The design and analysis of adaptive sorting algorithms has made important contributions to both theory and practice. The main contributions from the theoretical point of view are: the description of the complexity of a sorting algorithm not only in terms of the size of a problem instance but also in terms of the disorder of the given problem instance; the establishment of new relationships among measures of disorder; the introduction of new sorting algorithms that take advantage of the existing order in the input sequence; and, the proofs that several of the new sorting algorithms achieve maximal (optimal) adaptivity with respect to several measures of disorder. The main contributions from the practical point of view are: the demonstration that several algorithms currently in use are adaptive; and, the development of new algorithms, similar to currently used algorithms that perform competitively on random sequences and are significantly faster on nearly sorted sequences. In this survey, we present the basic notions and concepts of adaptive sorting and the state of the art of adaptive sorting algorithms.

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The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic metalanguage for the definition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions, although only regular expressions that denote words unambiguously, in the sense of the ISO standard, are allowed. In general, a word that is denoted by a regular expression is witnessed by a sequence of occurrences of symbols in the regular expression that match the word. In an unambiguous regular expression as defined by Book et al. (1971, IEEE Trans. Comput. C-20(2), 149 153), each word has at most one witness. But the SGML standard also requires that a witness be computed incrementally from the word with a onesymbol lookahead; we call such regular expressions 1-unambiguous. A regular language is a 1-unambiguous language if it is denoted by some 1-unambiguous regular expression. We give a Kleene theorem for 1-unambiguous languages and characterize 1-unambiguous regular languages in terms of structural properties of the minimal deterministic automata that recognize them. As a result we are able to prove the decidability of whether a given regular expression denotes a 1-unambiguous language; if it does, then we can construct an equivalent 1-unambiguous regular expression in worst-case optimal time.

Intracellular transport of cargo particles is performed by multiple motors working in concert. However, the mechanism of motor association to cargos is unknown. It is also unknown how long individual motors stay attached, how many are active, and how multimotor cargos would navigate a densely crowded filament with many other motors. Prior theoretical and experimental biophysical model systems of intracellular cargo have assumed fixed teams of motors transporting along bare microtubules or microtubules with fixed obstacles. Here, we investigate a regime of cargos transporting along microtubules crowded with free motors. Furthermore, we use cargos that are able to associate or dissociate motors as it translocates. We perform in vitro motility reconstitution experiments with high-resolution particle tracking. Our model system consists of a quantum dot cargo attached to kinesin motors, and additional free kinesin motors that act as traffic along the microtubule. Although high densities of kinesin motors hinder forward motion, resulting in a lower velocity, the ability to associate motors appears to enhance the run length and attachment time of the quantum dot, improving overall cargo transport. These results suggest that cargos that can associate new motors as they transport could overcome traffic jams.axonal transport | cytoplasmic dynein

Abstract.An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each of n given line segments in the plane is presented. As a matter of fact, the algorithm computes a description of all stabbing lines. A purely geometric fact is proved which infers that this description requires O(n) space to be .specified. Our algorithm computes it in O(n log n) time which is optimal in the worst case.Using the description of the stabbing lines, we are able to decide in O(Iog n) time whether or not a specified line is a stabbing line. Finally, the problem of maintaining the description of all stabbing lines while inserting and deleting line segments is addressed.