SEARCH · PubMed Health

Results for “Probability”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12Linked to original sources

PubMed2005

The influence of vocabulary size, phonotactic probability, and wordlikeness on nonword repetitions of children with and without specific language impairment.

Research has shown that children repeat high-probability phoneme sequences more accurately than low-probability ones. This effect attenuates with age, and its decrease is predicted by developmental changes in the size of the lexicon (J. Edwards, M. E. Beckman, & B. Munson, 2004; B. Munson, 2001; B. Munson, J. Edwards, & M. Beckman, 2005). This study expands on these findings by examining relationships between vocabulary size and repetition accuracy of nonwords varying in phonotactic probability by 16 children with specific language impairment (SLI), 16 chronological-age-matched (CA) peers with typical speech and language development, and 16 younger children matched with the children with SLI on vocabulary size (VS). As in previous research, children with SLI repeated nonwords less accurately than did CA children. The children with SLI and the VS children showed similar levels of nonword repetition accuracy. Phonotactic probability affected repetition accuracy more for children with SLI and VS children than for CA children. Regression analyses showed that measures of vocabulary size were the best predictor of the difference in repetition accuracy between high- and low-probability sequences. Analyses by items showed that measures of phonotactic probability were stronger predictors of repetition accuracy than judgments of wordlikeness. Taken together, the results support research demonstrating that vocabulary size mediates the influence of phonotactic probability on nonword repetition, perhaps due to its influence on the ongoing refinement of phonological categories.

Analysis of Variance↗

PubMed2006

Differentiating phonotactic probability and neighborhood density in adult word learning.

PURPOSE: The purpose of this study was to differentiate effects of phonotactic probability, the likelihood of occurrence of a sound sequence, and neighborhood density, the number of words that sound similar to a given word, on adult word learning. A second purpose was to determine what aspect of word learning (viz., triggering learning, formation of an initial representation, or integration with existing representations) was influenced by each variable. METHOD: Thirty-two adults were exposed to 16 nonwords paired with novel objects in a story context. The nonwords orthogonally varied in phonotactic probability and neighborhood density. Learning was measured following 1, 4, and 7 exposures in a picture-naming task. Partially correct (i.e., 2 of 3 phonemes correct) and completely correct responses (i.e., 3 of 3 phonemes correct) were analyzed together and independently to examine emerging and partial representations of new words versus complete and accurate representations of new words. RESULTS: Analysis of partially correct and completely correct responses combined showed that adults learned a lower proportion of high-probability nonwords than low-probability nonwords (i.e., high-probability disadvantage) and learned a higher proportion of high-density nonwords than low-density nonwords (i.e., high-density advantage). Separate analysis of partially correct responses yielded an effect of phonotactic probability only, whereas analysis of completely correct responses yielded an effect of neighborhood density only. CONCLUSIONS: These findings suggest that phonological and lexical processing influence different aspects of word learning. In particular, phonotactic probability may aid in triggering new learning, whereas neighborhood density may influence the integration of new lexical representations with existing representations.

Adolescent↗

PubMed2002

Central auditory dysfunction may precede the onset of clinical dementia in people with probable Alzheimer's disease.

OBJECTIVES: To document the prognostic significance of a central auditory speech-processing deficit for the subsequent onset of probable Alzheimer's disease. DESIGN: Prospective cohort study. SETTING: Framingham Heart Study. PARTICIPANTS: Seven hundred forty dementia-free volunteers from the Framingham Heart Study cohort with symmetric hearing thresholds at biennial examination 15 (1983-1985). MEASUREMENTS: The diagnosis of probable Alzheimer's disease was made prospectively using the National Institute of Neurological and Communicative Disorders and Stroke-Alzheimer's Disease Related Disorder Association criteria. A central auditory speech-processing deficit was defined as a score of 50% of less correct on the Synthetic Sentence Identification with Ipsilateral Competing Message test in at least one ear with normal word recognition ability in both ears. Cox proportional hazards regression assessed the relationship between a central auditory speech-processing deficit and the age at diagnosis of probable Alzheimer's disease. RESULTS: Forty subjects (5.4%) received a diagnosis of probable Alzheimer's disease during an average of 8.4 years (range 3-12) of follow-up; seven (17.5%) of these had a central auditory speech-processing deficit. The presence of a central auditory speech-processing deficit had an age-adjusted risk ratio for probable Alzheimer's disease of 10.8 (95% CI = 4.6-25.2), and the estimated risk ratio adjusted for age, gender, education level, apolipoprotein allele E4 presence, and hearing level was 23.3 (95% CI =6.6-82.7). A central auditory speech-processing deficit had a positive predictive value for subsequent probable Alzheimer's disease of 47% but the sensitivity was only 17.5%. CONCLUSION: Central auditory speech-processing deficits may be an early manifestation of probable Alzheimer's disease and may precede the onset of dementia diagnosis by many years.

