Combining overlap and containment for gene assembly in ciliates

Gene assembly in ciliates is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been introduced. This restriction has subsequently been defined as a string rewriting system. We show that, by extending the notion of overlap graph to also represent containment, it is possible to define an equivalent graph rewriting system for two of the three types of rules that make up simple gene assembly. It turns out that this graph rewriting system is often less involved to study than its corresponding string rewriting system. We illustrate this by giving characterizations of the ‘power’ of both types of graph rewriting rules. Also, a first step is made towards a characterization of the “extended overlap graphs”.     

Parallel complexity of signed graphs for gene assembly in ciliates

We consider a graph-based model for the study of parallelism in ciliate gene assembly, where a signed graph is associated to each micronuclear gene and the gene assembly is modeled as a graph rewriting process. A natural measure of complexity for gene assembly counts the minimal number of parallel steps needed to reduce the associated signed graph. We investigate the complexity of several classes of the graphs, so far found graphs of parallel complexity up to six. The general problem of whether there exists a finite upper bound for the graph parallel complexity still remains open.     

How ciliates manipulate their own DNA – A splendid example of natural computing

DNA computing is a novel and vivid researcharea which is genuinely interdisciplinary –computer scientists and molecular scientistscollaborate to investigate the use of DNAmolecules for the purpose of computing. DNAcomputing in vivo is the investigation ofcomputations taking place naturally in a livingcell, with the goal of understandingcomputational properties of DNA molecules intheir native environment. Gene assembly inciliates (single cell organisms) is perhaps themost involved process of DNA manipulation yetknown in living organisms. The computationalnature of this process has attracted muchattention in recent years. The resultsobtained so far demonstrate that this processof gene assembly is a splendid example ofcomputing taking place in nature, i.e., NaturalComputing. Indeed, DNA computing in vivomay be far more widespread in nature than wecurrently recognize. This paper is a tutorialon (computational nature of the) gene assemblyin ciliates, which is intended for a broadaudience of researchers interested in NaturalComputing. In particular, no knowledge ofmolecular biology is assumed on the part of themotivated reader.     

Lattice structure on some fuzzy algebraic systems

In this paper, we study the lattice structure of some fuzzy algebraic systems such as (G-)fuzzy groups, some fuzzy ordered algebras and fuzzy hyperstructures. We prove that under suitable conditions, these structures form a distributive or modular lattice. This research partially is supported by the “ Fuzzy Systems and its Applications Center of Excelence, Shahid Bahonar University of Kerman, Iran”.     

On the status and prospects of systems analysis methods in ukraine

The paper deals with the role and place of systems analysis methods in the solution of complex problems in various spheres of human activity in Ukraine. The social and socio-economic prerequisites for development of theory and applied methods are being considered. The main characteristics of the problems to which these methods are applied are formulated. The hierarchy of problems and methods used for solution of complex problems based on systems analysis methods is presented, and the main spheres of their application in Ukraine are presented. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 101–109, January–February, 2000.     

On Complexity of Computation of Partial Derivatives of Boolean Functions Realized by Zhegalkin Polynomials

The combinational complexity of a system of partial derivatives in the basis of linear functions is established for a Boolean function of n variables that is realized by a Zhegalkin polynomial. An algorithm whose complexity equals 3ⁿ – 2ⁿ modulo 2 additions is proposed for computation of all partial derivatives of such a function from the coefficients of its Zhegalkin polynomial.     

On very true operators on pocrims

Hájek introduced the logic enriching the logic BL by a unary connective vt which is a formalization of Zadeh’s fuzzy truth value “very true”. algebras, i.e., BL-algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of Partially ordered commutative integral residuated monoids (pocrims) are common generalizations of both BL-algebras and Heyting algebras. The aim of our paper is to introduce and study algebraic properties of pocrims endowed by “very-true” and “very-false”-like operators. Research is supported by the Research and Development Council of Czech Government via project MSN 6198959214.     

On the representation of shift-invariant operators by transfer functions

We give simple sufficient conditions on a function space on (0, ∞) to ensure that all shift-invariant operators defined on it are represented by transfer functions. This enables us to extend the result of Weiss on L_p(0, ∞) for 1 p < ∞ (but not p = ∞) to more general situations.     

On the strict logic foundation of fuzzy reasoning

This paper focuses on the logic foundation of fuzzy reasoning. At first, a new complete first-order fuzzy predicate calculus system K^* corresponding to the formal system L^* is built. Based on the many-sort system K_ms^* corresponding to K^*, the triple I methods of FMP and FMT for fuzzy reasoning and their consistency are formalized, thus fuzzy reasoning is put completely and rigorously into the logic framework of fuzzy logic.The author is indebted to anonymous referee for his useful comments which have helped to improve the paper.     

On pure H reduced-order dynamic controllers: an erratum

There are at least two approaches advocated to obtain a pure H^∞ reduced-order dynamic controller for a given augmented plant. One approach is to eliminate completely the H² aspect from a standard H²/H^∞ setting. A second approach is to equate the H² aspect with the H^∞ aspect in that same setting. This paper invalidates the first approach but affirms the second approach and produces the correct equations resulting therefrom.     

