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Autoimmunity as an immune defense against degenerative processes: a primary mathematical model illustrating the bright side of autoimmunity.

Self-tolerance, or the ability of the immune system to refrain from destroying the organism's own tissues, is a prerequisite for proper immune system operation. How such self-tolerance is achieved is still a subject of debate. The belief that autoimmunity poses a continuous threat to the organism was challenged by data demonstrating that autoimmunity has a protective function after traumatic injury to the central nervous system. This finding led us to suggest the 'comprehensive immunity' approach by which autoimmunity is viewed as a special case of immunity, namely as a defense mechanism that operates by fighting against the threat of potential destructive activity originated or mediated within the organism, similarly to the immune defense that operates against the threat from exogenous pathogens. We present a primary mathematical spatio-temporal model that supports this concept. The numerical solutions of this model illustrate the beneficial operation of a well-controlled immune response specific to self-antigens residing in the site of lesion. The model also explains how the response to self might be tolerated on a day-to-day basis. In addition, we demonstrate that the same autoimmune response, operating at different levels of regulation, can lead to either an autoimmune disease or a degenerative disorder. This preliminary qualitative model supports our contention that the way autoimmunity is perceived should be revised.

Animals↗

Computers in nuclear medicine: introductory concepts.

Computers play an important role in image and data processing in nuclear medicine. Applications extend from relatively simple mathematical processing of in vitro specimen assays to more sophisticated image reconstruction procedures for emission tomography. The basic concepts and terminology associated with computer applications in image and data processing in nuclear medicine are presented here.

Computers↗

A theory of drug tolerance and dependence I: a conceptual analysis.

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.

Adaptation, Physiological↗

The dynamical attainability of ESS in evolutionary games.

In this paper, the attainability of ESS of the evolutionary game among n players under the frequency-independent selection is studied by means of a mathematical model describing the dynamical development and a concept of stability (strongly determined stability). It is assumed that natural selection and small mutations cause the phenotype to change gradually in the direction of fitness increasing. It is shown that (1) the ESS solution is not always evolutionarily attainable in the evolutionary dynamics, (2) in the game where the interaction between two species is completely competitive, the Nash solution is always attainable, and (3) one of two species may attain the state of minimum fitness as a result of evolution. The attainability of ESS is also examined in two game models on the sex ratio of wasps and aphids in light of our criterion of the attainability of ESS.

Animals↗

[Considerations regarding Goldmann's rheologic equation].

PURPOSE: The aim of this paper is to verify if Goldmann's rheological concept is still valid. That is because the validity of this concept has been contested. (Beneyto P., Fernandez-Vila P.C., Perez T.M--An experimental approximation to the law of Goldmann: study of the dynamics of the aqueous humor outflow. Ann. Ophthalmol. Glaucoma, 1995, 27, 3, 160-166, Abstract in Glaucoma abstracts 1995, Vol. 6, nr. 3, 63.) MATERIAL: The authors sustained that Goldmann's equation has never been verified. On 42 normal eyes and 54 glaucomatous eyes (POAG) they determined aqueous flow by fluorophotometry, IOP by aplanotonometry and considered a value of 9mmHg as normal episcleral veins pressure. The results they obtained showed that in 47% of the cases the fluorophotometric values were with over 1microl/min higher then the calculated values using Goldmann's equation. So, they concluded that Goldmann's equation could be wrong. METHOD: There are two outflow pathways for the aqueous humor, trabecular and uveoscleral. Obviously, the uveoscleral outflow (Fu) summed with the trabecular outflow (Ftr) must be equal with the aqueous flow (FIN), and the total outflow facility (CTRU) must be the sum of the trabecular outflow facility (Ctr) and uveoscleral facility (Cu). Thereby Goldmann's equation can be written: FIN = Ftr + Fu = (Pio-Pv) * CTRU and Ftr = (Pio-Pv) * Ctr, Fu = (Pio-Pv) * Cu. With the authors' data we verified the previous equations. RESULTS: There is correspondence between clinical and mathematically deducted parameters. CONCLUSIONS: 1. Goldmann's rheological concept is still valid. 2. With proper modifications Goldmann's equation is still valid.

