Chance Expectation Research Articles

Gender Differences in the Validity of Career Interest Inventories

Predictive validity (including hit rates, kappa coefficients, and chance expectancy rates) between standard scoring and person matching was compared by gender based upon ex post facto data collected on 5143 medical students who had taken a career interest inventory and entered their medical residency. Hit rate accuracy for person matching with females and males in this study was lower than standard scoring. However, person matching demonstrated greater gender balancing in first match hit rates. Additionally, person matching increased career interest inventory validity over standard scoring as it has the greater ability to a) differentiate between and b) assign to specific occupational groups for females and males. Furthermore, person matching has the potential to offer female and male test takers the ability to receive narrative career data, which could improve the career decision making process over the scoring reports of career interest inventories using standard scoring.

Songs of the Eastern Phoebe, a suboscine songbird, are individually distinctive but do not vary geographically

Animal displays may vary both within and among individuals and also within and among populations. This variation may contain important information used by animals for individual recognition. Suboscine birds are thought to develop song by fully innate mechanisms and are poorly studied relative to oscine birds, where song learning results in significant variation in song structure among individuals and the development of dialects. Recent research, however, demonstrates that suboscine song is often individually distinctive and in some cases shows signs of regional variation. We used spectrogram cross-correlation and canonical discriminant function analysis to examine individual and geographic variations in songs of Eastern Phoebes (Sayornis phoebe), suboscine birds with two song types. Both song types were individually distinctive and showed significantly higher cross-correlations within than among individuals. Discriminant function analysis correctly assigned 85.3% of “phee-bee” and 90.0% of “phee-b-be-bee” songs to the correct male, levels that are significantly higher than expected by chance. The individually distinctive characters of songs were also significantly repeatable among recording sessions. Eastern Phoebe song did not vary geographically between two populations separated by 640 km; permuted discriminant function analysis assigned 65% of “phee-bee” and 70% of “phee-b-be-bee” songs to the correct population, which did not differ significantly from chance expectations. Variation among males in song characteristics could be used by both males and females to discriminate among individuals. These detailed bioacoustic analyses support the idea that individual distinctive acoustic signals are widespread across suboscine birds.

Disentangling the drivers of metacommunity structure across spatial scales.

Metacommunity theories attribute different relative degrees of importance to dispersal, environmental filtering, biotic interactions and stochastic processes in community assembly, but the role of spatial scale remains uncertain. Here we used two complementary statistical tools to test: (1) whether or not the patterns of community structure and environmental influences are consistent across resolutions; and (2) whether and how the joint use of two fundamentally different statistical approaches provides a complementary interpretation of results. Grassland plants in the French Alps. We used two approaches across five spatial resolutions (ranging from 1 km × 1 km to 30 km × 30 km): variance partitioning, and analysis of metacommunity structure on the site-by-species incidence matrices. Both methods allow the testing of expected patterns resulting from environmental filtering, but variance partitioning allows the role of dispersal and environmental gradients to be studied, while analysis of the site-by-species metacommunity structure informs an understanding of how environmental filtering occurs and whether or not patterns differ from chance expectation. We also used spatial regressions on species richness to identify relevant environmental factors at each scale and to link results from the two approaches. Major environmental drivers of richness included growing degree-days, temperature, moisture and spatial or temporal heterogeneity. Variance partitioning pointed to an increase in the role of dispersal at coarser resolutions, while metacommunity structure analysis pointed to environmental filtering having an important role at all resolutions through a Clementsian assembly process (i.e. groups of species having similar range boundaries and co-occurring in similar environments). The combination of methods used here allows a better understanding of the forces structuring ecological communities than either one of them used separately. A key aspect in this complementarity is that variance partitioning can detect effects of dispersal whereas metacommunity structure analysis cannot. Moreover, the latter can distinguish between different forms of environmental filtering (e.g. individualistic versus group species responses to environmental gradients).

Hybrid Binomial Distribution

Buckley and Eslami (2003) introduced a discrete distribution, namely Fuzzy Binomial distribution, that is intended to suit situations wherein impreciseness and randomness coexist. Using the approach of Liu (2008), a hybrid (combination of imprecision and randomness) version of Binomial distribution is developed. With the help of genetic algorithms the process of computing the chance distributions, expectation and variance of the distribution that is developed in this paper are illustrated. Illustrative examples are given to justify the usefulness of the distribution.

