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Results for “Probability Theory”

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At least 433 records · Page 24Linked to original sources
PubMed1981

Deviations from Michaelis-Menten kinetics. Computation of the probabilities of obtaining complex curves from simple kinetic schemes.

1. It is possible to calculate the intrinsic probability associated with any curve shape that is allowed for rational functions of given degree when the coefficients are independent or dependent random variables with known probability distributions. 2. Computations of such probabilities are described when the coefficients of the rational function are generated according to several probability distribution functions and in particular when rate constants are varied randomly for several simple model mechanisms. 3. It is concluded that each molecular mechanism is associated with a specific set of curve-shape probabilities, and this could be of value in discriminating between model mechanisms. 4. It is shown how a computer program can be used to estimate the probability of new complexities such as extra inflexions and turning points as the degree of rate equations increases. 5. The probability of 3 : 3 rate equations giving 2 : 2 curve shapes is discussed for unrestricted coefficients and also for the substrate-modifier mechanisms. 6. The probability associated with the numerical values of coefficients in rate equations is also calculated for this mechanism, and a possible method for determining the approximate magnitude of product-release steps is given. 7. The computer programs used in the computations have been deposited as Supplement SUP 50113 (21 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem, J. (1978) 169, 5.

Binding Sites↗
PubMed1977

An extension of a familiar index of observer agreement.

A popular index of observer agreement is a/(a + d) in which a and d represent the number of agreements and disagreements. This article provides a rationale for the extension of the index to the multiple-observer case, a comparison with another frequently used index, a description of situations for which the index is appropriate, and an analysis of factors related to interpreting the magnitude of the index.

Attention↗
PubMed1999

Morphology, morphometry and probability mapping of the pars opercularis of the inferior frontal gyrus: an in vivo MRI analysis.

The pars opercularis occupies the posterior part of the inferior frontal gyrus. Electrical stimulation or damage of this region interferes with language production. The present study investigated the morphology and morphometry of the pars opercularis in 108 normal adult human cerebral hemispheres by means of magnetic resonance imaging. The brain images were transformed into a standardized proportional steoreotaxic space (i.e. that of Talairach and Tournoux) in order to minimize interindividual brain size variability. There was considerable variability in the shape and location of the pars opercularis across brains and between cerebral hemispheres. There was no significant difference or correlation between left and right hemisphere grey matter volumes. There was also no significant difference between sex and side of asymmetry of the pars opercularis. A probability map of the pars opercularis was constructed by averaging its location and extent in each individual normalized brain into Talairach space to aid in localization of activity changes in functional neuroimaging studies.

Adult↗
PubMed1979

Analysis of probability as an aid in the clinical diagnosis of coronary-artery disease.

The diagnosis of coronary-artery disease has become increasingly complex. Many different results, obtained from tests with substantial imperfections, must be integrated into a diagnostic conclusion about the probability of disease in a given patient. To approach this problem in a practical manner, we reviewed the literature to estimate the pretest likelihood of disease (defined by age, sex and symptoms) and the sensitivity and specificity of four diagnostic tests: stress electrocardiography, cardiokymography, thallium scintigraphy and cardiac fluoroscopy. With this information, test results can be analyzed by use of Bayes' theorem of conditional probability. This approach has several advantages. It pools the diagnostic experience of many physicians ans integrates fundamental pretest clinical descriptors with many varying test results to summarize reproducibly and meaningfully the probability of angiographic coronary-artery disease. This approach also aids, but does not replace, the physician's judgment and may assit in decisions on cost effectiveness of tests.

Adult↗
PubMed2006

High resolution vacuum ultraviolet emission spectrum of D(2) from 78 to 103 nm: The D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) band systems.

The emission spectrum of the D(2) molecule has been studied at high resolution in the vacuum ultraviolet region 78.5-102.7 nm. A detailed analysis of the two D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) electronic band systems is reported. New and improved values of the level energies of the two upper states have been derived with the help of the program IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656 (1993)], originally developed for atomic spectral analysis. A detailed comparison is made between the observed energy levels and solutions of coupled equations using the newest ab initio potentials by Wolniewicz and co-workers [J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); J. Mol. Spectros. 212, 208 (2002); 220, 45 (2003)] taking into account the nonadiabatic coupling terms for the D (1)Pi(u) state with the lowest electronic states B (1)Sigma(u) (+), C (1)Pi(u), and B(') (1)Sigma(u) (+). A satisfactory agreement has been found for most of the level energies belonging to the D and D(') states. The remaining differences between observation and theory are probably due to nonadiabatic couplings with other higher electronic states which were neglected in the calculations.

