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PubMed1995

Indicating acts during counting by a chimpanzee (Pan troglodytes).

A chimpanzee (Pan troglodytes) experienced in counting arrays of 0-7 items and trained for comprehension of number symbols, spontaneously displayed a variety of indicating acts (e.g., pointing, touching, and rearranging items) during counting. Twenty-five sessions were videotaped, and all trials were evaluated for the relations among number of items presented, number of indicating acts displayed, and the Arabic number selected to represent the array. Significant correlations included the relations between number of items and the cardinal number selected by the animal, between the number of items and indicating acts displayed by the chimpanzee, and between the number of indicating acts and the numeral selected. These data suggest that the use of indicating acts by this animal may have functional significance and serves as an organizing schema, comparable to similar behaviors observed in children in the early stages of learning to count.

Animals↗
PubMed2005

Counting on neurons: the neurobiology of numerical competence.

Numbers are an integral part of our everyday life - we use them to quantify, rank and identify objects. The verbal number concept allows humans to develop superior mathematical and logic skills that define technologically advanced cultures. However, basic numerical competence is rooted in biological primitives that can be explored in animals, infants and human adults alike. We are now beginning to unravel its anatomical basis and neuronal mechanisms on many levels, down to its single neuron correlate. Neural representations of numerical information can engage extensive cerebral networks, but the posterior parietal cortex and the prefrontal cortex are the key structures in primates.

Animals↗
PubMed2002

Multistage carcinogenesis and radiation.

We will briefly review the concept of multistage carcinogenesis and the mathematical models built on this idea, including a class of models recently developed to describe the pathogenesis of colon cancer. The simplest model that explicitly accounts for cell proliferation kinetics is the two-stage clonal expansion model. It has been applied to a number of experimental and epidemiological data sets and has generated several thought-provoking hypotheses, especially as they relate to the role of promotion in radiation-induced carcinogenesis. The model generates hazard functions (used to estimate age-specific cancer incidence) that are not always intuitive because of the stochastic nature of the clonal expansion process involved. However, the model does make specific predictions depending on whether initiation, promotion or malignant conversion is affected by a carcinogen. A recent analysis of a large cohort of radiation workers exemplifies this behaviour.

Animals↗
PubMed1973

Mathematical Analysis of Plant Growth zea mays Primary Roots.

A new mathematical treatment is given to the concept of relative elemental growth rate, the limiting value at a point of the relative rate of tissue growth. The new point of view requires consideration of a coordinate system in which each point on the root surface is defined by its initial position on the root axis. The resultant technique of plotting growth parameters provides the ability to distinguish between waves of growth propagating toward the root tip away from cells and waves which tend to propagate along with the cells. Thus it is possible to model the plant growth-regulatory process in terms of auxin and other regulators, considering both cell-associated maxima of regulator concentration and maxima which propagate through the tissue.

Journal Article↗
PubMed2006

Toddler subtraction with large sets: further evidence for an analog-magnitude representation of number.

Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies were presented and then covered. The experimenter visibly subtracted cookies from the hidden sets, and the children were asked to choose which of the resulting sets had more. In Experiment 1, performance was above chance when high proportions of objects (3 versus 6) were subtracted from large sets (of 9) and for the subset of older participants (older than 3 years, 5 months; n = 15), performance was also above chance when high proportions (10 versus 20) were subtracted from the very large sets (of 30). In Experiment 2, which was conducted exclusively with older 3-year-olds and incorporated an important methodological control, the pattern of results for the subtraction tasks was replicated. In both experiments, success on the tasks was not related to counting ability. The results of these experiments support the hypothesis that young children have access to an analog-magnitude system for representing large approximate quantities, as performance on these subtraction tasks showed a Weber's Law signature, and was independent of conventional number knowledge.

Child Development↗
PubMed1995

A mathematical model for shear-induced hemolysis.

The time-varying history of stress exposure within a rotary blood pump makes it difficult to arrive at a quantifiable design criterion for predicting cell traumatization. Constant stress experiments have revealed that there is a threshold stress level above which damage to blood cells occurs depending upon the time of exposure. The shear stress history experienced by cells within a rotary blood pump, however, is highly unsteady. In order to better predict cell trauma under these realistic conditions, a mathematical damage model based on a concept of "damage accumulation" has been developed. This model is evaluated within the context of red cell trauma. Experimental results support the hypothesis that the rate of damage accumulation increases nonlinearly with the stress level as well as the age of the cell.

Erythrocytes↗
PubMed1986

Quantitative assessment of the two-component model of intestinal circulation.

Recently a two-component model of the intestinal circulation was proposed to explain the effects of vasodilators on intestinal oxygenation. This model assumes that the intestine is composed of two regions: one region in which oxygen uptake is blood flow independent (well perfused and normoxic) and a second region in which oxygen uptake is blood flow dependent (under-perfused and hypoxic). The model predicts that total intestinal oxygen uptake is increased by a vasodilator only if the blood flow-dependent region is affected. We used a systems analysis approach to predict the various boundary conditions that must be imposed on the two-component model for it to simulate experimental observations. The mathematical model was based on current concepts and available data regarding intestinal hemodynamics and oxygen exchange. The model simulations predict that 30-70% of the intestine must be hypoxic (regions where oxygen uptake is blood flow dependent) for the two-component hypothesis to adequately explain published observations. Since the existence of such an extensive hypoxic region seems unlikely for the normal intestine, the predictive value of the two-component hypothesis may be of limited value for describing the effects of vasodilators on oxygen uptake in the normal intestine. However, the two-component model may be useful in predicting the effects of vasodilators on intestinal oxygen uptake in the ischemic intestine.

