Mathematical skills: intergenerational features and relationships with cognitive and linguistic abilities

This thesis aimed to investigate the cognitive underpinnings of math skills, with particular reference to cognitive, and linguistic markers, core mechanisms of number processing and environmental variables. In particular, the issue of intergenerational transmission of math skills has been deepened, comparing parents’ and children’s basic and formal math abilities. This pattern of relationships amongst these has been considered in two different age ranges, preschool and primary school children. In the first chapter, a general introduction on mathematical skills is offered, with a description of some seminal works up to recent studies and latest findings. The first chapter concludes with a review of studies about the influence of environmental variables. In particular, a review of studies about home numeracy and intergenerational transmission is examined. The first study analyzed the relationship between mathematical skills of children attending primary school and those of their mothers. The objective of this study was to understand the influence of mothers' math abilities on those of their children. In the second study, the relationship between parents’ and children numerical processing has been examined in a sample of preschool children. The goal was to understand how mathematical skills of parents were relevant for the development of the numerical skills of children, taking into account children’s cognitive and linguistic skills as well as the role of home numeracy. The third study had the objective of investigating whether the verbal and nonverbal cognitive skills presumed to underlie arithmetic are also related to reading. Primary school children were administered measures of reading and arithmetic to understand the relationships between these two abilities and testing for possible shared cognitive markers. Finally, in the general discussion a summary of main findings across the study is presented, together with clinical and theoretical implications.

The spatial association of numbers and mathematical symbols

The "SNARC effect" refers to the finding that people respond faster to small numbers with the left hand and to large numbers with the right hand. This effect is often explained by hypothesizing that numbers are represented from left to right in ascending order (Mental Number Line). However, the SNARC effect may not depend on quantitative information, but on other factors such as the order in which numbers are often represented from left to right in our culture. Four experiments were performed to test this hypothesis. In the first experiment, the concept of spatial association was extended to nonnumeric mathematical symbols: the minus and plus symbols. These symbols were presented as fixation points in a spatial compatibility paradigm. The results demonstrated an opposite influence of the two symbols on the target stimulus: the minus symbol tends to favor the target presented on the left, while the plus symbol the target presented on the right, demonstrating that spatial association can emerge in the absence of a numerical context. In the last three experiments, the relationship between quantity and order was evaluated using normal numbers and mirror numbers. Although mirror numbers denote quantity, they are not encountered in a left-to-right spatial organization. In Experiments 1 and 2, participants performed a magnitude classification task with mirror and normal numbers presented together (Experiment 1) or separately (Experiment 2). In Experiment 3, participants performed a new task in which quantity information processing was not required: the mirror judgment task. The results show that participants access the quantity of both normal and mirror numbers, but only the normal numbers are spatially organized from left to right. In addition, the physical similarity between the numbers, used as a predictor variable in the last three experiments, showed that the physical characteristics of numbers influenced participants' reaction times.

Mathematical methods to analyze and interpret calcium signals of astrocytes

Astrocytes are the most numerous glial cell type in the mammalian brain and permeate the entire CNS interacting with neurons, vasculature, and other glial cells. Astrocytes display intracellular calcium signals that encode information about local synaptic function, distributed network activity, and high-level cognitive functions. Several studies have investigated the calcium dynamics of astrocytes in sensory areas and have shown that these cells can encode sensory stimuli. Nevertheless, only recently the neuro-scientific community has focused its attention on the role and functions of astrocytes in associative areas such as the hippocampus. In our first study, we used the information theory formalism to show that astrocytes in the CA1 area of the hippocampus recorded with 2-photon fluorescence microscopy during spatial navigation encode spatial information that is complementary and synergistic to information encoded by nearby "place cell" neurons. In our second study, we investigated various computational aspects of applying the information theory formalism to astrocytic calcium data. For this reason, we generated realistic simulations of calcium signals in astrocytes to determine optimal hyperparameters and procedures of information measures and applied them to real astrocytic calcium imaging data. Calcium signals of astrocytes are characterized by complex spatiotemporal dynamics occurring in subcellular parcels of the astrocytic domain which makes studying these cells in 2-photon calcium imaging recordings difficult. However, current analytical tools which identify the astrocytic subcellular regions are time consuming and extensively rely on user-defined parameters. Here, we present Rapid Astrocytic calcium Spatio-Temporal Analysis (RASTA), a novel machine learning algorithm for spatiotemporal semantic segmentation of 2-photon calcium imaging recordings of astrocytes which operates without human intervention. We found that RASTA provided fast and accurate identification of astrocytic cell somata, processes, and cellular domains, extracting calcium signals from identified regions of interest across individual cells and populations of hundreds of astrocytes recorded in awake mice.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Evaluation Of Fe Uptake And Translocation In Transgenic And Non-transgenic Soybean Plants Using Enriched Stable (57)fe As A Tracer.