Visual perception of fatigued lifting actions

Fatigue-related changes in lifting kinematics may expose workers to undue injury risks. Early detection of accumulating fatigue offers the prospect of intervention strategies to mitigate such fatigue-related risks. In a first step towards this objective, this study investigated whether fatigue detection was accessible to visual perception and, if so, what was the key visual information required for successful fatigue discrimination. Eighteen participants were tasked with identifying fatigued lifts when viewing 24 trials presented using both video and point-light representations. Each trial comprised a pair of lifting actions containing a fresh and a fatigued lift from the same individual presented in counter-balanced sequence. Confidence intervals demonstrated that the frequency of correct responses for both sexes exceeded chance expectations (50%) for both video (68%±12%) and point-light representations (67%±10%), demonstrating that fatigued lifting kinematics are open to visual perception. There were no significant differences between sexes or viewing condition, the latter result indicating kinematic dynamics as providing sufficient information for successful fatigue discrimination. Moreover, results from single viewer investigation reported fatigue detection (75%) from point-light information describing only the kinematics of the box lifted. These preliminary findings may have important workplace applications if fatigue discrimination rates can be improved upon through future research.

Variation in habitat use of coexisting rodent species in a tropical dry deciduous forest

Use of habitat is a critical component related to structure of small-mammal communities, with partitioning occurring primarily along dimensions of microhabitat, although use of microhabitat often does not explain fully use at a macrohabitat level. Through grid studies of small mammals in coastal Colima, Mexico (during January 2003–2005), we appraised influence of available habitat, species richness, abundance, and cumulative abundance of other small mammals on variation in habitat used by species. We evaluated 14 habitat variables (reflecting ground cover, slope, canopy, and vegetation density on vertical and horizontal axes) and developed a composite variable (principal component 1) reflecting general openness of habitat through which we addressed habitat use. For the four most common mammalian species (Sigmodon mascotensis, Heteromys pictus, Baiomys musculus, and Oryzomys couesi), two measures of variation in habitat used were employed to estimate niche breadth, one of which assessed variation in habitat use relative to variation present on a grid. Sigmodon mascotensis and B. musculus preferred areas that were more open, and H. pictus and O. couesi occupied less-open areas; breadth of habitat use did not differ interspecifically. Habitat use was more variable on grids with more variability in habitat, although not greater than chance expectations. Findings do not lend support to the resource-breadth hypothesis as an explanation for population densities of species at a local level or the habitat-heterogeneity hypothesis as a predictor of species richness. Variation in habitat used by S. mascotensis did not proportionally increase when diverse habitat was available but was greater when the species was more abundant. For H. pictus, when cumulative abundance of other small mammals was greater, breadth of habitat used was greater. Intraspecific density-dependent habitat selection may result in S. mascotensis selecting a greater variety of habitats, while greater interspecific abundance is related to a greater range in use of habitats by H. pictus. Baiomys musculus used a higher proportion of habitat relative to that available when more species were present on a grid. Variation in habitat used by O. couesi was unrelated to any factor examined. Overall, the four species responded in notably different ways with respect to availability of habitat, abundance, and presence of other species.

Using Bayes’ theorem in behavioural crime linking of serial homicide

Purpose. The study extends research by Santtila et al. (2008) by investigating the effectiveness of linking cases of serial homicide using behavioural patterns of offenders, analysed through Bayesian reasoning. The study also investigates the informative value of individual behavioural variables in the linking process.Methods. Offender behaviour was coded from official documents relating to 116 solved homicide cases belonging to 19 separate series. The basis of the linkage analyses was 92 behaviours coded as present or absent in the case based on investigator observations on the crime scene. We developed a Bayesian method for linking crime cases and judged its accuracy using cross‐validation. We explored the information added by individual behavioural variables, first, by testing if the variable represented purely noise with respect to classification, and second, by excluding variables from the original model, one by one, by choosing the behaviour that had the smallest effect on classification accuracy.Results. The model achieved a classification accuracy of 83.6% whereas chance expectancy was 5.3%. In simulated scenarios of only one and two known cases in a series, the accuracy was 59.0 and 69.2%, respectively. No behavioural variable represented pure noise but the same level of accuracy was achieved by analysing a set of 15, as analysing all 92 variables.Conclusion. The study illustrates the utility of analysing individual behavioural variables through Bayesian reasoning for crime linking. Feasible applied use of the approach is illustrated by the effectiveness of analysing a small set of carefully chosen variables.