Aged↗

PubMed2003

Fixation probability and time in subdivided populations.

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.

Alleles↗

PubMed2002

The epidemiological and control implications of HIV transmission probabilities within partnerships.

BACKGROUND: The spread of HIV is in part determined by the probability of transmission within a sexual partnership. GOAL: The goal of the study was to examine the relationship between the per-partnership and per-act transmission probability and explore how different assumptions influence the measurement of cofactors and interventions. STUDY DESIGN: We defined the mathematical relationship between the transmission probability of HIV per sex act and per partnership for the proposed biologic mechanisms. For completeness we included the original assumption of a per-partnership transmission probability and also the simple binomial model, which cannot be ruled out completely because of potential measurement error in discordant partner studies. RESULTS: A constant per-act or per-partnership transmission probability provides unsatisfactory models of the observed relationship between the number of sex acts and the likelihood of transmission. Either there is extreme heterogeneity in the transmission likelihood between partnerships or the transmission likelihood within a partnership decreases over time. These models cause the relative risk for a partnership in which a cofactor STD is present to decrease more rapidly than would be expected. The transmission probability per-partnership is substantially reduced only when there is a dramatic reduction in unprotected acts (e.g., condom use) or the transmission probability per act (e.g., due to antiretrovirals or STD treatment). Combining interventions can sometimes generate a more-than-additive impact, particularly with extreme heterogeneity. CONCLUSION: More empirical studies are needed to develop realistic models of transmission providing quantitative understanding of the HIV transmission process.

Disease Transmission, Infectious↗

PubMed1998

Using gene carrier probability to select high risk families for identifying germline mutations in breast cancer susceptibility genes.

Germline mutations in highly penetrant autosomal dominant genes explain about 5% of all breast cancer, and heritable mutations in the BRCA1 breast and ovarian cancer susceptibility gene account for 2-3% of breast cancer in the general population. Nevertheless, the presence of such mutations is highly predictive of disease development. Since screening for mutations is still technically laborious, we investigated whether the prior probability of being a carrier of a dominant breast cancer susceptibility gene in the youngest affected family member could be used to identify families in which the probability of finding a mutation is sufficiently high. Sixty German families with three or more cases of breast/ovarian cancer with at least two cases diagnosed under the age of 60 were screened for mutations by SSCP/CSGE and subsequent direct sequencing. Thirteen germline truncating/splicing mutations in BRCA1 were found in 33% (6/18) of the breast-ovarian cancer families and in 17% (7/42) of breast cancer only families. All the families showing mutations in BRCA1 had carrier probabilities of 0.65 or higher. In families with prior carrier probabilities above 0.6, the proportion detected was 0.46 in breast-ovarian cancer families and 0.26 in breast cancer only families. The average age at diagnosis of breast or ovarian cancer in families with BRCA1 mutations was 41.9 years and significantly lower than in families without mutations (p < 0.05). Mutation carriers and obligate carriers were also found to have cancers at other sites. The probability of being a susceptibility gene carrier, taking into account the complete pedigree information, allows uniform characterisation of all types of families for identifying those in which mutation analysis for BRCA1/2 is warranted. However, prior probabilities calculated using this method can be reduced when the correlation between genotype and phenotype is imperfect. A larger series of families needs to be investigated in this fashion to provide better estimates of the detection rate for different ranges of carrier probabilities.

Adult↗

PubMed1997

Probability of successful defibrillation at multiples of the defibrillation energy requirement in patients with an implantable defibrillator.