On alpha-adic expansions in Pisot bases

We study α-adic expansions of numbers, that is to say, left infinite representations of numbers in the positional numeration system with the base α, where α is an algebraic conjugate of a Pisot number β. Based on a result of Bertrand and Schmidt, we prove that a number belongs to if and only if it has an eventually periodic α-adic expansion. Then we consider α-adic expansions of elements of the ring when β satisfies the so-called Finiteness property (F). We give two algorithms for computing these expansions — one for positive and one for negative numbers. In the particular case that β is a quadratic Pisot unit satisfying (F), we inspect the unicity and/or multiplicity of α-adic expansions of elements of . We also provide algorithms to generate α-adic expansions of rational numbers in that case.     

On stability, -gain and control for switched systems

This paper addresses the issues of stability, L₂-gain analysis and H_∞ control for switched systems via multiple Lyapunov function methods. A concept of general Lyapunov-like functions is presented. A necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an L₂-gain characterization and a design method for stabilizing switching laws. A solution to the H_∞ control problem for switched systems is also provided.     

On the gap between H2 and entropy performance measures in H∞ control design

Recent papers have considered the problem of minimizing an entropy functional subject to an H_∞ performance constraint. Since the entropy is an upper bound for the H₂ cost, there remains a gap between entropy minimization and H₂ minimization. In this paper we consider a generalized cost functional involving both H₂ and entropy aspects. This approach thus provides a means for optimizing H₂ performance within H_∞ control design.     

A Model in κ for DNA Addition

DNA computing is a hot research topic in recent years. Formalization and verification using theories(π-calculus, bioambients, κ-calculus and etc.) in Computer Science attract attention because it can help prove and predict to a certian degree various kinds of biological processes. Combining these two aspects, formal methods can be used to verify algorithms in DNA computing, including basic arithmetic operations if they are to be included in a DNA chip. In this paper, we first introduce a newly-designed algorithm for solving binary addition with DNA, which contributes to a unit in DNA computer processor, and then formalize the algorithm in κ-calculus(a formal method well suited for describing protein interactions) to show the correctness of it in a sense, and a sensible example is provided. Finally, some discussion on the described model is made, in addition to a few possible future improvement directions.     

On the complexity of computing the diameter of a polytope

We show that it isD ^P -hard to determine the combinatorial diameter of a polytope specified by linear inequalities with integer data. Our result partially resolves a long-term open question.     

A sensitive and selective sensor for dopamine determination based on a molecularly imprinted electropolymer of o-aminophenol

A simple and reliable method was proposed for preparing a selective dopamine (DA) sensor based on a molecularly imprinted electropolymer of o-aminophenol. The sensor is selective for the determination of DA in the presence of high concentrations of ascorbic acid (AA), with a maximum molar ratio of 1/1000. The molecular imprinted (MIP) sensor was tested by cyclic voltammetry (CV) as well as differential pulse voltammetry (DPV) to verify the changes in oxidative currents of ferricyanide. In optimized conditions, DA at concentrations of 2 × 10⁻⁸ to 0.25 × 10⁻⁶ mol/L could be determined with a detection limit of 1.98 × 10⁻⁹ mol/L (S/N = 3). The MIP sensor showed high selectivity, sensitivity, and reproducibility. Determination of DA in simulated samples of dopamine hydrochloride showed good recovery.     

Distinct squares in run-length encoded strings

Squares are strings of the form ww where w is any nonempty string. Two squares ww and w^′w^′ are of different types if and only if w≠w^′. Fraenkel and Simpson [Avieri S. Fraenkel, Jamie Simpson, How many squares can a string contain? Journal of Combinatorial Theory, Series A 82 (1998) 112-120] proved that the number of square types contained in a string of length n is bounded by O(n). The set of all different square types contained in a string is called the vocabulary of the string. If a square can be obtained by a series of successive right-rotations from another square, then we say the latter covers the former. A square is called a c-square if no square with a smaller index can cover it and it is not a trivial square. The set containing all c-squares is called the covering set. Note that every string has a unique covering set. Furthermore, the vocabulary of the covering set are called c-vocabulary. In this paper, we prove that the cardinality of c-vocabulary in a string is less than , where N is the number of runs in this string.     

On Nonparametric Predictive Inference and Objective Bayesianism

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A _(n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A _(n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A _(n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism.     

On the closure of the diagonal of a T1-space

Let X be a topological space. The closure of Δ={(x,x):xX} in X×X is a symmetric relation on X. We characterise those equivalence relations on an infinite set that arise as the closure of the diagonal with respect to a T₁-topology.     

On approximate stochastic realization

The problem considered here is to represent a stationary stochastic processy with a low-dimensional stochastic model. This problem occurs when the state space of an exact realization ofy has a very large dimension. The reduction is obtained in this large state space, exploiting its markovian structure to characterize all markovian subspaces, among which a reducedk-dimensional model is sought. The concept of markovian basis is introduced, and its equivalence with the Malmquist basis in the spectral domain is shown. An algorithm with polynomial complexity to compute an approximate model is given.