Journal Article↗
PubMed2005

Probabilistic assessment of "dangerous" climate change and emissions pathways.

Climate policy decisions driving future greenhouse gas mitigation efforts will strongly influence the success of compliance with Article 2 of the United Nations Framework Convention on Climate Change, the prevention of "dangerous anthropogenic interference (DAI) with the climate system." However, success will be measured in very different ways by different stakeholders, suggesting a spectrum of possible definitions for DAI. The likelihood of avoiding a given threshold for DAI depends in part on uncertainty in the climate system, notably, the range of uncertainty in climate sensitivity. We combine a set of probabilistic global average temperature metrics for DAI with probability distributions of future climate change produced from a combination of several published climate sensitivity distributions and a range of proposed concentration stabilization profiles differing in both stabilization level and approach trajectory, including overshoot profiles. These analyses present a "likelihood framework" to differentiate future emissions pathways with regard to their potential for preventing DAI. Our analysis of overshoot profiles in comparison with non-overshoot profiles demonstrates that overshoot of a given stabilization target can significantly increase the likelihood of exceeding "dangerous" climate impact thresholds, even though equilibrium warming in our model is identical for non-overshoot concentration stabilization profiles having the same target.

Climate↗
PubMed2002

Statistical learning of new visual feature combinations by infants.

The ability of humans to recognize a nearly unlimited number of unique visual objects must be based on a robust and efficient learning mechanism that extracts complex visual features from the environment. To determine whether statistically optimal representations of scenes are formed during early development, we used a habituation paradigm with 9-month-old infants and found that, by mere observation of multielement scenes, they become sensitive to the underlying statistical structure of those scenes. After exposure to a large number of scenes, infants paid more attention not only to element pairs that cooccurred more often as embedded elements in the scenes than other pairs, but also to pairs that had higher predictability (conditional probability) between the elements of the pair. These findings suggest that, similar to lower-level visual representations, infants learn higher-order visual features based on the statistical coherence of elements within the scenes, thereby allowing them to develop an efficient representation for further associative learning.

Association Learning↗
PubMed1974

A probabilistic approach to cooperativity of ligand binding by a polyvalent molecule.

Cooperativity of ligand binding is defined operationally in terms of the Hill parameter n, whose values uniquely define the shape of the binding curve. When n is everywhere equal to 1 the system behaves as if the sites were all the same and independent. If at any point n is unequal to 1 the system is either cooperative (n > 1) or anticooperative (n < 1) at that point. This means that the binding of ligand at any site is influenced by the presence or absence of ligand at other sites. In the present paper this influence is formulated in terms of probabilities of the various binding events and of conditional probabilities which relate them. The result is a network of linked probabilities which determine the cooperativity or anticooperativity of the system. This probabilistic formulation supplements the more usual one in terms of free energies and places the subject in a broader perspective.

Binding Sites↗
PubMed1992

Protein folding funnels: a kinetic approach to the sequence-structure relationship.

A lattice model of protein folding is developed to distinguish between amino acid sequences that do and do not fold into unique conformations. Although Monte Carlo simulations provide insights into the long-time processes involved in protein folding, these simulations cannot systematically chart the conformational energy surface that enables folding. By assuming that protein folding occurs after chain collapse, a kinetic map of important pathways on this surface is constructed through the use of an analytical theory of probability flow. Convergent kinetic pathways, or "folding funnels," guide folding to a unique, stable, native conformation. Solution of the probability flow equations is facilitated by limiting treatment to diffusion between geometrically similar collapsed conformers. Similarity is measured in terms of a reconfigurational distance. Two specific amino acid sequences are deemed foldable and nonfoldable because one gives rise to a single, large folding funnel leading to a native conformation and the other has multiple pathways leading to several stable conformers. Monte Carlo simulations demonstrate that folding funnel calculations accurately predict the fact of and the pathways involved in folding-specific sequences. The existence of folding funnels for specific sequences suggests that geometrically related families of stable, collapsed conformers fulfill kinetic and thermodynamic requirements of protein folding.

Algorithms↗