BACKGROUND: The probability of successful defibrillation has been determined in normal animals but not in patients undergoing defibrillator implantation. Therefore, the purpose of this prospective study was to determine the probability of successful defibrillation in humans on the basis of a step-down defibrillation energy requirement. METHODS AND RESULTS: Fifty-three consecutive patients underwent five separate inductions of ventricular fibrillation after the defibrillation energy requirement was determined with the use of small decrements and a step-down protocol (20, 15, 12, 10, 8, 6, 5, 4, 3, 2, 1, and 0.8 J). The first shock energy for defibrillation was either 1.0, 1.3, 1.5, 1.7, or 2.0 times the defibrillation energy requirement, and the likelihoods of successful defibrillation were 70+/-27%, 84+/-12%, 86+/-25%, 80+/-29%, and 88+/-32%, respectively (P=.03). The frequencies of uniformly successful defibrillation (5 of 5 defibrillation attempts) were 30%, 27%, 60%, 64%, and 73%, respectively (P=.01). Seven patients in whom the defibrillation energy requirement was <4 J had an overall rate of successful defibrillation of 54+/-20% compared with 86+/-20% in the remaining 47 patients (P=.002). The likelihood of successful defibrillation at twice the defibrillation energy requirement was 98% in the 46 patients with a defibrillation energy requirement of >4 J and 67% in the 7 patients with a defibrillation energy requirement of <4 J (P=.17). An absolute safety margin of 7 J was associated with a 96% probability of successful defibrillation. CONCLUSIONS: The probability of successful defibrillation is 70% at the defibrillation energy requirement. The probability plateaus at 88%, at twice the defibrillation energy requirement. A 96% probability of successful defibrillation is achieved at an absolute safety margin of 7 J, and a 98% success rate is achieved at energies that are twice the defibrillation energy requirement if the defibrillation energy requirement is >4 J. If the defibrillation energy requirement is <4 J, larger multiples of the defibrillation energy requirement are needed to achieve a high probability of successful defibrillation.

Arrhythmias, Cardiac↗

PubMed1997

Neuroprotection with NBQX in rat focal cerebral ischemia. Effects on ADC probability distribution functions and diffusion-perfusion relationships.

BACKGROUND AND PURPOSE: We have previously shown that treatment with glutamate receptor antagonists after focal ischemia can partially reverse acute lesions measured with diffusion-weighted MRI. The goal of this study was to examine the quantitative nature of these effects of neuroprotection. METHODS: Rats were subjected to permanent occlusion of the middle cerebral artery under halothane anesthesia and treated with 2,3-dihydroxy-6-nitro-7-sulfamoyl-benzo(F)quinoxaline (NBQX) (30 mg/kg IP; two doses given immediately after ischemia and 1 hour after ischemia) or given injections of saline. Diffusion-weighted MRI scans were performed to map the changes in water diffusivity during the first 3 hours after ischemia. Apparent diffusion coefficients (ADCs) within the ischemic hemisphere were calculated, and ischemic changes were expressed as absolute reductions and as a percentage of contralateral mean values. Relative perfusion deficits in the ischemic hemisphere were assessed with dynamic MRI of transient changes in transverse relaxation rates (delta R2*). RESULTS: Analysis with ADC probability distribution functions showed that focal ischemia was present with gradients in ADC reductions emanating from the center to the periphery of the lesion. Ischemic evolution in control rats was manifested as a progressive shift of the probability distribution functions over time. NBQX treatment resulted in a reverse shift of these probability functions. By 3 hours after occlusion, probability distribution functions were significantly improved in treated rats (P < .05). Because of the temporal evolution of the probability distribution functions, ADC thresholds that correlated with histological outcomes of infarction changed over time. NBQX did not alter the cerebral perfusion index, measured as delta R2* peak values. CONCLUSIONS: The results indicate that ADC probability distribution functions can be used to quantitatively evaluate the effects of neuroprotective treatment on the gradients of injury in focal cerebral ischemia. The probability functions also allow for intrasubject comparisons and may therefore be useful for exploring therapeutic windows.

Animals↗

PubMed1997

Pediatric mortality probability estimated from pre-ICU severity of illness.

