Francesco Fabris

Shannon Information Theory and Molecular Biology

Abstract The role and the contribution of Shannon Information Theory to the development of Molecular Biology has been the object of stimulating debates during the last thirty years. This seems to be connected with some semantic charms associated with the use of the word “information” in the biological context. Furthermore information itself, if viewed in a broader perspective, is far from being completely defined in a fashion that overcomes the technical level at which the classical Information Theory has been conceived. This review aims at building on the acknowledged contribution of Shannon Information Theory to Molecular Biology, so as to discover if it is only a technical tool to analyze DNA and proteinic sequences, or if it can rise, at least in perspective, to a higher role that exerts an influence on the construction of a suitable model for handling the genetic information in Molecular Biology.

Splitting the BLOSUM score into numbers of biological significance

Mathematical tools developed in the context of Shannon information theory were used to analyze the meaning of the BLOSUM score, which was split into three components termed as the BLOSUM spectrum (or BLOSpectrum). These relate respectively to the sequence convergence (the stochastic similarity of the two protein sequences), to the background frequency divergence (typicality of the amino acid probability distribution in each sequence), and to the target frequency divergence (compliance of the amino acid variations between the two sequences to the protein model implicit in the BLOCKS database). This treatment sharpens the protein sequence comparison, providing a rationale for the biological significance of the obtained score, and helps to identify weakly related sequences. Moreover, the BLOSpectrum can guide the choice of the most appropriate scoring matrix, tailoring it to the evolutionary divergence associated with the two sequences, or indicate if a compositionally adjusted matrix could perform better.

On a measure of possibilistic non-compatibility with an application to data transmission

Abstract Inspired by Zadeh’s non-interactivitiy, we introduce a measure of non-compatibility between possibility distributions (πds), which is a possible mathematical counterpart to Mutual Information (which pertains to Information Theory). The measure is obtained by following the same mathematical guide lines used for mutual information, and can be associated to a model of data transmission and decoding over a noisy channel, in which possibilities are used instead of probabilities.

PolyMorph: A P300 Polymorphic Speller

P300 is an electric signal emitted by brain about 300 milliseconds after a rare, but relevant-for-the-user event. Even if it is hard to identify and it provides a low-rate communication channel, it can be used in cases in which other evoked potentials fail. One of the applications of this signal is a speller that enables subjects who lost the control of their motor pathways to communicate by selecting one by one each character of a sentence in a matrix containing all the alphabet symbols. This paper provides an improvement of this paradigm and it aims at reducing both the error rate and the time required to spell a sentence by exploiting the redundancy which is present in all the natural languages.

Informational analysis: a Shannon theoretic approach to measure the performance of a diagnostic test

AbstractDiagnostic test accuracy, based on sensitivity, specificity, positive/negative predictive values (dichotomous case), and on ROC analysis (continuous case), should be expressed with a single, coherent index. We propose to modelize the diagnostic test as a flow of information between the disease, that is, a hidden state of the patient, and the physicians. We assume that (1) sensitivity, specificity, and false-positive/false-negative rates are the probabilities of a binary asymmetric channel; (2) the diagnostic channel information is measured by mutual information. We introduce two summary measures of accuracy, namely the information ratio (IR) for the dichotomous case, and the global information ratio (GIR) for the continuous case. We apply our model to a study by Pisano et al. (N Engl J Med 353(17):1773–1783, 2005), who compared digital versus film mammography, in diagnosing breast cancer in a screening population of 42,760 women. In film mammography, the maximum IR (0.178) corresponds to the standard cutoff of sensitivity and specificity provided by the ROC analysis (GIR 0.200). Maximum IR and GIR for digital mammography are higher (0.201 and 0.229, respectively), but IR corresponds to a cutoff with higher sensitivity but lower specificity, thus suggesting that larger information provided by digital mammography carries the risk of more false-positive cases.

