > 0.05). We observed an association between the noise exposure time and the reduction of audiometric values for both ears. Significant differences existed for cargo carriers in relation to other groups. This evidence may be attributed to different forms of exposure. A slow and progressive deterioration appeared as the exposure time increased.

Teste de banco : adequação da altura do ergometro a estatura, para individuos a partir de 09 anos de idade, de ambosos sexos, praticantes e não praticantes de atividade fisica

Universidade Estadual de Campinas. Faculdade de Educação Física

Síndrome do X Frágil com variante de Dandy-Walker: estudo clínico das manifestações comunicativas orais e escritas

A síndrome do X Frágil é a causa mais frequente de deficiência intelectual hereditária. A variante de Dandy-Walker trata-se de uma constelação específica de achados neurorradiológicos. Este estudo relata achados da comunicação oral e escrita de um menino de 15 anos com diagnóstico clínico e molecular da síndrome do X-Frágil e achados de neuroimagem do encéfalo compatíveis com variante de Dandy-Walker. A avaliação fonoaudiológica foi realizada por meio da Observação do Comportamento Comunicativo, aplicação do ABFW - Teste de Linguagem Infantil - Fonologia, Perfil de Habilidades Fonológicas, Teste de Desempenho Escolar, Teste Illinois de Habilidades Psicolinguísticas, avaliação do sistema estomatognático e avaliação audiológica. Observou-se: alteração de linguagem oral quanto às habilidades fonológicas, semânticas, pragmáticas e morfossintáticas; déficits nas habilidades psicolinguísticas (recepção auditiva, expressão verbal, combinação de sons, memória sequencial auditiva e visual, closura auditiva, associação auditiva e visual); e alterações morfológicas e funcionais do sistema estomatognático. Na leitura verificou-se dificuldades na decodificação dos símbolos gráficos e na escrita havia omissões, aglutinações e representações múltiplas com o uso predominante de vogais e dificuldades na organização viso-espacial. Em matemática, apesar do reconhecimento numérico, não realizou operações aritméticas. Não foram observadas alterações na avaliação audiológica periférica. A constelação de sintomas comportamentais, cognitivos, linguísticos e perceptivos, previstos na síndrome do X-Frágil, somada às alterações estruturais do sistema nervoso central, pertencentes à variante de Dandy-Walker, trouxeram interferências marcantes no desenvolvimento das habilidades comunicativas, no aprendizado da leitura e escrita e na integração social do indivíduo.

Benign focal seizures of adolescence and neuropsychological findings in patients from community

RATIONALE: Benign focal seizures of adolescence (BFSA) described by Loiseau et al in 1972, is considered a rare entity, but maybe underdiagnosed. Although mild neuropsychological deficits have been reported in patients with benign epilepsies of childhood, these evaluations have not so far been described in BFSA. The aim of this study is to evaluate neuropsychological functions in BFSA with new onset seizures (<12 months). METHODS: Eight patients with BFSA (according to Loiseau et al, 1972, focal or secondarily tonic clonic generalized seizures between the ages of 10-18 yrs., normal neurologic examination, normal EEG or with mild focal abnormalities) initiated in the last 12 months were studied between July 2008 to May 2009. They were referred from the Pediatric Emergency Section of the Hospital Universitário of the University of Sao Paulo, a secondary care regionalized facility located in a district of middle-low income in Sao Paulo city, Brazil. The study was approved by the Ethics Committee of the Institution. All patients performed neurological, EEG, brain CT and neuropsychological evaluation which consisted of Raven's Special Progressive Matrices - General and Special Scale (according to different ages), Wechsler Children Intelligence Scale-WISC III with ACID Profile, Trail Making Test A/B, Stroop Test, Bender Visuo-Motor Test, Rey Complex Figure, Rey Auditory Verbal Learning Test-RAVLT, Boston Naming Test, Fluency Verbal for phonological and also conceptual patterns - FAS/Animals and Hooper Visual Organization Test. For academic achievement, we used a Brazilian test for named "Teste do Desempenho Escolar", which evaluates abilities to read, write and calculate according to school grade. RESULTS: There were 2 boys and 6 girls, with ages ranging from 10 yrs. 9 m to 14 yrs. 3 m. Most (7/8) of the patients presented one to two seizures and only three of them received antiepileptic drugs (AEDs). Six had mild EEG focal abnormalities and all had normal brain CT. All were literate, attended regular public schools and scored in a median range for IQ, and seven showed discrete higher scores for the verbal subtests. There were low scores for attention in different modalities in six patients, mainly in alternated attention as well as inhibitory subtests (Stroop test and Trail Making Test part B). Four of the latter cases who showed impairment both in alternated and inhibitory attention were not taking AEDs. Visual memory was impaired in five patients (Rey Complex Figure). Executive functions analysis showed deficits in working memory in five, mostly observed in Digits Indirect Order and Arithmetic tests (WISC III). Reading and writing skills were below the expected average for school grade in six patients according to the achievement scholar performance test utilized. One patient of this series who had the best scores in all tests was taking phenobarbital. CONCLUSIONS: Neuropsychological imbalance between normal IQ and mild dysfunctions such as in attention domain and in some executive abilities like working memory and planning, as well as difficulties in visual memory and in reading and writing, were described in this group of patients with BFSA from community. This may reflect mild higher level neurological dysfunctions in adolescence idiopathic focal seizures probably caused by an underlying dysmaturative epileptogenic process. Although academic problems often have multiple causes, a specific educational approach may be necessary in these adolescents, in order to improve their scholastic achievements, helping in this way, to decrease the stigma associated to epileptic seizures in the community.