OBJECTIVE: The Pediatric Risk of Mortality (PRISM) score is a measure of illness severity based on abnormalities observed in the bedside examination and laboratory assessment. PRISM scores obtained after pediatric intensive care unit (PICU) admission predict mortality probability, but no previous efforts to evaluate mortality risk before PICU admission have been reported. Our study was performed on patients admitted to PICUs at four pediatric tertiary care centers to derive a quantitative estimate of hospital mortality probability as a function of PRISM scores obtained at referring hospitals before PICU transfer. Performance of the model was tested by evaluating accuracy of mortality predictions obtained from pre-ICU PRISM scores in a separate validation set of patients. METHODS: Patients were randomized to the derivation or validation sets. Data were recorded prospectively from observations made at hospitals referring to the study PICUs. Patients included 780 infants and children with medical and surgical emergencies and trauma. Electively admitted patients were excluded from analysis. RESULTS: The relationship between mortality probability (P) and the pre-ICU PRISM score is expressed by the equation: P = er/(1 + er). In this equation, r is an empirical function of the pre-ICU PRISM score: r = .197 x PRISM - 4.705. The mortality probability rises from near 0 at low scores, approaching 1 (certainty) above a PRISM score of 40. Mortality probability exceeds 10% at a score of 13 and exceeds 50% at a score of 24. Performance of predictions in the validation set of patients was evaluated for five categories of mortality probability. The observed number of deaths corresponded to predicted mortality across the range of illness severity. When compared for each tertiary institution, observed mortality rates were similar to predictions for three of four institutions. For data obtained at institution D, the observed mortality of 17% significantly exceeded the 7% predicted rate. In infants younger than 1 year, as well as children 1 year and older, observed mortality rates were similar to predicted. CONCLUSIONS: The pre-ICU PRISM score as a measure of illness severity provides an estimate of hospital mortality probability. Further investigation is required to determine the use of pre-ICU mortality estimates in making clinical decisions.

Humans↗

PubMed1975

Molecular contingencies: reinforcement probability.

Pigeons obtained food by responding in a discrete-trials two-choice probability-learning experiment involving temporal stimuli. A given response alternative, a left- or right-key peck, had 11 associated reinforcement probabilities within each session. Reinforcement probability for a choice was an increasing or a decreasing function of the time interval immediately preceding the choice. The 11 equiprobable temporal stimuli ranged from 1 to 11 sec in 1-sec classes. Preference tended to deviate from probability matching in the direction of maximizing; i.e., the percentage of choices of the preferred response alternative tended to exceed the probability of reinforcement for that alternative. This result was qualitatively consistent with probability-learning experiments using visual stimuli. The result is consistent with a molecular analysis of operant behavior and poses a difficulty for molar theories holding that local variations in reinforcement probability may safely be disregarded in the analysis of behavior maintained by operant paradigms.

Journal Article↗

PubMed1992

Differences in cerebrospinal fluid gangliosides between "probable Alzheimer's disease" and normal aging.

The four major brain gangliosides, GM1, GD1a, GD1b, and GT1b, were determined in cerebrospinal fluid (CSF) of 43 patients with "probable Alzheimer's disease (AD)" and 40 healthy controls without psychiatric or neurological disorders. The total concentration of the four gangliosides did not differ significantly between "probable AD" group (116 +/- 58 nmol/L) and controls (92 +/- 31 nmol/L), but the proportion between the gangliosides was changed. In the "probable AD" group compared with the age-matched control group, there was an increase in both the GM1 (22.6 +/- 9.3% vs 12.6 +/- 4.1%; p < 0.0001) and GD1a (32.1 +/- 9.8% vs 23.3 +/- 5.7%; p < 0.0005) proportion, and a decrease in the GD1b (20.0 +/- 6.6% vs 23.8 +/- 6.0%; p < 0.05) and GT1b (25.3 +/- 7.9 vs 40.3 +/- 9.3%; p < 0.0001) proportion. The proportion of GM1 showed a positive correlation with age in the control group (r = 0.45; p < 0.01), but a negative correlation with age in the "probable AD" group (r = -0.37; p < 0.05). Thus, although the increase in proportion GM1 in the "probable AD" group was preferentially found in younger "probable AD" patients, it was not caused by age differences. While the pathogenetic mechanism for these changes in CSF-gangliosides in "probable AD" remains to be established, it may reflect the degeneration of nerve cells and synapses.

Adolescent↗

PubMed2001

Comparison of exercise test scores and physician estimation in determining disease probability.

