Auxiliary Symbols Research Articles

Differential direct coding: a compression algorithm for nucleotide sequence data

While modern hardware can provide vast amounts of inexpensive storage for biological databases, the compression of nucleotide sequence data is still of paramount importance in order to facilitate fast search and retrieval operations through a reduction in disk traffic. This issue becomes even more important in light of the recent increase of very large data sets, such as metagenomes. In this article, I propose the Differential Direct Coding algorithm, a general-purpose nucleotide compression protocol that can differentiate between sequence data and auxiliary data by supporting the inclusion of supplementary symbols that are not members of the set of expected nucleotide bases, thereby offering reconciliation between sequence-specific and general-purpose compression strategies. This algorithm permits a sequence to contain a rich lexicon of auxiliary symbols that can represent wildcards, annotation data and special subsequences, such as functional domains or special repeats. In particular, the representation of special subsequences can be incorporated to provide structure-based coding that increases the overall degree of compression. Moreover, supporting a robust set of symbols removes the requirement of wildcard elimination and restoration phases, resulting in a complexity of O(n) for execution time, making this algorithm suitable for very large data sets. Because this algorithm compresses data on the basis of triplets, it is highly amenable to interpretation as a polypeptide at decompression time. Also, an encoded sequence may be further compressed using other existing algorithms, like gzip, thereby maximizing the final degree of compression. Overall, the Differential Direct Coding algorithm can offer a beneficial impact on disk traffic for database queries and other disk-intensive operations.

Sequential monotonicity for restarting automata

As already 2-monotone R-automata accept NP-complete languages, we introduce a restricted variant of j -monotonicity for restarting automata, called sequential j -monotonicity . For restarting automata without auxiliary symbols, this restricted variant still yields infinite hierarchies. However, for restarting automata with auxiliary symbols, all degrees of sequential monotonicity collapse to the first level, implying that RLWW-automata that are sequentially monotone of degree j for any j ≥ 1 only accept context-free languages.

A P300-based brain—computer interface

The goal of this work was to describe a system for real-time typing controlled by brain biopotential signals. A 6 ( 6 matrix containing Russian alphabet letters and auxiliary symbols was shown on PC screen. Electroencephalogram was taken, and the P300 component was extracted (this component appeared only upon presentation of a significant stimulus). A combination of several detection methods was used to identify the P300 component, which made it possible to increase the probability of correct identification to 91.6 (5.2%. It was shown that the developed interface could be implemented on the basis of a single active electrode in Pz (Cz) position.

Degrees of non-monotonicity for restarting automata

In the literature various notions of monotonicity for restarting automata have been studied. Here we introduce two new variants of monotonicity for restarting automata and for two-way restarting automata: left-monotonicity and right-left-monotonicity. It is shown that for the various types of deterministic and nondeterministic (two-way) restarting automata without auxiliary symbols, these notions yield infinite hierarchies, and we compare these hierarchies to each other. Further, as a tool used to simplify some of the proofs, the shrinking restarting automaton is introduced, which is a generalization of the standard (length-reducing) restarting automaton to the weight-reducing case. Some of the consequences of this generalization are also discussed.

Restarting automata with restricted utilization of auxiliary symbols

The restarting automaton is a restricted model of computation that was introduced by Jančar et al. to model the so-called analysis by reduction, which is a technique used in linguistics to analyse sentences of natural languages. The most general models of restarting automata make use of auxiliary symbols in their rewrite operations, although this ability does not directly correspond to any aspect of the analysis by reduction. Here we put restrictions on the way in which restarting automata use auxiliary symbols, and we investigate the influence of these restrictions on their expressive power. In fact, we consider two types of restrictions. First, we consider the number of auxiliary symbols in the tape alphabet of a restarting automaton as a measure of its descriptional complexity. Secondly, we consider the number of occurrences of auxiliary symbols on the tape as a dynamic complexity measure. We establish some lower and upper bounds with respect to these complexity measures concerning the ability of restarting automata to recognize the (deterministic) context-free languages and some of their subclasses.

Hierarchies of weakly monotone restarting automata

It is known that the weakly monotone restarting automata accept exactly the growing context-sensitive languages. We introduce a measure on the degree of weak monotonicity and show that the language classes obtained in this way form strict hierarchies for the various types of deterministic and nondeterministic restarting automata without auxiliary symbols.

The language of RNA: a formal grammar that includes pseudoknots.