A tracer experiment is carried out with transgenic T (variety M 7211 RR) and non-transgenic NT (variety MSOY 8200) soybean plants to evaluate if genetic modification can influence the uptake and translocation of Fe. A chelate of EDTA with enriched stable (57)Fe is applied to the plants cultivated in vermiculite plus substrate and the (57)Fe acts as a tracer. The exposure of plants to enriched (57)Fe causes the dilution of the natural previously existing Fe in the plant compartments and then the changed Fe isotopic ratio ((57)Fe/(56)Fe) is measured using a quadrupole-based inductively coupled plasma mass spectrometer equipped with a dynamic reaction cell (DRC). Mathematical calculations based on the isotope dilution methodology allow distinguishing the natural abundance Fe from the enriched Fe (incorporated during the experiment). The NT soybean plants acquire higher amounts of Fe from natural abundance (originally present in the soil) and from enriched Fe (coming from the (57)Fe-EDTA during the experiment) than T soybean ones, demonstrating that the NT soybean plants probably absorb higher amounts of Fe, independently of the source. The percentage of newly incorporated Fe (coming from the treatment) was approximately 2.0 and 1.1% for NT and T soybean plants, respectively. A higher fraction (90.1%) of enriched Fe is translocated to upper parts, and a slightly lower fraction (3.8%) is accumulated in the stems by NT plants than by T ones (85.1%; 5.1%). Moreover, in both plants, the Fe-EDTA facilitates the transport and translocation of Fe to the leaves. The genetic modification is probably responsible for differences observed between T and NT soybean plants.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Anaerobic And Aerobic Performances In Elite Basketball Players.

THE PURPOSE OF THIS STUDY WAS TO PROPOSE A SPECIFIC LACTATE MINIMUM TEST FOR ELITE BASKETBALL PLAYERS CONSIDERING THE: Running Anaerobic Sprint Test (RAST) as a hyperlactatemia inductor, short distances (specific distance, 20 m) during progressive intensity and mathematical analysis to interpret aerobic and anaerobic variables. The basketball players were assigned to four groups: All positions (n=26), Guard (n= 7), Forward (n=11) and Center (n=8). The hyperlactatemia elevation (RAST) method consisted of 6 maximum sprints over 35 m separated by 10 s of recovery. The progressive phase of the lactate minimum test consisted of 5 stages controlled by an electronic metronome (8.0, 9.0, 10.0, 11.0 and 12.0 km/h) over a 20 m distance. The RAST variables and the lactate values were analyzed using visual and mathematical models. The intensity of the lactate minimum test, determined by a visual method, reduced in relation to polynomial fits (2nd degree) for the Small Forward positions and General groups. The Power and Fatigue Index values, determined by both methods, visual and 3rd degree polynomial, were not significantly different between the groups. In conclusion, the RAST is an excellent hyperlactatemia inductor and the progressive intensity of lactate minimum test using short distances (20 m) can be specifically used to evaluate the aerobic capacity of basketball players. In addition, no differences were observed between the visual and polynomial methods for RAST variables, but lactate minimum intensity was influenced by the method of analysis.

Supercritical Carbon Dioxide Extraction Of Capsaicinoids From Malagueta Pepper (capsicum Frutescens L.) Assisted By Ultrasound.

Extracts from malagueta pepper (Capsicum frutescens L.) were obtained using supercritical fluid extraction (SFE) assisted by ultrasound, with carbon dioxide as solvent at 15MPa and 40°C. The SFE global yield increased up to 77% when ultrasound waves were applied, and the best condition of ultrasound-assisted extraction was ultrasound power of 360W applied during 60min. Four capsaicinoids were identified in the extracts and quantified by high performance liquid chromatography. The use of ultrasonic waves did not influence significantly the capsaicinoid profiles and the phenolic content of the extracts. However, ultrasound has enhanced the SFE rate. A model based on the broken and intact cell concept was adequate to represent the extraction kinetics and estimate the mass transfer coefficients, which were increased with ultrasound. Images obtained by field emission scanning electron microscopy showed that the action of ultrasonic waves did not cause cracks on the cell wall surface. On the other hand, ultrasound promoted disturbances in the vegetable matrix, leading to the release of extractable material on the solid surface. The effects of ultrasound were more significant on SFE from larger solid particles.

Characterization Of Cumulative Joint Damage Patterns In Patients With Rheumatoid Arthritis: A Clinical, Serological, And Gene Polymorphism Perspective.