BACKGROUND: The recent American College of Cardiology/American Heart Association exercise testing guidelines provided equations to calculate treadmill scores and recommended their use to improve the predictive accuracy of the standard exercise test. However, if physicians can estimate the probability of coronary artery disease as well as the scores can, there would be no reason to add this complexity to test interpretation. To compare the exercise test scores with physician's estimation of disease probability, we used clinical, exercise test, and coronary angiographic data to compute the recommended scores and print patient summaries and treadmill reports. OBJECTIVE: To determine whether exercise test scores can be as effective as expert cardiologists in diagnosing coronary disease. METHODS: Five hundred ninety-nine consecutive male patients without previous myocardial infarction with a mean +/- SD age of 59 +/- 11 years were considered for this analysis. With angiographic disease defined as any coronary lumen occlusion of 50% or more, 58% had disease. The clinical/treadmill test reports were sent to expert cardiologists and to 2 other groups, including randomly selected cardiologists and internists, who classified the patients as having high, low, or intermediate probability of disease and estimated a numerical probability from 0% to 100%. RESULTS: Forty-five expert cardiologists returned estimates on 336 patients, 37 randomly chosen practicing cardiologists returned estimates on 129 patients, 29 randomly chosen practicing internists returned estimates on 106 patients, 13 academic cardiologists returned estimates on 102 patients, and 27 academic internists returned estimates on 174 patients. When probability estimates were compared, the scores were superior to all physician groups (0.76 area under the receiver operating characteristic curve to 0.70 for experts [P=.046], 0.73 to 0.58 for cardiologists [P=.003], and 0.76 to 0.61 for internists [P=.006]). Using a probability cut point of greater than 70% for abnormal, predictive accuracy was 69% for scores compared with 64% for experts, 63% to 62% for cardiologists, and 70% to 57% for internists. CONCLUSION: Although most similar to the disease estimates of the presence of clinically significant angiographic coronary artery disease provided by the expert cardiologists, the scores outperformed the nonexpert physicians.

Adult↗

PubMedDate not supplied

A detailed evaluation of patients with acute pulmonary embolism and low- or very-low-probability lung scan interpretations.

BACKGROUND: To determine the clinical characteristics of patients with pulmonary embolism (PE) and low- or very-low-probability ventilation-perfusion lung scan interpretations. METHODS: A retrospective analysis of the data obtained during the Prospective Investigation of Pulmonary Embolism Diagnosis study was performed. The clinical characteristics of patients with acute PE and low- or very-low-probability lung scan interpretation (false-negative interpretations) were compared with patients who had low- or very-low-probability lung scan interpretations and no evidence of acute PE (true-negative interpretations). RESULTS: Of the 1493 patients who gave consent to participate in the Prospective Investigation of Pulmonary Embolism Diagnosis study, 399 patients had angiographic or autopsy evidence of acute PE. Pulmonary embolism was excluded in 960 patients. Patients with false-negative lung scan interpretations more commonly had a history of immobilization (P < .0001), trauma to the lower extremities (P < .003), recent surgery (P < .002), or central venous instrumentation (P < .04) compared with patients with true-negative lung scan interpretations. In patients with low- or very-low-probability lung scan interpretations and none of the above-mentioned risk factors, the prevalence of PE was only 4.5%. In contrast, for patients with low- or very-low-probability lung scan interpretations and two or more of the above-mentioned risk factors, the prevalence of PE was 21%. CONCLUSIONS: Patients with a history of immobilization, trauma to the lower extremities, recent surgery, or central venous instrumentation were more likely to have false-negative lung scan interpretations. Therefore, this population warrants special attention when deciding on the need for peripheral venous studies or angiography in patients with low- or very-low-probability lung scan interpretation.

Acute Disease↗

PubMed1999

Constructing meiotic maps with known error probability.

We propose methods to construct meiotic gene maps while controlling the probability of a decision-error. First, a single step gene ordering procedure is presented whose decision-error probability is bounded above by a prespecified threshold. The bound for the error probability is valid under quite general circumstances. The ordering procedure is optimal in the sense of having maximal predictive probability of correct ordering among all procedures subject to the same bound on the error probability. Second, to reduce the number of hypotheses to be tested, a stepwise ordering procedure is presented. A Monte Carlo simulation study demonstrated the integrity of the proposed error bound for the stepwise procedure under a wide variety of situations, including data coming from different laboratories and marker typing errors. The stepwise procedure was applied to version 2 of the public database maintained by the Cooperative Human Linkage Center and maps of the 23 chromosomes were generated such that the probability that the order of the markers in a given chromosome is incorrect is less than 1%.