Transcriptome asymmetry within mouse zygotes but not between early embryonic sister blastomeres

Transcriptome regionalization is an essential polarity determinant among metazoans, directing embryonic axis formation during normal development. Although conservation of this principle in mammals is assumed, recent evidence is conflicting and it is not known whether transcriptome asymmetries exist within unfertilized mammalian eggs or between the respective cleavage products of early embryonic divisions. We here address this by comparing transcriptome profiles of paired single cells and sub-cellular structures obtained microsurgically from mouse oocytes and totipotent embryos. Paired microsurgical spindle and remnant samples from unfertilized metaphase II oocytes possessed distinguishable profiles. Fertilization produces a totipotent 1-cell embryo (zygote) and associated spindle-enriched second polar body whose paired profiles also differed, reflecting spindle transcript enrichment. However, there was no programmed transcriptome asymmetry between sister cells within 2- or 3-cell embryos. Accordingly, there is transcriptome asymmetry within mouse oocytes, but not between the sister blastomeres of early embryos. This work places constraints on pre-patterning in mammals and provides documentation correlating potency changes and transcriptome partitioning at the single-cell level.

Proteins encoded in genomic regions associated with immune-mediated disease physically interact and suggest underlying biology.

Genome-wide association studies (GWAS) have defined over 150 genomic regions unequivocally containing variation predisposing to immune-mediated disease. Inferring disease biology from these observations, however, hinges on our ability to discover the molecular processes being perturbed by these risk variants. It has previously been observed that different genes harboring causal mutations for the same Mendelian disease often physically interact. We sought to evaluate the degree to which this is true of genes within strongly associated loci in complex disease. Using sets of loci defined in rheumatoid arthritis (RA) and Crohn's disease (CD) GWAS, we build protein–protein interaction (PPI) networks for genes within associated loci and find abundant physical interactions between protein products of associated genes. We apply multiple permutation approaches to show that these networks are more densely connected than chance expectation. To confirm biological relevance, we show that the components of the networks tend to be expressed in similar tissues relevant to the phenotypes in question, suggesting the network indicates common underlying processes perturbed by risk loci. Furthermore, we show that the RA and CD networks have predictive power by demonstrating that proteins in these networks, not encoded in the confirmed list of disease associated loci, are significantly enriched for association to the phenotypes in question in extended GWAS analysis. Finally, we test our method in 3 non-immune traits to assess its applicability to complex traits in general. We find that genes in loci associated to height and lipid levels assemble into significantly connected networks but did not detect excess connectivity among Type 2 Diabetes (T2D) loci beyond chance. Taken together, our results constitute evidence that, for many of the complex diseases studied here, common genetic associations implicate regions encoding proteins that physically interact in a preferential manner, in line with observations in Mendelian disease.

Habitat use and demographic characteristics of the west Mexican cotton rat (Sigmodon mascotensis)

Abstract In tropical deciduous forest along the Pacific coast in Colima, Mexico, we conducted eight-night mark-recapture studies of Sigmodon mascotensis (January 2003–2005), evaluating habitat preferences and demography. Yearly we established five grids with 100 trapping stations (one ground and one elevated trap; 24,000 trap-nights), each evaluated for 14 environmental measures. We captured 96 S. mascotensis 274 times on 10 grids, most at ground level (85.6%), with densities of 0.84–25.31 individuals/ha. Adults predominated (88.2%), sex ratio (males:females) was 1:0.74, and males were heavier. Sigmodon mascotensis co-occurred with Oryzomys couesi and Baiomys musculus more often and Heteromys pictus less often than chance expectation. For 2004, univariate analyses indicated that stations frequented had more ground cover in woody plants, forbs and grasses; less in litter and bare ground; more vegetation low and less high; lower and more open canopy; and longer distance to nearest tree. Logistic regression indicated preference for open canopy, dense low vegetation, little litter and longer distance to nearest tree. Nonparametric multiplicative regression showed occurrence likelihood decreased as litter increased and increased with increasing slope, average hits at 1 m and average distance to nearest tree. The likelihood was high with no or low canopy, as well as high canopy.

