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PubMed1997

Detection, visualization and animation of abnormal anatomic structure with a deformable probabilistic brain atlas based on random vector field transformations.

This paper describes the design, implementation and preliminary results of a technique for creating a comprehensive probabilistic atlas of the human brain based on high-dimensional vector field transformations. The goal of the atlas is to detect and quantify distributed patterns of deviation from normal anatomy, in a 3-D brain image from any given subject. The algorithm analyzes a reference population of normal scans and automatically generates color-coded probability maps of the anatomy of new subjects. Given a 3-D brain image of a new subject, the algorithm calculates a set of high-dimensional volumetric maps (with typically 384(2) x 256 x 3 approximately 10(8) degrees of freedom) elastically deforming this scan into structural correspondence with other scans, selected one by one from an anatomic image database. The family of volumetric warps thus constructed encodes statistical properties and directional biases of local anatomical variation throughout the architecture of the brain. A probability space of random transformations, based on the theory of anisotropic Gaussian random fields, is then developed to reflect the observed variability in stereotaxic space of the points whose correspondences are found by the warping algorithm. A complete system of 384(2) x 256 probability density functions is computed, yielding confidence limits in stereotaxic space for the location of every point represented in the 3-D image lattice of the new subject's brain. Color-coded probability maps are generated, densely defined throughout the anatomy of the new subject. These indicate locally the probability of each anatomic point being unusually situated, given the distributions of corresponding points in the scans of normal subjects. 3-D MRI and high-resolution cryosection volumes are analyzed from subjects with metastatic tumors and Alzheimer's disease. Gradual variations and continuous deformations of the underlying anatomy are simulated and their dynamic effects on regional probability maps are animated in video format (on the accompanying CD-ROM). Applications of the deformable probabilistic atlas include the transfer of multi-subject 3-D functional, vascular and histologic maps onto a single anatomic template, the mapping of 3-D atlases onto the scans of new subjects, and the rapid detection, quantification and mapping of local shape changes in 3-D medical images in disease and during normal or abnormal growth and development.

Anatomy, Cross-Sectional↗
PubMed2004

Interelectronic angle densities of equivalent electrons in Hartree-Fock theory of atoms.

The interelectronic angle density A(theta12) is the probability density function that the angle thetaij (0 < or = thetaij < or = pi) subtended by the vectors ri and rj of any two electrons i and j becomes theta12. For equivalent electrons in atoms, it is shown that the density A(theta12) in the Hartree-Fock theory is given by a simple polynomial of cos theta12. Detailed expressions are reported for all LS terms arising from s2, pN (N = 2-6), dN (N = 2-10), and f(N) (N = 2,12) electron configurations. With no modifications, the present results apply as well to the interelectronic angle density A(theta12) in momentum space, where theta12 is the angle between two electron momenta.

Journal Article↗
PubMed1982

Toward a theory of patient satisfaction.

Despite the widespread concern in health care literature with patients'--or clients'--satisfaction, there has been no explicit definition of that concept nor systematic consideration of its determinants and consequences. The definition of satisfaction proposed here is derived from Fishbein and Ajzen's attitude theory and from job satisfaction research. Among the various probable determinants of a patient's satisfaction with health care are his/her attitudes and perceptions prior to experiencing that care; after reviewing relevant social science theories, we hypothesize five such social psychological variables which affect satisfaction ratings. The present attempt to define the concept patient satisfaction and to hypothesize some of its determinants can be regarded as first steps in building a theory of patient satisfaction.

Attitude to Health↗
PubMed2002

Metabolic oxidation of carcinogenic arylamines by p450 monooxygenases: theoretical support for the one-electron transfer mechanism.