Algorithms↗

PubMed2001

Probability binning and testing agreement between multivariate immunofluorescence histograms: extending the chi-squared test.

BACKGROUND: A key problem in immunohistochemistry is assessing when two sample histograms are significantly different. One test that is commonly used for this purpose in the univariate case is the chi-squared test. Comparing multivariate distributions is qualitatively harder, as the "curse of dimensionality" means that the number of bins can grow exponentially. For the chi-squared test to be useful, data-dependent binning methods must be employed. An example of how this can be done is provided by the "probability binning" method of Roederer et al. (1,2,3). METHODS: We derive the theoretical distribution of the probability binning statistic, giving it a more rigorous foundation. We show that the null distribution is a scaled chi-square, and show how it can be related to the standard chi-squared statistic. RESULTS: A small simulation shows how the theoretical results can be used to (a) modify the probability binning statistic to make it more sensitive and (b) suggest variant statistics which, while still exploiting the data-dependent strengths of the probability binning procedure, may be easier to work with. CONCLUSIONS: The probability binning procedure effectively uses adaptive binning to locate structure in high-dimensional data. The derivation of a theoretical basis provides a more detailed interpretation of its behavior and renders the probability binning method more flexible.

Chi-Square Distribution↗

PubMed1987

Paternity testing 3: exclusion probabilities.

Blood typing with several blood systems is used in many countries to determine paternity or nonpaternity with respect to an alleged father. Various probabilities are usually presented, in particular: the conditional probability of excluding a random man as father given a particular mother-child phenotype combination, and the expected (unconditional) exclusion probability for all mother-child combinations can be calculated for a given blood system. Because these probabilities are of general interest in paternity studies, explicit formulae for the unconditional probabilities have been derived for some of the systems. Algorithms suitable for a microcomputer are given here for finding the exclusion probabilities for any system. These algorithms avoid the need for developing new formulae whenever a new system is introduced or a current system is extended through the addition of further alleles.

Algorithms↗

PubMed1996

Continuous probability distribution (CUPID) analysis of potentials for internal rotations.

The continuous probability distribution (CUPID) approach for analyzing the rotamer populations from NMR spin-spin couplings and nuclear Overhauser enhancements [Z. Dzakula, W.M. Westler, A.S. Edison, and J.L. Markley, J. Amer. Chem. Soc. 114, 6195 (1992)] can be expanded to allow computation of the rotational potential from the Fourier coefficients of the angular probability distribution. This approach provides a general solution to the nonnegativity problem, which appears when lack of data causes a serious truncation in the Fourier series that defines the probability distribution. In favorable cases, this approach also allows thermodynamic characterization of internal rotation. Use of this extension of the CUPID method is illustrated by the analysis of internal rotations in an amino acid, two peptides, and an oligosaccharide from published experimental data. Three strategies have been devised for dealing with cases where the experimental input data do not provide enough information for complete reconstruction of the potential: (1) two-dimensional grid search for the undetermined third-order Fourier coefficients of the potential, (2) transfer of these coefficients from related model compounds, and (3) restriction of the magnitudes of the Fourier coefficients as required by the assumption of fast-exchange averaging of the input parameters. In addition, equations for translating uncertainties in experimental NMR input data into errors in calculated continuous probability distributions of rotamers are presented. The dependence of errors on various features of the distributions has been studied systematically from simulations. The results show that, typically, the confidence intervals are +/- 30-40 degrees for dihedral angles and +/- 0.2 for rotamer populations. For chi 1 rotamers of amino acids, the analysis is most sensitive to the uncertainties in C'-H beta couplings. A critical reexamination of the use of Gaussian functions to reconstruct a probability distribution is presented. In particular, the simplifying assumption of identical widths for all Gaussian probability peaks has been justified by showing that it does not lead to large errors in other CUPID parameters. finally, the angular dependencies of cross-relaxation rates, their uncertainties, and the potential for their use in studying chi 1 internal rotations in amino acids are discussed.

Electron Spin Resonance Spectroscopy↗

PubMed1996

Establishment probability in fluctuating environments: a branching process model.

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.

Demography↗