Differential aggression in genetically different morphs of the white-throated sparros (Zonotrichia albicollis).

To see if genetic differences correlate with differences in agonistic behavior, 225 encounters within and between color morphs of the white-throated sparrow (Zonotrichia albicollis) were observed in feeding groups of different sizes and morphic compositions. Tan morphs lack the M chromosome that replaces either of two chromosomes in the white morph. The data were analysed using quantitative models accounting for the proportions of morphs present, and the principal finding was that morphs are equally frequent recipients of aggression but the white morph was the aggressor more frequently than by chance expectation--regardless of the morph of the recipient, the size of the group or the morphic composition of the group.

Genetic Control of Individual Differences in Gene-Specific Methylation in Human Brain

We have observed extensive interindividual differences in DNA methylation of 8590 CpG sites of 6229 genes in 153 human adult cerebellum samples, enriched in CpG island "shores" and at further distances from CpG islands. To search for genetic factors that regulate this variation, we performed a genome-wide association study (GWAS) mapping of methylation quantitative trait loci (mQTLs) for the 8590 testable CpG sites. cis association refers to correlation of methylation with SNPs within 1 Mb of a CpG site. 736 CpG sites showed phenotype-wide significant cis association with 2878 SNPs (after permutation correction for all tested markers and methylation phenotypes). In trans analysis of methylation, which tests for distant regulation effects, associations of 12 CpG sites and 38 SNPs remained significant after phenotype-wide correction. To examine the functional effects of mQTLs, we analyzed 85 genes that were with genetically regulated methylation we observed and for which we had quality gene expression data. Ten genes showed SNP-methylation-expression three-way associations-the same SNP simultaneously showed significant association with both DNA methylation and gene expression, while DNA methylation was significantly correlated with gene expression. Thus, we demonstrated that DNA methylation is frequently a heritable continuous quantitatively variable trait in human brain. Unlike allele-specific methylation, genetic polymorphisms mark both cis- and trans-regulatory genetic sites at measurable distances from their CpG sites. Some of the genetically regulated DNA methylation is directly connected with genetically regulated gene expression variation.

Object familiarization and novel-object preference in rats

We investigated whether object familiarization was related to novel-object preference in the novel-object preference (NOP) test in rats. In Experiment 1, we found that no significant correlation existed between the time spent investigating 2 identical copies of a sample object and the degree of preference for a novel object. In Experiment 2, rats investigated 2 identical sample objects for a total of 5, 30, 60, 90 or 120s. Investigatory preference for the novel object was compared to chance expectancy as well as between the groups. Only the 90-s group and the 120-s group displayed above-chance investigatory preference for the novel object, but novel-object preference for these 2 groups did not differ from each other, suggesting that a minimal amount of sample object investigation is necessary for rats to develop a novel-object preference, beyond which no increase in novel-object preference was found. In Experiments 3 and 4, normal rats and rats with hippocampal lesions were given repeated test trials, with the same sample object presented with a different novel object, at 24-h and (Experiment 3) and 35-s intervals (Experiment 4). In both experiments, novel-object preference did not increase in magnitude with repeated sample object exposures, suggesting that increased familiarity with the sample object does not result in increased novel-object preference. Rats with lesions of the dorsal hippocampus showed an unreliable investigatory preference for the novel object. These results are discussed in terms of the potential limitations of the NOP test as a tool for the assessment of object-recognition memory in rats.

A computational approach identifies two regions of Hepatitis C Virus E1 protein as interacting domains involved in viral fusion process