In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However, a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. Here we show a one-to-one correspondence between that algorithm and a formal transformational grammar. This grammar class encompasses the context-free grammars and goes beyond to generate pseudoknotted structures. The pseudoknot grammar avoids the use of general context-sensitive rules by introducing a small number of auxiliary symbols used to reorder the strings generated by an otherwise context-free grammar. This formal representation of the residue correlations in RNA structure is important because it means we can build full probabilistic models of RNA secondary structure, including pseudoknots, and use them to optimally parse sequences in polynomial time.

A circuit approach to field computation

Many design objectives can be expressed more directly in terms of circuit parameters, such as capacitance and inductance, than in terms of the field vectors E and B. A simple, although radical, change is suggested to provide a closer link between the field and circuit views. The electric potential phi and magnetic vector A are defined, in energy terms, as the primary field quantities, and they are visualized as measures of the capacitance and inductance, respectively. E and B become auxiliary symbols denoting derivatives, so that the customary roles of the potentials and field vectors are reversed. Some of the practical advantages of the change are examined and are illustrated by example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Development of radiological and functional changes in silicosis during the long term follow-up

The report follows up the development of radiologic changes and functional disorders in 200 patients with silicosis who were repeatedly examined over a period of time. The patients were divided according to the X-ray findings, when first detected, into groups of simple silicosis, complicated silicosis, and simple silicosis passing into the complicated stage during the study. Each group was divided into 3 time periods of follow-up: 3 to 5 yrs, 6 to 10 yrs, and 11 to 17 yrs between the first and the last examinations. The results disclosed the following conclusions: 1. Changes of the radiologic picture evaluated according to the International Classification of Pneumoconiosis ILO 1971 proceeded in the course of time into more serious forms with respect to size and profusion of nodules. With complicated silicosis, possibly with the transient form, the auxiliary symbols increased with time, particularly “ax”, “pl”, “em”, “es”, “tbu”, and “tba”. The classification proved satisfactory for expressing shifts of X-ray changes; it did not suffice alone, however, for answering the question when a dust finding reaches the stage at which it is to be declared an occupational disease. This would require more criteria, chiefly tomography of the lungs and assessment of the dynamics of development in radiologic changes. 2. The trend of the ventilatory-function decrease differed only slightly in a mutual comparison of the groups. This means that in the intermediate and long time periods the decrease in ventilatory function is similar because the patients with severe functional disorders do not live long enough for long-term studies. This was proved by an analysis of the mortality rate in the groups. 3. We ascertained more significant differences in the ventilatory function within the individual groups in patients with signs of chronic bronchitis when compared with patients without bronchitis. The important influence especially of the obstructive form associated with complicated silicosis was evident here. 4. Part of the group was also studied from the aspect of blood gases and acid-base status over periods of 3 to 5 and 6 to 10 yrs. With both forms of silicosis the values of the first and last examinations differed only insignificantly. Pronounced changes of the respiratory function cannot be expected when the organism is able to compensate the disorder of ventilation. The finding of global respiratory insufficiency with rapid progress of silicosis always indicated a limited life expectancy.

Nonsequential languages

In this paper context-free languages are investigated according to their ordering properties. For this end O ( n )-grammars and languages are defined. It is shown that the class of O (0)-languages is identical with the well known sequential context-free languages. Furthermore, for each nonnegative integer n , the class ℒ T n of O ( k )-languages ( k ⩽ n ) is not empty. The most interesting characterization of nonsequential languages is by the complexity of the corresponding context-free expressions. It is proved that an arbitrary context-free language L belongs to the class ℒ T n only if the minimal context-free expressions for L contain at most n + 1 auxiliary symbols. Finally, some undecidability results for the complexity classes are established.

Optimum Symbols for Radar Displays

Experiments were conducted to determine: 1) sets of geometric symbols which can be discriminated from each other and recognized with high accuracy under a variety of display conditions, especially those involving degradation of the image in ways similar to those that occur on radar displays, and 2) the size and strokewidth to height ratio desirable for symbols to be used on complex displays. The recommended symbols are illustrated in the report; symbol height should be 1/2 inch or more and the strokewidth should be 1/8 to 1/10 of the height. Suggestions for combining auxiliary symbols with primary symbols are given.

Mesomerism and Tautomerism

THE recognition of valency exchange degeneracy as a matter of primary importance in relation to the energy1 and reactivity2 of organic molecules makes it the more necessary clearly to indicate the nature of the conception. It envisages both completely and incompletely degenerate states collectively called ‘mcsomeric’ states; and these states are described by first setting up. unperturbed structures, which correspond to classical chemical formulae but (according to the theory) not exactly to reality, and then correcting these structures by supposing them to undergo a perturbation, the nature of which may be indicated by auxiliary symbols.