Blood Flow Velocity↗
PubMed1989

Number concepts of preschool children.

Using the format of the tin game described by Hughes in 1986, this study investigated the extent and variety of written representations of small numbers of objects used spontaneously and meaningfully by a sample of 39 preschool children.

Child Development↗
PubMed2004

The swimsuit becomes us all: ethnicity, gender, and vulnerability to self-objectification.

Self-objectification theory posits and past research has found that Caucasian women's body image is negatively affected by a stigma of obesity and sociocultural norm of thinness that leads women to self-focus from a critical external perspective. However, research in this area is limited by its methodology and the restricted demographic composition of its study participants. The current study tested 176 men and 224 women of Caucasian, African American, Hispanic, and Asian American descent in a situation that induced a state of self-objectification (e.g., wearing a one-piece Speedo bathing suit) or that served as a control condition (e.g., wearing a sweater). Contrary to previous research, when put in a self-objectifying situation, men and women of every ethnicity experienced negative outcomes (e.g., lower math performance) that parallel those previously found for Caucasian women.

Adult↗
PubMed1994

Chaos theory and some nursing considerations.

The alleged synthesis of nursing and public health has not produced the expected community-as-client emphasis. Public health is characterized as disease-focused, with masculine domination, using a causal model. The explanatory model of chaos challenges nurses to reexamine nursing's theoretical base by questioning assumptions associated with linear thinking. The selected chaotic concepts of aperiodicity, attractors, sensitive dependence on initial conditions, phase space, and fractals are discussed here. Each concept's connection to physics and mathematics is cited and considerations for nursing science are outlined. Conclusions include redefining health, nursing, and community in chaotic terms and renaming nursing practice, which has this aperiodic and holistic paradigm, as ecologic health nursing.

Community Health Nursing↗
PubMed2005

The quantitation of buffering action II. Applications of the formal & general approach.

BACKGROUND: The paradigm of "buffering" originated in acid-base physiology, but was subsequently extended to other fields and is now used for a wide and diverse set of phenomena. In the preceding article, we have presented a formal and general approach to the quantitation of buffering action. Here, we use that buffering concept for a systematic treatment of selected classical and other buffering phenomena. RESULTS: H+ buffering by weak acids and "self-buffering" in pure water represent "conservative buffered systems" whose analysis reveals buffering properties that contrast in important aspects from classical textbook descriptions. The buffering of organ perfusion in the face of variable perfusion pressure (also termed "autoregulation") can be treated in terms of "non-conservative buffered systems", the general form of the concept. For the analysis of cytoplasmic Ca++ concentration transients (also termed "muffling"), we develop a related unit that is able to faithfully reflect the time-dependent quantitative aspect of buffering during the pre-steady state period. Steady-state buffering is shown to represent the limiting case of time-dependent muffling, namely for infinitely long time intervals and infinitely small perturbations. Finally, our buffering concept provides a stringent definition of "buffering" on the level of systems and control theory, resulting in four absolute ratio scales for control performance that are suited to measure disturbance rejection and setpoint tracking, and both their static and dynamic aspects. CONCLUSION: Our concept of buffering provides a powerful mathematical tool for the quantitation of buffering action in all its appearances.

Animals↗
PubMed2000

Use of number by crows: investigation by matching and oddity learning.

Hooded crows were trained in two-alternative simultaneous matching and oddity tasks with stimulus sets of three different categories: color (black and white), shape (Arabic Numerals 1 and 2, which were used as visual shapes only), and number of elements (arrays of one and two items). These three sets were used for training successively and repeatedly; the stimulus set was changed to the next one after the criterion (80% correct or better over 30 consecutive trials) was reached with the previous one. Training was continued until the criterion could be reached within the first 30 to 50 trials for each of the three training sets. During partial transfer tests, familiar stimuli (numerals and arrays in the range from 1 to 2) were paired with novel ones (numerals and arrays in the range from 3 to 4). At the final stage of testing only novel stimuli were presented (numerals and arrays in the range from 5 to 8). Four of 6 birds were able to transfer in these tests, and their performance was significantly above chance. Moreover, performance of the birds on the array stimuli did not differ from their performance on the color or shape stimuli. They were capable of recognizing the number of elements in arrays and comparing the stimuli by this attribute. It was concluded that crows were able to apply the matching (or oddity) concept to stimuli of numerical category.

Animals↗
PubMed1977

Concept of visual sensation.

A direct-realist account of visual sensation is outlined. The explanatory notion of elements in visual sensation (atomic sensations) is reinterpreted, and the suggested interpretation is formally justified by constructing a Boolean algebra for visual sensations. The related notion of sensory levels (visual field vs visual world) is discussed.

Color Perception↗