BackgroundThe E1 protein of Hepatitis C Virus (HCV) can be dissected into two distinct hydrophobic regions: a central domain containing an hypothetical fusion peptide (FP), and a C-terminal domain (CT) comprising two segments, a pre-anchor and a trans-membrane (TM) region. In the currently accepted model of the viral fusion process, the FP and the TM regions are considered to be closely juxtaposed in the post-fusion structure and their physical interaction cannot be excluded. In the present study, we took advantage of the natural sequence variability present among HCV strains to test, by purely sequence-based computational tools, the hypothesis that in this virus the fusion process involves the physical interaction of the FP and CT regions of E1.ResultsTwo computational approaches were applied. The first one is based on the co-evolution paradigm of interacting peptides and consequently on the correlation between the distance matrices generated by the sequence alignment method applied to FP and CT primary structures, respectively. In spite of the relatively low random genetic drift between genotypes, co-evolution analysis of sequences from five HCV genotypes revealed a greater correlation between the FP and CT domains than respect to a control HCV sequence from Core protein, so giving a clear, albeit still inconclusive, support to the physical interaction hypothesis.The second approach relies upon a non-linear signal analysis method widely used in protein science called Recurrence Quantification Analysis (RQA). This method allows for a direct comparison of domains for the presence of common hydrophobicity patterns, on which the physical interaction is based upon. RQA greatly strengthened the reliability of the hypothesis by the scoring of a lot of cross-recurrences between FP and CT peptides hydrophobicity patterning largely outnumbering chance expectations and pointing to putative interaction sites. Intriguingly, mutations in the CT region of E1, reducing the fusion process in vitro, strongly reduced the amount of cross-recurrence further supporting interaction between this region and FP.ConclusionOur results support a fusion model for HCV in which the FP and the C-terminal region of E1 are juxtaposed and interact in the post-fusion structure. These findings have general implications for viruses, as any visualization of the post-fusion FP-TM complex has been precluded by the impossibility to obtain crystallised viral fusion proteins containing the trans-membrane region. This limitation gives to sequence based modelling efforts a crucial role in the sketching of a molecular interpretation of the fusion process. Moreover, our data also have a more general relevance for cell biology as the mechanism of intracellular fusion showed remarkable similarities with viral fusion

A Rapid Online Telepathy Test

In an automated online telepathy test, each participant had four senders, two actual and two virtual, generated by the computer. In a series of 12 30-sec. trials, the computer selected one of the senders at random and asked him to write a message to the subject. After 30 sec., the participant was asked to guess who had written a message. After the computer had recorded his guess, it sent him the message. In a total of 6,000 trials, there were 1,559 hits (26.7%), significantly above the chance expectation of 25%. In filmed tests, the hit rate was very similar. The hit rate with actual senders was higher than with virtual senders, but there was a strong guessing bias in favour of actual senders. When high-scoring subjects were retested, hit rates generally declined, but one subject repeatedly scored above chance.

Association networks in spider monkeys (Ateles geoffroyi)

We use two novel techniques to analyze association patterns in a group of wild spider monkeys (Ateles geoffroyi) studied continuously for 8 years. Permutation tests identified association rates higher or lower than chance expectation, indicating active processes of companionship and avoidance as opposed to passive aggregation. Network graphs represented individual adults as nodes and their association rates as weighted edges. Strength and eigenvector centrality (a measure of how strongly linked an individual is to other strongly linked individuals) were used to quantify the particular role of individuals in determining the network's structure. Female–female dyads showed higher association rates than any other type of dyad, but permutation tests revealed that these associations cannot be distinguished from random aggregation. Females formed tightly linked clusters that were stable over time, with the exception of immigrant females who showed little association with any adult in the group. Eigenvector centrality was higher for females than for males. Adult males were associated mostly among them, and although their strength of association with others was lower than that of females, their association rates revealed a process of active companionship. Female–male bonds were weaker than those between same-sex pairs, with the exception of those involving young male adults, who by virtue of their strong connections both with female and male adults, appear as temporary brokers between the female and male clusters of the network. This analytical framework can serve to develop a more complete explanation of social structure in species with high levels of fission–fusion dynamics.

How proteins find their genomic targets in vivo? Implications for epigenetic inheritance

DNA‐binding proteins have a specificity of ~104 to 105, which corresponds to approximately 7‐8 bp of DNA sequence information. As a consequence, sequence motifs for DNA‐binding proteins should occur many times in genomes simply by chance expectation. This is true for E. coli (4 million bp), even more so for yeast (12 million bp), and dramatically so for human (3 billion bp). How do DNA‐binding proteins select their "correct" genomic targets in vivo while avoiding "incorrect" motifs that occur by chance? It turns out that organisms have different strategies. In E. coli, all motifs are bound, and selectivity is attained by DNA‐binding proteins with high specificity and evolutionary selection against motifs in non‐biological locations. In yeast, promoter regions are have DNA sequences that intrinsically disfavor nucleosome formation, thereby favoring binding (by a factor of 5‐30) to sites in promoter regions as compared to coding regions. In mammalian cells, the vast majority of motifs are unbound in vivo, and many bound sites lack motifs. This indicates that site selection in human cells requires cooperative binding, and a model for such cooperative binding in the absence of direct protein‐protein interactions is proposed. The issue of how proteins find their genomic targets underlies the issue of epigenetic inheritance, and I will discuss a model for position‐effect variegation and more generally how patterns of gene regulation are epigenetically inherited. In this model, epigenetic inheritance is mediated primarily through transcriptional regulatory proteins and transcription itself, with the role of chromatin being to reinforce the specific decisions made by these proteins. In particular, epigenetic inheritance is ultimately reduced to a question of binding affinities for different genomic regions, and the combined contributions of the various protein‐DNA and protein‐protein interactions.