N-oxidation by cytochrome p450 enzymes is an initial step in the metabolic activation of aromatic amine compounds. Once metabolized, these compounds are converted to DNA-reactive species which can exhibit potent mutagenic and/or carcinogenic activity. The precise mechanism of p450 enzyme oxidation is not completely understood, although various theories, involving either one-electron transfer, two-electron transfer or addition-rearrangement, have been debated. In previous studies, selection of the most probable mechanism has been based on consideration of Hückel theory charge distribution calculations and experimentally-derived enzyme metabolism data. This approach can now be improved by incorporating contemporary, ab initio quantum chemical methods to accurately determine the chemical properties of p450 aromatic amine substrates. In this work, we have re-examined the feasibility of three proposed p450 oxidation mechanisms by comparing the experimental oxidation yields and rates of 1-naphthylamine (1-NA), 2-naphthylamine (2-NA) and 2-aminofluorene (2-AF). This data has then been analyzed with respect to ab initio-calculated charge distributions and energies of reactants, oxidation products and proposed intermediates. Our analysis of theoretical and experimental data indicates that the one-electron model is more consistent with oxidation rate data for 1-NA, 2-NA, and 2-AF. We therefore conclude, in contrast to earlier studies, that the one-electron mechanism is more likely to be the pathway for p450-catalyzed aromatic amine oxidation.

1-Naphthylamine↗
PubMedDate not supplied

[Criticism of the current theories concerning the formation of the immunological repertory].

Application of the probability calculus to the variational structure of the immunoglobulins leads to demonstrate the impossibility of the random production of the repertory's antibodies. Physical and Cybernetic considerations lead, instead, to demonstrate the necessary existence of aspecific recognition of the antigen, i.e. of the antigen's activity. Application of the theory of stochastic convergence, at last, leads to demonstrate that, if there would be a connection between this aspecific recognition and the antibody's production, the latter would be possible. This connection, as a consequence, must exist.

Antibody Formation↗
PubMed1996

In defence of the right shift theory.

The right shift (RS) theory of a gene for left-cerebral dominance which increases the probability of right-handedness is outlined, together with two proposed alternatives, the 1985a genetic theory of McManus and the 1993 developmental instability theory of Yeo and Gangestad. Similarities and differences among the three theories are reviewed. Both of the genetic theories can predict the distribution of handedness in families and in twins more efficiently than the developmental instability theory, and the RS theory better than the McManus theory.

Adult↗
PubMed1978

The elderly and the control of simple behaviour by probabilistic information.

The probabilities of events in the environment are important as controllers of how we cope with that environment. Attention is deployed to parts of the visual field where important events are most likely to happen; in predicting what will happen next in a situation, probable things tend to be predicted. This paper assess adult age differences in the use of probabilistic information, using the laboratory task-settings of choice reaction time, simple prediction, and selective attending. In almost all situations the elderly are less influenced by event probabilities than their juniors, although they are just as capable of registering the probabilities involved. This consistent age effect contradicts the predictions of Griew's theory which assumes that behavioural experience operates by increasing the use of probabilistic information. A second finding was that value and reward manipulations which alter the response patterns of the young do not influence the elderly to the same extent. It is tentatively concluded that attenuated use of probability information characterises the elderly, as does a reduced response to simple payoffs. Some avenues of theoretical exploration are discussed, together with some caveats concerning the applicability of the findings.

Adult↗
PubMed2000

Exponential or polynomial learning Curves? - case-based studies

Learning curves exhibit a diversity of behaviors such as phase transition. However, the understanding of learning curves is still extremely limited, and existing theories can give the impression that without empirical studies (e.g., cross validation), one can probably do nothing more than qualitative interpretations. In this note, we propose a theory of learning curves based on the idea of reducing learning problems to hypothesis-testing ones. This theory provides a simple approach that is potentially useful for predicting and interpreting (a diversity of) learning curve behaviors qualitatively and quantitatively, and it applies to finite training sample size and finite learning machine and for learning situations not necessarily within the Bayesian framework. We illustrate the results by examining some exponential learning curve behaviors observed in Cohn and Tesauro (1992)'s experiment.

Journal Article↗
PubMedDate not supplied

Relative entropy as a measure of diagnostic information.