Algorithms↗

Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

Child↗

Mathematical modeling of lag phases in microbial growth.

This paper describes a mathematical method of the lap phases of Saccharomyces cerevisiae that incorporates the basic concepts previously presented in a two-stage deterministic model for the growth of this organism under conditions of oxygen excess with a sugar as the growth-limiting substrate. The model structure was suggested by an extensive investigation of the causes of the lap phases of S. cerevisiae which found that, in contrast to the traditionally accepted trends, the length of the lap phase was not inoculum-size dependent. This was consistent with other previously published work which suggested that a major factor in the length of the lag phases in S. cerevisiae was the need to synthesize adequate levels of glycolytic and respiratory enzymes. These suggestions were confirmed experimentally with lag-age data. Based on this conclusion a mathematical model was developed incorporating a description of the levels of glycolytic and respiratory enzymes and their effect on the growth rate and metabolism. This model was tested experimentally and the initial results indicate that many aspects of the lag phase of this organism may be described mathematically. The experimental findings further support the concept of primary regulatory control proposed by Bijkerk and Hall.

Glycolysis↗

The dimensional approach to clinical psychopharmacology: a polysemous concept.

The last decade has seen significant progress in the development and specific clinical application of selective psychotropes. The dimensional approach to clinical psychopharmacology views the behavioral targets of psychotropes as phenomena existing on a continuum and as components, in varying degrees, of most psychopathologies. The modern concept of dimension has been used in different contexts. In psychology it has a mathematical sense, whereas in biological psychiatry it is associated more with biological function. This paper reviews these two concepts and the recent models attempting to merge them into one. The heuristic value of the dimensional approach, as well as some of its pitfalls and new avenues of research, are discussed.

Adult↗

Investigating the influence of achievement on self-concept using an intra-class design and a comparison of the PASS and SDQ-1 self-concept tests.

BACKGROUND: The formation and measurement of self-concept were the foci of this research. AIMS: The study aimed to investigate the influence of achievement on academic self-concept and to compare the Perception of Ability Scale for Students (PASS, Boersma & Chapman, 1992) with the Self-Description Questionnaire-1 (SDQ-1, Marsh, 1988). SAMPLE: The participants were 479 grade 5 (mean age 126.6 months) coeducational Australian students, located in 18 schools. METHOD: An intra-class research design was used to investigate the influence of frame-of-reference on self-concept development. RESULTS: As students' academic scores rose above their class mean their self-concepts increased and as students' academic scores fell below their class mean their self-concepts decreased. Students' difference from class mean predicted their self-concept scores. This finding was consistently shown across the reading, spelling, and mathematics domains using test and teaching rating data. A comparison between the PASS and the SDQ-1 demonstrated concurrent validity across self-concept domains. CONCLUSION: The findings support the notions that the social environment is a significant agent that influences self-concept, and that teacher ratings and standardised tests of achievement and the PASS and the SDQ-1 are valid measures for self-concept research.

Achievement↗

Arithmetic education and learning disabilities in Italy.

In the first part of this article, we briefly present the context of mathematics education in Italy and its specific programs, teaching and assessment methods, use of psychological concepts, and policies in favor of pupils with difficulties. We illustrate the importance and the role of mathematics teachers' associations. In the second part, we focus more directly on the issue of arithmetic learning and learning disabilities in Italy. Despite the absence of a specific strong tradition in the field, new perspectives regarding mathematics education are evident in Italy. The preparation of new assessment tools has proceeded together with an effort toward the identification of subtypes of arithmetic learning disabilities. A basic distinction has been made between difficulties in number processing/calculation and problem-solving tasks. Within the area of calculation, a finer distinction between numerical knowledge, speed, and accuracy seems critical, but a more articulated differentiation of subcomponents relying on modern cognitive-neuropsychological models can be used also.

Child↗

Development of foamed emulsion bioreactor for air pollution control.

