MinMax-Profiles: A Unifying View of Common Intervals, Nested Common Intervals and Conserved Intervals of K Permutations

Common intervals of K permutations over the same set of n elements were firstly investigated by T. Uno and M.Yagiura (Algorithmica, 26:290:309, 2000), who proposed an efficient algorithm to find common intervals when K=2. Several particular classes of intervals have been defined since then, e.g. conserved intervals and nested common intervals, with applications mainly in genome comparison. Each such class, including common intervals, led to the development of a specific algorithmic approach for K=2, and - except for nested common intervals - for its extension to an arbitrary K. In this paper, we propose a common and efficient algorithmic framework for finding different types of common intervals in a set P of K permutations, with arbitrary K. Our generic algorithm is based on a global representation of the information stored in P, called the MinMax-profile of P, and an efficient data structure, called an LR-stack, that we introduce here. We show that common intervals (and their subclasses of irreducible common intervals and same-sign common intervals), nested common intervals (and their subclass of maximal nested common intervals) as well as conserved intervals (and their subclass of irreducible conserved intervals) may be obtained by appropriately setting the parameters of our algorithm in each case. All the resulting algorithms run in O(Kn+N)-time and need O(n) additional space, where N is the number of solutions. The algorithms for nested common intervals and maximal nested common intervals are new for K>2, in the sense that no other algorithm has been given so far to solve the problem with the same complexity, or better. The other algorithms are as efficient as the best known algorithms.Comment: 25 pages, 2 figure

Space-Time Intervals Underlie Human Conscious Experience, Gravity, and a Theory of Everything

Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time intervals by the brain; space-time intervals are the source of conscious experience (observed physical reality). Human conscious experience is modeled by Einstein’s special theory of relativity, a theory designed specifically from the general covariance of space-time intervals (for inertial frames of reference). General relativity is our most accurate description of gravity. In general relativity, the general covariance of space-time intervals is extended to all frames of reference (inertial and non-inertial), including gravitational reference frames; space-time intervals are the source of gravity in general relativity. The general covariance of space-time intervals is further extended to quantum mechanics; space-time intervals are the source of quantum gravity. The general covariance of space-time intervals seamlessly merges general relativity with quantum field theory (the two grand theories of the universe). Space-time intervals consequently are the basis of a Theory of Everything (a single all-encompassing coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe). This theoretical framework encompasses our observed physical reality (conscious experience) as well; space-time intervals link observed physical reality to actual physical reality. This provides an accurate and reliable match between observed physical reality and the physical universe by which we can carry on our activity. The Minkowski metric, which defines generally covariant space-time intervals, may be considered an axiom (premise, postulate) for the Theory of Everything

Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.Comment: 11 pages, 6 figures; incorporating changes as in the published versio

Dynamics of male meiotic recombination frequency during plant development using Fluorescent Tagged Lines in Arabidopsis thaliana

Meiotic homologous recombination plays a central role in creating genetic variability, making it an essential biological process relevant to evolution and crop breeding. In this study, we used pollenspecific fluorescent tagged lines (FTLs) to measure male meiotic recombination frequency during the development of Arabidopsis thaliana. Interestingly, a subset of pollen grains consistently shows loss of fluorescence expression in tested lines. Using nine independent FTL intervals, the spatio-temporal dynamics of male recombination frequency was assessed during plant development, considering both shoot type and plant age as independent parameters. In most genomic intervals assayed, male meiotic recombination frequency is highly consistent during plant development, showing no significant change between different shoot types and during plant aging. However, in some genomic regions, such as I1a and I5a, a small but significant effect of either developmental position or plant age were observed, indicating that the meiotic CO frequency in those intervals varies during plant development. Furthermore, from an overall view of all nine genomic intervals assayed, both primary and tertiary shoots show a similar dynamics of increasing recombination frequency during development, while secondary and lateral shoots remain highly stable. Our results provide new insights in the dynamics of male meiotic recombination frequency during plant development

Adding HL7 version 3 data types to PostgreSQL

The HL7 standard is widely used to exchange medical information electronically. As a part of the standard, HL7 defines scalar communication data types like physical quantity, point in time and concept descriptor but also complex types such as interval types, collection types and probabilistic types. Typical HL7 applications will store their communications in a database, resulting in a translation from HL7 concepts and types into database types. Since the data types were not designed to be implemented in a relational database server, this transition is cumbersome and fraught with programmer error. The purpose of this paper is two fold. First we analyze the HL7 version 3 data type definitions and define a number of conditions that must be met, for the data type to be suitable for implementation in a relational database. As a result of this analysis we describe a number of possible improvements in the HL7 specification. Second we describe an implementation in the PostgreSQL database server and show that the database server can effectively execute scientific calculations with units of measure, supports a large number of operations on time points and intervals, and can perform operations that are akin to a medical terminology server. Experiments on synthetic data show that the user defined types perform better than an implementation that uses only standard data types from the database server.Comment: 12 pages, 9 figures, 6 table

Efficient Genomic Interval Queries Using Augmented Range Trees

Efficient large-scale annotation of genomic intervals is essential for personal genome interpretation in the realm of precision medicine. There are 13 possible relations between two intervals according to Allen's interval algebra. Conventional interval trees are routinely used to identify the genomic intervals satisfying a coarse relation with a query interval, but cannot support efficient query for more refined relations such as all Allen's relations. We design and implement a novel approach to address this unmet need. Through rewriting Allen's interval relations, we transform an interval query to a range query, then adapt and utilize the range trees for querying. We implement two types of range trees: a basic 2-dimensional range tree (2D-RT) and an augmented range tree with fractional cascading (RTFC) and compare them with the conventional interval tree (IT). Theoretical analysis shows that RTFC can achieve the best time complexity for interval queries regarding all Allen's relations among the three trees. We also perform comparative experiments on the efficiency of RTFC, 2D-RT and IT in querying noncoding element annotations in a large collection of personal genomes. Our experimental results show that 2D-RT is more efficient than IT for interval queries regarding most of Allen's relations, RTFC is even more efficient than 2D-RT. The results demonstrate that RTFC is an efficient data structure for querying large-scale datasets regarding Allen's relations between genomic intervals, such as those required by interpreting genome-wide variation in large populations.Comment: 4 figures, 4 table