Relative entropy is a concept within information theory that provides a measure of the distance between two probability distributions. The author proposes that the amount of information gained by performing a diagnostic test can be quantified by calculating the relative entropy between the posttest and pretest probability distributions. This statistic, in essence, quantifies the degree to which the results of a diagnostic test are likely to reduce our surprise upon ultimately learning a patient's diagnosis. A previously proposed measure of diagnostic information that is also based on information theory (pretest entropy minus posttest entropy) has been criticized as failing, in some cases, to agree with our intuitive concept of diagnostic information. The proposed formula passes the tests used to challenge this previous measure.

Clinical Medicine↗
PubMed2002

"Slip and fall" theory--extreme order statistics.

Classical "slip and fall" analysis was reformulated in this paper to account for the stochastic nature of friction. As it turned out, the new theory, arising from this analysis, was a precise statement of the distribution function for the smallest value among n independent observations. This made it possible to invoke an important result from the asymptotic theory of extreme order statistics that reduced the theory to a simple and elegant relationship among the probability of slipping, the critical friction criterion, the distance traveled by the walker, and the average, spread and asymmetry of the distribution of friction coefficients. The new theory reveals that short walks lead to fewer falls; low friction floors are sometimes better than high friction ones.

Accidental Falls↗
PubMed2006

The influence of improper sets of information on judgment: how irrelevant information can bias judged probability.

This article introduces 2 new sources of bias in probability judgment, discrimination failure and inhibition failure, which are conceptualized as arising from an interaction between error prone memory processes and a support theory like comparison process. Both sources of bias stem from the influence of irrelevant information on participants' probability judgments, but they postulate different mechanisms for how irrelevant information affects judgment. The authors used an adaptation of the proactive interference (PI) and release from PI paradigm to test the effect of irrelevant information on judgment. The results of 2 experiments support the discrimination failure account of the effect of PI on probability judgment. In addition, the authors show that 2 commonly used measures of judgment accuracy, absolute and relative accuracy, can be dissociated. The results have broad implications for theories of judgment.

Analysis of Variance↗
PubMed2003

Minimal entropy probability paths between genome families.

We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non-rich vectors, does not involve variational theory and does not involve differential equations, but is a better approximation of the minimal entropy path distance than the distance //b-a//(2). We compute minimal entropy distance matrices for examples of DNA myostatin genes and amino-acid sequences across several species. Output tree dendograms for our minimal entropy metric are compared with dendograms based on BLAST and BLAST identity scores.

Algorithms↗
PubMed1980

The extinction of slowly evolving dynamical systems.

The time evolution of slowly evolving discrete dynamical systems xi + 1 = T(ri, xi), defined on an interval [0, L], where a parameter ri changes slowly with respect to i is considered. For certain transformations T, once ri reaches a critical value the system faces a non-zero probability of extinction because some xj psi [0, L]. Recent ergodic theory results of Ruelle, Pianigiani, and Lasota and Yorke are used to derive a simple expression for the probability of survival of these systems. The extinction process is illustrated with two examples. One is the quadratic map, T (r, x) = rx (1 - x), and the second is a simple model for the growth of a cellular population. The survival statistics for chronic myelogenous leukemia patients are discussed in light of these extinction processes. Two other dynamical processes of biological importance, to which our results are applicable, are mentioned.

Biological Evolution↗
PubMed1990

Amplitude variations in P300 component due to unpredictable stepwise change of stimulus probability.

The present study investigates whether the amplitude of the P300 in 'normal' subjects adapts to unexpected changes in global stimulus probability. The adaptation level (AL) metrics (in terms of Helson's [1964] theory) was applied to explain the variations in the P300 amplitude. In an oddball paradigm the probability of the deviant tone (target 1000 Hz, 80 dB, 50 ms) occurring randomly in a train of standard ones (non-target 1100 Hz, 80 dB, 50 ms) was changed in a stepwise way from 0.5 to 0.3 and then to 0.1 in 3 blocks without interruption of the stimulus presentation. Two experiments were performed. In the first one the subjects did not receive any prior information about the changes in the stimulus probability, whereas in the second experiment they were aware of such changes. The task always required the subject to silently count the deviants. EEG was recorded monopolarly from Fz, Cz and Pz in a total of 15 subjects. The block averaged P300 increased monotonically with probability, the increase being larger in Expt. II. In contrast to the block averaged P300, the variations in the P300 amplitude following the abrupt change in probability showed a non-linear dependency. On the basis of the AL a simulation of the time course of the P300 variations with probability was performed and a clear similarity between the simulated P300 and the experimental data was found. Some properties of the AL model are discussed.