To characterize cumulative joint damage (CJD) patterns in rheumatoid arthritis (RA) and determine their associations with demographic/clinical features and HLA-DRB1 gene polymorphism. Hand and foot radiographs were obtained from 404 patients with RA. CJD patterns were determined by 3 derivations from Sharp/van der Heijde scores, obtained by the mathematical division of scores for hands/feet (Sharp-h/f score), fingers/wrists (Sharp-f/w score), and erosion/space narrowing (Sharp-e/sn score), respectively. DNA and serum were obtained for determination of HLA-DRB1 polymorphism, rheumatoid factor (RF), and anticitrullinated protein antibodies (ACPA). Patients with wrist-dominant CJD pattern were more likely to have severe RA than those with finger-dominant pattern (68.4% vs 46.0%; p = 0.036) as were those with foot-dominant vs hand-dominant CJD pattern (76.5% vs 56.4%; p = 0.044). HLA-DRB1 shared epitope (SE) alleles were associated with erosion-dominant CJD pattern (p = 0.021). Patients with erosion-dominant CJD pattern had higher levels of RF and ACPA than those with space-narrowing-dominant CJD pattern (median RF 71.35 U/ml vs 22.05 U/ml, respectively; p = 0.003; median ACPA 187.9 U/ml vs 143.2 U/ml, respectively; p < 0.001). The majority of triple-positive patients (SE+, RF+, ACPA+) had erosion-dominant CJD pattern (62.3%) while the majority of triple-negative patients (SE-, FR-, ACPA-) had space narrowing-dominant CJD pattern (75%; p = 0.017). ACPA was associated with HLA-DRB1 SE alleles (p < 0.05). Patients with foot-dominant CJD pattern were taller than those with hand-dominant CJD pattern (p = 0.002); those with erosion-dominant CJD pattern had higher weight and body mass index than those with space narrowing-dominant CJD pattern (p = 0.014, p = 0.001). CJD patterns were associated with disease severity, HLA-DRB1 SE status, presence and titer of ACPA and RF, and morphometric features.

Diagramas de Ellingham e de Van't Hoff: algumas considerações

The main subject of this article is to show the parallelism betwen the Ellingham and Van't Hoff diagrams. The first one is a graphic representation of the changes in the standard Gibbs free energy (deltarGtheta) as a function of T and was introduced by Ellingham in 1944, in order to study metallurgic processes involving oxides and sulphides. On the other hand, the Van't Hoff diagram is a representation of the function ln K versus (1/T). The equivalence between both diagrams is easily demonstrated, making simple mathematical manipulations. In order to show the parallelism between both diagrams, they are presented briefly and two examples are discussed. The comparison of the both diagrams surely will be helpful to students and teachers in their learning and teaching activities, and will certainly enrich important aspects of chemical thermodynamics.

Condutividade e difusividade térmica do figo (Ficus carica L.) Roxo de Valinhos

The post harvest cooling and/or freezing processes for horticultural products have been carried out with the objective of removing the heat from these products, allowing them a bigger period of conservation. Therefore, the knowledge of the physical properties that involve heat transference in the fig fruit Roxo de Valinhos is useful for calculating projects and systems of food engineering in general, as well as, for using in equations of thermodynamic mathematical models. The values of conductivity and thermal diffusivity of the whole fig fruit-rami index were determined, and from these values it was determined the value of the specific heat. For these determination it was used the transient method of the Line Heat Source. The results shown that the fig fruit has a thermal conductivity of 0.52 W m-1°C, thermal diffusivity of 1.56 x 10-7 m² s-1, pulp density of 815.6 kg m-3 and specific heat of 4.07 kJ kg-1 °C.

Modelagem matemática e simulação numérica do resfriamento rápido de morango com ar forçado

This work approaches the forced air cooling of strawberry by numerical simulation. The mathematical model that was used describes the process of heat transfer, based on the Fourier's law, in spherical coordinates and simplified to describe the one-dimensional process. For the resolution of the equation expressed for the mathematical model, an algorithm was developed based on the explicit scheme of the numerical method of the finite differences and implemented in the scientific computation program MATLAB 6.1. The validation of the mathematical model was made by the comparison between theoretical and experimental data, where strawberries had been cooled with forced air. The results showed to be possible the determination of the convective heat transfer coefficient by fitting the numerical and experimental data. The methodology of the numerical simulations was showed like a promising tool in the support of the decision to use or to develop equipment in the area of cooling process with forced air of spherical fruits.

Identificação eletrônica para avaliação do comportamento dos suínos na fase de gestação

The efficiency of swine production performance depends on the herd administration, such as good nutrition, sanitary control, facilities and appropriate environmental conditions. The concept of this production model is directly related with the reduction of selective losses and the process control. Each production segment is controlled to reach the optimization in the system totality, it is necessary to apply animals handling concepts, environmental control implementation, diseases control, nutrition control, information concerning in guaranteeing the animal welfare and individual identification. The present work presents as objective the development of the mathematical model to evaluate interactions among the internal atmosphere of the installation and the thermal animals preference, in the expectation of detecting a relationship among the frequency access to the drinking fountain and the atmosphere conditions - temperature, black globe temperature and relative humidity, using as tool the electronic identification. The results obtained by the mathematical model, allowed to conclude accurately the evaluation of the swine thermal preference correlating with the climatic variables in the pregnancy stage.

Projeto de um cortador de base para colhedora de cana-de-açúcar utilizando otimização matemática

A base-cutter represented for a mechanism of four bars, was developed using the Autocad program. The normal force of reaction of the profile in the contact point was determined through the dynamic analysis. The equations of dynamic balance were based on the laws of Newton-Euler. The linkage was subject to an optimization technique that considered the peak value of soil reaction force as the objective function to be minimized while the link lengths and the spring constant varied through a specified range. The Algorithm of Sequential Quadratic Programming-SQP was implemented of the program computational Matlab. Results were very encouraging; the maximum value of the normal reaction force was reduced from 4,250.33 to 237.13 N, making the floating process much less disturbing to the soil and the sugarcane rate. Later, others variables had been incorporated the mechanism optimized and new otimization process was implemented .