A new type of bioreactor for air pollution control has been developed. The new process relies on an organic-phase emulsion and actively growing pollutant-degrading microorganisms, made into a foam with the air being treated. This new reactor is referred to as a foamed emulsion bioreactor (FEBR). As there is no packing in the reactor, the FEBR is not subject to clogging. Mathematical modeling of the process and proof of concept using a laboratory prototype revealed that the foamed emulsion bioreactor greatly surpasses the performance of existing gas-phase bioreactors. Experimental results showed a toluene elimination capacity as high as 285 g(toluene) m(-3) (reactor) h(-1) with a removal efficiency of 95% at a gas residence time of 15 s and a toluene inlet concentration of 1-1.3 g x m(-3). Oxygen limited the reactor performance at toluene concentration above about 0.7-1.0 g x m(-3); consequently, performance was significantly improved when pure oxygen was added to the contaminated air. The elimination capacity increased from 204 to 408 g x m(-3) h(-1) with >77% toluene removal at toluene inlet concentrations of 2-2.2 g x m(-3). Overall, the results show that the performance of the FEBR far exceeds that of currently used bioreactors for air pollution control.

Air Pollutants↗

Relationship between EEG amplitude and subjective rating of task strain during performance of a calculating task.

With the use of a calculating work tester, a paced calculating task consisting of addition or subtraction of two 2-digit numbers was imposed for five minutes at each of eight grades of workload upon 24 healthy male students. The subject's scalp EEG was recorded for 10 s at the occipital midline (Oz) during rest and task performance, and the average amplitude was obtained for each of the five spectral bands. The subjective rating of the hardness of each task was adopted as a subjective measure of mental task strain. The logarithm of percentage of errors, the amplitudes of the alpha, beta 1, and beta 2 bands and the subjective ratings of hardness of the task increased in linear proportion to the workloads of the task. The highest correlation was found between the subjective ratings and the percentage increases of the Oz beta 2 amplitude over the resting level. It was suggested that these two measures would be useful for the measurement of mental task strain. In addition, it was judged that workloads of more than 90% of capacity induce excessive mental task strain in the subject.

Adult↗

A fast method for arranging DNA sequence fragments.

A method is described which allows efficient arrangement of DNA sequence fragments and, based on this arrangement, reconstruction of a complete DNA sequence. The concepts and algorithms used are based on the mathematical theory of graphs. The amount of human interaction required is considerably reduced compared to existing methods. An experiment with a set of 168 fragments yields a DNA sequence of about 5800 bases almost automatically.

Base Sequence↗

Number and language: how are they related?

Does the ability to develop numerical concepts depend on our ability to use language? We consider the role of the vocabulary of counting words in developing numerical concepts. We challenge the 'bootstrapping' theory which claims that children move from using something like an object-file - an attentional process for responding to small numerosities - to a truly arithmetic one as a result of their learning the counting words. We also question the interpretation of recent findings from Amazonian cultures that have very restricted number vocabularies. Our review of data and theory, along with neuroscientific evidence, imply that numerical concepts have an ontogenetic origin and a neural basis that are independent of language.

Concept Formation↗

Automatic karyotyping of metaphase cells with overlapping chromosomes.

Image analysis research aimed at analyzing images of banded, human chromosomes is described. An experimental automated karyotyping system (AKS) has been assembled. The goal of the system is to label the chromosomes from a metaphase image with minimal human intervention. The AKS is unique in that it is designed to automatically process cells containing overlapping chromosomes. It also has four novel algorithmic features: the use of cross section sequence graphs, an over-segmentation-based segmentation strategy, the use of the 'pale path' concept for banded chromosomes and the application of mathematical programming for cell-level chromosome classification in cells with overlapping chromosomes. System performance was analyzed using a variety of metaphase images exhibiting various levels of overlapping chromosomes.

Algorithms↗

The wrath of math. Deficiencies of mathematical mastery in the school child.

Mastery of mathematics involves the interactions of multiple developmental pathways. Children with mathematics disabilities often experience profound feelings of intellectual inadequacy that can erode self-esteem and academic motivation. This article delineates 16 interactive subcomponents that students who underachieve in mathematics can encounter. The article also discusses assessment and management issues for children with mathematics disabilities.

Child↗