Observations on Haemagogus janthinomys Dyar (Diptera: Culicidae) and other mosquito populations within tree holes in a gallery forest in the northwestern region of Sao Paulo state, Brazil

In 2000, an outbreak of sylvatic yellow fever possibly occurred in gallery forests of the Grande river in the Paraná basin in the northwestern region of São Paulo state. The aim of this study was to obtain information on the bionomics of Haemagogus and other mosquitoes inside tree holes in that area. Eighteen open tree holes were sampled for immature specimens. Adults were collected twice a month in the forest in Santa Albertina county from July 2000 to June 2001. The seasonal frequency of fourth instars was obtained by the Williams geometric mean (Mw), while the adult frequency was estimated either by hourly arithmetic or the Williams' means. Cole's index was applied to evaluate larval inter-specific associations. Among the ten mosquito species identified, the most abundant was Aedes terrens Walker followed by Sabethes tridentatus Cerqueira and Haemagogus janthinomys Dyar. Larval and adult abundance of these species was higher in summer than in winter. Although larval abundance of Hg. janthinomys peaked in the rainy season, correlation with rainfall was not significant. Six groups of larval associations were distinguished, one of which the most positively stable. The Hg. janthinomys and Ae. terrens association was significant, and Limatus durhamii Theobald was the species with most negative associations.

Evaluation of Cadaveric Renal Vein Lengths and Their Extension Loss with Three Types of Ligature and Section

Background and Purpose: The right kidney has been less frequently used in live donor nephrectomy, because of the shorter length of the right renal vein (RRV) that is associated with technical difficulties and higher rates of venous thrombosis. In live open donor or deceased donor transplant nephrectomy, an additional cuff of the inferior vena cava is usually removed, but this is a more difficult and risky maneuver in laparoscopic nephrectomy. For this reason, laparoscopic right nephrectomy (LRN) for renal transplantation (RT) is not frequently performed in most medical institutions. We evaluate the difference between RRV and left renal vein (LRV) lengths in cadavers, as harvested for RT by three clamping methods. Our objective was to obtain information that could clarify when LRN for RT should be encouraged or avoided with regard to conventional surgery. Materials and Methods: Ninety adult fresh unfrozen cadavers were randomly divided into three groups of 30, according to the clamping device used: Satinsky, stapler, and Hem-o-lok clip. The abdominal viscera were removed through a median xyphopubic incision, and the veins were measured on the bench. Two lateral limits were used: The renal hilum and the tangential line of the renal poles. As for medial limits, the inferior vena cava or the laparoscopic clipping device on the RRV were used on the right side, while on the LRV, the medial border of the emergence of the adrenal vein was considered. After section of the renal vein, a slight traction of the extremity was applied for the measurement. All measurements were obtained three times using a metallic millimetric ruler, and the arithmetic mean was considered. The chi-square, one-way analysis of variance, and paired t tests were used for statistical analysis. Statistical significance was accepted at P <= 0.05. Results: The groups of cadavers were homogeneous in demographic characteristics. Regardless of the clamping method and considering the useful length of the LRV, the RRV was statistically smaller. The evaluation of the vein length did not depend on the lateral limit considered. Independent of the clamping method, on both sides, the lengths after the vein section were larger than before the section, a fact attributed to traction. Use of a stapler and a single Hem-o-lok presented the same waste of vein length on the right side. On average, the RRV was 13.7% shorter than the LRV. Conclusions: With the wide acceptance of laparoscopic live donor nephrectomy, the length difference between the veins of both kidneys is an important issue, and the right kidney is therefore used less than the left, compared with conventional surgery. This article represents the first step to quantify the anatomic length of renal veins in different situations. Certainly, more imagenologic or surgical studies should be carried out before decisions can be made for better selection of patients for LRN.

Relationship Between Surface Topography and Energy Density Distribution of Er,Cr:YSGG Beam on Irradiated Dentin: An Atomic Force Microscopy Study

Objective: The aim of this study was to assess by atomic force microscopy (AFM) the effect of Er,Cr:YSGG laser application on the surface microtopography of radicular dentin. Background: Lasers have been used for various purposes in dentistry, where they are clinically effective when used in an appropriate manner. The Er, Cr: YSGG laser can be used for caries prevention when settings are below the ablation threshold. Materials and Methods: Four specimens of bovine dentin were irradiated using an Er, Cr:YSGG laser (lambda = 2.78 mu m), at a repetition rate of 20 Hz, with a 750-mu m-diameter sapphire tip and energy density of 2.8 J/cm(2) (12.5 mJ/pulse). After irradiation, surface topography was analyzed by AFM using a Si probe in tapping mode. Quantitative and qualitative information concerning the arithmetic average roughness (Ra) and power spectral density analyses were obtained from central, intermediate, and peripheral areas of laser pulses and compared with data from nonirradiated samples. Results: Dentin Ra for different areas were as follows: central, 261.26 (+/- 21.65) nm; intermediate, 83.48 (+/- 6.34) nm; peripheral, 45.8 (+/- 13.47) nm; and nonirradiated, 35.18 (+/- 2.9) nm. The central region of laser pulses presented higher ablation of intertubular dentin, with about 340-760 nm height, while intermediate, peripheral, and nonirradiated regions presented no difference in height of peritubular and interperitubular dentin. Conclusion: According to these results, we can assume that even when used at a low-energy density parameter, Er, Cr: YSGG laser can significantly alter the microtopography of radicular dentin, which is an important characteristic to be considered when laser is used for clinical applications.