Acoustic Stimulation↗
PubMed2003

Natural selection and the emergence of a mutation phenotype: an update of the evolutionary synthesis considering mechanisms that affect genome variation.

Most descriptions of evolution assume that all mutations are completely random with respect to their potential effects on survival. However, much like other phenotypic variations that affect the survival of the descendants, intrinsic variations in the probability, type, and location of genetic change can feel the pressure of natural selection. From site-specific recombination to changes in polymerase fidelity and repair of DNA damage, an organism's gene products affect what genetic changes occur in its genome. Through the action of natural selection on these gene products, potentially favorable mutations can become more probable than random. With examples from variation in bacterial surface proteins to the vertebrate immune response, it is clear that a great deal of genetic change is better than "random" with respect to its potential effect on survival. Indeed, some potentially useful mutations are so probable that they can be viewed as being encoded implicitly in the genome. An updated evolutionary theory includes emergence, under selective pressure, of genomic information that affects the probability of different classes of mutation, with consequences for genome survival.

Bacteria↗
PubMed2006

Fixational eye movements and motion perception.

Small eye movements are necessary for maintained visibility of the static scene, but at the same time they randomly oscillate the retinal image, so the visual system must compensate for such motions to yield the stable visual world. According to the theory of visual stabilization based on retinal motion signals, objects are perceived to move only if their retinal images make spatially differential motions with respect to some baseline movement probably due to eye movements. Motion illusions favoring this theory are demonstrated, and psychophysical as well as brain-imaging studies on the illusions are reviewed. It is argued that perceptual stability is established through interactions between motion-energy detection at an early stage and spatial differentiation of motion at a later stage. As such, image oscillations originating in fixational eye movements go unnoticed perceptually, and it is also shown that image oscillations are, though unnoticed, working as a limiting factor of motion detection. Finally, the functional importance of non-differential, global motion signals are discussed in relation to visual stability during large-scale eye movements as well as heading estimation.

Afterimage↗
PubMed2003

Non-Gaussian statistics of soliton timing jitter induced by amplifier noise.

Based on first-order perturbation theory of the soliton, the Gordon-Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Both frequency and timing jitter have larger tail probabilities than Gaussian distribution given by the linearized perturbation theory. The timing jitter has a larger discrepancy from Gaussian distribution than does the frequency jitter.

Journal Article↗
PubMed2003

Evaluation of the ranking probabilities for partial orders based on random linear extensions.

Partial order theory and Hasse diagrams appears to be a promising tool for decision-making in environmental issues. Alternatives or objects are said to be partial ordered when it is impossible to find a mutual relationship (< or >) for all criteria. This is often the case in complicated real life situations. However, sometimes it is attractive to apply a total order, i.e. linear rank, and not just the partial order. Based on ranking probabilities and linear extensions it is possible to derive a total order. A linear extension is a projection of the partial order into a total order that comply with all the relations in the partial order. When all linear extensions are known the ranking probabilities can be found as the probability for an object to occupy a specific rank. However, the total number of linear extensions is proportional with the faculty of the number of objects in the partial order. Therefore it is practically impossible to identify all possible linear extensions for partial orders with more than around 20 objects. This study reviews and evaluates a method which estimates the ranking probability based on sampling of a minor random fraction of the linear extensions. Using standard statistics the necessary number of random linear extensions is described as a function of the ranking probability estimate and the restrictions on the confidence interval around the ranking probability. The analysis reveals a smaller systematic uncertainty, which occurs due to the random selection of ranking between two incomparable objects. The discrepancy appears to be dependent on the structure of the partial order. The method using random linear extensions thus appears as a valuable tool for analysing larger partially ordered sets, which are practically impossible to handle using the total set of linear extensions.

Decision Making↗