Mental disorders among persons with diabetes—Results from the World Mental Health Surveys

Objective To estimate 12-month prevalence rate of mood, anxiety, and alcohol-use disorders among community samples of diabetic persons. We assess whether associations of specific mental disorders with diabetes are consistent across diverse countries after controlling for age and gender. Research design and methods Eighteen surveys of household-residing adults were conducted in two phases across 17 countries in Europe, the Americas, the Middle East, Africa, Asia, and the South Pacific (Part 1, N=85,088). Mental disorders, identified by the World Mental Health–Composite International Diagnostic Interview, included anxiety disorders (generalized anxiety disorder, panic disorder/agoraphobia, posttraumatic stress disorder, and social phobia), mood disorders (dysthymia and major depressive disorder), and alcohol abuse/dependence. Diabetes was ascertained by self-report (Part 2, N=42,697). Association was assessed by age–gender adjusted odds ratios. Results Risk of mood and anxiety disorders was slightly higher among persons with diabetes relative to those without: odds ratio of 1.38 for depression (95% CI=1.15–1.66) and 1.20 for anxiety disorders, (95 % CI=1.01–1.42), after adjusting for age and gender. Odds ratio estimates across countries did not differ more than chance expectation. Alcohol-use disorders were uncommon among persons with diabetes in most countries, and not associated with diabetes in pooled survey data. Conclusions Population sample surveys revealed mood and anxiety disorders occurred with somewhat greater frequency among persons with diabetes than those without diabetes. Prevalence of major depression among persons with diabetes was lower in the general population than suggested by prior studies of clinical samples. Strength of association did not differ significantly across disorders or countries.

Behavioural crime linking in serial homicide

The present study aimed to identify dimensions of variation in serial homicide and to use these dimensions to behaviourally link offences committed by the same offender with each other. The sample consisted of 116 Italian homicides committed by 23 individual offenders. Each offender had committed at least two homicides. As some offenders had worked together and some murders involved more than one victim, there were 155 unique pairings of offenders and victims. Dichotomous variables reflecting crime features and victim characteristics were coded for each case. Using Mokken scaling, a nonparametric alternative to factor analysis, seven dimensions of variation were identified. Five of the dimensions described variations in the motivation for the killings. Three of these were concerned with aspects of instrumental motivation whereas two of the motivational scales described variations in sexual motivation. The two remaining dimensions dealt with the level of planning evident in the crime scene behaviour of the offender. Two dimensions were identified: one consisting of behaviours suggesting a higher level of control and another describing impulsiveness. Using discriminant function analysis with the dimensions as independent variables and the series an offence belonged to as dependent variable, 62.9% of the cases could be correctly assigned to the right series (chance expectation was 6.2%). The implications of the results for serial homicide investigations are discussed.

Relative occurrence of amino acid-nucleotide contacts assessed by Voronoi-Delaunay tessellation of protein-DNA interfaces

The data for 1109 protein-DNA complexes in PDB were analyzed for direct contacts between particular amino acid residues and nucleotides by rigorous space partitioning (Voronoi-Delaunay tessellation). When the actual occurrence of each kind of residue-nucleotide contact in the interface was related to its chance expectation, the most abundant contacts (made by Arg or Lys as well as by Ser or Thr) proved indiscriminate to heterocyclic bases, whereas a number of other, rarer contacts were clearly nonrandom, being significantly overrepresented or underrepresented in the sample of interfaces. Especially remarkable was the high overrepresentation of G/C contacts with negatively charged Asp/Glu. The nonrandom combinations showed no distinctions between purines and pyrimidines. This first step in formal analysis provides some hints concerning the accessibility of the “protein-DNA recognition code.”