Binary List Decoding Beyond Covering Radius

Abstract Wus list decoding algorithm, when restricted to binary codes, allows decoding up to the binary Johnson bound. Unfortunately, in the vast majority of cases, this bound is not capable to reach the covering radius R of the code, and this implies that some n-tuples do exist that are not list decodable. Nevertheless we prove that a class of Reed-Muller codes it exists, for which the decoding radius τwu is greater than or equal to the covering radius. This situation is the list decoding counterpart of perfect codes.

A Lower Bound on the Expected Complexity in the Set of n-Tuples of Given Weight

Abstract In this paper we determine a lower bound on the average complexity distribution over the set of the n-tuples with a prefixed weight k; besides, a formula is given to calculate the probability of obtaining n-tuples with low complexity.

Stream Ciphering Techniques Based on n-Tuples Juxtaposition Sequences

Abstract In this paper it is shown that the family of periodic sequences obtained by arbitrarily juxtaposing the 2 n different binary n-tuples have good pseudo-randomness performance, since they pass several pseudo-randomness tests (namely Golomb’s postulates, the k-tuples frequency test and the serial test) more and more accurately as n goes to infinity. Besides, the behaviour of the sequences complexity profile is investigated, a lower bound for the expected linear complexity and an upper bound for the probability of obtaining a complexity less than some prefixed constant are derived. Also, some experimental results, related with the distribution of complexity over the set of sequences, are communicated. Finally it is shown that the stream ciphering techniques are a possible application area for the given results.

PolyMorph: Increasing the Spelling Efficiency of P300 by Selection Matrix PolyMorphism and Sentence-Based Predictions

ABSTRACT One application of the P300 brain electric signal is sentence spelling, which enables subjects who have lost control of their motor pathways to communicate by selecting characters in a matrix containing all alphabet symbols. This technology still suffers from both low communication/high error rates. A P300 speller, named PolyMorph, which jointly introduces the selection matrix polymorphism (reducing the matrix size by removing useless symbols) and sentence-based predictions (which forecast words on the basis of language statistics) is presented. This is accomplished by using a custom dynamic knowledge-base, tailored to the subject lexicon, and updated in real time with the selections of the subject. The effectiveness of the presented speller is measured in vivo and in silico. The results suggest that the use of PolyMorph increases the number of spelt characters per time unit and reduces the error rate.

Differentiating small (≤1 cm) focal liver lesions as metastases or cysts by means of computed tomography: a case-study to illustrate a fuzzy logic-based method to assess the impact of diagnostic confidence on radiological diagnosis.

Purpose. To quantify the impact of diagnostic confidence on radiological diagnosis with a fuzzy logic-based method. Materials and Methods. Twenty-two oncologic patients with 20 cysts and 30 metastases ≤1 cm in size found at 64-row computed tomography were included. Two readers (R1/R2) expressed diagnoses as a subjective level of confidence P(d) in malignancy within the interval [0,1] rather than on a “crisp” basis (malignant/benign); confidence in benignancy was 1 − p(d). When cross-tabulating data according to the standard of reference, 2 × 2 table cells resulted from the aggregation between p(d)/1 − p(d) and final diagnosis. We then assessed (i) readers diagnostic performance on a fuzzy and crisp basis; (ii) the “divergence” δ(F, C) (%) as a measure of how confidence impacted on crisp diagnosis. Results. Diagnoses expressed with lower confidence increased fuzzy false positives compared to crisp ones (from 0 to 0.2 for R1; from 1 to 2.4 for R2). Crisp/fuzzy accuracy was 94.0%/93.6% (R1) and 94.0/91.6% (R2). δ(F, C) (%) was larger in the case of the less experienced reader (R2) (up to +7.95% for specificity). According to simulations, δ(F, C) (%) was negative/positive depending on the level of confidence in incorrect diagnoses. Conclusion. Fuzzy evaluation shows a measurable effect of uncertainty on radiological diagnoses.